UDK 621.791.05:539.5                                                                                                                                                   ISSN 1580-2949
Original scientific article/Izvirni znanstveni članek                                                                                      MTAEC9, 40(2)49(2006)
SMALL-PUNCH TESTING OF A WELD’S HEAT-AFFECTED ZONES
TESTIRANJE LEZENJA TOPLOTNO VPLIVANIH PODROČIJ VARA Z UPORABO MAJHNEGA BATA
1 Roman Šturm, 2Yingzhi Li
!Institute of Metals and Technology, Lepi pot 11, 1000 Ljubljana, Slovenia
2KEMA Nederland BV, Utrechtseweg 310, Arnhem 6800ET, Netherlands
roman.sturmŽfs.uni-lj.si
Prejem rokopisa – received: 2005-09-05; sprejem za objavo - accepted for publication: 2006-01-12
Small-punch creep tests were performed on four different zones of a P91 welded joint: the base metal (BM), the weld metal (WM), the heat-affected zone on the base-metal side (HAZ-BM) and the heat-affected zone on the weld-metal side (HAZ-WM). In addition to the creep-rupture times, full creep-deflection curves were also available, from which the creep properties of different HAZ zones could be derived.
In this paper an analytic approach based on Chakrebarty’s membrane-stretch model and Kachanov’s creep law is used to interpret the creep-deflection curves of different zones. First of all, the strains and stresses are derived from the observed deflection curves according to Chakrebarty’s membrane-stretch model, then the Kachanov parameters are determined by attempting to minimize the sum of the squares of the residuals (the difference between the derived strains and the calculated strains at each time point). With the Kachanov parameters known, all the creep properties of the different zones of the welded joint can be obtained.
Keywords: small punch creep tests, welded joint, Kachanov parameters
Preskušanje lezenja z majhnim batom je bilo opravljeno na štirih različnih področjih P91 varjenega spoja, in sicer na osnovnem materialu (BM), na varu (WM), na toplotno vplivnem področju na strani osnovnega materiala (HAZ-BM) in na toplotno vplivnem področju na strani vara (HAZ-WM). Poleg samih časov lezenja do loma so na razpolago tudi celotne krivulje upogib preizkušanca–čas, na osnovi katerih je možno določiti lastnosti lezenja različnih toplotno vplivnih področij. V prispevku smo uporabili analitičen način interpretacije krivulj lezenja (odvisnost upogib preizkušanca–čas) preizkušancev, vzetih iz različnih območij varjenega spoja P91. Analitični način temelji na Chakrebartyjevem modelu raztezanja membrane in na Kachanovem zakonu lezenja. Najprej se iz časovno odvisnih krivulj upogibanja preizkušanca izračuna napetosti in deformacije po Chakrebartyjevem modelu raztezanja membrane. Potem se določijo Kachanovi parametri z minimiziranjem vsote kvadratov ostankov (to je razlika med dobljenimi raztezki in izračunanimi raztezki v vsaki časovni točki). Ko poznamo Kachanove parametre, lahko ocenimo vse lastnosti lezenja posameznega področja varjenega spoja.
Ključne besede: preskušanje lezenja z majhnim batom, varjeni spoj, Kachanovi parametri
1 INTRODUCTION
Reducing the consumption of energy by improving the efficiency of thermal power plants has become an important issue in the development of modern materials. Advanced power plants need to use higher working temperatures and higher steam pressures, and this requires materials with superior properties that can operate under such conditions 1,2. The creep properties of new metals for high-temperature applications, i.e., for the welded components of power plants with higher steam temperatures and pressures, are extremely important. These materials exhibit a pronounced change in their microstructure during exposure to high-temperature service conditions, which determines their remnant creep life. It is important to remember that it is necessary to achieve good creep resistance for the welded joint as a whole, and not just for the welding consumables. Experience has shown that the first cracks always appear in the welded joints, and so the creep properties for different HAZs are very important for the life assessment of welded structures 3.
The creep properties of a welded joint can be measured with cross-weld specimens 4,5; however, the ongoing micro-mechanisms in particular zones of a welded joint cannot be identified for certain. Therefore, a new creep-measuring technique, known as small-punch creep testing (SPCT), can be used. As only a small amount of material is needed for SPCT, this represents a new method for determining the creep properties for a weld’s HAZs. The SPCT was carried out on P91 steel at the Institute of Metals and Technology, Ljubljana, Slovenia. This paper describes how to derive the creep properties from the SPCT curves.
2 EXPERIMENTAL PROCEDURE
