VSEBINA – CONTENTS
PREGLEDNI ZNANSTVENI ^LANKI – REVIEW ARTICLES
Structural steels with micrometer grain size: a survey
Konstrukcijska jekla z mikrometrskimi kristalnimi zrni: pregled
F. Vodopivec, D. Kmeti~, F. Tehovnik, J. Vojvodi~-Tuma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
IZVIRNI ZNANSTVENI ^LANKI – ORIGINAL SCIENTIFIC ARTICLES
The implementation of an online mathematical model of billet reheating in an OFU furnace
Implementacija simulacijskega modela za spremljanje ogrevanja gredic v OFU-pe~i
A. Jakli~, F. Vode, T. Marolt, B. Kumer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
The behaviour of coarse-grain HAZ steel with small defects during cyclic loading
Vedenje jekla grobozrnatega TVP z napakami pri cikli~ni obremenitvi
Vladimir Gliha, Toma` Vuherer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
The effect of cold work on the sensitisation of austenitic stainless steels
Vpliv hladne deformacije na pove~anje ob~utljivosti nerjavnih jekel
M. Dománková, M. Peter, M. Roman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Fatigue-crack propagation near a threshold region in the framework of two-parameter fracture mechanics
Dvoparametrska lomno mehanska analiza hitrosti utrujenostne razpoke blizu praga propagacije
S. Seitl, P. Hutaø . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Modelling of the solidification process and the chemical heterogeneity of a 26NiCrMoV115 steel ingot
Modeliranje procesa strjevanja in kemi~ne heterogenosti ingota iz jekla 26NiCrMoV115
M. Balcar, R. @elezný, L. Martínek, P. Fila, J. Ba`an . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Frekven~na odvisnost rezidualnega trenja viskoznostnega vakuumskega merilnika z lebde~o kroglico
Frequency dependence of spinning rotor gauge residual drag
J. [etina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
STROKOVNI ^LANKI – PROFESSIONAL ARTICLES
A wet-steam pipeline fracture
Prelom cevovoda za vla`no paro
R. Celin, D. Kmeti~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
15. KONFERENCA O MATERIALIH IN TEHNOLOGIJAH / 8. – 10. oktober, 2007, Portoro`, Slovenija
15th CONFERENCE ON MATERIALS AND TECHNOLOGY / 8–10 october, 2007, Portoro`, Slovenia . . . . . . . . . . . . . . . . . . . . . . . 155
ISSN 1580-2949
UDK 669+666+678+53 MTAEC9, 41(3)109–154(2007)
MATER.
TEHNOL.
LETNIK
VOLUME 41
[TEV.
NO. 3
STR.
P. 109–154
LJUBLJANA
SLOVENIJA
MAY-JUNE
2007

F. VODOPIVEC ET AL.: STRUCTURAL STEELS WITH MICROMETER GRAIN SIZE.
STRUCTURAL STEELS WITH MICROMETER GRAIN SIZE:
A SURVEY
KONSTRUKCIJSKA JEKLA Z MIKROMETRSKIMI KRISTALNIMI ZRNI:
PREGLED
Franc Vodopivec, Dimitrij Kmeti~, Franc Tehovnik, Jelena Vojvodi~-Tuma
Institute of Metals and Technology, Lepi pot 11, 1000 Ljubljana, Slovenia
franc.vodopivec imt.si
Prejem rokopisa – received: 2006-11-17; sprejem za objavo – accepted for publication: 2007-03-01
Experimental findings and their theoretical interpretation related to the achieving of a µm grain size in structural steels with a
microstructure of ferrite and pearlite are summarised. Several laboratory processing methods can be used to achieve this grain
size. It seems that only DIFT (deformation induced ferrite transformation) offers the possibilty of industrial use for thin sheets,
while for thicker products DIFT can ensure the small grain size only for a thiN surface layer. By very small grain size yield
stress and tensile strength are increased, while elongation, reduction of area and strain hardening are decreased. For a grain size
of 1.3 µm upper shelf notch toughness is smaller, toughness transition temperature is lower and lower shelf notch toughness is
higher than by the steel with the grain size of 6.8 µm.
Key words: structural steels, ultrafine grain size, processing methods, effect of deformation and temperature, mechanical
properties
Predstavljeni in interpretirani so eksperimentalni izsledki raziskovanja s ciljem doseganja mikrometrskih velikosti kristalnih zrn
v konstrukcijskih jeklih z mikrostrukturo iz ferita in perlita. Tako velikost zrn je mogo~e dose~i z ve~ metodami
laboratorijskega procesiranja. Po dosedanjih spoznanjih je primerna za industrijsko uporabo za izdelavo tankih trakov le metoda
DIFT (deformacijsko inducirana transformacija ferita). Po tej metodi je mogo~e pri debelej{ih plo{~ah ustvariti zelo majhna
zrna samo v tanki plasti ob povr{ini. Pri zelo majhni velikosti zrn se pove~ata meja plasti~nosti in trdnost, zmanj{ajo pa se
razteznost, kontrakcija in deformacijska utrditev. Pri jeklu z velikostjo zrn 1,3 µm je v obmo~ju duktilnega loma zarezna
`ilavost manj{a, prehodna temperatura `ilavosti je tudi manj{a, `ilavost pod to temperaturo pa ve~ja kot pri jeklu z velikostjo
zrn 6,8 µm.
Klju~ne besede: konstrukcijska jekla, zelo majhna kristalna zrna, metode procesiranja, vpliv deformacije in temperature,
mehanske lastnosti
1 INTRODUCTION
Yield stress (RE) increases with decreasing grain size
because the grain boundaries hinder the movement of
dislocations produced by the cold deformation of metals
according to the Hall-Petch equation:
RE = Ro + k · d
1/2 (1)
With: Ro – constant depending on the chemical and
phase composition of the steel and k – constant charac-
teristic for the effect of linear grain size (d).
For steels having an essentially ferritic micro-
structure the following relations were developped for the
yield stress and for the notch toughness transition
temperature1:
RE /MPa = 104.1 + 32.6 w(Mn) + 84 w(Si) +
+ 17.5 d–1/2 (2)
ITT /°C = 19 + 44 w(Si) + 700 w(N) – 11.5 d–1/2 (3)
By smaller grain size the temperature of cleavage of
ferrite is lower and the yield stress greater. Other ferrite
strengthening mechanisms increase also the temperature
of cleavage fracture. For this reason, their exploitation
for the increase of yield stress of structural steels is
limited. It is predicted2 that for a steel with a grain size
of 5 µm the 50 % fracture appearance transition
temperature of –100 °C would decrease to below –200
°C for a grain size of 1 µm. The extent of the beneficial
effect of grain size is shown in Table 1 by comparison
of the chemical composition and the share of other of
strengthening mechanisms for three structural steels with
a microstructure of ferrite and pearlite3. The industrial
exploitation of the effect of grain size depends on the
benefit obtained with the decrease of production costs
which may result from the smaller content of alloying
elements, the incresed costs of the technology to achieve
the aimed grain size rsp. properties and the benefit of the
use of the steel with increased yield strength for
structures. In the last benefit several costs are included,
f.i. lower transportation and erection costs for structures
and a smaller quantity of welding consumables. Some-
times, the user can consider as important for the choice
of steel also other criteria, f.i. the resistance of the steel
to hydrogen embrittlemenst which is of essential
importance for steels for vessels for liquid hydrocarbons.
It is shown in Figure 1 than steel C with a grain size of
about 3 µm conserves a much greater reduction of area
after the NACE test of tensile test after a determined
time of maintaninig the specimens at stress level of 80 %
of the yield stress in water saturated with H2S than the
Materiali in tehnologije / Materials and technology 41 (2007) 3, 111–117 111
UDC/UDK 669.14.018.298 ISSN 1580-2949
Review scientific article/Pregledni znanstveni ~lanek MTAEC9, 41(3)111(2007)
steel B with a grain size of about 25 µm inspite the by
1/3 greater yield stress of the first4. The fine grained steel
in capable to retain in solution and in traps much more
hydrogen than the coarse grained steel before the
ductility is deteriorated to a significant extent. It is, thus,
more resisting to hydrogen embrittlement and also more
resistant to the delayed fracture due to the accumulation
hydrogen at grain boundaries2.
Iz is shown later that there are processing routes
which have the potential to obtain a grain size of 1 µm in
flat products with substatial thickness. These steel will
find cost effective applications, but not major markets5.
The reason is in the fact that the effect different major
parameters affecting the grain size, f.i. steel chemistry,
relation temperature – deformation intensity, cooling rate
and transformation is not knovn to the extent allowing
the industrial exploitation or the explotation would
require significant investments in the hot working
technology, at least for products used for steel structures.
Thus, by analysing the potential effect of grain size on
structural steels, two aspects should be considered: the
scientific and the technological – commercial.
By a given chemical composition, the parameters of
hot working of steels of essential importance for the
achieving of a small grain size are: the hot working
temperature range, the finishing rolling temperature, the
per pass deformation and the total plastic deformation in
the range of temperature affecting the must the
nucleation and the growth of recrystallised grains in
deformed austenite or ferrite. One of the problems to
overcame is the rate interpass growth of recrystallised
grains and the rate of growth of ferrite grains after the
austenite to ferrite transformation.
In Figure 2 the effect of rolling temperature range of
56 mm slabs to 12 mm plates in 6 passes temperature is
shown for structural steels with different chemical
composition6,7. All slabs were soaked at 1250 °C and
cooled to a different initial rolling temperature. It is
evident, that by several passes rolling the initial size of
austenite grains does not affect the grain size in the
F. VODOPIVEC ET AL.: STRUCTURAL STEELS WITH MICROMETER GRAIN SIZE
112 Materiali in tehnologije / Materials and technology 41 (2007) 3, 111–117
Table 1: Chemical composition and share of strengthening mechanisms for three structural steels
Tabela 1: Kemi~na sestava in masni dele` mehanizmov utrditve za tri konstrucijska jekla
Composition Element in mass fractions w/%
C Mn Si Al Nb Cr Ni Cu Mo
Steel A 0.21 0.51 0.25 0.027 – 0.02 0.04 0.10 –
Steel B 0.17 1.32 0.32 0.009 – 0.21 0.13 – –
Steel C 0.08 0.36 0.34 0.052 0.058 0.54 0.27 0.36 0.27
Share of yield stress increase, RE/MPa
SM 1 SM 2 SM 3 Sm 4 Sm 5 SM 6 SM7 YSth YSexp
Steel A 30 50 17 56 85 – 20 258 265
Steel B 30 61 17 104 135 – 28 372 377
Steel 3 30 15 17 136 254 9 43 504 522
SM 1 – ferrite yield stress, SM 2 – content of pearlite, SM 3 – Interstitial solution, SM 4 – Substitutional solution, SM 5 – Grain size, SM 6 –
Dispersion, SM 7 – Precipitation in γ phase, YSth – calculated yield stress, YSexp – Experimental yield stress
Figure 2: Effect of finishing rolling temperature on linear grain size
for several structural steels rolled from 55 mm slabs in 6 passes to 16
mm plates and cooled in air on a warm bed
Slika 2: Vpliv temperature konca valjanja na linearno intercepcijsko
dol`ino za ve~ konstrukcijskih jekel, ki so bila izvaljana iz 55-mili-
metrskih slabov v 16-milimetrske plo{~e v {estih vtikih in ohlajena na
zraku na topli podlagi
Figure 1: Results of the NACE test for the steels B and C in Table 1
and a microalloyed normalised steel with yield stress of 470 MPa4
Slika 1: Rezultati preizkusa NACE za jekli B in C iz tabele 1 in za
mikrolegirano normalizirano jeklo z mejo plasti~nosti 470 MPa4
rolled and air cooled steel. Also, in the applied rolling
conditions, the effect of niobium carbide precipitation
was very limited, since, only a slightly greater
ferrite-pearlite grain size was obtained in steels with
similar carbon content and without niobium although the
virtually complete precipitation of niobium carbide
during the rolling. In Figure 3 the effect of finishing
temperature on grain size is shown for steels with 0.04 %
C to 0.13 % C8. The rolling regime was virtually iden-
tical to that for steels in Figure 2. At the same finishing
temperature the grain size in the range of 7 µm to 33 µm
was obtained. The shape of the curves for different steels
on Figure 3 shows that after a temperature, which
depends on the content of carbon, coarser grain size is
obtained at lower than by higher finishing rolling
temperature. By a finishing temperature of 800 °C the
grain size decreases virtually proportionally to the
content of carbon in steel (Figure 4). From the shape of
the relation ship in Figures 3 and 4 and considering the
chemical composition of the steels, it was concluded that
the difference between the theoretical transformation
temperature of austenite and the real transformation
temperature during the rolling was very small and that it
depends mostly on the content of carbon in the steel.
Also, Figures 3 and 4 show that the growth of ferrite
grains after the last pass (last partial deformation of
about 20 %), is very fast. The strong effect of carbon on
grain size in as rolled steels is explained with the
increasing share of rolling performed in ferrite range
with a per pass deformation of approximately 20 %,
which is lower than that necessary for the static
recrystallisation of this phase, which is of about 60 %9,10.
According to11,12 for the static recrystallisation of
austenite only a per pass deformation of above 10 % is
necessary. In absence of recristallisation, the grain
growth of ferrite, termed strain induced coarsening,
occurs with a much greater rate than the growth of grains
of ferrite produced with the transformation of
recrystallised austenite at lower temperature. With the
transformation of deformed and non recrystallised grains
of austenite in Nb microalloying steel bainite grains of
size more than one order of magnitude greater than the
size of ferrite and pearlite grains in the surrounding
matrix and formed by transformation of recrystallised
austenite grains, were obtained, while the transformation
of grains of deformed austenite in low carbon steel
produced lenticular colonies of coarser, partially acicular
ferrite and pearlite grains (Figure 5). It is clear, thus,
F. VODOPIVEC ET AL.: STRUCTURAL STEELS WITH MICROMETER GRAIN SIZE
Materiali in tehnologije / Materials and technology 41 (2007) 3, 111–117 113
Figure 5: (magn. 200 times) Microstructure of the steel K from
Figure 3 rolled in the temperature range from 900 °C to 774 °C
Slika 5: (pov. 200-kratna) Mikrostruktura jekla K s slike 3, ki je bilo
izvaljano v razponu temperature od 900 °C do 774 °C
Figure 3: Effect of finishing rolling temperature on the ferrite pearlite
grain size for steels with the content of carbon in the range of 0.04 %
to 0.13 %. The tests were carried out in the same way as those in
Figure 2
Slika 3: Vpliv konca temperature valjanja na velikost zrn ferita in
perlita za jekla z ogljikom v razponu med 0,04 % in 0,12 %. Preizkusi
so bili izvr{eni na enak na~in kot pri jeklih na sliki 2
Figure 4: Relationship grain size versus carbon content for steels in
Figure 3 rolled in the temperature range from 900 °C to 790 °C
Slika 4: Velikost zrn v odvisnosti of vsebnosti ogljika za jekla s slike
3, ki so bila izvaljana v razponu temperature med 900 °C in 790 °C
that the achievement of µm and smaller size of ferrite
grains in structural steels is a problem of rolling tech-
nology, and for a given chemical composition of the
steel, it depends on the deformation and the temperature
of final rolling passes, the austenite to ferrite transfor-
mation temperature and the cooling of the rolled steel. It
is usefull to remember that the general tendency in the
development of modern structural steeels is assotiated
with a constant lowering of the content of carbon13, as
shown in Figure 6.
In this survey the parameters related to the grain size
of structural steels will be discussed considering the tests
aimed to determine what can be achieved in laboratory
and is, in this moment and in the near future, outside the
potential of the present technology and what may be
achieved with acceptable changes of the present
technology.
2 THEORETICAL ROUTES TO ACHIEVE A
SMALL GRAIN SIZE
The benefit of grain size is achieved with small
crystal grains with high angle boundaries able to stop
moving dislocations produced by cold deformation by
testing of tensile properties at room temperature. High
angle boundaries are achieved with recrystallisation of
austenite and ferrite, mostly static, and with the austenite
to ferrite transformation. It is, thus, logical to assume,
than small grain size involving the phase transformation
can be obtained only from austenite with very small
grain size and the prevention of ferrite grain growth. If
the small grain size is to be obtained with static
recrystallisation of ferrite at hot rolling, a very great
plastic deformation is necessary, in one pass or in several
passes on condition of incomplete per pass relaxation of
deformation energy.
The recrystallisatuon behaviour of austenite depends
on the steel chemistry. For the calculations of the
temperature of the end of static recrystallisation of
austenite the following equation was deduced for the
effect of different alloying elements in wt %14:
Tnr = 887 + 464 w(C) + 890 w(Ti) – 357 w(Si) +
+ 6445 w(Nb) – 644 w(Nb)1/2 + 363 w(Al) (3)
The effect of nobium is the greater and it is related to
the precipitation of niobium carbide (NbC). For the
calculation of the temperature of precipitation of this
carbide the following relation was proposed14:
TNbC/°C = −6770/{lg [w(Nb) × w(C)] – 2.26} – 273 (4)
The rate of precipitation of NbC is at the same
temperature for approximately three orders of magnitude
greater during the deformation of austenite and for two
orders of magnitude greater in deformed austenite15,16
than in recrystallised austenite and the increase of strain
rate lowers the recrystallisation and the precipitation
temperature17. The explanation of the delaying effect of
niobium is that strain induced precipitates hinder the
growth recrystallisation nuclea from reaching the critical
size required for their growth in deformed austenite.
Within this explanation it is not clear why the effect of
titatium is smaller than that of niobium. By equal weight
content, the atomic content of titanium is greater and the
solubility product for titanium carbide is even smaller
than that for NbC. For this reason, a similar effect of
titanium would be expected even at higher temperature
than that of niobium. It is interesting to note, with
respect to the mechanism of the effect of niobium on
recystallisation of austenite, that it was found with
dilatometric investigations of recrystallitaion and pre-
cipitation, that niobium in solid solution in ferrite
delayed the recrystallisation of this phase14. Other
alloying elements have a much smaller effect of the
temperature of static recrystallisation of austenite and,
for this reason, can not be, exploited for the achieving of
small grain size. In all cases, the presence of a
determined number of precipitates is necessary to
prevent the growth of recrystallised austenite and ferrite
grains.
The microstructure of fine grained structural steels
consists of ferrite, pearlite and bainite in different
combinations and can be achieved with the trasformation
of fine grained austenite. For a given steel chemistry, the
austenite grain size depends on the extent of deformation
and the growth of recrystallised grain in interpass time,
the time of cooling below the minimal grain growth
temperature or the time to the transformation to ferrite. It
was found that, indepenedently on the cooling rate, after
holding of the deformed austenite for 100 s at 900 °C,
the steel had a ferrite grain size 1 µm greater than
without holding time14. The explanation was in the rapid
coarsening of NbC precipitates.
In laboratory, it is possible to vary in a large range all
the parameters affecting the grain size. At this time, the
smallest grain size is achieved with ECAP18 (equal
channel angular pressing) or hot pressing. The defor-
mation energy is dispersed motly as heat, for this reason,
test with great deformation or deformation rate are not
isothermal. The rate of plastic deformation is generally
F. VODOPIVEC ET AL.: STRUCTURAL STEELS WITH MICROMETER GRAIN SIZE
114 Materiali in tehnologije / Materials and technology 41 (2007) 3, 111–117
Figure 6: Evolutionary trend for high strength steels for linepipes
Slika 6: Smer evolucije visokotrdnih jekel za cevi
high and, for this reason, the deformation energy may be
generated adiabatically and the steel in the deformation
zone heated significantly above the nominal deformation
temperature.
With ECAP processing18 a grain size below 1 µm can
be obtained with interstitial free steels. With 4 passes of
ECAP at 623 K a ferrite grain size of 0.3 µm and
severely deformed pearlitic cementite were achieved in a
steel with 0.15 % C, 0.25 % Si and 1.1 % Mn and the
initial intercept length of ~ 30 µm. The yield stress was
increased from 300 MPa to 944 MPa, while, the ductility
was decreased to less than one half of the initial level.
