EFFECTS OF BIAXIAL STRESS CONDITION FOR FATIGUE PROPERTIES
OF TITANIUM
Y. Itoha, b, A. Shimamotob, D. Y. Hwangb, T. Nemotoa and H. Matuuraa
a
National Institute for Longevity Sciences
National Center for Geriatrics and Gerontology
36-3, Gengo, Morioka, Obu, Aichi, 474-8522, Japan
b
Advanced Science Laboratory
Saitama Institute of Technology
1690 Fusaiji, Fukaya, Saitama, 369-0293, Japan
a
[email protected], [email protected]
ABSTRACT
Machines and structures, such as automobiles are usually subjected to biaxial or three-axial stresses instead of uniaxial stress.
However, research on a fatigue failure under multi-axial stress has not been fully presented because such experiments are
difficult. To solve this problem, we developed the servo biaxial fatigue-testing machine. Authors already investigated the
fatigue crack progress behavior of the magnesium alloy under biaxial stress. As a result, it was suggested that existence of a
stress parallel to a crack affects crack progress velocity in AZ31B. In this research, fatigue crack propagation tests of pure
titanium were conducted under conditions of biaxial and uniaxial loading by using a cruciform specimen in a biaxial fatigue
machine, in order to investigate the effect of non-singular stress cycling on the fatigue crack growth properties. It is because
the crystal structure of titanium is the same as magnesium. As a result, we clarified effects of biaxial stress condition for fatigue
properties of pure titanium. The fatigue characteristics of pure titanium found that there was little effect of biaxial load stress
ratio as a result of this research.
Introduction
The density of pure titanium is about 3/5 of that of steel. Pure titanium is excellent also not only in specific strength but the
difficulty of rusting, the heat conductivity, and bio-compatibility. Therefore, use of titanium to medical equipment, an assisted
living instrument, and a life tool is increasing in recent years. When applied to such a purpose, the fatigue characteristics of
titanium are indispensable in order to create the design which ensures the reliability and the safety in long-distance run.
The effect of non-singular stress acting parallel to the crack plane on fatigue crack propagation is one of the basic problems of
fatigue crack propagation in biaxial stress fields. According to linear fracture mechanics the crack growth rate is controlled by
the stress intensity factor (SIF), so the non-singular stress has no effect on the growth rate. While several experimental data by
Kitagawa et al. and Liu et al. more or less support this principle, some data indicate that the non-singular stress does influence
the crack growth rate [1, 2]. For example, Tanaka et al. and Miller reported that the action of a stress parallel to a crack affects
crack progress velocity [3-5]. Above results suggest that there is no general consensus how biaxial stress exerts on fatigue
crack propagation.
In this research, fatigue crack propagation tests of pure titanium were conducted under conditions of biaxial and uniaxial
loading by using a cruciform specimen in a biaxial fatigue testing device, in order to investigate the effect of non-singular stress
cycling on the fatigue crack growth properties. As a result, the authors obtained the fundamental data about the biaxial fatigue
characteristics of pure titanium. Since validity of a servo biaxial fatigue-testing machine is essential for this study, we verified it
before conducting the fatigue tests. We present this result as well as the results from the fatigue tests.
Verification of the Performance and the Effectiveness of the Biaxial Fatigue Testing Machine
A uniaxial and an equal biaxial tensile test were carried out to verify the effectiveness of the biaxial fatigue testing device
shown in figure 1 which authors developed. The performance of the device is shown in table 1. The test specimens were
fabricated as the shape and size shown in figure 2 (a) and (b). To create test specimens, we processed the plates (aluminum
alloy 2024-T3, a thickness, t = 2.54mm, its mechanical properties are given in table 2.) with an end mill with a vertical
machining center. The thin strain gauges (KFEL -5-120-C1L3M2R: Kyowa Dengyo) were adhered to the front and back of the
center part of the uniaxial specimens as shown in figure 2 (a). In the case of the biaxial test specimens, we attached the thin
strain gauges to the front and back of the center part and also at a position of 80 % coverage of the biaxial stress field (in the
dotted lines in figure 2 (b)). For the experimental conditions, we set tension speed at 0.02 mm/s in both the uniaxial and the
biaxial tests. Strain under each load was measured with a memory recorder analyzer (EDX-1500 A-16AD: Kyowa Dengyo).
Figure 3-5 shows the results of the relationship between the load and the strain. As shown in figure 3 and figure 4, we confirm
that the experimental values are very well in agreement with the FEM analysis values. Figure 5 shows the relationship
between the load and the strain at the center, and in the 80 % coverage of the biaxial stress field of the test specimens. It
shows that the relationships have good proportionality up to the measured strain though there are some small deviations. The
result suggests that our testing device generates a uniformity biaxial stress field as intended.
Figure 1. Biaxial fatigue testing device
Table 1. Performance of examination machine
Name
Size
AS2000 Ver1.0
Length
2433mm
Side
2266mm
The maximum load
50kN
Displacement
±15mm
Frequency range
0.001-10Hz
The maximum velocity
1.5cm/s
Size of test specimen
300mm×300mm
Control method
Feedback control of displacement
Control software
SAGINOMIYA tiredness examination Software
Table 1. Mechanical properties of aluminum alloy
Tensile strength [MPa]
Proof stress [MPa]
Elongation [%]
461
320
17.9
.2
Strain Gauge
0
R2
20
25
60
O6
17
70
120
160
300
70
Unit : mm
(a) uniaxial test specimen
CH3
30 36.5
140
CH2
Triaxial
gauge
Biaxial strain gauge
CH1~CH6 : Strain Gauge
CH6
CH5
23.3
5.