The creep examination procedure for the P91 welded joint can be described as follows. High-alloyed P91 consumables were used for welding (a modified J-type weld, i.e., a half V-shape) the two parts of the main steam pipes manufactured from the same P91 steel. The welded joint was then tempered for 1000 h at 565 °C in order to relieve the internal stresses and to simulate the
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R. ŠTURM, Y. LI: SMALL-PUNCH TESTING OF A WELD’S HEAT-AFFECTED ZONES
SP specimens WM
BM
«-HAZ-BM -HAZ-WM
nnpii|iiiHiiiiii|iiiiŠ
Figure 1: Welded joint of P91 base metal and P91 weld metal. Slika 1: Varjeni spoj P91 osnovnega materiala in P91 varjenega materiala
operating conditions in the material where no external stress is applied. The SPCT specimens were cut from the base material, from the HAZ and from the weld itself (Figure 1). The undiluted all-weld metal chemical composition for the experimental consumables is shown in Table 1.
The SPCT technique was used for the creep test with a disk-shaped test specimen that was cut from the weld with a diameter of 8 mm and a thickness of 0.5 mm. As shown in Figure 2, the small-punch test equipment used is similar to a constant-load cantilever creep machine. The test specimens are placed on the central axis of the lower die of the specimen holder and fixed by the upper die so that there is a loose fitting, i.e., neglecting the friction between the upper die and the specimen. The ball and the puncher are inserted into the hole in the upper die of the holder. The assembled holder is then put into reverting grips and suspended in the creep machine. During the test a constant load acts on the specimen by means of a ceramic ball with radius R = 1.25 mm. The radius of the hole, a, is equal to 2 mm, and its shoulder radius, rs, is equal to 0.2 mm. The temperature of the specimen is measured by means of a thermocouple placed very close to the specimen. The displacement of the puncher, i.e., the central deflection of the disk specimen, is measured using a very accurate inductive transducer (repeatability of 1 µm), and is recorded continuously with a computer. A constant load of 520 N and a test temperature of 620 °C was applied during the SPCT.
2.1 Experimental Testing Results
The results of the SPCT are summarized in Table 2, including the rupture time and the deflection at rupture.
Figure 2: Schematic illustration of the dies in the small-punch creep-test equipment.
Slika 2: Shematični prikaz čeljusti pri napravi za preskušanje lezenja z majhnim batom
Table 2: Test results of SPCT Tabela 2: Rezultati SPCT
	Rupture time tr/h	Deflection ô /mm due to load	Deflection <r/mm at rupture
BM	20.094	1.531	2.467
WM	22.504	0.904	2.287
HAZ-BM	8.286	1.743	2.584
HAZ-WM	16.556	1.343	2.664
The deflection curves of four different zones of the P91 welded joint are shown in Figure 3. The load was added at one time within 3 seconds and the applied stress is higher than the yield strength. Taking into account the influence of plasticity, the deflection due to load can be determined from the intersection point of two lines: the
20-
I
&   o
•§ o
00
HAZrWM
WM
Load = 520N Temperature = 620 °C
0        200      400      600        00       000      200      400
Time to rupture f/min
Figure 3: SPCT deflection curves of four different zones of the P91 welded joint
Slika 3: SPCT krivulje upogibanja za štiri različne cone P91 varjenega spoja
Table 1: Chemical composition of P91 material Tabela 1: Kemična sestava materiala P91
Si
Mn
Cr
Mo
V
Ni
Nb
N
w/%
0.10
0.27
0.53
0.007
0.01
8.76
0.91
0.2
0.35
0.04
0.0038
50
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R. ŠTURM, Y. LI: SMALL-PUNCH TESTING OF A WELD’S HEAT-AFFECTED ZONES
tangential line of the initial load deflection and the tangential line of the creep deflection. The deflections due to the load for four different zones are also listed in Table 2.
3 STATE OF THE ART FOR THE DETERMINATION OF CREEP PROPERTIES
Until now there has only been a little work on interpreting the creep curves from SPCT. In this paragraph, one of the existing approaches is described first.
3.1 Equivalent stress concept
The basic idea of the equivalent stress concept is to answer the question: "What load should be used in the SPCT to obtain the same time-to-rupture as in a 1-D conventional constant-load test?"
In total, four equations were found in the literatures 6,7,8, which are listed in the round-robin report 9. The symbols used are listed as follows (see Figure 4 for details):
Fsp: applied load on the SPCT specimen t : thickness of the disc t0: initial thickness of the disc a: radius of the disc between supports R: radius of the punch r: current radius a: membrane stress
<p: angle made by the surface normal to the vertical axis 6: angle <p at r = a 0: angle <p at the contact boundary ô: central deflection of the disc
One of the formulations proposed by Chakabarty was for stretch forming over hemispherical punch heads as 8:
F„„
a
t = tn
2pRt sin2 en
1 + cos00 1 + cos <p
(1)
(2)
where t is the current specimen thickness and t0 is the initial thickness.
3.2 Relations between strains, stresses and deflections
With the increasing deflection the disc shows an extension of the fibers on the tensile side. Tettamanti and Crudeli proposed that the extension of the arc, which insists on the same chord, can be calculated using a simple geometric diagram. The creep strain rate of the fibers on the tensile side of the disc can be derived from the deflection curve 6. This idea was adopted by Yingzhi Li to derive the creep strain from the deflection and obtain the creep properties 10.
A better expression of the relation between the strain s and the central deflection ô was proposed by Chakra-
barty based on the so-called membrane-stretch model for the stretch forming of a circular blank over a hemispherical punch head. It is assumed that the rigid punch is well lubricated in order to neglect the effect of friction; it was also assumed that the material was rigid-plastic. In addition, the deformation of the disc was assumed to take place under membrane stresses alone because the thickness of the disc was small in comparison to the radius of the punch. According to Chakra-barty, the general formula for compressive thickness strain is 8:
2ln
(1 + cos <p)(1+ coso) (1+cosö0 )2
(3)
The maximum strain at the centre of the disc (<p = 0)
is:
Ł = 2ln
2(1 +coso) (1+cosö0 )2
The strain at the contact boundary (p = 0O) is: (1 + coso)
2ln-
(1+cos0„)
(4)
(5)
Chakrabarty proved that the radius strain Łr is equal to the circumferential strain Łc, together with the volume incompressible condition; the compressive thickness strain Ł turns out to be the equivalent strain.
Meanwhile, Chakrabarty gave the expression for the central deflection of the disc, which equals the value of z at <p = 0 (Figure 4), as:
ň = a sin 6 ln
tan(00/2) tan(0/2)
+ R(1-cos 6 0)
An equation relating 6 and 0O is shown as:
sin0:
R
sin2 0.
(6)
(7)
Zhen Yang and Zhiwen Wang 11 gave the relation between the maximum equivalent strain Ł at the disc center and the deflection ô from Equations (4)-(7). A set of Ł and ô values are computed by inputting the actual specimen sizes a and R, and setting 0O to values in the
Figure 4: Geometry of deformation ' Slika 4: Geometrija deformacije diska
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R. ŠTURM, Y. LI: SMALL-PUNCH TESTING OF A WELD’S HEAT-AFFECTED ZONES
range from 0 to 90°. Then by fitting the values of Ł and ô using a polynomial expression, a relationship between Ł and ô (in units of mm) is finally obtained. Zhen Yang and Zhiwen Wang also gave the relation between the stress o and the deflection ô using an exponential expression.
The strain Ł at the contact boundary is more important than that at the disc center, as the former can be used to derive the stress o at the contact boundary with the strain-hardening law. From Equations (4)-(7) and a similar procedure to that mentioned above, the relation between the equivalent strain Ł at the contact boundary and the deflection ô is built with a polynomial fitting. For the European round-robin 9, the specimen dimensions were a = 2.0 mm and R = 1.25 mm. The relationship between the equivalent strain Ł at the contact boundary and deflection ô (in units of mm) is expressed as follows.
Ł = 014718Ô +0.03653Ô2 + 0.00772(53
(8)
A general relation between Fsp/a and the deflection ň can be derived from the equilibrium equation (1) together with Equations (6) and (7). The relationship between Fsp/o (Fsp in units of N, o in units of MPa) and deflection ň (in units of mm) is expressed in the form
F sp/o-
¦¦ 1.26613(5 -012866(52 - 0.04344(53 (for ň > 0.8 mm)
(9)
When the deflection ô tends to zero, Fsp/o also tends to zero, i.e., the membrane stress a tends to infinity. Thus the formula is not valid in the small-deformation stage as the bending is neglected. Based on an engineering judgment, the results of a large deformation are valid if the deflection is larger than 20 % of the maximum structural dimension. Therefore, the stresses given by Equation (9) are valid, even in creep analysis, if the deflection is larger than 20 % of the hole diameter, i.e., 0.8 mm.
4 AN ANALYTIC PROCEDURE TO DETERMINE THE CREEP PROPERTIES
The analytical procedures represent a critical aspect of the interpretation of SPCT. The procedures consist of the following steps:
1.   Derive strains and stresses from the observed deflection curve according to the membrane-stretch model provided by Chakrabarty.
2.   The Kachanov parameters can be estimated by attempting to minimize the sum of the squares of the residuals (difference between the derived strains and the calculated strains at each time point) considering the stress variation.
3.   By using Kachanov’s obtained parameters, determine the creep properties at the test temperature.