The addition of 0.06 % V to the steel had no visible
effect on the properties after ECAP inspite of the fact,
that the initial grain size was of ~ 10 µm, thus only 1/3 of
that in the case of the vanadium free steel. The increase
of ECAP passes from 4 to 8 did not affect the grain size
and the yield stress, it increased however the misorien-
tation of the grain boundaries19,20. The conclusions were
that that by multiple ECAP the effect of initial grain size
is not significant.
The tensile properties were changed significantly
after ECAP deformation of the 0.15 % C, 0.25 % Si,
1.12 % Mn, 0.34 % V and 0.012 % N, yield stress was
increased from 435 MPa to 920 MPa, tensile strength for
568 MPa to 920 MPa, uniform elongation was decreased
from 17 % to 2 % and total elongation from 28 % to 9 %
(Figure 7)21. If during the ECAP test nanosize precipi-
tation of vanadium carbide occured, the precipitates
improved the thermal stability of nanostructure and of
tensile properties of the steel, while, the particles
obtained with normalisation before ECAP had no
significant effect of the thermal stability of the ECAP
nanostructure21.
With ECAP at 500 °C and intercritical annealing of
the 0.15 % C,0.25 % Si and 1.1 % Mn the achieved grain
size of ferrite grains and martensite islands was of 0.8
µm22, the yield stress, of 540 MPa, tensile stregth of 890
MPa, uniform elongation of 9.8 % and total elongatiopn
of 17.6 %. By difference of results achieved with other
types of steel, the investigated steel exibited an extensive
strain hardening.
With four pass compression with a total strain of ε =
1.6 in the temperature range from 1143 °C to 823 °C the
grains size of a 0.22 % C and 0.74 % Mn steel was
diminished from 6.8 µm to 1.3 µm, yield stress increased
from 360 MPa to 540 MPa23 and the elongation was
decreased from 31 % to 16 %. This decrease was
explained in terms of smaller strain hardening due to the
spreading of dislocation in the grain boundaries of ferrite
grains. Of special interest in the finding that by small
grain size the upper shelf absorbed energy was smaller
than by coarse grain size, while the transition
temperature was lower and the transition range was
greater (Figure 8). The greater notch toughness below
the value of half upper shelf energy was explained in
terms of delamination occurring at the fracturing in
lower temperature range, which may be related to a
stronger texture of crystal grains in the fracture plane.
The one pass hot pressing eliminates the changes of
micro/nano structure during the interpass time, avoids
the multi axial deformation and enables the analysis of
the micro/nano structure obtained at different strain
level24. The transformation grain refinement (TGR) and
recrystallisation grain refinement (RGR) are suggested
as potential routes to achieve µm grain size. Both routes
can be carried out f.i., with tests of ECAP, hot pressing
or warm rolling. By one pass pressing of 0.16 % C, 0.41
% Si and 1.43 % Mn at 823 °C and 10–1s they were able
to distinguish the different steps of the formation of
small grains. First the original grain are compressed and
elongated in the direction of metal flow and low angle
boundaries are introduced because of the parallel
rotation of elongated grains. At the strain of 2.5 fine
equiaxed grains appear at high angle boundaries of initial
F. VODOPIVEC ET AL.: STRUCTURAL STEELS WITH MICROMETER GRAIN SIZE
Materiali in tehnologije / Materials and technology 41 (2007) 3, 111–117 115
Figure 8: Effect of test temperature on absorbed energy for two steels
with grain size 6.8 µm and 1.3 µm
Slika 8: Vpliv temperature preizkusa na energijo preloma za dve jekli
z velikostjo zrn 6,8 µm in 1,3 µm
Figure 7: Stress-strain curves for two steels before V(1) and after
ECAP V(2)
Slika 7: Odvisnosti napetost-deformacija za dve jekli pred ECAP
V(1) in po njem V(2)
grains, at the strain of 4 the share of fine new grains is
significant and it increases continously with the
increasing plastic deformation. The formation of these
grains is explained with work hardening accompanied
with grain subdivision and dynamical recovery occuring
simultateusly at warm working temperatures. With warm
pressing deformation in four passes with the per pas
deformation of of ε = 0.4 in temperatrure range from 600
°C to 710 °C in a 0.36 % C, 0.53 % Mn, 0.22 % Si
equiaxed ferrite grains of size 1 µm to 2 µm and an
uniform distribution of even smaller cementite particles
were attained25.
The different routes to achieve small grain size are
discussed also in26 where also experimental work was
performed with the aim to verify the exploitation of the
deformation induced ferrrite transformation (DIFT) and
the accumulative roll bonding. The investigation was
performed in the frame of a ECSC project aimed to
identify whether ultrafine grained steels were a potential
commercial opportunity or just an academic curiosity. It
was established that deformation induced ferrite
transformation (DIFT) occurs at a critical strain, which is
related to the chemistry of the steel and that carbon in
solution in austenite increases the critical strain and
retards the DIFT.
The process of DIFT consists of rolling a coarse
grained steel close to the Ar1 level with a reduction of
30–40 %27. The undecooling due to the roll chilling and
the high shear strain at the sheet surface, increases
greatly the nucleation rate in austenite grains. In this
way, a very rapid austenite transformation is achieved
over the whole austenite grain. It seems that the strain
enegy of deformed austenite may induce the transfor-
mation to ferrite slightly above the Ar3 point28,29,30, in
agreement with Figure 3.
In the thermodinamic analyis of DIFT31 it is assumed
that the deformation elongates austenite grains, increases
the grain boundary area and enhances the disorder of the
grain boundary structure and the grain boundary energy
per unit area. Analytical relations were developped to
calculate the increase of free energy in dependence of
the deformation degree and rate. Two nucleation sites for
the transformation induced ferrite (DIF) were observed:
austenite grain boundaries and two sites in the interior of
austenite grains: deformation bands and the new formed
g/a interface. The share of DIFT in the steels increases
strongly with the deformation and it is of approximately
25 % by a strain of 0.4 and of 80 % by a strain of 1.2.
With laboratory DIFT rolling of a 0.09 %C, 0.47 %Si,
1.38 %Mn, 0.1 %V, 0.04 %Nb, 0.02 %Al and 0.018 %N
steel in the temperature range of 1473 K to1093 K with a
strain of 0.93 at the final thre passes grain size of 1.5 µm
was obtained.
With DIFT in a microalloyed structural low carbon
steel32 (X65 steel) a grain size of 1.22 µm and the
volume share of DIFT ferrite of 71 % were obtained by
the hot rolling reduction of 69 %, the grain size of 0.92
µm and a volume share of DIFT ferrite of 98 % were
obtained after a deformation of 88 %. The precipitation
of niobium should occurr before the final rolling passes.
If not achieved, coarser grain size, similar to that in
Figure 5, is obtained after air cooling.
The 0.08 %C, 1,74 %Mn and 0.18 %Ti steel was
rolled rolled in 6 passes from 30 mm to 5 mm with the
finishing temperature in the range 790 °C to 820 °C and
cooled with the rate in the range od 20 °C/s to 40 °C/s to
the coiling temperature of 550 °C33. A microstructure
consisting of ferrite of average linear size of approxi-
mately 1.5 µm by a cooling velocity of 20 °C/s and
bainite by a cooling rate of 30 °C/s were obtained. With
the microstructure of ferrite the yield stress of 500 MPa
and the elongation of 27 % were obtained, while with a
microstructure of 90 % of bainite the yield stress was of
835 MPa and the elongation of 20 %.
The ferrite grain size of approximately 2 µm seems to
be the minimal size, which can be abtained by he DIFT
mechanims and heavy rolling deformation of super-
cooled austenite using the existing rolling facilities34.
Further refining doesn’t seems to improve the mecha-
nical properties as compared to the effects to be made. In
this reference three temperature (Td) domains of grain
refinenement by heavy deformation are mentioned.
Deformation of supercooled austenite (Td > Ar3) and
DIFT refinement mechanism and limit grain size of 2
µm, deformation of a duplex austenite + ferrite initial
microstructure (Ar3 > Td >Ar1) and refining by DIFT or
DRX (dynamic recrystallisation of ferrite) and limit
grain size of 1 µm and deformation of ferrite (Td < Ar1)
with the limit grain size of 0.6 µm. Ferrite grain size
obtained with dynamic transformation is finer than that
obtained with static recrystallisation. No data on the
extent of deformation are given in this reference.
3 CONCLUSION
Micrometer grain size can be obtained for low carbon
structural steels with several methods. Virtually all of
them are suited for laboratory processing, only DIFT
(deformation induced ferrite transformation) and low
temperature transformation of recrystallised austenite
seems to offer the industrial feasibility. Several authors
confirm that by µm grain size yield stress and tensile
strength are greatly increased, while and elongation is
significantly decreased. In one reference it was found,
that by the upper shelf ductile fracturing energy was
lower for the same steel by the 1.3 µm than by the 6.8
µm grain size. On the contrary below the temperature of
half of the maximal fracture energy, the toughness was
greater for the steel with smaller grain size.
The DIFT processing seems to be suited for the
production of thin sheets, for thicker product the µm size
of grains can be obtained only in a relatively this surface
layer. For thicker plates, a small grain size can be
achieved with strictly controlled termomechanical
F. VODOPIVEC ET AL.: STRUCTURAL STEELS WITH MICROMETER GRAIN SIZE
116 Materiali in tehnologije / Materials and technology 41 (2007) 3, 111–117
rolling involving the completed recrystallisation of
plastically deformed austenite, it transformation to
polygonal ferrite at a low temperature, and a sufficiently
rapid cooling to prevent the ferrite grain growth. For
such processing only niobium microalloyed steel are
suited. The chemical composition of the steel should
ensure a low temperature of precipitation of niobium
carbide and and a low transformation temperature of
recrystallised austenite to polygonal ferrite.
4 REFERENCES
1 F. B. Pickering, T. Gladman: Metallurgical Development in carbon
steels; ISI, 1963, 10–20
2 Ultra Steels for the 21st Century; Center for Structural Materials
Research, National Institute for Materials Research, Japan, 2001
3 F. Vodopivec, J. Vojvodi~ - Tuma, M. Lovre~i~ - Sara`in: Kovine
Zlit. Tehnol. 32 (1998), 463
4 S. A`man, L. Vehovar, J. Vojvodi~-Tuma: Razvoj ~elika mikro-
legiranog niobijem i molibdenom (Development of a steel micro-
alloyed with niobium and molybdenum), Zavarivanje 96, Beograd,
58–60
5 J. A. A. Hove: Mat. Sci. Techn. 16 (2000), 1264
6 F. Vodopivec, M. Gabrov{ek, J. @vokelj: @elez. zb. 17 (1985),17
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(1988) 117
9 D. N. Hawkins: Metals Techn. 5 (1978), 37
10 S. Gohda, T. Watanebe, J. Hashimoto: Trans. ISIJ 21 (1981), 6
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UCC Corpor., Nery York, 1975, 107
12 I. Kozasu, C. Ouchi, T. Sampei, T. Okita: Microlloying 75, UCC
Corpor., New York, 1975, 120
13 G. Buzzichelli, E. Anelli: ISIJ Intern. 42 (2002), 1354
14 C. Mesplont: Grain refinement and high precipitation hardening by
combining microalloying and ultra fast cooling; Proceedings of the
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Italy, 2–4 Nov. 2005
15 I. Weiss, J. J. Jonas: Metall. Trans. 11 A (1980), 403
16 J. J. Jonas, I. Weiss: Met. Sci. 3 (1979), 238
17 S. F. Medina, A. Quispe: Mat. Sci. Techn 16 (2000), 635
18 Z. Horita, M. Furukawa, M. Nemoto, T. G.Langdon: Mat. Sci.
Techn. 16 (2000), 1239
19 D. H. Shin, J. J. Park, S.Y Chang, Y. K. Lee, K. T. Park: ISIJ Intern.
42 (2002), 1490
20 D. H. Shin, W. G. Kim, J. Y Ahn, K. T. Park, N. J. Kim: Fabrication
and tensile properties of ultrafine grained steels; Proceedings of the
1th International Conference on super – high strength steels, Rome,
Italy, 2–4 Nov., 2005
21 K. T. Park, S. Y Han, D. H. Shin, Y. K. Lee, K. S. Lee: ISIJ Intern. 4
(2006), 1057
22 K. T. Park, Y. K. Lee, D. H. Shin: I/SIJ Intern. 45 (2005) 9, 750
23 R. Song, D. Ponge, D. Raabe: Mechanical properties of an ultrafine
grained C-Mn steel; Proceedings of the 1th International Conference
on super – high strength steels, Rome, Italy, 2–4 Nov., 2005
24 S. V. S. Narayama Murty, S. Torizuka, K. Nagai: ISIJ Intern. 45
(2005), 1651
25 L. Sorojeva, R. Kaspar, D. Ponge: ISIJ Intern. 44 (2004), 1211
26 I. Salvatori: Ultrafine grained steels by advanced thermomechanical
processes and severe plastic deformation; Proceedings of the 1th
International Conference on super – high strength steels, Rome,
Italy, 2–4 Nov., 2005
27 P. J. Hurley, B. C. Module, P. D. Hogson in Thermomechanical
Processing of steels 2000, London, Mai 2000, 476 (loc. cit. ref. 24)
28 M. R. Higson, P. D. Hogson: Mater. Sci. Technol. 15 (2000), 85
29 J. K. Choi, D. H. Seo, K. Umk, W. Y. Choo: ISIJ Intern. 43 (2003),
764
30 S.C. Hong, S. H. Lim, H. S. Hong, K. J. Lee, D. H. Shin, K. S Lee:
Mat. Sci. Techn. 20 (2004), 207
31 X. Sun, Q. Liu, H. Dong: Deformation induced ferrite transformation
and grain refinement in low carbon steel; Proceedings of the 1th
International conference on Super – high strength steels, Rome, Italy,
2–4 Nov. 2005
32 H. Dong, Y. Gan,Y. Weng: Research activities on advanced steels in
Nercast; Proceedings of the 1th International conference on Super –
high strength steels, Rome, Italy, 2–4 Nov., 2005
33 J. K. Choi: Development of high strength and high performance
steels at Posco through Hipers-21 project; Proceedings of the 1th
International conference on Super – high strength steels, Rome, Italy,
2–4 Nov. 2005
34 H. L. Yi, L. X. Du, G. D. Wang, X. H. Liu: ISJ Intern. 46 (2006),
754
F. VODOPIVEC ET AL.: STRUCTURAL STEELS WITH MICROMETER GRAIN SIZE
Materiali in tehnologije / Materials and technology 41 (2007) 3, 111–117 117

A. JAKLI^ ET AL.: HE IMPLEMENTATION OF AN ONLINE MATHEMATICAL MODEL ...
THE IMPLEMENTATION OF AN ONLINE
MATHEMATICAL MODEL OF BILLET REHEATING IN
AN OFU FURNACE
IMPLEMENTACIJA SIMULACIJSKEGA MODELA ZA
SPREMLJANJE OGREVANJA GREDIC V OFU-PE^I
Anton Jakli~1, Franci Vode1, Toma` Marolt2, Boris Kumer2
1In{titut za kovinske materiale in tehnologije, Lepi pot 11, 1000 Ljubljana, Slovenia
2[tore Steel, d. o. o., @elezarska cesta 3, 3220 [tore, Slovenia
anton.jaklicimt.si
Prejem rokopisa – received: 2007-01-15; sprejem za objavo – accepted for publication: 2007-03-29
We present the implementation of an online mathematical model for billet reheating in the OFU walking-beam furnace at the
[tore Steel d.o.o. steelworks in Slovenia. For the real-time operation of the simulation model the data about furnace charging
and real-time measurements in the furnace are needed. The simulation model is connected to the existing information system of
the OFU furnace, which can ensure the required data. The simulation is performed for all the billets (up to 125) that are
currently charged in the furnace. The modeling of the reheating process in a gas-fired walking-beam furnace consists of
descriptions of complex partial mechanisms. For the validation of the model, measurements of the billet reheating in the OFU
furnace were made. These measurements involved a test billet and five trailing thermocouples. The comparison of the
measurements and the simulation results, which are stored in a local database, shows good agreement across the whole
temperature range of the reheating process. For a user-friendly presentation of the simulation-model results we developed a
graphical user interface. This GUI allows the selection of particular billet from a visualization on the screen of the billets in the
furnace. The temperature field and the history of reheating for individual positions of the billet in the furnace are shown for the
selected billet. The system has been used online in the production process since May 2006.
Key words: simulation of reheating, billet reheating, real-time simulation, reheating furnace, walking-beam furnace
V prispevku je opisana implementacija simulacijskega modela za spremljanje ogrevanja gredic v OFU-pe~i v valjarni
[tore-Steel, d. o. o. Simulacijski model za delovanje v realnem ~asu potrebuje podatke o trenutnih meritvah temperatur con pe~i
in podatke o zalo`itvi pe~i, zato je povezan na obstoje~ informacijski sistem OFU-pe~i. Simulacija se izvaja v realnem ~asu za
vse gredice, ki so zalo`ene v pe~i (do 125). Modeliranje ogrevnega procesa v plinsko ogrevani kora~ni pe~i je sestavljeno iz
obravnave kompleksnih delnih mehanizmov. Vrednotenje simulacijskega modela je bilo izvedeno z meritvami ogrevanja
gredice v OFU pe~i. Meritve ogrevanja so bile izvedene med proizvodnim procesom na preizkusni gredici s petimi vle~nimi
termoelementi hkrati. Primerjava izra~una in meritev ka`e dobro ujemanje v celotnem poteku ogrevanja. Rezultati simulacije se
shranjujejo v lokalno bazo podatkov. Za uporabni{ko prijazen prikaz rezultatov simulacije je bil razvit grafi~ni uporabni{ki
vmesnik. Ta omogo~a izbiro poljubne gredice med prikazanimi gredicami, ki so zalo`ene v pe~i. Za izbrano gredico se prika`e
trenutno temperaturno polje in celotna zgodovina ogrevanja po posameznih polo`ajih v pe~i. Sistem se v rednem proizvodnem
procesu uporablja od maja 2006.
Klju~ne besede: simulacija ogrevanja, ogrevanje gredic, simulacija v realnem ~asu, ogrevna pe~, kora~na pe~
1 INTRODUCTION
A computer-controlled hot-rolling process for steel
billets requires high-quality reheated billets in terms of
time, temperature, thermal profile and furnace
atmosphere. When the furnace operates in steady-state
conditions the reheating history of every billet is very
similar; this type of operation can normally not be
achieved. During the normal, non-steady-state, pro-
duction process various transient operating conditions
occur in the furnace : planned and unplanned stoppages
in the mill’s operation, changing steel grades with
varying drop-out temperatures and different thermo-
dynamic properties, changing the stock dimensions, etc.
During this kind of transient operation every billet is
reheated under different reheating conditions. Therefore,
the reheating history of almost every billet is different.
For transient-type furnace operation information about
the temperature field for all (up to 125) billets in the
furnace is very important for successful furnace control
and operation. Unfortunately, however, existing
measuring methods cannot provide the temperature
fields of billets in the furnace. Nevertheless, by using
trailing thermocouples it is possible to measure the
reheating at a few measuring points inside the test billet.
By contrast, measurements using optical pyrometers or
thermal cameras in the furnace only give information
about the surface temperature of the billets. The use of
an online simulation model is the most appropriate way
to acquire the real-time temperature fields of billets in
the furnace.
In the [tore Steel, d. o. o. steelworks a continuous
walking-beam furnace (Figure 1) is used for the
reheating of steel billets. The furnace has three control
zones. The material flow through the furnace is
discontinuous, with fixed walking-beam steps. The
furnace has 125 billet positions; however, it is possible
to charge only every second or every third walking-beam
Materiali in tehnologije / Materials and technology 41 (2007) 3, 119–124 119
UDC/UDK 621.77.014:519.68 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 41(3)119(2007)
step in order to shorten the residing time of the billets in
the furnace.
