M. DING et al.: FATIGUE-STRENGTH ANALYSIS IN THE VERY-HIGH-CYCLE REGIME ...
311–320
FATIGUE-STRENGTH ANALYSIS IN THE VERY-HIGH-CYCLE
REGIME OF THE TC17 TITANIUM ALLOY WITH MICRO
SCRATCHES
VPLIV MIKRORAZ NA VISOKOCIKLI^NO TRAJNO NIHAJNO
TRDNOST TITANOVE ZLITINE TC17
Mingchao Ding
1
, Yuanliang Zhang
1*
, Jinlong Wang
1
, Huitian Lu
2
,
Hongwei Xian
1
, Ning Hu
1
, Zexin Li
1
1
School of Mechanical Engineering, Dalian University of Technology, Dalian, Liaoning 116023, China
2
College of Engineering, South Dakota State University, Brookings, South Dakota 57007, United States of America
Prejem rokopisa – received: 2019-05-27; sprejem za objavo – accepted for publication: 2019-12-23
doi:10.17222/mit.2019.114
The effect of surface defects, especially micro scratches, on the fatigue strength of the TC17 titanium alloy is studied in this
paper. An ultrasonic fatigue experiment was conducted to obtain the geometric parameters of the surface scratches and the
corresponding fatigue data. Fatigue failure of the specimens occurred from the scratches in this experiment. A new parameter
area
Δ
is proposed to describe the fatigue damage caused by mechanical scratches; it is defined as the square root of the
triangular area of a scratch section. A modified fatigue strength model of TC17 with a consideration of the mechanical scratches
is established by applying the Murakami model and the term area
Δ
. Compared with the reported models, the new model is
demonstrated to be more suitable for the fatigue-strength prediction of TC17.
Keywords: TC17 titanium alloy, surface defects, micro mechanical scratches, scratch measurement, non-metallic inclusion,
surface fatigue failure, fatigue strength
V ~lanku avtorji opisujejo vpliv povr{inskih defektov, {e posebej raz mikronske velikosti, na trajno nihajno trdnost titanove
zlitine TC17. Izvedli so ultrazvo~ne preizkuse utrujanja materiala, da bi dobili geometrijske parametre povr{inskih raz in
odgovarjajo~e podatke o utrujanju materiala. Poru{itev vzorcev zaradi utrujanja materiala je posledica raz na njihovi povr{ini.
Avtorji predlagajo nov parameter area
Δ
za opis utrujenostnih po{kodb zaradi mehanskih raz, ki je definiran kot kvadratni koren
trikotnega preseka raze. Modificiran model za trajno trdnost titanove zlitine TC17 z upo{tevanjem mehanskih raz, temelji na
Murakamijevem modelu in izrazu area
Δ
. Primerjava z `e prej predlaganimi (objavljenimi) modeli je pokazala, da je novi
model primernej{i za napoved trajne nihajne trdnosti Ti zlitine TC17.
Klju~ne besede: titanova zlitina TC17, povr{inski defekti, mikromehanske raze, merjenje velikosti raz, nekovinski vklju~ki,
po{kodbe povr{ine zaradi utrujanja, trajna nihajna trdnost
1 INTRODUCTION
Titanium alloys have been the workhorse materials of
industrial fields such as the aerospace industry for many
years. The TC17 titanium alloy possesses numerous
great mechanical properties, such as high strength, low
relative density and excellent high-temperature oxidation
resistance. It is widely used in the manufacturing of core
mechanical parts in aero-engines, such as advanced
compressor blisk.
Even though the high surface quality of TC17 blisk is
carefully controlled in engineering practice, the micro
scratches still exist on the part’s surface. These scratches
are caused by the manufacturing or assembly process
due to unintentional or wrong operation generally. The
geometrical size of the micro scratch is small (the width
is less than 50 μm and the depth is less than 10 μm),
these scratches have a significant impact on fatigue
strength of the parts.