4.1 Kachanov model
The finite-element package ANSYS 5.7 is used in the calculations. In ANSYS the standard creep laws only contain the primary and the secondary creep regions. This means that a user-defined creep law is needed in order to be able to describe the tertiary creep region. The Kachanov creep law is used to define the total creep behavior in the calculation.
According to the Kachanov model, a creep curve can be governed by the following coupled equations (for details see 12):
At
m = Bt
-m(	r	°  )
\	v1	-a))
-m		ov
(1-«)'
(10)
(11)
In which A, B, n, v and t] are the Kachanov parameters; co denotes the damage factor, cd = 0 for untouched and cd = 1 for failure. For a constant-stress situation, the coupled equations (10) and (11) can be solved by integration and give explicit expressions for the strain Ł and the damage cd, see 12 for details.
By knowing the Kachanov parameters, the creep properties of the material can be determined. For constant-stress conditions, Equations (10) and (11) can be integrated to give:
v+1
(12)
Where
1-m
B(rj+1)ov
1
1-m
(13)
(14)
Here, A, B, n,v, tj and m are the six Kachanov parameters. If the primary creep stage can be neglected, then the parameter m = 0, and the number of parameters is five.
With the Kachanov parameters known, the creep properties of the material can be determined as follows. The minimum creep strain rate will be:
emin=At-on                      (15)
The rupture time tR and the rupture strain eR are already given in Equations (13) and (14) respectively. If the primary creep stage can be neglected, i.e., m = 0, from Equation (15), the creep strain rate can be determined in the form of the Norton creep law.
Aon
(16)
The rupture time can be derived from Eq. (13) as follows,
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1
B(1] + 1)(Jv
(17)
The rupture strain can be determined from Equations (14) and (15), and the rupture strain can be expressed in the form of the Dobes-Milicka relation 7:
where
Čmin t R
Tj + 1
(n+1-n)
(18)
(19)
The obtained material parameters are derived at the test temperature. If a set of creep curves at different temperatures is available, a set of parameters is derived at a different temperature. A least-square method can be used to determine the relations between the material parameters and the temperature. Dorn’s equation can be used to describe the temperature dependency. For example, Norton’s creep law can be expressed in the form:
: Ao n exp
RT
(20)
4.2 Determination of the Kachanov parameters and the creep properties
First, the strain curves should be checked to ensure a monotonous increase. In the mathematical software package MATLAB there is a function FMINCON that can carry out a non-linear minimization procedure with constrained conditions. However, it is difficult to get the results as the matrix is singular and depends strongly on the starting, estimated values. The practical method is to specify a broad range of parameters and directly carry out the optimization scheme.
It is easy to specify the range for parameters n, v and tj. They are usually between 3 and 12. The range of parameter m is between 0.05 and 1. The Dobes-Milicka
constant 2 must be greater than 1 and less than 6, thus rj > 6/5*n-1. It is difficult to specify the range of parameters A and B (from Equations (16) and (17)). The obtained Kachanov parameters are listed in Table 3. A comparison of the predicted and observed strain curves for the base metal (BM) is shown in Figure 5. Good agreement is found up to the tertiary creep region.
Table 3: Kachanov parameters of test material (at 620 °C) Tabela 3: Kachanovi parametri preskušanja materiala (pri 620 °C)
Parameter	A	B	n	v	t]	m
BM	2.262 X 10-21	5.099 x 10-31	7.235	11.000	8.647	0.844
WM	5.067 X 10-12	1.082 x 10-11	3.571	3.571	3.571	0.438
HAZ-BM	7.513 X 10-23	5.591 x 10-13	8.143	4.143	9.857	0.693
HAZ-WM	1.628 X 10-24	1.558 x 10-17	8.714	5.857	11.000	0.564
Based on the obtained Kachanov parameters, the creep properties of the test material can be derived if the primary creep is neglected. Taking the base metal (BM) as an example:
The Norton creep law:
Ł .   =Aon
min
with A = 2.262 X 1021 and n = 7.235
According Equation (17), the rupture time vs. stress:
tR = A-0-n'
With:
A' = 1/ŠB(?/+1)] = 2.033 x 1029 and n ’ = v = 11000
According to Equation (19), the Dobes-Milicka constanti:
2 = (7+1)(7+1-n) = 4.0
The predicted rupture time vs. stress for the four different zones are summarized and shown in Figure 6. From Figure 6 it is obvious that the weakest part of the P91 weld was the inter-critically quenched HAZ-BM.
0.6
<n  0.1
10                  15
Rupture time tr/h
20
25
Figure 5: Comparison of predicted and observed creep strains (BM) Slika 5: Primerjava napovedanih in izmerjenih deformacij lezenja (BM)
1.00000E+05
1.00000E+04
1.00000E+03
1.00000E+02
1.00000E+01
													