In recent years, simulation models of reheating
furnaces that calculate the actual temperature distribution
in the stock have been developed with increasing
computational power. The current state of the art are
one- or two-dimensional calculations of the stock
temperature 1,2,3,4. However, the first attempts were made
to calculate the stock temperature in three dimensions
5,6,7 for different types of reheating furnaces, but not in
real-time. A 3D online simulation model of reheating in
a walking-beam furnace is presented in 8. The imple-
mentation of an online simulation model in a pusher-type
furnace is presented in 9.
In this paper we present the implementation of the
3D online simulation model of the OFU walking-beam
furnace.
2 EXPERIMENTAL WORK
The implementation of the simulation model for the
online operation of the furnace includes the development
of modules to provide real-time measuring data from the
furnace, to provide and recognize the current furnace
charge, to provide the thermal properties of different
steel grades, to store the simulation results in a database,
and to present the simulation results in a user-friendly
form.
2.1 Mathematical model
The online mathematical model used in the
implementation is presented in detail in 8,10. The
determination of the temperature fields of the billets is
based on algorithms that include the main physical
phenomena associated with the reheating process in a
natural-gas-fired walking-beam furnace. Thermal
radiation represents the dominant contribution of heat
transfer in a high-temperature reheating furnace. The
heat exchange between the furnace gas, the furnace wall
and the billet surface is calculated using the three-
temperature model of Heiligenstaedt.11 Heat radiation
between the surfaces inside the furnace (the furnace-wall
surfaces and the billet surfaces) is described using a
view-factor matrix. This matrix is obtained before the
simulation using the Monte Carlo method. The heat
conduction in the billets is calculated using a 3D
finite-difference method. The algorithms in the model
are optimized to allow a real-time simulation.
2.2 Obtaining the real-time data
For the online operation of the simulation model the
real-time data of furnace charging and furnace
measurements are needed. The simulation model is
connected to the existing furnace-process computer of
the OFU furnace (Figure 2), which provides the
real-time data about furnace-charging measurements in
the furnace. Both computers are connected by an
Ethernet connection. The data transfer is performed with
ASCII files using file-transfer protocol (FTP).
A data file "OFU.DAT" is generated every 30 s by
the OFU furnace-process computer. It contains both
online measurement data and charging data. The
measurement data include:
• Date and time of the measurements
• Temperature measurements of the three control zones
• The gas/air flows of individual control zones
• Oxygen measurements
• Pressure measurements
• Measurements of the recuperator temperatures.
The charging data are written in table form and
include information about current positions and other
important information about the billets in the furnace.
The data for an individual billet in the table consist of:
• Billet position
• Working order
• Serial number of the billet in the working order
• Steel grade
• Billet dimensions
• Date and time of charging
The "OFU.DAT" file is transferred from the
furnace-process computer to a computer with the
simulation model at regular intervals (i.e., every 20 s) by
the process "ftp-transfer", which runs on the computer
with the simulation model. After the transfer the file is
A. JAKLI^ ET AL.: HE IMPLEMENTATION OF AN ONLINE MATHEMATICAL MODEL ...
120 Materiali in tehnologije / Materials and technology 41 (2007) 3, 119–124
Figure 1: a) OFU walking-beam furnace, b) billets in the furnace
Slika 1: a) OFU-kora~na pe~ za ogrevanje gredic, b) gredice v pe~i
a
b
deleted on the main process computer. The intervals for
transferring the data file have to be shorter than the
intervals for writing the data to the file to prevent data
loss.
2.3 Thermal properties data
The thermal properties (the specific heat and the heat
conduction) of steel billets have a significant influence
on the reheating process. Generally speaking, these
properties are temperature dependent. In the model the
tables are written in ASCII files. In the production
process different steel grades with different thermal
properties are reheated in the furnace; however, some of
them have similar thermal properties. Therefore, all
types of steel grades are classified into main groups, and
for these groups the thermal properties were measured or
obtained from the literature. The automatic classification
is based on a uniform classification table, where the
corresponding steel group is written for each steel grade
in the table. When the billet is added to the charging list
the corresponding steel group is recognized on the basis
of the steel billet’s grade. The system then reads from
the files the temperature-dependant specific heat and the
heat-conduction tables for the recognized steel group.
These data are used for the calculation of the thermal
conduction inside the billet.
2.4 Automatic recognition of the charging events
The system is capable of automatic recognition of the
charging events and the charging interventions of the
furnace operator on the basis of a comparison between
the billet-charging table and the charging file. At the end
of the event-recognition process the charging table and
charging file have to be harmonized. The recognition of
charging events is a three-stage process.
In the first stage every billet in the charging table is
tested to see if it is present in the charging file. The
billets that are absent are deleted from the charging
table; their reheating history is saved in the archive
directory.
In the second stage every billet in the charging file is
tested to see if it is on the charging list. The billets that
are absent are added to the charging list and a new file
with billet data is opened and filled with the initial data.
After the first and second stages we can be sure that
the same billets are included in the charging list and in
the charging file. In the third stage the billets in the
charging list are sorted into the same order as in the
charging file. The position of every billet in the charging
list is compared to that in the charging file. If the
position is different, then the position in the list is
changed and the current calculated temperature field and
the position data are written in the reheating file of that
billet. The same algorithm is used for single and for
double charging and also for transitional operations:
single-to-double and double-to-single charging.
2.5 Database structure
All the results of the simulation model are stored in a
local database named "ofu" (Figure 3). The system uses
the open-source database system MySQL. The database
can be accessed locally by the online simulation model
and the human-machine interface (HMI) or through an
Ethernet connection by PC workstations in the local area
network (LAN).
The database consists of data tables. At every
simulation step (30 seconds) the simulation model
creates the data table "ofu_online" (Figure 3). The
records in the table correspond to the billets in the
furnace. Each record in the table includes basic billet
data (Working order, Serial number in the working
A. JAKLI^ ET AL.: HE IMPLEMENTATION OF AN ONLINE MATHEMATICAL MODEL ...
Materiali in tehnologije / Materials and technology 41 (2007) 3, 119–124 121
LAN
PLC
OFU furnace
Furnace process
computer
On-line simulation
model
Figure 2: The connection of the simulation model to the OFU furnace-process computer
Slika 2: Povezava simulacijskega modela s procesnim ra~unalnikom OFU pe~i
order, Steel grade, Billet width, Billet height, Billet
length, Charging time, Real-time of last calculation,
Number of the walking-beam step, Position in the
furnace, Residing time at the position, Residing time in
furnace) and the characteristic points of the last-calcu-
lated temperature field of the billet (Figure 4).
In cases when the charging situation in the furnace is
changed (new billet charged, billet discharged,
walking-beam step) the simulation model writes changes
into the "Working order tables" (the names of the tables
are working-order names, i.e., "066L0001686"). For
those billets for which the position is changed the model
writes the record of the last calculated temperature field
into the table with the name that corresponds to the billet
working order. The record has the same fields as the
record for the table "ofu_online". Therefore, the
"Working order tables" include the position-dependent
history of reheating in the furnace for all the billets of
the working order.
When new measurements from the furnace are
available (every 30 seconds) the simulation model adds
the record with the measurement data to the data table
"ofu_meritve" (Figure 3). The record consists of the
following: Time of measurement, Temperature zone 1,
Temperature zone 2, Temperature zone 3, Fuel-con-
sumption zone 1, Air-consumption zone 1, Fuel-
consumption zone 2, Air-consumption zone 2,
Fuel-consumption zone 3, Air-consumption zone 3,
Furnace pressure, Oxygen probe 1, Oxygen probe 2,
Oxygen probe 3, Combustion-air temperature, Waste-gas
temperature before recuperator, Waste-gas temperature
after recuperator.
2.6 Human-machine interface
The human-machine interface (HMI) (Figure 5) was
developed for the user-friendly presentation of the
real-time results of the simulation model. The HMI
process runs parallel to the simulation model. The HMI
gets all the data from the "ofu" database. There are two
modes of HMI operation: real-time and archive.
When the HMI runs in real-time mode the top view
of the furnace containing charged billets is shown in the
upper part of the window (Figure 5). The billet is
selected with a mouse click. In the lower part of the
window are detailed data about the selected billet:
Working order, serial number, steel grade, dimensions,
etc. The calculated temperatures of the characteristic
points on the cross-section are presented numerically and
using a thermal scale. Different diagram presentations,
such as the reheating temperatures of three selected
points in the billet, the temperatures of individual
furnace-control zones, the gas consumption of individual
control zones, the oxygen content, the pressure in the
furnace, the holding time of a billet at a particular
position in the furnace (Figure 6), can be selected. The
archive mode allows a preview of the reheating process
A. JAKLI^ ET AL.: HE IMPLEMENTATION OF AN ONLINE MATHEMATICAL MODEL ...
122 Materiali in tehnologije / Materials and technology 41 (2007) 3, 119–124
Figure 3: Database structure and availability
Slika 3: Struktura in dostopnost baze podatkov
Figure 5: The human-machine interface of the simulation model –
calculated temperatures of characteristic points of the cross-section
Slika 5: Grafi~ni uporabni{ki vmesnik simulacijskega modela –
izra~unane temperature karakteristi~nih to~k prereza
SE
SC SD
DE
DF
1
CE
S
3
2
Figure 4: Characteristic points on the billet cross-sections
Slika 4: Karakteristi~ne to~ke na prerezih gredice
of already-reheated billets. Billets in the archive list are
sorted by discharge time. The HMI is developed using
the XFORMS graphical library.
3 RESULTS AND DISCUSSION
The model was validated on the basis of
measurements from the OFU walking-beam furnace at
the [tore Steel steelworks in Slovenia. The test billet
(CK45 steel grade, dimensions 140 mm x 140 mm x
3500 mm) was reheated during the normal production
process. The temperature measurements were performed
using five trailing thermocouples (Type K,   = 4.5 mm,
L = 35 m). These five thermocouples were mounted
inside a test billet, as shown in Figure 7. Thermocouple
TC1 was mounted 10 mm under the upper slab surface;
TC2 was mounted 10 mm from the left billet surface, 70
mm deep; TC2 was mounted 10 mm from the right billet
surface, 70 mm deep; TC4 was mounted 10 mm from the
bottom billet surface, 130 mm deep; and TC5 was
mounted in the centre of the billet.
The simulation model was compared with the
measurements at all five measuring points, TC1, TC2,
TC3, TC4 and TC5. The model was tuned by adjusting
the temperature profile of the furnace’s ceiling and
sidewalls. After tuning the model, all the parameters of
the model were observed to be real physical values.
Good agreement was obtained between the measured and
the calculated temperatures at all five comparison points
for the whole reheating process (Figures 8 and 9). The
graph was divided into two graphs–the first for the time
interval 0–60 min (Figure 8) and the second for the time
interval 60–120 min (Figure 9) – in order to distinguish
between the measured and the calculated values. The
small vertical lines at the bottom of the graphs show the
walking-beam step intervals of the furnace.
The validation phase shows that the developed
algorithms of the simulation model for billet reheating in
A. JAKLI^ ET AL.: HE IMPLEMENTATION OF AN ONLINE MATHEMATICAL MODEL ...
Materiali in tehnologije / Materials and technology 41 (2007) 3, 119–124 123
0
100
200
300
400
500
600
0 10 20 30 40 50
S
t
T
imulation
Measurement
Figure 8: Validation of the simulation model for the test billet
(material: CK45, 140 mm x 140 mm x 3500 mm) for the time interval
0–60 min
Slika 8: Vrednotenje simulacijskega modela na preskusni gredici
(material: CK45, 140 mm x 140 mm x 3500 mm) v ~asovnem
intervalu 0–60 min
Figure 6: The human-machine interface of the simulation model –
diagram of the residing time of the billet at a particular position in the
furnace
Slika 6: Grafi~ni uporabni{ki vmesnik simulacijskega modela –
diagram ~asa zadr`evanja gredice na posameznem mestu v pe~i
Figure 7: Measuring points in the test billet
Slika 7: Merilne to~ke na preizkusni gredici
500
600
700
800
900
1000
1100
60 70 80 90 100 110
Simulation
Measurement
t
T
Figure 9: Validation of the simulation model for the test billet
(material: CK45, 140 mm x 140 mm x 3500 mm) for the time interval
60–120 min
Slika 9: Vrednotenje simulacijskega modela na preskusni gredici
(material: CK45, 140 mm x 140 mm x 3500 mm) v ~asovnem
intervalu 60–120 min
the OFU furnace are in good agreement with the real
physical behavior of the reheating process.
The system was developed using only open-source
solutions, and the Linux platform ensures stable running
of the system. The system has been used online in the
regular production process at the [tore Steel, d. o. o.
steelworks in Slovenia since May 2006.
4 CONCLUSIONS
The implemented system allows online monitoring of
non-measurable values (the 3D temperature fields of
billets in the furnace). The system is connected to the
furnace-process computer to ensure real-time measuring
and charging data from the furnace.
The simulation model’s results are stored in an SQL
database, which allows internet access to the data. Good
agreement between the measured and the calculated
heating curves shows that the model includes the main
physical phenomena occurring during the reheating
process in the OFU walking-Beam furnace. The
developed HMI allows a user-friendly presentation of
the simulation model’s results. The system has been used
online in the regular production process at the [tore
Steel, d. o. o., steelworks in Slovenia since May 2006.
5 REFERENCES
1 Staalman, D. F. J.: Process control in reheating furnaces, IoM
Conference Challenges in Reheating Furnaces, Conference Papers,
October 2002, London, 267–285
2 Dahm, B., Klima, R.: Feedback control of stock temperature and
oxygen content in reheating furnaces, IoM conference Challenges in
Reheating Furnaces, Conference Papers, October 2002, London,
287–296
3 Kolenko, T.; Glogovac, B., Jaklic, A.: An analysis of a heat transfer
model for situations involving gas and surface radiative heat transfer.
Commun. numer. methods eng., 15 (1999), 349–365
4 Jakli~ A., Kolenko T., Glogovac B.: Supervision of slab reheating
process using mathematical model, 3rd IMACS Symposium on
Mathematical Modelling MATHMOD, February 2–4, Vienna.
Proceedings, (ARGESIM Report No. 15), Vienna, 2 (2000), 755–759
5 Leden, B., Lindholm, D. and Nitteberg, E.: The use of STEEL-
TEMP® software in heating control, La Revue de Métallurgie-CIT,
96 (1999) 3, 367–380
6 Leden, B.: STEELTEMP® for temperature and heat-transfer analysis
of heating furnaces with on-line applications, IoM Conference
Challenges in Reheating Furnaces, Conference Papers, October
2002, London, 297–307
7 ECSC Steel RTD Programme, Contract No. 7210-PA/278, 7210-
PB/278, 7210-PC/278, Rules based system for the improved
monitoring and guidance of reheating furnaces
8 Jakli~ A., Kolenko, T., Glogovac, B.: A real-time simulation model
of billet reheating in the Allino walking-beam furance. Zborník
referátov : `iaromateriály, pece a tepelné izolácie: refractories,
furnaces and thermal insulations. Ko{ice: Hutnícka fakulta
Technickej univerzity, 2004, 237–242
9 Jakli~ A., Vode F., Robi~ R., Perko F., Strmole B., Novak J., Triplat
J.: The implementation of an online mathematical model of slab
reheating in a pusher-type furnace Mater. tehnol., 39 (2005) 6,
215–220
10 Jakli~ A., Kolenko T., Zupan~i~ B.: The influence of the space
between the billets on the productivity of a continuous walking-beam
furnace. Appl. therm. eng..  Print ed., 25 (2005) 5–6, 783–795
11 Heiligenstaedt W.: Wärmetechnische Rechnungen für Industrieöfen,
Verlag Stahleisen mbH, Düsseldorf, 1966
A. JAKLI^ ET AL.: HE IMPLEMENTATION OF AN ONLINE MATHEMATICAL MODEL ...
124 Materiali in tehnologije / Materials and technology 41 (2007) 3, 119–124
V. GLIHA, T. VUHERER: THE BEHAVIOUR OF COARSE-GRAIN HAZ STEEL WITH SMALL DEFECTS ...
THE BEHAVIOUR OF COARSE-GRAIN HAZ STEEL
WITH SMALL DEFECTS DURING CYCLIC LOADING
VEDENJE JEKLA GROBOZRNATEGA TVP Z NAPAKAMI PRI
CIKLI^NI OBREMENITVI
Vladimir Gliha, Toma` Vuherer
University of Maribor, Faculty of Mechanical Engineering, Smetanova 17, 2000 Maribor, Slovenia
vladimir.glihauni-mb.si/ tomaz.vuhereruni-mb.si
Prejem rokopisa – received: 2006-05-17; sprejem za objavo – accepted for publication: 2007-01-15
The effects of small, artificial surface defects on the fatigue strength of coarse-grain HAZ material found at the weld toe were
studied. The size of the defects did not exceed the grain size, which is the most relevant microstructural unit of polycrystalline
metals. The artificial defects were made by indenting the material with a Vickers pyramid and by drilling holes. The samples of
coarse-grain HAZ material were prepared using a welding thermal-cycle simulator or a furnace.
The experimentally determined bending fatigue strength versus the properly evaluated defects size was compared with the
propagation of long cracks. Residual stresses appear when making small artificial defects. The crack initiation from the defects
was analysed and the influence of residual stresses is discussed.
Key words: HAZ, weld toe, coarse grain, fatigue strength, artificial defect, residual stresses, non-propagating crack
Raziskan je bil vpliv majhnih umetnih napak na dinami~no trdnost grobozrnatega dela TVP ob robu zvarov. Napake niso bile
ve~je od kristalnih zrn, ki so najbolj pomembna enota polikristalnih materialov. Umetne napake smo ustvarili z odtiskovanjem
Vickesove piramide in vrtanjem. Preizku{ance z grobozrnatim jeklom TVP smo pripravili v simulatorju termi~nega cikla in v
pe~i.
Eksperimentalno dolo~eno upogibno dinami~no trdnost v odvisnosti od velikosti napake smo primerjali s propagacijo dolgih
razpok. S pripravo umetnih napak nastanejo zaostale napetosti. V razpravi je govor o za~etku razpoke iz napak in o vplivu
zaostalih napetosti.
Klju~ne besede: TVP, rob zvara, groba zrna, dinami~na trdnost, umetne napake, stabilna razpoka
1 INTRODUCTION
Defects decrease the fatigue strength of welds. In the
past, S-N curves were the only available tool to predict
the fatigue life of real quality welds until LEFM
concepts started to be applied to welds with macroscopic
crack-like defects.
Murakami and co-workers treated the influence of
variously shaped small defects in the same way as
cracks, i.e., using LEFM concepts 1–3. The square root of
the projection of defects onto the plane perpendicular to
the cyclic stress is a parameter reflecting the effect of
small defects on the fatigue strength of metallic mate-
rials. However, LEFM greatly underestimates the propa-
gation rates of short cracks within the local plastic zones
that develop as a result of the stress concentration 4,5.
Small cracks, much smaller than the smallest
microstructural units (microstructurally small defects),
have no influence on the fatigue strength of metals
(endurance limit) although these cracks can propagate
unexpectedly quickly at the beginning. Nevertheless, the
propagation decelerates gradually when approaching
microstructural obstacles such as grain boundaries. The
propagation can even stop, and the cracks then become
non-propagating. However, in the presence of cracks
whose size is comparable to the microstructural units of
a metal, the fatigue strength of metals is lowered. The
behaviour of metals with cracks from the smallest (short
cracks) to the biggest (long cracks) is described with the
use of a Kitagawa-Takahashy diagram 6.
The crack-initiation times in the highest-quality
butt-welds are shorter than predicted by LEFM if the
cracks initiate at the weld toe. Therefore, the possibility
of crack initiation at the weld toe, where a substantial
stress concentration exists, is of greatest importance for
the load-carrying capacity of cyclically loaded welded
structures (Figure 1). Because of the concentrated stress,
Materiali in tehnologije / Materials and technology 41 (2007) 3, 125–130 125
UDC/UDK 621.791.05:620.178.152.3 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 41(3)125(2007)
Figure 1: Macrograph of a K-butt weld with a remote homogeneous
stress. Arrows indicate the weld toes: the positions of the concentrated
stress field.