1,2
Hence, there is a need to
investigate the effect of micro mechanical scratches on
the fatigue strength to have an empirical prediction
model on TC17.
Many research results have been published on the
study of the effect of surface condition, including micro
mechanical scratches, on the fatigue property of metallic
materials. If the scratch is regarded as a propagating
crack, then fracture mechanics can be used to calculate
the lifetime to failure.
3
Fatigue-crack development from
mechanically induced scratches is a small notch fatigue
problem, where the stress concentrators are a few
microns deep.
4
The well-known term of area proposed
by Murakami makes a great contribution to the study the
effect of surface defects on fatigue strength.
5
M.
Filippini
6
studied the fatigue sensitivity to small defects
of a Gamma-titanium-aluminide alloy by an artificial
defect of area = 644 μm. The relevant parameters that
govern the specific mechanisms of failure such as the
range of stress-intensity factor, the threshold stress-inten-
Materiali in tehnologije / Materials and technology 54 (2020) 3, 311–320 311
UDK 67.017:669.295:539.536 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 54(3)311(2020)
*Corresponding author's e-mail:
zylgzh@dlut.edu.cn (Yuanliang Zhang)

sity factor range are evaluated by employing the Mura-
kami model. M. Åman
7
carried out a bending fatigue test
on notched specimens having different notch root
radiuses and a small drilled hole at the notch root. The
fatigue result shows that the area parameter model can
be extensively applied to consider the effects of stress
concentration, stress gradient and stress-intensity factors
in combined linear and uniform loading. Y. Nishimura
8
evaluated the sensitivity of fatigue strength to small
scratches based on the area parameter model. As
expected, the scratch depth exerts a significant effect on
the fatigue limit.
Researchers have made an effort to modify the
Murakami fatigue-strength model with the purpose of
improving its applicability. M. Zhang
9
assumed that the
fatigue crack that initiated from the internal inclusion is
a circumferential crack around a spherical cavity. Based
on the assumption, Murakami’s model was modified and
its accuracy was checked by 28 groups of high-strength
steels from the literature. The fatigue strength model
with surface defects was modified by simplifying the
surface defects as cracks using fracture mechanics.
10
However, to the author’s knowledge, little attention has
been focused on the effect of actual mechanical scratches
from machining defects on the fatigue performance for
TC17.
It is worth noting that artificial defects with regular
section shape are introduced in the above researches. The
main reason for this method is that area can be ob-
tained through simple section area calculation. However,
the scratches from engineering practice are mainly
caused by accidental operation. The formation of a
mechanical scratch depends on the forces involved, the
angle of the force, and the geometry of the object.
11
Thus, the section shape of scratches from engineering
practice cannot be regular. Moreover, the scratches are
micron size in depth and width. So, artificial defects may
not be suitable for the simulation of actual mechanical
scratches from engineering practice.
Using standard surface-roughness parameters such as
R
a
and R
z
is one traditional type of characterizing the
surface quality. Nevertheless, researchers have pointed
out that it cannot be applied directly to express the
fatigue-failure performance with these parameters. D.
Arola
12
pointed out that the average surface roughness
does not account for the process-dependent profile valley
radii, which has a critical influence on the stress-concen-
tration factor. H. Javadi
13
found that classic surface-
roughness parameters such as Ra are not the most
efficient parameters to quantify the fatigue surface
quality and the amplitude distribution parameter Mr2,
which represents the valley material component, showed
the highest direct correlation. J. C. Lacerda
14
analyzed
the evolution of the surface roughness of low-carbon
steel. They found that the ratio between the inclination of
the evolution curves of the peaks and valleys of the
roughness could be one more indicator for predicting the
failure of SAE 1020. It may be inadequate to express the
fatigue damage caused by scratches using traditional
surface-roughness parameters. So, it is obligatory to
establish a new fatigue-damage parameter for micro
mechanical scratches in order to set up an analytical
connection between the fatigue strength and the
scratches for TC17.
