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Surface crack initiation in pure titanium under various stress frequencies
EngineeringFracrwc MechanicsVol. 49, No. 2. PP. 317-321. 1994 Copyrigh1~
001~7!Wl(94)Eo110-3
1994 Ekvicr
scicna
Ltd
Printed in Great Britain. All ri%ts mserved 0013-7944j94 87.00+ 0.00
SURFACE CRACK INITIATION IN PURE TITANIUM UNDER VARIOUS STRESS FREQUENCIES HIDETOSHI
SAKAMOTO
and HIROYUKI
SAIKI
Department of Mechanical Engineering, Kumamoto University, 2-39-l Kurokami Kumamoto 860, Japan and KIYOTAKA TAKANO Yamaha Motor Co. Ltd. 2500 Shinkai Iwata 438, Japan Abatrac-The effect of stress frequency on fatigue surface crack initiation in 99.5% pure titanium, which has remarkable strain rate dependence in the plastic region, was studied by experiment and FE analysis. Surface crack initiation teats were carried out under three different stress frequencies. In this analysis, 3D elasto-v&o-plastic FEM-code was used. A comparison between the surface crack initiation life and the behaviors of the stress concentration part by analysis was made.
1. INTRODUCTION MANY MACHINE and structure materials have strain rate dependence at room temperature. In such materials fatigue strength, that is, fatigue crack initiation and propagation rate more or less depend upon stress frequency [l-4]. However, in many cases, the effect of stress frequency was almost ignored except for the case of consideration of chemical effects and elevated temperature, and fatigue strength was evaluated by the results of fatigue tests under a constant stress frequency. This conventional evaluation is likely to over/underestimate fatigue strength, and it is very important from a practical point of view (fatigue design, precise prediction of fatigue life, etc.) to make clear the effect on stress frequency on fatigue crack initiation life, because fatigue crack initiation life occupies a large part of fatigue life. So, in strain rate dependent materials, the present study makes clear the effect of stress frequency on surface crack initiation from stress concentration parts by the following experiments and analysis. (1) Evaluation of strain rate dependence of material. (2) Making clear the effect of stress frequency on surface crack initiation life by fatigue tests. (3) 3D_elasto-visco-plastic FEM analysis of the stress concentration part. (4) Comparison of the experimental results with the calculation ones by FEM, and propose an evaluation parameter of effect of stress frequency on surface crack initiation life.
2. SURFACE CRACK INITIATION TESTS 2.1. Material and specimen The material used in this study was 99.5% pure titanium bar, which has remarkable strain rate dependence. The chemical composition is given in Table 1. The geometry and dimensions of the specimen of the surface crack initiation test is shown in Fig. 1. Mean size of the crystal grain of this material is about 50 pm. A circular hole of 0.5 mm diameter and 0.5 mm depth was made at the center of the specimen surface to serve as a stress concentration part. All specimens were annealed under argon atmosphere at 540°C for 1 h after machining. The surfaces of the specimens were polished with No. 1500 emery paper and 0.3 pm-alumina polishing suspension for microscopic observation. 2.2. Experimental method Before fatigue tests, the strain rate dependence of the material was made clear by monotonic and cyclic tensile tests under different constant tensile speeds. An Instron-type universal testing machine was used. EFM 49n--Y
317
318
H. SAKAMOTO et al. Table I. Chemcial composition Fe
N
0
H
0.08
0.01
0.12
0.0028
Fatigue tests were performed in a hydraulic servo-type fatigue testing machine. In order to observe the effect of stress frequency on surface fatigue crack initiation life, pulsating loads in tension (Aa = 157, 176 MPa) with three different constant frequencies cf = 0.2, 1, 20 Hz), were applied. Crack initiation from the circular hole was observed with a travelling microscope (x 50). In the case of 20 Hz, the crack lengths were measured by synchronizing a stroboscope. After crack initiation on a surface of the specimen was recognized, crack length was measured at constant interval cycles. The ratio of crack depth and surface crack length was calculated by a bench mark on the fracture surface. 2.3. Experimental results The stress strain relations obtained by monotonic and cyclic tensile tests were shown in Figs 2 and 3. It is found that the stress level increased with higher strain rate in the plastic region both monotonic and cyclic ones and both of the ratio of strain rate dependence were approximately same. Figure 4 shows relation between surface crack initiation life Ni and stress frequency J Crack initiation life was defined as the number of cycles when the crack grew to 0.1 mm under consideration of detectable crack length by travelling microscope ( x 50). This defined length corresponds to about two grain sizes. From this figure, it is observed that crack initiation life depends upon stress frequency. For a low value of frequencyf, a short crack initiation life Ni was obtained. 4. 3D-ELASTO-VISCO-PLASTIC
ANALYSIS OF STRESS CONCENTRATION
PART
For the purpose of introducing strain rate dependence, the Baushinger effect in the plastic region, 3D-elasto-v&o-plastic FEM-code was employed. The elasto-viscoplastic constitutive relation is as follows [5]: {E} = {EC>+ {EV} {E’}= [o’]-‘(u) (.p}
= y(@(F))
J 31aJ;) 2
JJ;
aa
(1)
where the dot denotes partial differentiation with respect of time, and y, E, v are coefficient of viscosity, Young’s modulus and Poisson’s ratio, respectively. The function (G(F)) is defined as follows: (@(F)) = 0 (Q(F))
(F G 0)
= @(F)
(F > 0)
F= (a - d*)/Q*,
Fig. 1. Geometry and dimensions of fatigue specimen.