										p.		11                     ------	
													
										-¦-WM			
										HAZ-BM ==			
													
										-X-HAZ-WM —			
													
													
F?*1													
													
													
													
													
													
								čj					
								p- '-Č					
													
													
													
													
													
													
1.00000E+00
100             200             300             400
Applied stress s/MPa
Figure 6: Rupture time vs. stress predicted by SPCT
Slika 6: Odvisnost časa loma vs. napetost,  napovedana s SPCT
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R. ŠTURM, Y. LI: SMALL-PUNCH TESTING OF A WELD’S HEAT-AFFECTED ZONES
5 CONCLUSION
Small-punch creep tests were performed on four different zones of a P91 welded joint: the base metal (BM), the weld metal (WM), the heat-affected zone on the base-metal side (HAZ-BM) and the heat-affected zone on the weld-metal side (HAZ-WM). In addition to the creep-rupture times, full creep-deflection curves were also available, from which the creep properties of the four different zones of the P91 welded joint were derived.
Engineering experiences show that the creep properties for the different HAZs are very important for a life assessment of welded structures. However, due to difficulties with the measurement, the creep properties of a weld’s HAZ can only be obtained indirectly. The proposed approach provides a non-empirical method to interpret creep-test data from a small-punch test curve, and makes it possible to derive the creep properties for different HAZs. The results of the rupture time vs. stress predicted by the SPCT are shown in Figure 6. Only a few SPCT of different zones of the welded joint are enough to obtain the Kachanov parameters, which can describe/predict the creep properties of these different zones of the welded joint over a wide range of applied stresses. This might be a new approach to determining the creep properties for the weld’s HAZ as only a small amount of material is needed for small-punch creep tests.
A verification should be carried out to compare the results of the small-punch and standard 1-D uniaxial creep tests. The 1-D creep tests of the P91 base metal are now in progress.
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