The main purpose of this study is to propose an
improved analytical model of the fatigue strength for
TC17 by redefining a new expression of area for micro
mechanical scratches. An ultrasonic fatigue experiment
was conducted to investigate the effect of mechanical
scratches on the fatigue strength of TC17. Firstly, a
physical scratch was predefined and quantitatively
measured in the width and depth processed by ZYGO`s
3D optical profiler instrument beforehand. Then, an
ultrasonic fatigue tensile experiment was carried out to
obtain fatigue data, and fracture characteristics were
observed with a Scanning Electron Microscope (SEM),
along with the test experiments.
A new fatigue-damage parameter for mechanical
scratches is defined as the square root of the triangular
area of the scratch section, marked as area
Δ
, combined
with the classic Murakami theory. A modified fatigue-
strength model for TC17 with the proposed parameter as
the main variable is described. The accuracy of this
model is proved by comparing with the results from the
reported models in lectures. It can be concluded that it is
more suitable to describe the characteristics of surface
mechanical scratches using the proposed parameter.
area
Δ
provides a new approach to the study of the
influence of the surface condition on fatigue perform-
ance.
2 FATIGUE EXPERIMENT OF TC17
2.1 Material and specimen
The mechanical properties of TC17 specimens in the
experiment are listed in Table 1.
The specimen used in the experiment is the hourglass
type with a minimum diameter of 3 mm, a radius
curvature of the reduced section (notch radius) of 58.9
mm, as shown in Figure 1. To remain the obvious
scratches that can be measured, there were no fine
M. DING et al.: FATIGUE-STRENGTH ANALYSIS IN THE VERY-HIGH-CYCLE REGIME ...
312 Materiali in tehnologije / Materials and technology 54 (2020) 3, 311–320
Table 1: Mechanical properties of TC17
Elastic modulus
E (GPa)
Tensile strength
R
m
(MPa)
Yield strength
R
p0.2
(MPa)
Vickers hardness
(Kgf/mm
2
)
Total elongation Reduction in area
111.5 1108.5 1060.5 356 15.8 % 42.0 %

grinding and polishing procedures in the final machining
step.
2.2 Ultrasonic fatigue experiment
Ultrasonic fatigue experiments are widely used to
investigate the fatigue property of TC17 because of its
high efficiency and low energy consumption.
15–17
In an
ultrasonic fatigue test, appropriately designed specimens
are stimulated to resonance vibrations at frequencies
close to 20 kHz. The specially designed specimens, as
shown in Figure 1, can meet the resonance requirement
of 20 kHz in the system. Vibrations are generated by a
piezoelectric ultrasonic converter and are magnified with
an amplifying horn. The fatigue test system is shown in
Figure 2. Some studies indicate that the frequency effect
is very small by using the ultrasonic testing machine.
18–20
The fatigue experiment of TC17 in this study is
carried out with an USF-2000 ultrasonic fatigue test
system with a constant load ratio of R = –1 at room
temperature (20 °C). The practical situation of an
aero-engine at high temperatures is not considered in this
study. The test temperature can be monitored in real time
by the temperature and monitoring device, as shown in
Figure 2. A cooling system is adopted to keep the testing
environment at room temperature. The characteristics of
the fatigue-fracture morphology are observed by SEM.
To obtain the stress amplitude when the specimens
break, loading stress increases from initial stress ampli-
tudes, 565 MPa, until fatigue failure occurs.
2.3 Measurement of depth and width of scratches
To study the effect of the mechanical scratches on
fatigue strength of TC17, the parameters that can reflect
the effective geometric characteristics of the scratches
should be measured before the fatigue experiment.