Slika 1: Makrografija K-zvara s homogeno napetostjo dale~ od spoja.
Pu{~ice ozna~ujejo robove zvarov in polo`aj koncentriranega polja
napetosti.
cracks at the weld toe initiate in the coarse-grain region
of the HAZ, the formation of which is the result of the
heat input needed for the fusion welding and, as a rule, it
is much harder than the base metal 7.
Artificial defects, especially small holes, are used
with great success in studies of the effects of small
defects on the endurance limit of metallic materials.
Extremely small weld defects, such as sharp transitions,
inclusions, scratches or cracks, present at the weld toe,
i.e., in the coarse-grain HAZ, can be modelled with
artificial defects, too.
Vickers indentations are suitable artificial defects.
The preparation of a proper indentation of the prescribed
size is easy to execute because only the hardness has to
be known. The problem of Vickers indentations used as
artificial weld defects is residual stresses. Any kind of
defect made in a mechanical way results in the
appearance of residual stresses. The reason is in the
irreversibility of the plastic deformation, which is very
extensive when indenting with Vickers pyramids. High
residual stresses affect the local stress/strain conditions
and change the actual shape of the artificial defect.
The behaviour of coarse-grain HAZ materials with
different types of microstructurally small defects in a
stress-concentrated condition was studied for cyclic
loading. The effects of the residual stresses were taken
into account.
2 EXPERIMENTAL
For this study samples of coarse-grained steel
characteristic of the HAZ at the weld toe in the
as-welded condition in the case of "cold" welding were
prepared by simulating the thermal conditions in the
material close to the weld on a welding thermal-cycle
simulator (Smitweld). The coarse-grain microstructure
was either pure martensite (M) or martensite with a
small portion of bainite (M+B).
The simulated coarse-grain HAZ microstructures
were designated as M1–M5. They were formed at
different cooling rates. The data on the cooling times, the
mechanical properties and the microstructures are shown
in Table 1.
The specimens for the fatigue-strength testing were
machined from samples with the simulated HAZ micro-
structure with the shape and size shown in Figure 2.
The specimens were notched in the region with the
simulated HAZ microstructure. The bottom of the notch
was ground and polished. The calculated stress
concentration caused by the notch was 1.74. The smooth
surface at the bottom of the notch is specified in Table 1
as test condition C1.
Artificial defects of different sizes and shapes were
made by indenting with a Vickers pyramid on the bottom
of the notch. As shown in Figure 3, they were single
indentations and a series of five indentations in a straight
line, perpendicular to the testing stress.
The average size of the single indentations, d, was
(105, 160, and 221) µm. These situations are specified in
Table 1 as the test conditions C2, C3 and C4.
The average length of a series of indentations, l, was
386 µm and 692 µm. These situations are specified in
Table 1 as the test conditions C5 and C6. The series were
composed of indentations with diagonals of length of
approximately 110 µm and 220 µm.
In the second part of this study, a coarse-grain HAZ
was prepared with furnace heating. During the first step
the samples of steel were heated to 1100 °C and held for
3 h. The grains grew to a size of 200 µm. This
coarse-grain annealing was followed by cooling in water.
The next step of the thermal treatment was heating to
870 °C and water quenching. The result of the combined
thermal treatment was a microstructure of pure
martensite.
The specimens were notched and artificial defects
made either before or after the quenching.
V. GLIHA, T. VUHERER: THE BEHAVIOUR OF COARSE-GRAIN HAZ STEEL WITH SMALL DEFECTS ...
126 Materiali in tehnologije / Materials and technology 41 (2007) 3, 125–130
Figure 2: Bend specimen with a notch in the simulated coarse-grain
HAZ steel
Slika 2: Upogibni preizku{anci z zarezo na podro~ju z jeklom
simuliranega grobozrnatega TVP
Table 1: Simulation parameters, mechanical properties, microstructures and test conditions
Tabela 1: Parametri simulacije, mehanske lastnosti, mikrostrukture in pogoji preizku{anja
Designation Cooling time t/s Yield strength
/MPa
Tensile strength
/MPa
Grain size
d/µm
Microstructure Condition
M1 5 981 1210 130 M C1,C2,C3,C4,C6
M2 9 935 1171 140 M+B C1, C2, C4, C6
M3 5.5 992 1192 180 M C1, C2, C4, C6
M4 9.5 939 1176 140 M+B C1, C2, C4, C5, C6
M5 9.5 921 1172 180 M+B C1, C2, C4, C5, C6
3 EXPERIMENTAL RESULTS AND DISCUSSION
Smooth and artificially surface-defected specimens
were bend-loaded in the first part of this study on a
resonant machine at room temperature in the load-
control mode. The frequency of the loading and the
stress rate were f ≅ 115 Hz and R ≅ 0, respectively.
The loading was increased in steps to 2 million
cycles or to fatigue crack initiation or specimen fracture.
A new specimen was used each time. The results of the
testing were S-N curves, valid for the test condition
C1–C6, and the coarse-grain HAZ materials M1–M5. The
highest stress range, ∆σΒ, at which the material still
resisted after 2 million cycles was taken as the bending
fatigue strength of the material, ∆σf-B. The numerical
results of the testing are shown in Table 2.
The depth of the artificial defects, b in Figure 3, is an
important parameter for the area evaluation, which
depends on the size of the indentation. The angle
between the opposite planes at the top of the Vickers
pyramid is 136°. The angle, α, between the opposite
edges that form the diagonal of the indentation, is
therefore somewhat bigger:
α = ⋅ °2 2 136
2
arctg tg( ); b
d= ⋅ °2
4
136
2
ctg (1)
The defect size parameter area was evaluated for
each of the used artificial defects, single indentations of
three sizes and a series of indentations of two sizes. A
special approach for the evaluation of long-shallow
small defects is available 8.
As shown in Figure 4, the area is the plane of the
actual defect projection for the single indentation and the
product of the maximum defect width with the length of
ten times the depth for the series of indentations 8.
area
d
ind
ctg= °
2 2
8
136
2
; area
d
ind
2ctg= °5 2
4
136
2
2
(2)
The relationships between the results of the testing
expressed as the fatigue strength ∆σf-B and the parameter
area are shown on a logarithmic-logarithmic scale in
Figure 5.
The shapes of the curves in Figure 5 agree quite well
with the Kitagawa-Takahashy plot. For that reason, three
dotted lines are entered in the figure, representing the
possible fatigue strengths of coarse-grained HAZ mate-
rials with long cracks. One of these lines could be the
right-hand side of the Kitagawa-Takahashy plot because
V. GLIHA, T. VUHERER: THE BEHAVIOUR OF COARSE-GRAIN HAZ STEEL WITH SMALL DEFECTS ...
Materiali in tehnologije / Materials and technology 41 (2007) 3, 125–130 127
Figure 4: Size of the image of a series of indentations and a single
indentation
Slika 4: Velikost plo{~ine niza odtisov in enega odtisa
Figure 3: Small artificial surface defects: a single indentation with
diagonal d and a series of five indentations with length l (cross-section
– a, ground plan – b)
Slika 3: Majhne umetne povr{inske napake: odtis z diagonalo d in niz
petih odtisov z dol`ino l (prerez – a, naris – b)
Table 2: Fatigue strength of the HAZs in terms of the quality of the surface at the bottom of the notch
Tabela 2: Trajna dinami~na trdnost TVP pri razli~ni kakovosti povr{ine na dnu zareze
Test condition C1 C2 C3 C4 C5 C6
Defect size, µm 0 d ≅ 105 d ≅ 160 d ≅ 221 l ≅ 386 l ≅ 692
Material ∆σf-B/MPa
M1 539 526 520 481 – 442
M2 546 507 – 468 – 442
M3 533 520 – 468 – 416
M4 533 533 507 442 – 416
M5 526 520 – 468 481 416
the ∆Kth-value for carbon structural steels corresponds to
5–10 MPa m.
Smooth and artificially surface-defected specimens
were bend-loaded in the second part of this study on a
rotary bending machine at room temperature in the
load-control mode. The frequency of the loading and the
stress rate were f ≅ 100 Hz and R = –1, respectively.
Single Vickers indentations and drilled small holes were
used as artificial weld defects. The defect size parameter
area was the same for both types of defect. Two
examples of these defects with already-initiated cracks
are shown in Figures 6 and 7.
The life of fatigue cracks has two stages: initiation
and propagation. The crack initiation from defects in the
presence of residual stresses is either easier or more
difficult because of the locally enhanced or reduced
stress/strain field caused by the defect preparation. Due
to the existing pre-stress, the local stress rate, R, is
changed. During the fatigue loading, at a sufficiently
high stress level, cracks appear due to the interactive
effect of the micro-defect and the loading.
To distinguish between the effects of micro-
structurally small defects assisted by local residual
stresses and microstructurally small defects acting alone,
a suitable approach to remove those stresses was
necessary. Electro-etching was not effective enough with
indentations, although it is often used with drilled holes.
Recrystallization in the last stage of CGHAZ simulation
using a furnace seemed a convenient way to remove the
local residual stresses without significantly changing the
defect’s geometry.
Two kinds of specimens with artificial defects were
prepared:
• specimens in the as-indented or as-drilled condition
• specimens in the stress-relieved condition
Local residual stresses due to indenting are
compressive, whilst with drilling they could be tensile.
When the defect is made before heating for water
quenching, local residual stresses do not exist after
quenching. The reason is the newly formed micro-
structure, caused by recrystallization during the
transformation. In contrast, the introduction of the defect
after the complete thermal treatment for coarse-grain
HAZ simulation induces local residual stresses.
In the first stage of fatigue testing, a microcrack
appears either at the surface, adjacent to the defects, or
inside the defects. Crack initiation occurs in individual
grains where the cyclic tangential stress in the weakest
crystal plane of randomly oriented grains exceeds a
determined level. If the remote stress level is not too
high the grain boundary arrests the crack propagation.
Local stress concentration due to the presence of defects
assists the crack initiation, but the effect is reduced with
the distance.
An array of initiated cracks on a specimen with a
smooth surface is seen in Figure 8. The cracks are not
longer than the average grain size, i.e., 200 µm. Their
orientation in the initiation stage is close to ± π/4.
V. GLIHA, T. VUHERER: THE BEHAVIOUR OF COARSE-GRAIN HAZ STEEL WITH SMALL DEFECTS ...
128 Materiali in tehnologije / Materials and technology 41 (2007) 3, 125–130
Figure 7: Drilled hole with a diameter of 90 µm. Cracks are initiated
on both sides of the hole.
Slika 7: Izvrtina s premerom 90 µm. Razpoki nastaneta na obeh stra-
neh izvrtine.
Figure 5: Dependence of the bending fatigue strength on the defect
size parameter area , calculated as illustrated in Figure 4
Slika 5: Odvisnost med upogibno dinami~no trdnostjo in parametrom
velikosti napake area , izra~unananim tako, kot je prikazano na sliki
4
Figure 6: Vickers indentation with a diagonal of 200 µm. Cracks are
visible at the ends of the indentation.
Slika 6: Vickers odtis z diagonalo 200 µm. Razpoki vidimo na konceh
odtisa.
In specimens where the crack is defected initiation
turns up in part of the grains where the intensity of the
cyclic stress/strain field is sufficient and it is parallel to
the shearing direction of the grain.
Figure 9 represents two separate cracks initiated at
the edges of the indentation. They are not connected at
the bottom of the indentation and did not spread over the
surface outside the indentation like the crack shown in
Figure 6. The reason for this is the existence of com-
pressive residual stresses, mostly at the bottom of the
indentation.
Figure 10 shows a single crack initiated at the edge
of a round hole. The difference between the two cracks
in Figure 7 and the single crack in Figure 10 is
explained by the absence of tensile residual stresses in
the close vicinity of the hole. Only the grain with the
initiated crack was oriented to enable crack initiation, the
orientation of the grain on the other side was less
suitable.
4 CONCLUSIONS
The shape of the relationship curve presenting the
bending fatigue strength, ∆σf-B, versus the defect size
parameter area shown in Figure 5 does not approach
the expected linear trend defined with several ∆Kth-
values up to the defect size parameter area ≅ 100 µm.
This is not surprising, because the threshold
stress-intensity factor, ∆Kth, which defines the fatigue
strength of materials with macroscopic cracks (the
long-crack propagation law) is grain-size dependent.
Because of coarse grains the ∆Kth-value is very likely
much higher than 7. On the other hand, it seems that the
defect size parameter area underestimates the fatigue
strength, thereby lowering the effect of a series of
indentations.
At this point it is not possible to conclude what is
more important for the unexpected shape of the relation-
ship curve ∆σf-B- area, the coarse grain size or the
indenting residual stresses. The length of the biggest
series of indentations is almost 700 µm (4–6 times the
average grain size); the depth of the indentations does
not exceed 31–32 µm (much less than the average grain
size). A logical question is which extension of the series
of indentations, length or depth, is more important? The
answer – that it depends on which direction the cracks
initiate – seems to be doubtful.
It was expected that specimens in the as-indented
condition would behave differently than those in the
stress-relieved condition. The reason is the presence of
the residual stresses:
If compressive residual stresses are the highest at the
deepest part of the indentation, cracks will initiate
separately at both loaded edges of the indentation. When
the stress level is sufficiently low those cracks become
non-propagating after their initiation. When stress level
is higher the cracks join at the deepest part of the
indentation and create a single crack. The effect of a
bigger single crack is greater than the effect of separate
cracks, although its size is almost equal to the sum of
their lengths.
V. GLIHA, T. VUHERER: THE BEHAVIOUR OF COARSE-GRAIN HAZ STEEL WITH SMALL DEFECTS ...
Materiali in tehnologije / Materials and technology 41 (2007) 3, 125–130 129
Figure 10: A single crack initiated from a hole
Slika 10: Ena sama razpoka, ki je nastala na izvrtini
Figure 8: Cracks initiated at the bottom of the notched specimen
without defects
Slika 8: Razpoke, ki so nastale na dnu zareze, ko ni napak
Figure 9: Two cracks initiated at both edges of a Vickers indentation
Slika 9: Razpoki, ki sta nastali na obeh robovih Vickers odtisa
In the absence of residual stresses the crack will
initiate as a single crack over the whole length of the
indentation. An initiated crack in the stress-relieved
condition that is longer than the indentation diagonal has
a stronger effect than the effect of two separate cracks in
the as-indented condition. The higher fatigue strength of
the specimens with compressive residual stresses than
those without residual stresses is logical.
Hole-drilled specimens behave differently than
indented specimens. The residual stresses due to drilling
are tensile; therefore, the opposite behaviour by the
drilled specimens was observed. The fatigue strength of
specimens with residual stresses is lower than the fatigue
strength of specimens without residual stresses.
Generally, compressive stresses at the surface
increase the fatigue strength, while the tensile stresses
decrease it.
5 REFERENCES
1 Murakami, Y. at al. Quantitative evaluation of effects of non-
metallic inclusions on fatigue strength of high strength steels – I:
Basic fatigue mechanism and evaluation of correlation between the
fatigue fracture stress and the size and location of non-metallic
inclusions, Int. J. of Fatigue, 9 (1989), 291–298
2 Murakami, Y., Usuki, H. Quantitative evaluation of effects of non-
metallic inclusions on fatigue strength of high strength steels – II:
Fatigue limit evaluation based on statistics for extreme values of
inclusion size, Int. J. of Fatigue, 9 (1989), 299–308
3 Murakami, Y. Effects of small defects and nonmetallic inclusions on
fatigue strength of metals, JSME International Journal I, 32 (1989) 2,
167–180
4 Miller, K. J. The behaviour of short fatigue cracks and their
initiation, Part I and Part II, Fatigue Fract. Engng. Mater. Struct., 10
(1987) 1, 75–91 and 10 (1987) 2, 93–113
5 Yasniy P-V. at al. Microcrack initiation and growth in heat-resistant
15Kh2MFA steel under cyclic deformation, Fatigue Fract. Engng.
Mater. Struct., 28 (2005) 4, 391–397
6 Kitagawa, H., Takahashi, S. Applicability of fracture mechanics to
very small cracks or the cracks in the early stage, 2nd International
Conference on the Behaviour of Materials, Boston, ZDA, 1976
7 Verreman, Y., Bailon, J-P., Masounave, J. Fatigue life prediction of
welded joints – A re-assessment, Fatigue Fract. Engng. Mater.
Struct., 10 (1987) 1, 17–36
8 Murakami, Y., Endo, M. Effects of hardness and crack geometries on
∆Kth of small cracks emanating from small defects, The behaviour of
short fatigue cracks, Edited by K. J. Miller, E. R. de los Rios,
Mechanical Engineering Publications, 1986
V. GLIHA, T. VUHERER: THE BEHAVIOUR OF COARSE-GRAIN HAZ STEEL WITH SMALL DEFECTS ...
130 Materiali in tehnologije / Materials and technology 41 (2007) 3, 125–130
M. DOMÁNKOVÁ ET AL.: THE EFFECT OF COLD WORK ON THE SENSITISATION OF AUSTENITIC ...
THE EFFECT OF COLD WORK ON THE SENSITISATION
OF AUSTENITIC STAINLESS STEELS
VPLIV HLADNE DEFORMACIJE NA POVE^ANJE
OB^UTLJIVOSTI NERJAVNIH JEKEL
Mária Dománková, Marek Peter, Morav~ík Roman
Faculty of Materials Science and Technology in Trnava, Slovak University of Technology in Bratislava,
Bottova 24, 917 24 Trnava, Slovakia
maria.domankova stuba.sk
Prejem rokopisa – received: 2006-09-20; sprejem za objavo – accepted for publication: 2007-01-15
The sensitisation behaviour of austenitic stainless steel is greatly influenced by several metallurgical factors, such as the
chemical composition, the degree of prior deformation, the grain size, and the ageing temperature and time. The precipitation
behaviour of AISI 316 and 304 austenitic stainless steels has been investigated after ageing at various temperatures from 500 °C
to 900 °C for 0.1 h to 1000 h. The TTS diagrams of the experimental steels after an oxalic-acid etch test ASTM A262 practice A
were constructed. It was demonstrated that the C curves of the TTS diagrams were displaced towards shorter times by the
increment of 20 % cold work (CW), since the sites inside the grain matrix have a high energy and the carbides can nucleate
there easily. Cold work increases the number of dislocations/dislocation pipes along which the diffusion rate of chromium is
very high. The sensitisation of the experimental steels accelerated the precipitation of M23C6. Besides M23C6, the σ-phase and
M6C were detected at the grain boundaries and in the austenitic matrix in the case of the cold-worked samples.
Key words: austenitic stainless steels, sensitisation, precipitation, cold working, intergranular corrosion
Ob~utljivost nerjavnih jekel je odvisna od ve~ metalur{kih dejavnikov, npr. od kemi~ne sestave, predhodne deformacije,
velikosti zrn, ~asa in temperature staranja. Izlo~ilno vedenje jekel AISI 316 in 304 je bilo raziskano po razli~no dolgem staranju
od 0,1 h do 1000 h pri temperaturah med 500 °C in 900 °C. TTS diagrami eksperimentalnih jekel so bili pripravljeni po
oksalnem preizkusu po ASTM 262 – metoda A. Dokazano je, da so C-krivulje TTS-diagramov premaknjene h kraj{im ~asom po
20-odstotni hladni deformaciji (CW), zato ker imajo tudi v zrnih mesta z veliko energijo, kjer nastanejo karbidni izlo~ki. Hladna
deformacija pove~a {tevilo dislokacij/dislokacijskih cevk, kjer je difuzija kroma zelo hitra. Pove~anje ob~utljivosti jekel je
pove~alo hitrost izlo~anja karbidov M23C6. σ-fazo in M6 karbide smo v hladno deformiranem jeklu opazili ob kristalnih mejah in
v avstenitni matrici.