4
CH4
R2
280
CH1
12.7
12.7
44.5
12.7
46.7
140
280
t=3
Unit : mm
(b) biaxial test specimen
Figure 2. Shape of test specimen and Position of strain gauges
Stress [MPa]
450
400
350
FEM
Experiment
300
250
200
150
100
50
0
0
1
2
3
4
Strain [%]
Figure 3. Relation between stress and strain under uniaxial loading condition
400
Stress [MPa]
350
FEM
Experiment
300
250
200
150
100
50
0
0
0.1
0.2
0.3
0.4
0.5
Strain [%]
Figure 4. Relation between stress and strain under biaxial loading condition
250
1ch
2ch
3ch
4ch
5ch
6ch
Stress [MPa]
200
150
100
50
0
0
0.05
0.1
0.15
0.2
0.25
Strain [%]
Figure 5. Measured stress-strain relation by strain gauges in biaxial loading test
Experimental Procedure
Pure titanium TP340C plates used for this research is 2.5mm thickness. The Chemical composition of TPC340C is shown in
Table 2. The mechanical property of TPC340C is shown in Table 3, and the dimension and form of a specimen are shown in
Figure 6. The radius of curvature of initial crack at the center of a specimen was set to 0.15mm. We made Y-axis of the
specimen as the rolling direction. The fatigue tester used for this experiment was the biaxial, electrically operated, oil-pressure
servo tension-compression fatigue tester. In the fatigue crack propagation tests, as shown in Figure 7, we put the stress, σx0
0
0
0
on X-axis and σy on Y-axis. The experiment was conducted on condition of the load stress ratio Rb = σx /σy =0, 0.25, 0.5,
0
0
0
0.75 and 1.0. The maximum values (σx max, σy max) of σx are shown in Table 4. We put stress with sinusoidal in shape, with the
0
0
stress ratio of σy min /σy max = 0, and the cycle speed of 10Hz.
Table 2. Chemical compositions of pure titanium TP340C (mass, %)
H
O
N
Fe
Ti
0.002
0.01
0.01
0.07
bal.
Table 3. Mechanical properties of pure titanium TP340C
Tensile strength
[MPa]
Proof stress
[MPa]
Elongation
[%]
Young’s modulus
[GPa]
Poisson’s
ratio
408
265
36
102.9
0.321
13.5
154.879
35.5
Y
25
69
300
a=30
X
22.4
12
23
24
140
300
Unit : mm
Figure 6. Shape and dimension of fatigue test specimen
Figure 7. Stress condition of fatigue test specimen
Table 4. Load stress in each biaxial load stress ratio
Rb ( = σx0/σy0)
0
0.25
0.5
0.75
1.0
σx0max [MPa]
0
11.43
22.86
34.29
45.72
σy0max [MPa]
45.72
45.72
45.72
45.72
45.72
Results and Discussion
As shown figure 8, in all experiments, cracks were propagated from the both ends of a pre-crack tip, and the fatigue crack
progressed in the direction of a pre-crack, i.e., the extended direction of a pre-crack tip. Figure 9 shows the relationship
between the half crack length a and the number of load cycles N obtained by fatigue tests. We used the laser beam
microscope for measurement of half crack length. Figure 9 shows that generating and progress of a fatigue crack become slow
in proportion to a stress parallel to a crack. However, in the case of Rb = 0.75, generating and progress of the fatigue crack
were the slowest. Existence of such a special biaxial load stress ratio is reported about magnesium [6-9]. However, the special
biaxial load stress ratio is not discovered with other materials. It is guessed that it is a phenomenon peculiar to a dense
hexagonal lattice that generating and progress of a fatigue crack become slow greatly under a specific biaxial load stress ratio.
Pre-crack
Crack tip
Crack tip
Figure 8. Test specimen after a fatigue test
0.04
Rb=
▲R b=
○R b=
×R b=
●R b=
Half crack length, a , m
□
0.03
0
0.25
0.5
0.75
1.0
0.02
0.01
0
100000
200000
300000
Number of cycles, N
Figure 9. Crack growth curves
400000
500000
Conclusions
The following knowledge was acquired as a result of verification of the performance of the biaxial fatigue-testing machine and
examining fatigue crack generation and progress process of pure titanium under various biaxial stress ratios.
1. The result of verification of the performance of the biaxial fatigue-testing machine suggests that our testing device
generates a uniformity biaxial stress field as intended.
2. It became clear that generating and progress of a fatigue crack become slow in proportion to the magnitude of a stress
parallel to a crack.
3. In the case of Rb = 0.75, generating and progress of the fatigue crack were the slowest. It is guessed that it is a
phenomenon peculiar to a dense hexagonal lattice that generating and progress of a fatigue crack become slow greatly
under a specific biaxial load stress ratio.
Acknowledgments
This research was sponsored by High-Tech Research Center of Saitama Institute of Technology.
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