The determination of the geometric parameters is
supported by ZYGO’s 3D optical profiler instrument for
a better understanding of the mechanical scratches, as
shown in Figure 3. ZYGO owns numerous advantages:
high precise, non-contact surface measurement and
nanoscale surface features. It consists of three core
M. DING et al.: FATIGUE-STRENGTH ANALYSIS IN THE VERY-HIGH-CYCLE REGIME ...
Materiali in tehnologije / Materials and technology 54 (2020) 3, 311–320 313
Figure 1: Specimen of TC17
Figure 3: ZYGO 3D optical profiler instrument: a) equipment of
ZYGO, b) operating system
Figure 2: Ultrasonic fatigue experiment system: a) display of external
equipment, b) loading specimen

components: optical information collector, a real-time
monitor to display the surface appearance of the speci-
men and a computer to process the geometric data.
Studies have reported that the angle and tip radius
have exhibited an important influence on the fatigue
property of the micro notched samples.
12–21
The
stress-concentration factor for a single surface notch is
subjected to these parameters. However, when it comes
to the actual micro mechanical scratch, there are many
obstacles in measuring these parameters due to the
irregular section shape and minimal geometric size, as
shown in Figure 4.
It will be convenient to evaluate the fatigue damage
using basic geometric parameters, such as the depth and
width of the scratch. Three sections on one scratch are
selected in Figure 4a and the schematic of the depth and
width of section 1 are given in Figure 4b. It can be seen
in Figure 4 that the depth and width of each section can
be clearly captured. Herein, W and D are defined as the
width and depth of a whole scratch, which can be
calculated as follows:
W
WWW
=
++
123
3
; D
DDD
=
++
123
3
(1)
Where W
1
, W
2
, and W
3
refer to the width of three
sections and D
1
, D
2
, and D
3
refer to the depth of three
sections in the scratch.
Since the width and depth of a whole scratch are
defined, the next work is to measure the depth and width
of the scratches. The specific measurement standards are
as follows:
Stress concentration will happen in the minimum
diameter area of the specimen due to the specially
designed shape, as shown in Figure 1. Thus, the fatigue
crack will choose and initiate from the scratches within
the minimum diameter area of the specimen. So, the
measurement area is selected at the minimum diameter
of the specimen.
There can be many scratches among the measure-
ment area. Due to the limit of the experimental
capability, a maximum of three obvious scratches in the
measurement area is collected instead of all the existing
ones.
ZYGO is equipped with a real-time monitor, as
shown in Figure 3a, which can display the appearance of
the scratches during the measurement. The observation
and selection for the obvious scratches can be achieved
with the assistance of the monitor.
Once a scratch is located, the corresponding R
a
and
R
z
of the sample area and the depth and width of the
scratch are determined at the same time.
For the locked scratch, three sections are selected at
the positions with larger sizes of depth and width,
instead of an equal distribution on the scratches Figure
4a.
Table 3 presents the measurement results of the
depth and width of each scratch. Moreover, the average
depth of scratches that will be used below is given in
Table 2.
Table 2: Data of width and depth (μm)
Speci-
men
Scratch 1 Scratch 2 Scratch 3
Average
depth W D W D W D
1 11.65 2.5 10.5 1.8 2.15
2 6.70 1.91 14.43 1.58 1.75
3 11.30 1.37 10.30 1.79 7.55 1.5 1.55
4 12.30 1.49 15.07 0.93 1.21
5 11.75 1.53 12.05 0.96 12 1.13 1.21
6 6.70 1.91 14.43 1.58 1.75
7 11.30 1.37 10.30 1.79 7.55 1.50 1.55
8 12.73 1.57 13.50 1.76 1.67
9 12.2 1.33 1.33
10 9.80 1.35 11.60 1.52 1.44
Surface roughness R
a
and R
z
can be directly read in
Figure 3b. Table 3 shows the corresponding average
value of the surface roughness R
a
and R
z
of the
measurement areas. Surface-roughness parameters are
measured beforehand in order to make a comparison of
the fatigue-strength prediction below.