Klju~ne besede: avstenitna nerjavna jekla, pove~anje ob~utljivosti, hladna deformacija, interkristalna korozija
1 INTRODUCTION
The intergranular corrosion (IGC) and stress-
corrosion cracking (SCC) of austenitic stainless steels
are the most important corrosion processes that affect the
service behaviour of these materials. Exposure to
temperatures in range 500–800 °C leads to the grain-
boundary precipitation of chromium-rich carbides
(Fe,Cr)23C6 and to the formation of chromium-depleted
regions. If the mass fraction of chromium content near
the grain boundaries drops under the passivity limit of 12
%, the steel becomes sensitised. The sensitisation
temperature range is often encountered during isothermal
heat treatment, slow cooling from the solution annealing
temperature, the improper heat treatment in the
heat-affected zone of the welds or welding joints or the
hot working of the material. The degree of sensitisation
(DOS) is influenced by factors such as the steel’s
chemical composition, the grain size, the degree of strain
or temperature and the time of isothermal annealing. The
sensitisation involves both the nucleation and growth of
carbides at the grain boundaries. Depending on the state
or the energy of the grain boundaries they can provide
preferential sites for carbide nucleation and act as a
favoured diffusion path for the growth of carbides.
Therefore, it has been suggested that the nature of grain
boundaries could also influence the DOS and IGC 1–4.
In this article we report on some preliminary
comparisons of the combined effects of chemical
composition, deformation, temperature and aging time
on sensitisation in AISI 304 and 316 stainless steels.
2 MATERIALS AND EXPERIMENTAL
PROCEDURES
The chemical composition of the experimental steels
is given in Table 1. The steels were mostly investigated
in the as-received condition with some in the
solution-annealed condition. The solution annealing was
conducted on the as-received materials at 1050 °C for 60
min followed by water quenching.
The steels were 20–40 % cold rolled by controlling
the thickness of the plates. The cold-worked samples
were heat treated at various temperatures in the range
500–900 °C for times of 0.1 to 1000 h. The samples
were then water quenched after the heat treatment.
The oxalic-acid etch test (ASTM A262 practice A)
was used to determine the steels’ sensitivity to inter-
granular corrosion. The specimens were electrolytically
etched in 10 % oxalic acid for 90 s at a current density of
Materiali in tehnologije / Materials and technology 41 (2007) 3, 131–134 131
UDC/UDK 669.14.018.8:620.193 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 41(3)131(2007)
1 A/cm2. The etched microstructure was then examined
at 250x, and was characterised as a step, dual or ditch
microstructure 5.
For the individual secondary-phase identification
transmission electron microscopy (TEM) of the carbon
extraction replicas was applied. TEM observations were
performed using a JEOL 200 CX operating at 200 kV.
The carbon extraction replicas were obtained from
mechanically polished and etched surfaces. The replicas
were stripped from the specimens in the solution of
CH3COOH : HClO4 = 4 : 1 at 20 °C and 20 V.
3 RESULTS
The results of the light microscopy examination are
summarised in Figure 1. The microstructure of AISI 304
after solution annealing consists of polyhedral austenitic
grains with twinning typical of an fcc microstructure.
The average austenitic grain size in this state is about
45 µm (Figure 1a). A small amount of  -ferrite was also
observed. No precipitates were detected at the grain
boundaries (GBs) of the solution-annealed steels. Figure
1b shows the microstructure of the AISI 304 after 40 %
of CW. The microstructures of the aged states are shown
in Figure 1c and Figure 1d. Figure 1c shows the
evolution of secondary phases precipitated at the
GB in the isothermally aged specimen (650 °C/0.5 h)
without cold work. The microstructure of the isother-
mally aged specimen (650 °C/0.5 h) and 40 % CW is
shown in Figure 1d. The precipitation of secondary
phases was observed at the GB and intragranularly and
within the matrix.
To compare the results of two austenitic stainless
steels, time-temperature-sensitisation (TTS) diagrams for
these steels for different degrees of CW ranging from 0
% to 40 % are presented in Figure 2. From the TTS
diagrams it can be seen that the nose of the C curve
corresponding to the maximum rate of sensitisation
M. DOMÁNKOVÁ ET AL.: THE EFFECT OF COLD WORK ON THE SENSITISATION OF AUSTENITIC ...
132 Materiali in tehnologije / Materials and technology 41 (2007) 3, 131–134
Table 1: Chemical composition (in mass fractions, w/%) of the austenitic stainless steels
Tabela 1: Kemi~na sestava (v masnih dele`ih, w/%) avstenitnih nerjavnih jekel
steel C N Si Mn P S Cr Ni Mo Fe
AISI 304 0.04 0.012 0.54 1.08 0.0032 0.008 18.52 8.47 0.21 bal.
AISI 316 0.05 0.032 0.47 0.86 0.0026 0.001 17.55 11.56 2.10 bal.
a b
c d
Figure 1: Microstructure of the AISI 304 a) after solution annealing – 0 % CW, b) after solution annealing – 40 % CW, c) after aging at 650
°C/0.5 h, 0 % CW, d) after aging at 650 °C/0.5 h, 40 % CW
Slika 1: Mikrostruktura jekla AISI 304 a) po topilnem `arjenju – 0 % CW, b) po topilnem `arjenju – 40 % CW, c) po staranju 650 °C/0,5 h, 0
% CW, d) po staranju 650 °C/0,5 h, 40 % CW
occurs at 800 °C for the AISI 316 in the 0 % CW
condition. As the degree of CW increases, the nose
temperature remains almost that same, but tmin decreases
with the increase in % CW up to 20 % and remains
constant thereafter. The TTS diagram of AISI 304 is
shifted towards shorter times than the 0 % CW material.
The tendency of the shift of the AISI 304 C curve is
similar to the case of AISI 316.
To identify the type of secondary phases precipitated
at the grain boundaries (GBs) during the isothermal
treatment, TEM analysis was carried out. First, M23C6
was detected at the grain boundaries after aging. In
addition to M23C6, the σ-phase and M6C were detected at
the grain boundaries (Figure 3 and Figure 4). Similar
precipitation trends were detected using TEM analysis at
M. DOMÁNKOVÁ ET AL.: THE EFFECT OF COLD WORK ON THE SENSITISATION OF AUSTENITIC ...
Materiali in tehnologije / Materials and technology 41 (2007) 3, 131–134 133
T
em
pe
ra
tu
re
,
/°
C
T
T
em
pe
ra
tu
re
,
/°
C
T
lg ( /s)thod.
lg ( /s)thod.
Figure 2: TTS diagrams for AISI type 316 and 304 stainless steels
with various degrees of CW established as per ASTM A262 practice
A test
Slika 2: TTS diagrama za nerjavni jekli 316 in 304 pri razli~ni stopnji
deformacije, dolo~eni z ASTM A262-preizkusom
Figure 6: Phase ratio in AISI 304 after aging at 650 °C
Slika 6: Razmerje faz v jeklu AISI 304 po staranju pri temperaturi
650 °C
Figure 3: Microstructure of AISI 316 (650 °C/300 h) – TEM
Slika 3: Mikrostruktura jekla AISI 316 (650 °C/300 h) – TEM
Figure 5: Phase ratio in AISI 316 after aging at 650 °C
Slika 5: Razmerje faz v jeklu AISI 316 po staranju pri temperaturi
650 °C
Figure 4: Microstructure of AISI 316 (650 °C/1000 h) - TEM
Slika 4: Mikrostruktura jekla AISI 316 (650 °C/1000 h) – TEM
the grain boundaries of the AISI 304 steel. The identified
secondary phases in the experimental steels and the
phase ratio are shown in Figures 5 and 6.
4 CONCLUSIONS
The precipitation behaviour of AISI 316 and 304
austenitic stainless steels was investigated during aging
at various temperatures in range from 500 °C to 900 °C
for times from 0.1 to 1000 h. The following conclusions
can be drawn:
TTS diagrams of the experimental steels after the
oxalic-acid etch test ASTM A262 practice A show that
the C curves of the TTS diagrams are displaced towards
shorter times with increasing amounts of CW.
After ≈20 % cold working, even the sites inside the
grain matrix have high energy and carbides can nucleate
there also. Cold work increases the number of
dislocations/dislocation pipes along which the diffusion
rate of chromium is faster.
Sensitisation of the experimental steels accelerated
the precipitation of M23C6. In addition to this carbide,
σ-phase and M6C were detected at the grain boundaries
and in the austenitic matrix in the cold-worked samples.
Acknowledgement
The authors wish to thank the Scientific Grant
Agency of the Slovak Republic (VEGA) for their
financial support of grant No. 1/2113/05.
5 REFERENCES
1 Murr L. E. Advani A., Shakar S., Atteridge D. G.: Effects of
deformation and heat treatment on grain boundary sensitisation and
precipitation in austenitic stainless steels. Material Characterization,
24 (1990), 135–158
2 Trillo E. A., Murr L. E.: Effects of carbon content, deformation and
interfacial energetics on carbide precipitation and corrosion
sensitisation in 304 stainless steel. Acta Materialia, 47 (1999) 1,
235–245
3 Janovec J., Blach J, Záhumenský P., Magula V., Pecha J.: Role of
intergranular precipitation in the fracture behaviour of AISI 316
austenitic stainless steel. Canadian Metallurgical Quartely, 38
(1999) 1, 53–59
4 Parvathavartini N., Dayal R. K: Influence of chemical composition,
prior deformation and prolonged thermal aging on sensitisation
characteristics of austenitic stainless steels. Journal of Nuclear
Materials, 305 (2002), 209–219
5 Standard Practice for Detecting Susceptibility to Intergranular
Corrosion of Austenitic Stainless Steels, ASTM, 2001
M. DOMÁNKOVÁ ET AL.: THE EFFECT OF COLD WORK ON THE SENSITISATION OF AUSTENITIC ...
134 Materiali in tehnologije / Materials and technology 41 (2007) 3, 131–134
S. SEITL, P. HUTA : FATIGUE-CRACK PROPAGATION NEAR A THRESHOLD REGION ...
FATIGUE-CRACK PROPAGATION NEAR A
THRESHOLD REGION IN THE FRAMEWORK OF
TWO-PARAMETER FRACTURE MECHANICS
DVOPARAMETRSKA LOMNO MEHANSKA ANALIZA HITROSTI
UTRUJENOSTNE RAZPOKE BLIZU PRAGA PROPAGACIJE
Stanislav Seitl, Pavel Huta 
Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Zizkova 22, 616 62 Brno, Czech Republic
seitl ipm.cz
Prejem rokopisa – received: 2006-05-17; sprejem za objavo – accepted for publication: 2007-03-09
A two-parameter constraint-based fracture mechanics method was applied to the problems of the fatigue-crack propagation rate
near a threshold region. Two geometries of specimens with different values of constraint were analyzed. The experimentally
obtained results were compared with numerical data. The presented result makes it possible to relate experimentally measured
data obtained from specimens with different geometries, and thus contributes to more reliable estimates of the residual fatigue
life of a structure.
Key words: constraint, T-stress, threshold values, fatigue crack growth rate, high cyclic fatigue,
Dvoparametrska vpetostna metoda je uporabljena pri problemu {irjenja utrujenostne razpoke blizu praga propagacije.
Analizirani sta dve geometriji preizku{anca z razli~no vpetostjo. Eksperimentalni podatki so primerjani z numeri~nimi.
Rezultati omogo~ajo, da se pove~a eksperimentalne izsledke s preizku{ancev z razli~no geometrijo in omogo~ajo bolj zanesljivo
oceno preostale trajnostne dobe neke strukture.
Klju~ne besede: vpetost, vrednosti praga, hitrost rasti utrujenostne razpoke, visokocikli~na utrujenost
1 INTRODUCTION
The understanding of constraint effects on the
fatigue-crack propagation rate (FCPR) is relevant for the
prediction of the operating life of engineering structures.
The elastic T-stress, the second term of Williams’s series
expansion1 for linear elastic crack-tip fields, represents
the stress acting parallel to the crack plane. In paper2
results relating to FCPR measurements for a 2024
aluminum alloy of two different specimen geometries
are investigated. The FCPR was found to be sensitive to
the specimen’s geometry in the Paris region of the
da/dN–K curve as well as in the threshold values. The
same trends are quantified for different levels of
constraint in the vicinity of the fatigue-crack tip by
means of the T-stress. This has been published for the
ratio R ≈ 0 in paper3. These findings are contradicted by
the results published in 4. The experiments are focused
on the fatigue-crack growth data from three different
specimen geometries obtained for nickel-based super-
alloys and mild steel. The recently published study5
describes experiments on edge-bending specimens
SE(B) and C(T) specimens to characterize the fatigue-
crack growth rates of Inconel 718, and in this study no
difference in the crack-growth rate between the two
kinds of specimens was observed.
Within two-parameter fracture mechanics (2PFM)
the stress field near the crack tip is expressed by means
of two parameters, i.e., the stress-intensity factor, K, and
the T-stress. The stress field at the crack tip can then be
expressed for a normal mode (mode I) of loading as
σ θ δ δij ij i j
K
r
f T= +1 1 1
2π
( ) (1)
where fij(θ) is a known function of the polar angle θ, and
δij and δ1j are the Cronecker deltas, taking the value 1 if
i and j are equal, and 1 and 0 otherwise.
The work reported here uses 2PFM for a description
of the different threshold values of a FCPR to predict the
effect of constraint on the retardation or acceleration of
the crack growth in high cyclic fatigue loading. The
corresponding calculations are performed according to
the finite-element method (FEM). The experimental
measurements of FCPR on two kinds of specimens with
a different geometries were compared and so were the
experimental data covering the effect of constraint.
2 TESTS OF THE FATIGUE-CRACK
PROPAGATION RATE NEAR TRESHOLD
VALUES
The effect of constraint on the fatigue-crack growth
rate near the threshold values was experimentally studied
in relation to two different specimens: the M(T) (the
middle-tension specimen) and C(T) (the compact-tension
specimen). The M(T) specimen produced a low level of
constraint (negative values of the T-stress) and the C(T)
specimen produced a high level of constraint (positive
Materiali in tehnologije / Materials and technology 41 (2007) 3, 135–138 135
UDC/UDK 539.42 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 41(3)135(2007)
values of the T-stress) e.g., 6. The thickness of both types
of specimens was the same, B = 10 mm. The experi-
mental results were obtained for steel with 0.45 % C.
The material properties corresponding to the cyclic
strain-stress curve (Figure 1) are: Young’s modulus E =
2.1⋅105 MPa, Poisson’s ratio ν = 0.3, cyclic yield stress
σ0 = 350 MPa and hardening exponent n = 0.314. All the
experiments were performed under the same conditions:
room temperature and a loading stress ratio R ≈ 0 (close
to a pulsating cycle R = 0.1). The crack length was
measured optically with a resolution of 0.01 mm. The
experimental data were evaluated according to ASTM
E6477. The threshold values were determined at crack-
growth rates of 10–8 mm/cycle.
The following results were obtained, see Figure 2.
The fatigue-crack growth rate was found to be higher for
the M(T) specimen with a negative value of T-stress
(low constraint) than for the C(T) specimen with a
positive value of T-stress (high constraint), when sub-
jected to the same nominal range of the stress-intensity
factor, ∆K. Significant differences were seen between
the threshold values of the FCPR. The corresponding
parameters of the Paris-Erdogan law are then: C = 6.607
· 10–11, m = 4.609 and Kth = 8.81 MPa m1/2 for the M(T)
specimen and C = 2.883 · 10–10, m = 3.662 and Kth = 9.66
MPa m1/2 for the C(T) specimen.
3 CONSTRAINT-BASED DESCRIPTION OF A
FATIGUE CRACK
The plastic-zone size around the crack tip depends
upon many variables, such as the yield stress, the applied
stress, the specimen geometry and the crack geometry.
According to one-parameter linear-elastic fracture
mechanics (LEFM), there is a single-valued relation
between the size of the plastic zone and the corres-
ponding value of the stress-intensity factor, KI, which
controls the FCPR (e.g.,8). Following this, one of the
parameters, say Rp = Rp(K), which characterizes the size
of the plastic zone, can be used as the controlling
variable, and the Paris-Erdogan law9 da/dN = C(K)m can
be rewritten in the form
[ ]d
d
p
a
N
F R K= ( ) (2)
Therefore, the size of the plastic zone can be
considered as a potential parameter with a direct physical
meaning to describe the FCGR. Based on the assump-
tions of the 2PFM, the size of the plastic zone depends
on the given value of K and the T-stress (the level of
constraint), Rp* = Rp*(K,T), and Equation (2) takes the
form:
[ ]d
d
p
a
N
F R K= * ( ) (3)
Equation (3) considers the effect of the stress field at
the crack tip on the FCPR, which included the non-
singular term (T-stress), and this Equation (3) can be
used to quantify the effect of the constraint.
In the present study, see e.g.3, the plastic-zone area,
Sp(K,T), is used as a parameter controlling the FCPR,
and it is assumed that the crack will propagate at the
same fatigue rate if the values of Sp(K,T) (corresponding
to different combinations of the K and T parameters) are
the same.
Let us take the level of constraint corresponding to
the zero value of the T-stress as a reference state and
denote the corresponding area of the plastic zone as Sp0 =
Sp(K,T = 0), based on the assumption of LEFM it is
Sp
0 = Sp(K,T = 0) = (,T = 0)(K/0)
4 (4)
where (,T = 0) is a function of Poisson’s ratio, ν, and
the cyclic yield stress, σ0 of the material used. The
function can be determined conventionally by
substituting the singular terms of the elastic stress field
into the von Mises’ yield criterion or numerically using
the FEM. Similarly, let us denote the area of the plastic
zone around the crack tip corresponding to a structure
S. SEITL, P. HUTA: FATIGUE-CRACK PROPAGATION NEAR A THRESHOLD REGION ...
136 Materiali in tehnologije / Materials and technology 41 (2007) 3, 135–138
0.9 1 1.1 1.2 1.3 1.4 1.5
lg∆K (MPa m1/2)
-8
-7
-6
-5
-4
lg
(
(
d
a
/d
N
)
)
m
m
/
/
/
r
Figure 2: The influence of the geometry of the specimen on the
threshold values and the fatigue crack propagating rate
Slika 2: Vpliv geometrije preizku{anca na vrednosti praga in hitrost
propagacije utrujenostne razpoke
0 0.01 0.02 0.03 0.04
ε
0
100
200
300
400
500
600
700
σ
/
M
P
a
Figure 1: Cyclic stress-strain curve of the material used for
experiments
Slika 1: Cikli~na napetost-deformacija odvisnost materiala, ki je bil
uporabljen za preizkuse
with a non-zero level of constraint as Sp = Sp(K,T  0),
and express it in the form
Sp(K,T  0) = ψ(ν,T  0)(K/σ0)
4 (5)
Both quantities, ψ(ν,T = 0) and ψ(ν,T  0), were
calculated numerically by using a modified boundary-
layer analysis (MBLA). The calculations of the
plastic-zone size and area were performed for different
values of the stress-intensity factor as a function of the
ratio of the T-stress and the yield stress, T/σ0, in an
interval of a real ratio < –0.8; 0.4 > (see also10). The
chosen values of the K factor and the ratio T/σ0
correspond to the applied levels of the external stress and
the constraint in the presented experiments. The depen-
dence obtained can then be expressed in the form
λ
σ σ σ σ
T T T T
0 0 0
2
0
1 0 33 066 0 445
⎛
⎝
⎜
⎞
⎠
⎟ = −
⎛
⎝
⎜
⎞
⎠
⎟ +
⎛
⎝
⎜
⎞
⎠
⎟ −. . .
⎛
⎝
⎜
⎞
⎠
⎟
3
,
see Figure 3.
The relation between the plastic-zone sizes with and
without using the T-stress was found in the form:
Sp(K,T) = 
4(T/0)Sp
0 (6)
Let us further define the effective value of the
stress-intensity factor, Keff, using the equality (6) that
relates the plastic-zone area for T = 0 and T ≠ 0 in the
form:
Keff(T) = (T/0)K(T = 0) (7)
Where the application of the Keff(T) for the
description of the fatigue-crack growth rate takes the
level of the applied stress and the constraint into account,
the Paris-Erdogan equation can be rewritten in the form
da/dN = C (T/0)K
m (8)
Equation (8) represents a modified form of the
Paris-Erdogan law and makes it possible to account for
the effect of the constraint on the fatigue-crack growth
rate. C and m are material constants obtained for condi-
tions corresponding to T = 0. The value of the T-stress
represents the level of constraint corresponding to the
given specimen geometry.