Table 3: Data of surface roughness (μm)
Specimen R
a
R
z
Specimen R
a
R
z
1 0.340 4.94 6 0.297 7.98
2 0.246 6.74 7 0.214 6.78
3 0.180 5.47 8 0.285 7.25
4 0.280 6.73 9 0.274 7.78
5 0.298 6.78 10 0.246 6.87
M. DING et al.: FATIGUE-STRENGTH ANALYSIS IN THE VERY-HIGH-CYCLE REGIME ...
314 Materiali in tehnologije / Materials and technology 54 (2020) 3, 311–320
Figure 4: Profile plots of a scratch by ZYGO: a) three sections on one
scratch, b) W
1
refers to the width of section 1 and D
1
refers to the
depth of section 1 in one scratch

3 FATIGUE EXPERIMENTAL DATA AND
OBSERVATIONS
Table 4 shows the results of the fatigue experiment.
Fatigue failure begins to occur when the stress amplitude
is above 615 MPa.
Table 4: Fatigue experiment data
Specimen
 a
(MPa)
Fracture
or not
Specimen
 a
(MPa)
Fracture
or not
1 565 No 6 615 No
2 600 No 7 620 Yes
3 610 No 8 630 Yes
4 615 No 9 645 Yes
5 615 No 10 645 Yes
Figure 5a shows a typical fracture characteristic,
including crack initiation, propagation area including
stable propagation and unstable propagation, and final
momentary fracture area. The crack-initiation area pre-
sents neatly a narrow strip shape, as shown in Figure 5b.
The fracture of the fatigue propagation is a river-shape
pattern in this experiment.
Figure 5b shows the fatigue crack initiated from the
root of the scratch. The slip mechanism that is induced
by localized inhomogeneous slip deformation is the main
reason for the surface failure. However, facets are not
observed in the fracture, which can conclude that surface
failure without facets is the fatigue failure mode in this
study.
22
A surface mechanical scratch can serve as stress
concentrator and produce localized stress concentrations
at the surface. The existence of surface scratches can be
regarded as micro notches, which accelerated the forma-
tion of the initial crack. As a result, at these positions
around the scratches where cyclic plastic deformation is
higher than the average, which caused fatigue failure.
23
As shown in Figures 5 and 6, there are no obvious
inherent defects, fish-eyes or granular bright facets
(GBFs) from the observation. However, the non-metallic
inclusions are detected by EDX, which are seen as the
black spots in Figure 6a. The analysis of a non-metallic
inclusion is given in Figure 6b. The main elements of
the non-metallic inclusions are carbon, oxygen,
magnesium and calcium and a little titanium. Even
though nonmetallic inclusions are scattered among
sub-surface, fatigue failures still occur from the surface,
M. DING et al.: FATIGUE-STRENGTH ANALYSIS IN THE VERY-HIGH-CYCLE REGIME ...
Materiali in tehnologije / Materials and technology 54 (2020) 3, 311–320 315
Figure 6: Nonmetallic inclusions of TC17: a) surface topography,
b) main elements of non-metallic inclusion by EDX
Figure 5: Surface topography of fatigue fracture: a) three parts in the
overall morphology of fracture, b) crack initiated from the root of
scratch

as shown in Figure 6a. As discussed above, it may be
reasonable to suppose that non-metallic inclusions have
no obvious effect on the fatigue-failure model of TC17
from this experiment.
4 SURFACE FATIGUE STRENGTH MODELS OF
TC17
Murakami conducted intensive studies on the effect
of surface defects on the fatigue behaviors of steel
alloys.
24–26
Y. Murakami et al.
27
proved the Vickers
hardness and area, simple and useful method, for the
prediction of the fatigue strength of materials containing
small defects. area is defined as the square root of the
area obtained by projecting a small defect or crack onto a
plane perpendicular to the maximum principal stress.
First of all, the origination of area in Murakami’s
research should be clarified. It is to be noted that
artificial defects on the specimens as shown in Figure 7
were pre-prepared by Murakami’s team.
27
Consequently,
the projection area of surface defect can be calculated
using simple area formulas. That is to say, area is a
pure geometrical parameter
28
and the initial size of a
defect is the crucial geometrical parameter that controls
the fatigue limit.
29
Therefore, an appropriate shape to
describe a section of the surface defect is the key step in
the fatigue strength analysis.
4.1 Current evaluations of surface fatigue strength
The stress-intensity factor builds a bridge between
the surface defect and the fatigue strength in fracture-
mechanics theory. It is well known that the threshold
stress-intensity factor range,  K
th
, depends on the a
crack size and decreases with a decreasing crack
size.
30–32
For a surface crack, K
Imax
is given approximately
as Equation (2), where  0
is the uniaxial tensile stress.
33
ΔK
Imax
area =× 065 2
0
.  π (2)
 K
th
is calculated by substituting the stress range at
fatigue strength, 2 w
, for  0
.
ΔK
th w
area =× 065 2 .  π (3)
ΔK
th
area ∝()
/ 13
is a significant finding to establish
the fatigue-strength model in Murakami`s work. The
well-known parameter model for the prediction of the
fatigue strength is given below:
  w
area
=
+ cH()
()
/
120
13
(4)
where Hv is the Vickers hardness, which is available
from a material test, c is a location parameter and c =
1.43 for the surface defect.
In early research, there are two dominant methods to
quantify fatigue damage in estimating the surface fatigue
strength: using the actual depth of a crack and the
surface roughness parameters.
For a single shallow circumferential crack, as shown
in Figure 8a, Equation (5) is used to estimate the
effective area, where 'a' is the depth of a very slender
crack.
34
area = 10a (5)
M. Zhang
35
substituted R
z
for 'a' in Equation (6), and
the prediction value is much closer to the experimental
value for FV520B.
area
z
= 10R (6)
Considering the effect of the surface roughness on
the fatigue strength, especially for a periodic surface
crack, as shown in Figure 8b, a more accurate
expression based on the accuracy of the depth and width
of the notches is given in Equation (7), where 'a'isthe
average depth of the surface scratches and '2b'i st h e
average peak distance.
36
And Equation (8) shows a much
more simplified expression for the surface defect.
37
M. DING et al.: FATIGUE-STRENGTH ANALYSIS IN THE VERY-HIGH-CYCLE REGIME ...
316 Materiali in tehnologije / Materials and technology 54 (2020) 3, 311–320
Figure 7: Geometries of artificial defects from Murakami's research: a) hole, b) Vickers indentation, c) notch, d) circumferential crack (redrawn
from
29
)

area
R
2
297
2
351
2
974
2
2
b
a
b
a
b
a
b
=
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ...
3
2
0195 for
a
b
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ < .
(7)
area =297 . a (8)
J. L. Wang
39
brought the effect of surface roughness
R
a
in fatigue life modelling of FV520B-I:
area
a
=297 . R (9)
Table 5 shows the prediction results of fatigue
strength using the above four different expressions,
Equations (5), (6), (8) and (9), where  a
refers to
experimental data and  w
refers to the predicted value.
The required data for 'a' is from Table 2. The prediction
error between experimental data and the predicted value
is calculated:
Prediction Error
aw
a
=
−
×
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 
 100 % (10)
The predicted value is more than 10% larger than the
experimental data when area =297 . Ra is applied to
describe the surface defect, which would produce a
potential danger in engineering practice. And more than
35 % error is produced by area
z
= 10R . When taking
the depth of the scratch into consideration, a much lower
prediction error, about 17 %, is generated by
area =297 . a and area = 10a.