4 DISCUSSION
The approach presented is a phenomenological one
and does not consider the effect of plasticity-induced
crack closure; it proceeds from the assumption of LEFM.
The two-parameter fracture methodology is based upon
the assumption that the fracture behaviour of two
different bodies is the same if both encompass the same
value of the stress-intensity factor, K, and the same range
of the constraint parameter T-stress. Note that the
positive values of the T-stress correspond to a high
constraint level and negative values to a low constraint.
The two-parameter description characterized the stress
state near the crack tip more accurately, and can explain
the effect of the outer geometry of the structure. On the
other hand, this approach does not take account of the
corresponding mechanism of the fatigue-crack growth
rate or the microstructure of the material.
The correlation of the dependence da/dN – K related
to a zero constraint level for the steel specimens is
shown in Figure 4. The corresponding Paris-Erdogan
law parameters are C = 1.473 · 10–10, m = 4.013 and Kth =
9.44 MPa m1/2. The points corresponding to the lower
level of constraint (M(T) specimen) are shifted to lower
values of the FCPR. Similarly, the points corresponding
to a higher level of constraint (the C(T) specimen) are
transformed into higher values of the FCPR. The scatter
of the experimental results after this transformation is
smaller in comparison to the data in Figure 2. Finally, it
is possible to make an approximation of all experimental
data by the one material curve, which is independent of
the outer geometry of the specimen, with reasonable
experimental scatter corresponding to a zero value of the
constraint.
Similarly, the influence of the constraint can be
described in the threshold region, see Figure 4.
S. SEITL, P. HUTA: FATIGUE-CRACK PROPAGATION NEAR A THRESHOLD REGION ...
Materiali in tehnologije / Materials and technology 41 (2007) 3, 135–138 137
0.9 1 1.1 1.2 1.3 1.4 1.5
-8
-7
-6
-5
-4
lg∆K (MPa m1/2)
lg
(
(
d
a
/d
N
)
)
m
m
/
/
/
r
Figure 4: The experimental data from Figure 2 correlated to a zero
value of the constraint
Slika 4: Eksperimentalne vrednosti s slike 2 korelirane na ni~no
vrednost vpetosti
– 0.8 – 0.6 – 0.4 – 0.2 0 0.2 0.4
T/σ0
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
λ
Figure 3: Dependence λ= λ(T/σ0)
Slika 3: Odvisnost λ= λ(T/σ0)
Following these observations it can be concluded that the
fatigue crack will not propagate if the threshold value for
zero T-stress is smaller than the effective range of the
stress-intensity factor.
Keff(K,T) < Kth(T = 0) (9)
5 CONCLUSIONS
This work describes the constraint effect for
fatigue-crack propagation near the threshold values in
the context of the requirement for improved life-
prediction methods. A combined experimental and
modeling approach is used. Experimental measurements
of the FCPR were made on two kinds of specimens with
different shapes: i.e., M(T) (low level of constraint) and
C(T) (high level of constraint) specimens.
The plastic zone is considered as a controlling
variable for near-threshold fatigue-crack behaviour and a
simple procedure makes it possible to estimate the
changes of the fatigue-crack propagation rate in the
threshold region due to different constraint levels
formulated quantitatively.
The effective stress-intensity factor, Keff, becomes
smaller (T > 0) or larger (T < 0) than the nominally
applied one, and hence the crack propagation is slower
or faster, and the threshold values are lower or higher,
than would be predicted without any knowledge of the
constraint effect.
ACKNOWLEDGEMENT
This investigation was supported by grants No.
101/04/P001 of the Grant Agency of the Czech Republic
and by the Institutional Research Plan AV OZ 204 105
07.
6 REFERENCES
1 M. L. Williams: On the stress distribution at the base of a stationary
crack. ASME Journal Applied Mechanics, 24 (1957), 109–123
2 R. S. Vecchio, J. S. Crompton, R. W. Hartyberg: The influence of
specimen geometry on near threshold fatigue crack growth, Fatigue
Fracture Engineering Mat. Structure, 10 (1987), 333–342
3 Z. Knesl, K. Bednar, J. C. Radon: Influence of T-stress on the rate of
propagation of fatigue crack, Physical Mesomechanics, (2000), 5–9
4 J. Tong: T-stress and its implications for crack growth, Engineering
Fracture Mechanics, 69 (2002), 1325–1337
5 J. A. Joyce: Evaluation of the Effect of Crack Tip Constraint on
Fatigue Crack Growth Rate in Inconel 718, Fatigue and Fracture
Mechanics: 34 (2004), ASTM STP 1461
6 Z. Knesl, K. Bednar: Two-parameters Fracture Mechanics: Calcu-
lation of Parameters and their Values, Institute of Physics of
Materials, Brno, Czech Republic, 1998
7 ASTM E647-05 Standard Test Method for Measurement of Fatigue
Crack Growth Rate. Vol. 03.01, 591–630
8 S. Suresh: Fatigue of Materials, Cambridge University Press,
Cambridge 1998
9 P. Paris, F. Erdogan: A critical analysis of crack propagation laws,
Journal Basic Engineering Trans. ASME, (1963), 528–534
10 S. Seitl, P. Hutaø: Influence of materials parameters on polynom used
for modification Paris law, 22nd conference with international
participation, Hrad Ne~tiny, 2 (2006), 543–550, Text in Czech
S. SEITL, P. HUTAØ: FATIGUE-CRACK PROPAGATION NEAR A THRESHOLD REGION ...
138 Materiali in tehnologije / Materials and technology 41 (2007) 3, 135–138
M. BALCAR ET AL.: MODELLING OF THE SOLIDIFICATION PROCESS ...
MODELLING OF THE SOLIDIFICATION PROCESS AND
THE CHEMICAL HETEROGENEITY OF A
26NiCrMoV115 STEEL INGOT
MODELIRANJE PROCESA STRJEVANJA IN KEMI^NE
HETEROGENOSTI INGOTA IZ JEKLA 26NiCrMoV115
Martin Balcar1, Rudolf @elezný1, Ludvík Martínek1, Pavel Fila1, Ji í Ba`an2
1@AS, a. s., Strojírenská 6, 591 71 @ár nad Sázavou, Czech Republic
2University V[B – TU Ostrava, FMMI, 17. listopadu 15, 708 33 Ostrava, Czech Republic
martin.balcar zdas.cz
Prejem rokopisa – received: 2006-08-29; sprejem za objavo – accepted for publication: 2006-12-12
Steel making at @AS, a.s. using secondary metallurgy technology makes it possible to produce liquid metal with high levels of
metallurgical cleanliness. During the casting and subsequent cooling of forging ingots, the steel solidification takes place.
Directional material solidification, grain size, chemical heterogeneity and discontinuities can have a negative effect on the
products’ final properties. The comparison of the chemical composition based on a numerical calculation with the heterogeneity
of the real ingot has proven the possibility of using MAGMA software to model the casting and solidification of ingots for
open-die forgings made from 26NiCrMoV115 steel.
Key words: forging ingot, solidification, heterogeneity, modelling of segregations
Za uporabo tehnologije sekundarne metalurgije se v @AS izdeluje teko~e jeklo z veliko metalur{ko ~istostjo. Med ulivanjem
in ohlajanjem kova{kih ingotov se izvr{i strjevanje. Usmerjeno strjevanje, velikost zrn, kemi~na heterogenost in diskontinuitete
lahko negativno vplivajo na lastnosti kon~nega proizvoda. Primerjava kemi~ne sestave z numeri~nim izra~unom heterogenosti
realnega ingota je dokazala mo`nost uporabe softvera MAGMA za modeliranje ulivanja in strjevanja ingotov za prosto kovanje
iz jekla 26NiCrMoV115.
Klju~ne besede: kova{ki ingot, strjevanje, heterogenost, modeliranje segregacij
1 INTRODUCTION
The manufacture of steel forgings for the rotary parts
of gas turbines requires an adherence to exactly defined
forming and heat-treatment rules. A prerequisite for the
successful production of highly stressed machine parts is
a high-quality initial blank or ingot.
The use of MAGMA software to model the ingot
casting and solidification, to forecast the internal quality
and the segregation of basic alloying elements and to
compare the theoretical prerequisites with practical
results makes it possible to evaluate the possibility of
also using software for other types of numerical
simulation related to the processing of ingots.
The evaluation of the chemical heterogeneity of the
forging ingot of type 8K8.4 cast at @AS, a.s. from
26NiCrMoV115 steel demonstrated the requirements for
an isotropic structure and mechanical properties of the
steel forging are met.
2 MODELLING OF THE INGOT CASTING AND
THE SOLIDIFICATION PROCESS
Using the MAGMA software a simulation of the
casting and solidification of the 8K8.4 forging ingot in
30NiCrMoV steel with the chemical composition shown
in Table 1 was carried out.
The results of the numerical modelling of the ingot
solidification process in the form of the location of the
solidus temperature for different solidification times are
shown in Figure 1. A graphical visualisation of the time
Materiali in tehnologije / Materials and technology 41 (2007) 3, 139–144 139
UDC/UDK 669.18 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 41(3)139(2007)
Figure 1: Development of the solidus temperature range depending on
time
Slika 1: ^asovna evolucija razpona solidusne temperature
zones when the temperature of the molten steel changes
through the phase between the liquidus and solidus lines
is shown in Figure 2.
The final phase of the solidification process is
intended for an immediate share of 100 % solid phase. 1
Along with the numerical simulation of the ingot
casting and the solidification, calculations of the
segregation and unmixing of the basic alloying and
tramp elements were also carried out. Significant
concentration changes throughout the steel ingot’s
cross-section were only noted for elements with greater
content. The concentration distribution of some elements
is shown in Figures 3 and 4.
It is obvious that the degree of segregation increases
from the ingot surface towards the axial part.
The concentration of the elements was deduced from
the concentration ranges in Figures 3 and 4 and
arranged in an ascending order, with numbers from 0 to
X, according to the local level of concentration. By
summing the local content of all the elements the values
in Table 2 were obtained showing the relative segre-
gation degree according to the location of the analyses
points in Figure 5.
Table 2: Relative segregation degree
Tabela 2: Relativna stopnja segregacije
Sample 1 2 3
H 18 8 0
S 14 9 4
P 7 8 4
M. BALCAR ET AL.: MODELLING OF THE SOLIDIFICATION PROCESS ...
140 Materiali in tehnologije / Materials and technology 41 (2007) 3, 139–144
Table 1: Chemical composition of steel as per the MAGMA software
Tabela 1: Kemi~na sestava jekla za softver MAGMA
MAGMA
C Mn Si P S Cr Ni Cu Mo V Al
w/%
30NiCrMoV 0.30 – – 0.025 0.006 1.40 3.00 – 0.40 – –
Figure 2: Stay of the melt in the phase boundary between the liquidus
and solidus temperatures
Slika 2: Zadr`anje taline na fazni meji med likvidusno in solidusno
temperaturo
Carbon Chromium Nickel Molybdenum
Figure 3: Concentration of some elements in the central vertical section of the ingot
Slika 3: Koncentracija nekaterih elementov na pokon~nem prerezu skozi sredino ingota
The highest values of the positive segregation
correspond to the ingot part marked with the index H1.
Compared with the other sampling points, all the
elements attain the maximum concentration here.
The lowest concentrations of the analysed elements
were found in H3 and events S3 and P3.
3 PRODUCTION PROCESSING AND SAMPLING
METHOD
Within the scope of the experimental work, the
26NiCrMoV115 steel melt with the chemical compo-
sition in Table 3 was made at @AS, a.s. The molten
M. BALCAR ET AL.: MODELLING OF THE SOLIDIFICATION PROCESS ...
Materiali in tehnologije / Materials and technology 41 (2007) 3, 139–144 141
Cross-section view below the ingot top
Figure 4: Concentration of some elements in the cross-section, view below the ingot top
Slika 4: Koncentracija nekaterih elementov na prerezu pod glavo ingota
Table 3: Chemical composition of steel – final melt test
Tabela 3: Kemi~na sestava jekla, kon~na analiza {ar`e
Melt analyse
C Mn Si P S Cr Ni Cu Mo V Al As Sn Sb Ca
w/% µg/g
30NiCrMoV 0.29 0.21 0.01 0.004 0.006 1.69 2.88 0.01 0.41 0.12 0.009 30 <5 <5 4
Figure 5: Steel ingot dividing and sampling diagram
Slika 5: Razdelitev ingota in skica odvzema vzorcev
metal was bottom cast in the mould of the 8K8.4 to form
an ingot with a mass of approximately 8 tonnes. 3
The solidification and the cooling of the ingot to
ambient temperature took place in the mould. In order to
facilitate the manipulation after the fettling, the ingot
was divided into three parts using a cutting machine, as
shown in Figure 5.
Figure 5 shows the sampling points for the speci-
mens taken for analysis from parts below the top, from
the middle and from the bottom of the ingot.
4 CHEMICAL COMPOSITION OF THE INGOT
IN THE MONITORED ZONES
The samples H1, H2, H3 were cut out from the body
part below the ingot top, the samples S1, S2, S3 from the
middle part and the samples P1, P2 and P3 from the
ingot’s bottom part. All the samples were submitted for
chemical analyses in the laboratory of ISPAT NOVÁ
HU, a.s. and the contents of several elements were
determined. 4
The chemical compositions of the samples, shown in
Table 4, only include the elements present in sufficient
concentrations with respect to the detection limits of the
analytical device.
If the concentrations of the elements from Table 4
are arranged in ascending order, with evaluation points
from 0 to X according to the increasing content, a sum
for all the elements indicating the relative segregation
degree in Table 5 is obtained.
Table 5: Relative segregation degree
Tabela 5: Relativna stopnja segregacije
Sample 1 2 3
H 27 8 18
S 7 11 9
P 10 19 9
In the zone corresponding to the ingot part marked
with H1 the highest positive segregations occur. In this
area most elements show a significant unmixing. Com-
pared with other sampling points, carbon, chromium,
nickel, molybdenum and vanadium attain the maximum
segregation; the lowest concentrations of the elements
analysed were found in the S1 and also in the S3 and P3
zones.
5 ELEMENT HETEROGENEITY
MEASUREMENT
The chemical heterogeneity of the steel samples was
determined at VTÚO Brno using a method previously
reported 5. For the energy-dispersion (ED) X-ray micro-
analysis a JEOL JXA8600/KEVEX Delta V Sesame
microscope was used.
The analyses were performed for elements with a
content higher than the detection limit for the ED
microanalysis. For each analysed element the content
was determined for 101 points. The analysed elements
were vanadium, chromium, manganese, iron, nickel and
molybdenum.
For each point analyses, the program also determined
some basic statistical parameters:
XS mean value
SX standard deviation
Min minimum value
IHet heterogeneity index IHet = SX/XS
Max maximum value
Is segregation index Is = Max/XS
The results are shown in Table 6. For the evaluation
of the chemical heterogeneity the maximum point
content for each element was considered and obtained
along a measured line of 1000 µm for each sample.
The dimensionless parameter known as the segre-
gation index (Is) was determined as the relationship
between the maximum concentration and the average
concentration in the given section (Is = Max/XS). The
results are shown in Table 7.
M. BALCAR ET AL.: MODELLING OF THE SOLIDIFICATION PROCESS ...
142 Materiali in tehnologije / Materials and technology 41 (2007) 3, 139–144
Table 4: Chemical composition of samples taken throughout the ingot
cross-section
Tabela 4: Kemi~na analiza vzorcev, izrezanih iz prereza ingota
In order to make it easier to understand, the
segregation index for the analysed elements is arranged
so that it emphasizes the maximum and minimum
segregation index. According to the position of the
samples in the ingot, the following indexes were
determined.
The distribution of the values of the maximum and
minimum segregation indexes of the elements shows that
it is not possible to decide unambiguously in which ingot
part the highest and/or lowest segregation intensity
occurs.
If we assign the same weight to the highest and/or the
lowest segregation index of each element (six analysed
elements with a mass of 1/6), the distribution of the
maximum and/or minimum segregation indexes of the
elements, the data in Table 8, are obtained.
Materiali in tehnologije / Materials and technology 41 (2007) 3, 139–144 143
M. BALCAR ET AL.: MODELLING OF THE SOLIDIFICATION PROCESS ...
Table 8: Maximum and minimum segregation indexes
Tabela 8: Najve~ji in najmanj{i indeksi segregacije
Table 9: Mass distribution of segregation indexes
Tabela 9: Razdelitev indeksov segregacije po masi
Maxima Minima
H1 H2 H3 H1 H2 H3
S1 S2 S3 S1 S2 S3
P1 P2 P3 P1 P2 P3
1 0 1 0 0 0
2 0 0 0 3 1
1 1 0 1 1 0
Table 7: IHet and Is indexes
Tabela 7: Indeks IHet in Is
Table 6: Basic statistics of samples and elements
Tabela 6: Osnovna statistika vzorcev in elementov
These data show that the highest segregation index is
obtained in the ingot axis area, where a fraction of 4/6 of
cases falls on the vertical column of samples H1-S1-P1
The smallest segregation index is found for samples
from the S2 ingot position. In terms of the fraction 3/6 it
means S2 takes half of all cases. The fraction 2/3 of
cases falls on the column H2, S2 and P2.
The minimum fraction 1/6 of the lowest measured
values of the segregation indexes falls on the vertical
columns H1–S1–P1 and H3–S3–P3, while in the column
H1–S1–P1 the weight of occurrence of the elements with
the maximum heterogeneity index is 2/3. It can be
concluded that the highest unmixing tendency is
expected in the ingot axis – column 1. The lowest
unmixing tendency can be expected at the surface of the
ingot – column 3.
The segregation behaviour of the elements Cr and
Mn is different, as shown in Table 9.
The smallest measured segregation indexes are found
for the ingot areas H2, S2 and P2. However, there are
also two exceptions to this rule, again the elements are
Cr and Mn.
Sequence according to the highest segregation index:
Table 11: Sequence of segregation indexes
Tabela 11: Sekvence indeksov segregacije
Segregation V Mo Mn Cr Ni Fe
Index 12.74 8.51 4.63 3.20 1.30 1.02
Sequence of elements according to the lowest
segregation index:
Segrgeation Mo V Mn Cr Ni Fe
Index 2.47 2.27 2.17 1.49 1.20 1.01
Both sequences are almost identical, i.e., Mo, V, Mn,
Cr, Ni and Fe and only two elements, molybdenum and
vanadium, exchange their places in the sequence.
In both sequences the elements V, Mo and Mn are in
the first three places and the sequence is ended by the
elements Cr, Ni and Fe. The reciprocal value of the
segregation index k » 1/Is represents, as a first approxi-
mation, the effective distribution coefficient of the
element 6.
6 CONCLUSION
The relatively good agreement of the results of the
measurements and the simulations of the maximum and
minimum segregation index sequence indicate the same
tendencies during the solidification and cooling of a steel
ingot with a given chemical composition.
On the basis of the measurements it can be concluded
that this tendency depends on the real value of the
effective distribution coefficient of the elements. It is
also possible to conclude on the basis of the
measurements that, of the external parameters, the
parameter referred to as the local solidification time
plays an important role, i.e., the time when the particular
measured area of the sample stays between the solidus
and liquidus temperatures.
The use of the MAGMA software to model the ingot
casting and solidification process and to predict the
behaviour of the basic alloying elements confirms the
relative agreement between the theoretical predictions
and the practical results.
The determination of the chemical heterogeneity of
the forging ingot type 8K8.4 of 26NiCrMoV115 steel
will contribute to an explanation of the causes of
possible occurrence of structural anisotropy of the steel
in connection with the end-use properties.