M. DING et al.: FATIGUE-STRENGTH ANALYSIS IN THE VERY-HIGH-CYCLE REGIME ...
Materiali in tehnologije / Materials and technology 54 (2020) 3, 311–320 317
Figure 8: a) very shallow surface crack (l>10 a) (redrawn from
35
), b) periodic surface crack (redrawn from
36
)
Table 5: Fatigue-strength prediction results and errors for the reported models
 a (MPa)
area
a
=297 . R area
z
= 10R area =297 . a area = 10a
 w
(MPa) Error  w
(MPa) Error  w
(MPa) Error  w
(MPa) Error
620 734 -18.6 % 408 34 % 527 15 % 522 16 %
630 699 -11.4 % 403 37 % 521 17 % 516 19 %
645 704 -9.7 % 399 40 % 541 16 % 535 18 %
645 717 -11.7 % 407 39 % 534 18 % 529 19 %
Figure 9: Triangle in mechanical scratch section: a) the appearance of scratch on intensity map, b) three sections on surface map, c) the profile
plots of three section

As discussed above, it may be inadequate to establish
a link between the fatigue strength and the actual
mechanical scratches in reported models for TC17.
Therefore, a new way to describe the surface mechanical
scratches is necessary for a fatigue-strength analysis of
TC17 in this study.
4.2 Surface fatigue-strength prediction based on area
Δ
For parts that require a high surface quality, micro
mechanical scratches from engineering practice are the
main source of the surface defects instead of visible
notches or holes. It can be conducted from the above
discussion that the determination of the section shape of
a scratch is the primary work in the fatigue strength
analysis. Figure 10 shows the geometric morphology of
micro scratches from engineering practice by ZYGO. As
shown in Figures 9a and 9b, one scratch can be captured
with a dark blue strip. Figure 9c shows the profile plot
of three sections 'a-a', 'b-b', 'c-c' in one scratch. It can be
inferred from the above observations that the approx-
imate section shape for the scratch is a triangle.
Scratches of all specimens were observed according
to the same method mentioned above to confirm the
universality of a triangle for the section shape. Exami-
nations of the surface map by ZYGO show that almost
all the scratches have the same section shape, as
observed in Figure 9c. Besides, all the specimens
machined with the same process can also ensure the
universality of a triangle for section shape. Apparently,
in general and despite some dispersion, a triangle should
be the closest approximate shape to describe the section
of the scratch.
It is necessary to study the relationship between
triangle area and the fatigue strength of TC17 based on
Murakami theory. Thus, area
Δ
is defined as the square
root of the triangle area of scratch section for a quanti-
tative characterization of the surface fatigue damage. It
takes the triangle area of the scratches section as a
crucial factor in the surface fatigue analysis, which can
reflect the effect of depth and width on the fatigue
strength for TC17.
The depth of the scratch is far smaller than the
length. Consequently, the calculation of the stress-inten-
sity factor does not take the length of the scratch into
consideration.
39,40
The square root of the triangle area of the scratch i
can be expressed as:
area
Δi
ll
WD
=
2
(11)
Where W
l
is the width of the scratch i and D
l
is the
depth of the scratch i, which can be calculated by
Equation (1).
The micro crack always initiates from the maximum
scratch due to the stress concentration. Therefore, fatigue
damage caused by a micro scratch is determined by the
maximum value area
Δi
:
{} area area
ΔΔ
== max , , , ,...,
i
in 123 (12)
Thus, a modified surface fatigue-strength model of
TC17 applying the Murakami model and the new term of
area
Δ
is given:
  w
area
Δ
Δ
=
+ cH()
()
/
120
16
(13)
Table 6 shows the prediction results using the new
model (13). The square root of the triangle area of every
scratch is also listed in Table 6. Figure 10 shows the
error comparison between the new model and the above
four models.
Table 6: Fatigue strength prediction of TC17 based on area
Δ
 a
(MPa)
area
Δ1
(μm)
area
Δ2
(μm)
area
Δ3
(μm)
area
Δ
 w MPa
Error
620 2.777 3.035 2.379 3.035 565.7 8.8 %
630 3.157 3.449 – 3.449 553.8 12.1 %
645 2.848 – – 2.848 571.7 11.4 %
645 2.575 2.965 – 2.965 567.9 12.0 %
The maximum error is 12.1 %, and the minimum
error is 8.8 % when area
Δ
is used to predict the fatigue
strength of TC17. Thus, compared with the reported four
models, model (13) possesses an advantage with a 10 %
prediction error in the fatigue-strength prediction
accuracy of TC17.
Fatigue failure always initiates from a local geo-
metric discontinuity, such as holes, micro notches and
scratches. This is because stress concentration will occur
in these specific surface defects. In this study, it is
observed that the micro mechanical scratches are the
main surface defects for the specimens. Surface-rough-
M. DING et al.: FATIGUE-STRENGTH ANALYSIS IN THE VERY-HIGH-CYCLE REGIME ...
318 Materiali in tehnologije / Materials and technology 54 (2020) 3, 311–320
Figure 10: Error comparison between five models for TC17

ness parameters can express the overall surface quality in
a region of the measured area. However, the geometric
characteristics of specific scratches that caused fatigue
failure cannot be reflected by the surface roughness. The
deficiency of the surface roughness in the fatigue-
strength analysis is consistent with the current research
results, as discussed in the introduction.
The depth of the scratch exerts a significant influence
on the fatigue performance.
8
Equations (5) and (8) can
reflect the effect of the depth of the scratches on the
fatigue strength and produce much lower prediction
errors, around 17 %. So, it is reasonable and useful to
analyze surface fatigue strength based on the geometric
size of specific mechanical scratches. Once the width
and depth of the scratches are reflected at the same time,
the prediction results become much better. Therefore, it
is reasonable to think of area
Δ
as an effective and suit-
able parameter to describe the fatigue damage caused by
mechanical scratches, which can be applied to a surface
fatigue-strength prediction for TC17.
area
Δ
provides a novel approach to the study of the
influence of the surface state on fatigue performance. Its
applicability is validated by TC17 in this study, but it
needs more validation experiments using other metals
and forms of scratch. This paper establishes a framework
on surface fatigue strength affected by micro mechanical
scratches with laboratory experimental tests and data. As
laboratories are expensive costs for both the test and the
time, the sample size for the statistical empirical model
may not be large enough for a comprehensive expres-
sion, but the primary practice and the results are pro-
mising, and could be the good examples of the research
in this realm.
5 CONCLUSIONS
In this study, the width and depth of the scratches are
measured by ZGYO to establish a new fatigue-damage
parameter for the micro mechanical scratches; experi-
mental data and observations are obtained from fatigue
experiments to analyze the fatigue property of TC17.
The main conclusions are summarized as follows:
• Failure model of fatigue crack initiation is revealed
and named as the surface failure without facets.
Crack initiation presents a neatly narrow strip shape.
Although the non-metallic inclusions are observed,
no experimental phenomenon or data indicate that the
inclusions would affect the surface fatigue failure
model in this study.
• The classic surface-roughness parameters such as R
a
and R
z
have larger prediction error in the fatigue
strength prediction from this experiment. This is
because that roughness cannot reflect the geometric
characteristics of specific mechanical scratches.
• A parameter by the term of area
Δ
is proposed to
describe the fatigue damage caused by mechanical
scratches, which is defined as the square root of the
triangle area of the micro scratch section.
• A fatigue strength model with the consideration of
micro mechanical scratches of TC17 is established by
the application of area
Δ
based on Murakami theory.
It is proved that the new model can be applied to a
surface fatigue prediction of TC17 with a smaller
error.
Acknowledgment
The authors gratefully acknowledge The National
Natural Science Foundation of China (No. 51875082 &
No. 51375074). Also gratefully acknowledge the Fun-
damental Research Funds for the Central Universities
(DUT17ZD230) and Key Research and Development
Projects of Hui Ningxia Autonomous Region
(2018BDE02045).
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