ACKNOWLEDGEMENTS
The investigations were performed within the
EUREKA programme of the E!3192 ENSTEEL project,
identification number 1P04EO169. The project was
funded partially with the financial support of the
Ministry of Education, Youth and Sport of the Czech
Republic
7 LITERATURE
1 Martínek, L., Balcar, M., Ba`an, J. et al.: Optimization of casting and
solidification with respect to the ingot structure and homogeneity.
Progress report from the solution of the EUREKA E!3192
ENSTEEL project, identification number 1P04OE169, 2005, 69 p.
2 Martínek, L., Balcar, M. @elezný, R.: Optimization of casting and
solidification with respect to the ingot structure and homogeneity.
Annex No. 4: Numerical simulation outputs and selected quality
parameters of the ingot. Progress report form the solution of the
EUREKA E!3192 ENSTEEL project, identification number
1P04OE169, 2005, 97 p.
3 Martínek, L., Balcar, M. et al.: Production of components from
high-clean steels for power equipment. Progress report on the
solution of the EUREKA E!3192 ENSTEEL project, 2004, 117 p.
4 Metallurgical and chemical laboratories ISPAT NOVÁ HU a.s.,
Test report, 2004
5 Ba`an, J. et al.: Comparison of influence of the contemporary, single
and combined processes of extra-furnace metallurgy and casting on
the end-use properties and expensiveness of high-grade steels.
/Opposed final report of the grant project GA^R 106/01/0365/.
V[B - TU Ostrava, 2003, 68 p.
6 Rek, A., Stránský, K.: Element heterogeneity in the 26NiCrMoV115
steel samples from the 8 t ingot. VTÚO Brno, 2004, 35 p.
M. BALCAR ET AL.: MODELLING OF THE SOLIDIFICATION PROCESS ...
144 Materiali in tehnologije / Materials and technology 41 (2007) 3, 139–144
Table 10: Limit values of the segregation indexes related to the
elements
Tabela 10: Mejne vrednosti za indekse segregacije za elemente
Maxima Minima
H1 H2 H3 H1 H2 H3
S1 S2 S3 S1 S2 S3
P1 P2 P3 P1 P2 P3
Fe Mn
V Ni Fe Ni Mo Cr
Mo Cr Mn V
J. ŠETINA: FREKVEN^NA ODVISNOST REZIDUALNEGA TRENJA VISKOZNOSTNEGA ...
FREKVEN^NA ODVISNOST REZIDUALNEGA TRENJA
VISKOZNOSTNEGA VAKUUMSKEGA MERILNIKA Z
LEBDE^O KROGLICO
FREQUENCY DEPENDENCE OF SPINNING ROTOR GAUGE
RESIDUAL DRAG
Janez [etina
In{titut za kovinske materiale in tehnologije, Lepi pot 11, 1000 Ljubljana, Slovenija
janez.setina@imt.si
Prejem rokopisa – received: 2007-04-18; sprejem za objavo – accepted for publication: 2007-05-07
Viskoznostni merilnik tlaka z lebde~o kroglico (SRG – Spinning Rotor Gauge) se je uveljavil v meroslovju nizkih tlakov kot
precizen in stabilen referen~ni etalon za obmo~je med 10–4 Pa in 1 Pa. Ob ustrezni kalibraciji s primarnimi vakuumskimi
standardi je v tem obmo~ju tlakov dosegljiva merilna negotovost pri komercialnih merilnikih ± 0,5 %. Med vplivnimi
veli~inami pri merjenjih z SRG-merilnikom je najpomembnej{e rezidualno trenje rotorja, ki se pojavi zaradi vrtin~nih
elektri~nih izgub pri magnetnem lebdenju in vrtenju kroglice. Rezidualno trenje lahko izmerimo pri zelo nizkem tlaku kot
ni~elni signal in ga nato upo{tevamo pri meritvi tlaka kot popravek. ^asovna stabilnost rezidualnega trenja dolo~a spodnjo
merilno mejo SRG-merilnika. Izka`e se, da je rezidualno trenje odvisno od frekvence vrtenja rotorja. Frekven~no odvisnost
lahko dolo~imo z linearno regresijo merjenih vrednosti rezidualnega trenja v odvisnosti od frekvence. Podrobneje smo raziskali
stabilnost in frekven~no odvisnost rezidualnega trenja pri razli~nih namestitvah dveh kroglic. Rezultati so pokazali, da je
frekven~na odvisnost slabo korelirana z absolutno vrednostjo rezidualnega trenja. V ve~ini primerov je frekven~na odvisnost
tako velika, da jo moramo upo{tevati pri izra~unu popravka rezidualnega trenja pri meritvah tlakov plina pod 1·10–3 Pa.
Klju~ne besede: viskoznostni vakuumski merilnik, rezidualno trenje, meritev vakuuma
Spinning rotor gauge (SRG) is well recognized in the field of low pressure metrology as precise and stable reference standard in
the range from 10–4 Pa to 1 Pa. The achievable measurement uncertainty of commercial SRG is ± 0,5%, assuring a suitable
calibration with a higher level primary standard. Important correction of SRG is the pressure independent contribution to the
measured signal known as residual drag. It is caused by eddy current losses in magnetic levitation system and metallic parts in
the close vicinity of the spinning rotor, and can be determined at very low gas pressure as a zero signal of the gauge. The
residual drag usually depends on the rotational frequency of the rotor. It can be approximated with a linear function which can
be determined by linear regression of measured values as a function of rotational frequency. We have investigated stability and
frequency dependence of residual drag for several different suspensions of two SRG rotors. Results showed that there is no
correlation between frequency dependence and magnitude of residual drag. The frequency dependence is in most cases large
enough to have significant influence on the measurements and has to be taken into account for precise pressure measurements
below 1·10–3 Pa.
Key words: spinning rotor gauge, residual drag, vacuum measurement
1 UVOD
Vsakr{no gibanje predmetov v plinu je ovirano zaradi
trkov z molekulami plina. Parameter, ki pove, kako
mo~no je gibanje v nekem plinu ovirano, je viskoznost.
Pojav molekularnega trenja je povezan s prenosom
gibalne koli~ine med molekulami plina in gibajo~im
predmetom. Enako kot toplotna prevodnost je tudi
viskoznost plinov pri nizkem tlaku plina (v moleku-
larnem podro~ju) sorazmerna s tlakom, kar lahko izkori-
stimo za posredno merjenje vakuuma.
Shematski prerez viskoznostnega vakuumskega
merilnika z lebde~o kroglico (angle{ko: SRG – Spinning
Rotor Gauge) je prikazan na sliki 1. Merilni element je
jeklena kroglica s premerom 4,5 mm, ki prosto lebdi v
magnetnem le`aju 1. Kroglica se nahaja v nekaj centi-
metrov dolgi cevki z notranjim premerom 8 mm. Cevka
je z ene strani zaprta, z druge strani pa je privarjena v
prirobnico, ki je povezana s posodo, v kateri merimo tlak
plina. Merilna glava, ki zagotavlja magnetno lebdenje,
pospe{evanje in induktivno merjenje frekvence kroglice,
se nahaja zunaj vakuuma. Kroglico pospe{imo (z vrte~im
se magnetnim poljem, podobno kot pri asinhronskem
elektromotorju) do frekvence 400 Hz in nato pustimo, da
se prosto vrti v razred~enem plinu. Trenje z molekulami
plina kroglico zavira. Merjena veli~ina je ~asovna odvis-
nost kotne hitrosti kroglice ω. Z &ω ozna~imo ~asovni
Materiali in tehnologije / Materials and technology 41 (2007) 3, 145–149 145
Slika 1: Prerez merilne glave SRG-merilnika
Figure 1: Cross section of a suspension head of SRG
UDK/UDC 621.5/.6:533.5 ISSN 1580-2949
Izvirni znanstveni ~lanek/Original scientific article MTAEC9, 41(3)145(2007)
odvod kotne hitrosti. Definirajmo relativni pojemek
kotne hitrosti ( / )− &ω ω , ki ga bomo zaradi la`jega pisanja
v nadaljevanju ozna~evali z DCR (okraj{ava iz angle{kih
besed Deceleration Rate):
DCR = −
&ω
ω
DCR je v molekularnem podro~ju sorazmeren s
tlakom plina 1:
p = Kp · DCR (1)
Sorazmernostni faktor Kp v ena~bi (1) je konstanta
ob~utljivosti SRG-merilnika:
K
a RT
M
p =
ρ
σ10
8π
(2)
Kp vsebuje gostoto ρ in premer kroglice a, molekul-
sko maso M in temperaturo plina T, koeficient prenosa
gibalne koli~ine σ ter plinsko konstanto R. Edini para-
meter v ena~bi (2), ki ga ne moremo zanesljivo izmeriti
ali napovedati je σ, zato ga moramo za izbrano kroglico
in vrsto plina dolo~iti s kalibracijo. V praksi se je
izkazalo 2, da je za plin du{ik na povr{ini gladkih jekle-
nih kroglic σ med 0,94 in 1,06. Razlike med razli~nimi
plini so v mejah ± 2 % 3,4.
SRG-merilnik je pomemben predvsem, ker v stabil-
nosti preka{a vse druge merilnike v visokovakuumskem
podro~ju. V razli~nih raziskavah so ugotovili, da se pri
pazljivem ravnanju konstanta ob~utljivosti SRG-meril-
nika v dalj{em ~asovnem obdobju (ve~ let) obi~ajno
spremeni za manj kot 1 %. Merilnik se je v vakuumskem
meroslovju uveljavil kot prenosni etalonski merilnik
oziroma sekundarni referen~ni merilnik 5. V Laboratoriju
za metrologijo tlaka na IMT je SRG-merilnik slovenski
nacionalni etalon v obmo~ju med 10–5 Pa in 0,1 Pa 6.
Zaradi majhnega delovnega volumna in inertnosti je
SRG merilnik {e posebej primeren za meritve tlaka in
netesnosti v majhnih hermeti~nih sistemih 7,8,9.
2 REZIDUALNO TRENJE ROTORJA
Poleg molekularnega trenja pri SRG-merilniku
opazimo tudi majhno, od tlaka in vrste plina povsem
neodvisno zaviranje kroglice. To je tako imenovano
rezidualno trenje, ki je navadno tako veliko, kot bi bilo
trenje v plinu (du{iku) pri tlaku med 10–4 Pa in 10–2 Pa.
Na prvi pogled se zdi, da zaradi rezidualnega trenja
sploh ne moremo natan~no meriti tlakov pod 10–2 Pa.
Vendar lahko rezidualno trenje predhodno izmerimo
tako, da sistem iz~rpamo do tlaka pod 1·10–6 Pa, ko
postane molekularno trenje zanemarljivo v primeri z
rezidualnim. Tedaj merilnik poka`e "ekvivalent tlaka",
ki ustreza rezidualnemu trenju kroglice in ga navadno
imenujemo "ofset" (OFS) oziroma ni~elni premik:
OFS = Kp · DCRp=0 (3)
Pri meritvi tlaka dobimo pravi tlak plina p, ki je
posledica molekularnega trenja tako, da v ena~bi 1 od
merjenega relativnega kotnega pospe{ka DCR od{tejemo
od tlaka neodvisni prispevek DCRp=0:
p = Kp · (DCR – DCRp=0) = Ψ – OFS (4)
Tu je Ψ prikazana vrednost tlaka brez popravka
rezidualnega trenja (osnovni signal). ^e popravek
rezidualnega trenja izra`amo v enotah tlaka (OFS),
moramo pri tem navesti, za katero vrsto plina velja, saj je
sorazmernostni faktor Kp odvisen od molekularne mase
plina. V nadaljevanju bomo vse vrednosti Ψ in OFS
izra`ali v ekvivalentu tlaka du{ika.
Rezidualno trenje izmerimo tako, da iz~rpamo sistem
s SRG-merilnikom do tlaka p, ki je ni`ji od negotovosti,
ki jo `elimo dose~i, in lahko naredimo pribli`ek OFS =
Ψ. Tako je za meritve v obmo~ju 10–1 Pa navadno
dovolj, da izmerimo ni~elni premik pri tlaku pod 10–4 Pa,
kar je manj kot 0,1 % merjenega tlaka. Za precizijske
meritve nizkih tlakov pod 10–3 Pa moramo ni~elni
premik izmeriti pri tlakih pod 10–6 Pa.
Obi~ajen postopek za popravek rezidualnega trenja,
ki ga priporo~a proizvajalec 10 v svojih navodilih, je
naslednji:
1. Iz~rpati sistem pod mejo lo~ljivosti (<10–6 Pa);
2. v kontrolni enoti nastaviti (resetirati) parameter OFS
na vrednost 0;
3. aktivirati nov merilni cikel in izmeriti ni~elni premik
(prikazana vrednost pri tlaku plina p ≈ 0), na primer
2,5678·10–4 Pa;
4. izmerjeno vrednost vnesti v kontrolno enoto kot novo
vrednost parametra OFS = 2,5678·10–4 Pa
Pri vseh nadaljnjih meritvah elektronska kontrolna
enota avtomati~no od{teva OFS od osnovne merjene
vrednosti in tako prika`e tlak s popravkom rezidualnega
trenja (ena~ba 4).
Rezidualno trenje nastopi zaradi ve~ pojavov. Pogla-
vitni vzrok rezidualnega trenja pri komercialnih SRG-
merilnikih so inducirani vrtin~ni tokovi 11. Pri tem
razlikujemo:
• vrtin~ne tokove, ki se inducirajo v sami kroglici, ~e
magnetno polje, v katerem lebdi kroglica, ni sime-
tri~no okrog osi vrtenja kroglice;
• vrtin~ne tokove, ki se inducirajo v kovinskih delih v
neposredni bli`ini kroglice zaradi vrte~e se kompo-
nente magnetnega momenta kroglice (ta nam v
detekcijskih tuljavah tudi inducira sinusni signal za
merjenje kotne hitrosti).
Zaradi induciranih vrtin~nih tokov se kroglici
zmanj{uje njena rotacijska energija, ki se pretvarja v
elektri~no delo oziroma toplotne izgube. ^eprav so te
izgube znatne v primeri z molekularnim trenjem pri niz-
kih tlakih, je segrevanje kroglice in njene okolice zaradi
njih prav neznatno. Mo~, ki ustreza rezidualnemu ali
molekularnemu trenju pri 10–3 Pa je namre~ le 10–10 W.
V praksi se je izkazalo, da velikosti rezidualnega
trenja za neko kroglico ne moremo vnaprej napovedati
ali izra~unati, saj je odvisna tako od asimetrije magnet-
nega polja, v katerem lebdi kroglica, kot tudi od velikosti
J. ŠETINA: FREKVEN^NA ODVISNOST REZIDUALNEGA TRENJA VISKOZNOSTNEGA ...
146 Materiali in tehnologije / Materials and technology 41 (2007) 3, 145–149
in smeri vrte~e se komponente magnetnega momenta
kroglice. Zato je rezidualno trenje za razli~ne kroglice
razli~no. Prav tako dobimo pri neki kroglici vsaki~
druga~no vrednost rezidualnega trenja, ~e kroglico
vzamemo iz merilne glave in jo nato ponovno
namestimo vanjo. Pri vsakem lebdenju se namre~
kroglica druga~e orientira v magnetnem polju. Poskusi,
da bi stabilizirali orientacijo kroglice v magnetnem polju
in s tem tudi rezidualno trenje, se niso obnesli 12. ^eprav
se rezidualno trenje ne vede ponovljivo, pa je na sre~o
pri ve~ini kroglic stabilno, ~e merilnika ne izklopimo in s
tem ne prekinemo lebdenja kroglice.
3 EKSPERIMENTALNO DELO
Pri meritvi z SRG-merilnikom je osnovni signal
vedno vsota rezidualnega in molekularnega trenja. Po
na{ih izku{njah lahko zavzame rezidualno trenje {irok
obseg vrednosti od 5·10–5 Pa do 10–2 Pa, a je naj-
pogosteje v obmo~ju med 2·10–4 Pa in 8·10–4 Pa.
Rezidualno trenje je najpomembnej{i popravek pri
SRG-merilniku v obmo~ju zelo nizkih tlakov.
Negotovost popravka je odvisna od negotovosti, ki jo
dose`emo pri merjenju rezidualnega trenja, in od
kratkoro~ne oziroma dolgoro~ne stabilnosti. Ker ne
moremo meriti hkrati tlaka plina in rezidualnega trenja,
lahko negotovost ni~elnega popravka v ~asu meritve
tlaka pravilno ocenimo le, ~e imamo dovolj podatkov o
njegovi stabilnosti.
Pri na{em eksperimentu smo SRG-merilnik iz~rpali
na ultravisokovakuumskem sistemu do tlaka pod 2·10–7
Pa in z ra~unalnikom neprekinjeno zapisovali frekvenco
rotorja in prikazano vrednost tlaka Ψ brez popravka
rezidualnega trenja. Meritev je trajala 4 dni. Pri
integracijskem intervalu 30 s bi v tem ~asu dobili ve~ kot
10 000 prikazanih vrednosti, zato smo v programu za
zajem podatkov uvedli povpre~enje 10 zaporednih
prikazanih vrednosti in v datoteko shranjevali povpre~ne
vrednosti frekvence in tlaka v ~asovnem intervalu 300 s.
S povpre~enjem se je tudi zmanj{al statisti~ni {um za
faktor 10. V nadaljevanju eksperimenta smo izmerili
frekven~no odvisnost rezidualnega trenja pri ve~jem
{tevilu razli~nih namestitev dveh rotorjev.
V kontrolno enoto SRG-merilnika so bili pri vseh
meritvah vneseni parametri za plin du{ik pri temperaturi
293 K (ena~ba 2).
4 REZULTATI IN DISKUSIJA
A – Frekven~na odvisnost in ~asovna stabilnost rezi-
dualnega trenja
Primer neprekinjene meritve osnovnega signala Ψ pri
tlaku pod 2·10–7 Pa v ~asovnem obdobju 100 h je pri-
kazan na sliki 2 a. Na sliki 2 b je prikazana tudi
frekvenca rotorja, ki smo jo merili hkrati s Ψ. Na sliki 2a
opazimo `agast potek signala, ki je koreliran s frekvenco
rotorja. @agast potek frekvence je povezan s samodejnim
pospe{evanjem rotorja. Ko pade frekvenca rotorja pod
spodnjo mejo 405 Hz, elektronska kontrolna enota rotor
ponovno pospe{i do zgornje frekven~ne meje 415 Hz. To
frekven~no okno je pri na{em tipu SRG-merilnika fiksno
in ga ne moremo spreminjati. Pri vsaki pospe{itvi rotorja
je ni~elni premik skokovito narasel in je nato enako-
merno padal, ko se je frekvenca po~asi s ~asom zmanj-
{evala (posledica izgub energije zaradi rezidualnega
trenja).
Merjene vrednosti Ψ s slike 2 a lahko prika`emo na
diagramu odvisnosti od frekvence (slika 3). V majhnem
obmo~ju frekvenc med 405 Hz in 415 Hz lahko frek-
ven~no odvisnost aproksimiramo z linearno funkcijo.
J. ŠETINA: FREKVEN^NA ODVISNOST REZIDUALNEGA TRENJA VISKOZNOSTNEGA ...
Materiali in tehnologije / Materials and technology 41 (2007) 3, 145–149 147
t / h
f/
H
z
t / h
Ψ
/ P
a
,
,
,
,
,
,
Slika 2: Prikazana vrednost SRG-merilnika (Ψ) v odvisnosti od ~asa
(t) pri tlaku pod 10–6 Pa (a) in potek frekvence rotorja (f) v dalj{em
~asovnem obdobju (b)
Figure 2: Displayed value of SRG (Ψ) versus time (t) at gas pressure
below 10–6 Pa (a), and rotor frequency (f) (b)
f / Hz
Ψ
/P
a
Slika 3: Prikazana vrednost SRG-merilnika (Ψ) s slike 2 v odvisnosti
od frekvence rotorja (f)
Figure 3: Displayed value of SRG (Ψ) from Figure 2 versus rotor
frequency (f)
Rezultati linearne regresije merjenih to~k z metodo
najmanj{ih kvadratov so podani v tabeli 1.
Popravek rezidualnega trenja v odvisnosti od frek-
vence lahko izra~unamo iz konstante C in naklona
premice kf iz tabele 1:
OFS(f) = kf · f + C (5)
Razlika merjenih vrednosti Ψ in linearne aproksi-
macije popravka OFS(f) je prikazana na sliki 4. Preostale
variacije merjenega signala z upo{tevanim popravkom
rezidualnega trenja so posledica nihanj temperature ter
vibracij in drugih vplivov 13. Ker je bil tlak v sistemu
manj{i od 2·10–7 Pa nam slika 4 prikazuje dolgoro~no
stabilnost popravka rezidualnega trenja. @e na prvi
pogled se zdi, da se povpre~na vrednost razlike Ψ –
OFS(f) v ~asu meritve ni bistveno spremenila, vendar pa
je kvantitativna ocena "na pogled" zaradi znatnega
raztrosa prakti~no nemogo~a. Ker imamo na razpolago
veliko {tevilo merjenih to~k, si lahko pomagamo s
statisti~nimi metodami in tudi v tem primeru kot merilo
za dolgoro~no stabilnost rezidualnega trenja vzamemo
naklon premice, ki jo dolo~imo z metodo najmanj{ih
kvadratov. Naklon premice na sliki 4 je –3·10–8 Pa/d s
standardno negotovostjo 7·10–8 Pa/d. To pomeni, da je
izra~unani naklon bistveno manj{i od standardne nego-
tovosti in lahko re~emo, da je bila vrednost rezidualnega
trenja z upo{tevanim frekven~nim popravkom ~asovno
neodvisna.
B – Ponovljivosti rezidualnega trenja za razli~ne name-
stitve rotorja
Eksperiment smo nadaljevali tako, da smo rotor
zaustavili, odstranili merilno glavo in jo ponovno
namestili na merilno cevko. Pri tem smo dobili novo
orientacijo rotorja v magnetnem le`aju glede na os
vrtenja. Postopek smo ve~krat ponovili in za vsako novo
namestitev dolo~ili frekven~no odvisnost rezidualnega
trenja.
Neodvisno od opisanega eksperimenta smo pridobili
podatke o frekven~ni odvisnosti rezidualnega trenja {e za
drug SRG-rotor v drugi merilni cevki, a z isto merilno
glavo in kontrolno enoto. Rezultati za oba rotorja so
podani v tabeli 2 in na sliki 5.
Glede na razmeroma majhno {tevilo ponovitev
meritve lahko re~emo, da se vrednost ofseta pri 410 Hz
bistveno ne razlikuje za rotorja A in B. Pri obeh rotorjih
je bila vrednost rezidualnega trenja med 3·10–4 Pa in
6·10–4 Pa. Opazna pa je razlika v koeficientu frekven~ne
odvisnosti kf, ki je pri rotorju A bistveno ve~ja. Pri
rotorju B smo pri eni namestitvi izmerili rezidualno
trenje, ki je bilo prakti~no brez frekven~ne odvisnosti. V
vseh drugih primerih pa je bila frekven~na odvisnost
znatna, tako da je bila pri pospe{itvi rotorja od 405 Hz
J. ŠETINA: FREKVEN^NA ODVISNOST REZIDUALNEGA TRENJA VISKOZNOSTNEGA ...
148 Materiali in tehnologije / Materials and technology 41 (2007) 3, 145–149
OFS
k f
,
,
, , , , , , ,
Slika 5: Ponovljivost rezidualnega trenja (OFS) in njegove frekven~ne
odvisnosti (kf) pri razli~nih namestitvah rotorja
Figure 5: Repeatability of residual drag (OFS) and frequency
dependence (kf) for different suspensions of the rotor
t / h
Ψ
–
/ P
a
O
FS
Slika 4: Merjeni signal s popravkom rezidualnega trenja (Ψ–OFS)
Figure 4: Measured signal with residual drag correction (Ψ–OFS)
(without and with a frequency dependence)
Tabela 2: Rezidualno trenje (OFS) pri 410 Hz in frekven~na
odvisnost (kf) za dva SRG-rotorja pri razli~nih namestitvah v
magnetnem le`aju. Pri obeh rotorjih sta bili uporabljeni ista kontrolna
enota in merilna glava.
Table 2: Residual drag (OFS) at 410 Hz and frequency dependence
(kf) for different suspensions of two SRG rotors. (The same
suspension head and SRG controller has been used for both rotors).
OFS (410 Hz) kf
Rotor A 5.715·10–4 1.42·10–6
4.339·10–4 1.38·10–6
3.141·10–4 1.88·10–6
4.207·10–4 1.80·10–6
4.302·10–4 2.11·10–6
5.327·10–4 1.95·10–6
Rotor B 3.597·10–4 5.95·10–8
2.930·10–4 3.67·10–7
4.901·10–4 7.17·10–7
4.081·10–4 4.52·10–7
3.398·10–4 7.16·10–7
Tabela 1: Rezultati linearne regresije merjenih vrednosti Ψ s slike 2
Table 1: Results of linear regression of measured values of Ψ from
figure 2
Rezultati linearne regresije:
Konstanta C = –9,8878·10–6 Pa
Standardni odmik konstante 1,0279·10–6 Pa
R2 0,94520
[tevilo prostostnih stopenj 1169
Naklon premice kf = 1,418·10
–6 Pa/Hz
Standardni odmik naklona 9,9·10–9 Pa/Hz
do 415 Hz sprememba rezidualnega trenja med 3,7·10–6
Pa in 2,1·10–5 Pa, kar ima znaten vpliv pri meritvah tlaka
v podro~ju pod 1·10–3 Pa.
5 SKLEPI
Rezidualno trenje SRG-rotorja je odvisno od
frekvence vrtenja. Le v~asih je frekven~na odvisnost
tako majhna, da jo lahko zanemarimo. Podobno kot
velikosti rezidualnega trenja tudi frekven~ne odvisnosti
ne moremo napovedati. Pri vsaki prekinitvi magnetnega
lebdenja in ponovni namestitvi rotorja se naklju~no
spremenita tako velikost rezidualnega trenja kot tudi
frekven~na odvisnost. Med njima ni zadostne korelacije,
da bi lahko `e iz velikosti rezidualnega trenja napovedali
frekven~no odvisnost. Poudariti pa velja, da navadno obe
vrednosti ostaneta konstantni med neprekinjenim
lebdenjem, tudi po ve~kratni pospe{itvi rotorja, tako da
lahko zanesljivo izra~unamo popravke rezidualnega
trenja pri meritvah tlaka.
6 REFERENCES
1 J. K. Fremerey, J. Vac. Sci. Technol. A3, (1985),, 1715
2 S. Dittmann, B. E. Lindenau, C. R. Tilford, J. Vac. Sci. Technol. A7,
(1989), 3356
3 J. K. Fremerey, Vacuum, 32, (1982), 685
4 G. Comsa, J. K. Fremerey, B. Lindenau, G. Messer, P. Röhl, J. Vac.
Sci. Technol. 17, (1980), 642
5 B. Erjavec, J. [etina, L. Irman~nik-Beli~, Mater. tehnol., 35, (2001),
143
6 J [etina, B. Erjavec, L. Irman~nik-Beli~, Mater. tehnol., 35, (2001),
321
7 J. [etina, R. Zava{nik, V. Nemani~, J. Vac. Sci. Technol. A5, (1987),
2650
8 V. Nemani~, J. [etina, J. Vac. Sci. Technol. A17, (1999), 1040
9 B. Erjavec, Vacuum, 64, (2001), 15
10 SRG 2CE, Instruction Manual, MKS Instruments, ZDA
11 J. K. Fremerey, Rev.Sci.Instrum. 43, (1972), 1413
12 C. Suk-Ho, S. Dittmann, C. R. Tilford, J. Vac. Sci. Technol. A8,
(1990), 4079
13 T. Bock, K. Jousten, Vacuum, 81, (2006), 234
J. ŠETINA: FREKVEN^NA ODVISNOST REZIDUALNEGA TRENJA VISKOZNOSTNEGA ...
Materiali in tehnologije / Materials and technology 41 (2007) 3, 145–149 149

R. CELIN, D. KMETI^: A WET-STEAM PIPELINE FRACTURE
A WET-STEAM PIPELINE FRACTURE
PRELOM CEVOVODA ZA VLA@NO PARO
Roman Celin, Dimitrij Kmeti~
Institute of Metals and Technology, Lepi pot 11, 1000 Ljubljana, Slovenia
roman.celin imt.si
Prejem rokopisa – received: 2007-02-02; sprejem za objavo – accepted for publication: 2007-02-21
The operational reliability of a system determines the system’s availability and costs during its lifetime. Taking care of the
reliability usually starts with knowledge of the operating conditions that need to be considered during the design, fabrication
and maintenance of the system. In the case of a system or component failure, it is necessary to know the causes and the
degradation mechanisms. An analysis of a fractured low-pressure wet-steam pipeline from a heat exchanger was performed. The
fracture was located in the fillet weld’s heat-affected zone. Visual testing, chemical analysis, hardness measurements and
metallographic examinations were carried out. The fracture surface was quite damaged, and so the number of fatigue-crack
propagation cycles could not be determined. An examination of the microstructure revealed that the fatigue crack occurred in
the heat-affected zone, where the plasticity and toughness had been diminished due to the material overheating at the welding.
As a result of the fracture analysis the industrial facility concerned extended the scope of its inspection of wet-steam pipelines.
Key words: pipeline, fracture, examination, fatigue failure
Zanesljivost obratovanja je lastnost sistemov ali komponent, ki dolo~a njihovo razpolo`ljivost in stro{ke v trajnostni dobi. Skrb
za zanesljivost je tudi poznanje pogojev obratovanja, ki jih je treba upo{tevati med konstruiranjem, izdelavo in uporabo sistema.
Pri okvari sistema ali komponente pa je treba natan~no poznati vzroke in mehanizme degradacije. Zaradi tega je bila opravljena
analiza preloma nizkotla~nega cevovoda za vla`no paro izmenjevalnika toplote. Prelom je nastal v toplotno vplivani coni
zvarjenega spoja. Izvedena je bila vizualna kontrola, kemijska analiza, meritve trdote in metalografska preiskava. Povr{ina
celega preloma je bila precej po{kodovana, zato na njej ni bilo mogo~e ugotoviti v koliko korakih je nastala utrujenostna
razpoka. Preiskava mikrostrukture je odkrila, da se je prelom cevi izvr{il v obmo~ju, kjer je bila plasti~nost, z njo pa tudi
`ilavost, zmanj{ana zaradi spremembe mikrostrukture pri varjenju zaradi pregretja materiala. Na osnovi rezultatov analize
preloma je bil v industrijskem obratu pove~an obseg kontrole cevovodov za mokro paro.
Klju~ne besede: cevovod, prelom, preiskave, utrujenostni prelom
1 INTRODUCTION
Reliability is defined as the probability that a certain
system will operate for a given time and under given
conditions without failure. Therefore, if a failure occurs
it is wise to analyse the system and determine the
probable cause of the failure1. In the case of metals, one
of the most commons reasons for failure is fatigue.
Fatigue failure is the phenomenon leading to fracture
under repeated or fluctuating stresses that are less than
the tensile strength of the material. There are three stages
of fatigue failure: initiation, crack propagation, and final
fracture2. The initiation site is always very small, never
extending for more than the size of a few grains around
the origin. The point of initiation is located at a stress
concentration and this stage may be extremely small, and
so difficult to distinguish from the succeeding stages of
propagation and crack growth. However, after the
original crack is formed, it becomes an extremely sharp
stress concentration that drives the crack even deeper
into the metal with each stress cycle. Whenever there is
an interruption in the propagation of a fatigue fracture,
characteristic marks or ridges may be observed.3 As the
propagation of the fatigue crack continues, gradually
reducing the cross-sectional area, it eventually weakens
the material so much that final, complete fracture occurs.
After 25 years in operation a failure occurred in a
low-pressure wet-steam pipeline. This failure was not a
catastrophic one, but it was severe enough to halt the
operation of the system. Figure 1 shows a sketch of the
pipeline and the position of the fracture. In this case the
fracture occurred in the heat-affected zone of the
flange’s fillet weld.
The dimensions of the tube were φ 60 mm × 4.8 mm.
No other data were available about the tube material or
the welding procedure used.
2 EXAMINATION
The fractured part of the pipeline was cut away from
the broken tube and the flanges. There are a number of
Materiali in tehnologije / Materials and technology 41 (2007) 3, 151–154 151
UDC/UDK 621.643:620.179 ISSN 1580-2949
Professional article/Strokovni ~lanek MTAEC9, 41(3)151(2007)
Figure 1: Sketch of the wet-steam pipeline with the fracture
Slika 1: Skica cevovoda mokre pare z mestom preloma
methods available for the detection and analysis of
fatigue cracks4. In this case it was decided to carry out a
careful visual examination, a chemical analysis, hardness
measurements and a metallographic examination.
3 RESULTS AND DISCUSSION
3.1 Visual examination
A visual examination of the inside area of the
fractured tube revealed a substantial loss of metal, which
is shown in Figure 2. The minimum thickness of the
tube was 3 mm. The affected area was smooth with
wavelike countours5. The minimum distance between the
affected area and the fracture was of 6 mm. Flanges are
not shown on Figure 2, becouse they were cut off.
The metal loss is oriented along the direction of the
wet steam’s flow and it is a classic feature of erosion-
corrosion, which can be defined as the accelerated
degradation of a material resulting from the joint action
of erosion and corrosion when the material is exposed to
rapidly moving droplets of water in a steam flow6.
Figure 3 shows the tube’s fracture surface. One area
of the initial crack is marked with the number 1, and it is
shown in more detail in Figure 4. It is clear that the
initial crack propagated in the circumferential direction
more quickly than in the radial direction.
The microstructure in the initial and fatigue-crack
propagation area is typical for an overheated steel. In the
area subject to the highest temperature the micro-
structure consists of a mesh of ferrite around large grains
of pearlite with many Widmanstätten ferrite needles.
Such a microstructure has a low deformability and a low
toughness and as such has a low fatigue strength.
Ridges are visible on the fracture surface marked
with the number 2 in Figure 3. The details are shown in
Figure 5.
The ridges are parallel with the tube’s circumference.
This kind of surface morphology is typical of rapid crack
propagation in steel without significal deformation. A
cross-section of the tube was cut and prepared for
R. CELIN, D. KMETI^: A WET-STEAM PIPELINE FRACTURE
152 Materiali in tehnologije / Materials and technology 41 (2007) 3, 151–154
Figure 3: Tube fracture surface
Slika 3: Povr{ina preloma cevi
Figure 4: Fatigue crack surface
Slika 4: Povr{ina utrujenostne razpoke
Figure 2: Tube with fracture and erosion-corrosion damage
Slika 2: Cev s prelomom in po{kodbami zaradi erozije – korozije
Figure 6: Crack on the fracture surface
Slika 6: Razpoka na povr{ini preloma
Figure 5: Ridges on the fracture surface
Slika 5: Brazde na povr{ini preloma
metallographic examination. The crack in Figure 6
shows transcrystal propagation typical for fatigue.
3.2 Chemical analysis
The chemical analysis of the tube material was made
with an ICP optical emission spectrometer7. This che-
mical composition is listed in Table 1.
Table 1: Chemical composition of the tube in mass fractions, w/%
Tabela 1: Kemijska sestava cevi v masnih dele`ih, w/%
C Mn Si P S Cr Ni Mo Al
0.21 0.74 0.17 0.003 0.017 0.04 0.01 0.02 0.012
A comparison of the values in Table 1 with the
reference data8 shows that the chemical composition of
the tube corresponds to the steel grade ASTM A 106 Gr.
B, which is widely used for the manufacturing of tubes.
3.3 Hardness measurement
A sample of the fillet weld was prepared for hardness
HV 0.3 measurements. The results are shown in Table 2.
The hardness indentations were 0.1 mm apart, starting in
the base metal, continuing across the heat-affected zone
(HAZ) and on into the weld deposit metal.
Table 2: Hardness HV 0.3 across the fillet weld
Tabela 2: Rezultati meritev trdot HV 0,3
base metal
1. 138 2. 142 3. 141 4. 141 5. 139 6. 141
heat-affected zone
7. 153 8. 145 9. 145 10. 152 11. 154 12. 156 13. 163
14. 162 15. 175 16. 165 17. 174 18. 165 19. 159 20. 162
21. 178 22. 176 23. 175 24. 171 25. 177 26. 178 27. 177
28. 173 29. 194 30. 199 31. 192 32. 199 33. 196 34. 199
35. 203 36. 201
weld deposit metal
37. 214 38. 211 39. 210 40. 212 41. 214 42. 218 43. 217
44. 213 45. 210 46. 215 47. 211
The average base metal hardness is HV 140.3; and it
is within the standard values for A 106 Gr. B steel. The
highest values measured were not in the HAZ, as would
be expected, but in the weld deposit metal. The average
value was HV 213, which should be considered as being
relatively high.
3.4 Metallographic examination of the fillet weld
The fillet weld between the tube and the flange, with
the base metal and the HAZ, is shown in Figure 7.
There is clear evidence of columnar crystals in the
weld deposit metal. The microstructure consists of
bainite with a small amount of ferrite in the grain
boundaries after the transformation (Figure 8). The
grains of austenite in the HAZ near the fusion line grew
in size because of the overheating.
At the cooling cooling the austenite transformed into
pearlite, bainite and a ferrite net. The microstructure of
the base metal (Figure 9) consist of uniform grains of
ferrite and pearlite. The wide HAZ indicates a very large
input of heat during the welding.
4 CONCLUSION
After our examinations we can conclude that the
fracture occurred in an area where plasticity and
toughness were diminished with the overheating during
the welding. The fracture took place in two stages. In the
first stage a fatigue crack started to grow from one point
on the outer tube surface. The propagation of this fatigue
crack was much faster in the circumferential direction
than in the radial direction. During the second stage the
crack propagated even faster, this time without any
plastic deformation. The fracture surface was damaged,
R. CELIN, D. KMETI^: A WET-STEAM PIPELINE FRACTURE
Materiali in tehnologije / Materials and technology 41 (2007) 3, 151–154 153
Figure 9: Microstructure of the tube’s base metal
Slika 9: Mikrostruktura osnovnega materiala cevi
Figure 7: Fillet weld with heat-affected zone
Slika 7: Kotni zvar s toplotno vplivanim podro~jem
Figure 8: Microstructure of the fillet-weld deposit material
Slika 8: Mikrostruktura deponiranega materiala zvara
and so it is impossible to determine how many steps it
took for the fatigue crack to start and how many steps it
took for the final fracture to take place. Based on
available data we can conclude that the main cause of the
fracture was a local increase in the bending stresses on
the outer tube surface because of uncontrolled, possibly
resonant, vibrations of the wet-steam pipeline during the
start up or the shut down of the system.
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1 D. J. Smith, Reliability, maintability and risk, 6th ed., Butterworth
Heinemann, Oxford 2001, 1–29
2 R. E. Smallman, R. J. Bishop, Modern physical metallurgy and mate-
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256–258
3 F. Vodopivec, Kovine in zlitine, IMT, Ljubljana 2002, 121
4 B. Kosec, G. Kova~i~, L. Kosec, Engineering Failure analysis, 9
(2002), 603–609
5 H. M. Herro, The Nalco guide to cooling water system failure
analysis, McGraw-Hill, New York 1993, 239–250
6 L. L. Shrerir, R. A. Jarman, G. T. Burstein, Corrosion Vol. 1, 3rd ed.,
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7 ASTM E 415 - 99a Standard Test Method for Optical Emission
Vacuum Spectrometric Analysis of Carbon and Low Alloy Steel
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R. CELIN, D. KMETI^: A WET-STEAM PIPELINE FRACTURE
154 Materiali in tehnologije / Materials and technology 41 (2007) 3, 151–154