(2)
Effect of stress frequency on surface crack initiation
319
b
b
0.5
1.0 &
1.5
1
2.0
%
Fig. 2. Monotonic stress-strain
curves.
3
2 &
Fig. 3. Cyclic stressstrain
(%) curves.
where d is equivalent stress and c* is quasi-static stress that was obtained from the cyclic stress-strain relation in the case of smallest strain rate (E = 2.47 x lo-‘). In this analysis, the yield condition used is von Mises’ criterion. Analytical model and crack initiation surface subdivision is shown in Fig. 5. Utilizing symmetry, l/4 of the region was analyzed. An eight-node complex element was used and the shortest side length of an element around the stress concentration part is 0.2 mm. 5. ANALYTICAL
RESULTS
AND DISCUSSION
Figure 6 shows the relation between equivalent visco-plastic strain range At? and stress frequencyfin logarithmic coordinates. It is found that AP has the increasing tendency for a lower value off, and this is approximately in inverse proportion to f”(n > 0). From this figure, plastic work or damage per cycle at the stress concentration part increases with the decrease of stress frequencyf. This relation corresponds well with the trend of the N&curve in Fig. 4 obtained from the surface crack initiation tests. The fact mentioned above suggests that surface crack initiation life can be expressed in terms of equivalent v&o-plastic strain range AI?’ at the stress concentration part. The relation between the number of cycles to crack initiation Ni in Fig. 4 and equivalent v&o-plastic strain range A.P is shown in Fig. 7. If Ni is plotted against in logarithmic coordinates, this relation is approximated by a straight line. Consequently, the dependence of surface crack initiation life is closely related to the equivalent v&o-plastic strain range at stress concentration part based on viscoplasticity of material.
f
cycle
Fig. 4. Relation between surface crack initiation life N, and stress frequency J
320
Ii. SAKAMOTO er al.
I
initial crack tm Fig. 5. Analytical model and subdivision.
6. CONCLUSIONS (I) It was found from fatigue crack initiation tests that the number of cycles to surface crack initiation Ni depended upon stress frequency J (2) The crack initiation life Ni is closely related to equivalent v&co-plastic strain range AP at stress ~n~ntration part by 3D-elasto-visco-plastic analysis. If & is plotted against AP, the relation can be approximately expressed by a straight line in logarithmic coordinates for any stress frequency. This relation is expressed as follows; AE’P(N;)” = c C,n:
(n > 0)
material constants. 0.014
0.014
d;! 0.013
*
e ‘W
a
(3)
0.013
0.012
P 1Q.I _.J 0.012
0.011
0.011
0.010lo-’
10’
1
f
il
102
cycle
Fig. 6. Relation between equivalent visco-plastic strain range Ass and stress frequency I:
0.010 1
5
10
50
* 10’
Ni
Fig. 7. Relation between number of cycles to crack initiation N, and equivalent visco-plastic strain range Aew.
Effect of stress frequency on surface crack initiation
321
REFERENCES [l] K. Yokobori and K. Sate, The effect of frequency on fatigue crack propagation rate and striation spacing in 2024-T3 aluminum alloy and SM-54 steel. Engng Fracfure Me& 8, 81-88 (1976). [2] E. N. Strova, Influence of loading frequency on the rate of fatigue crack growth in aluminum alloys. Zuuo&aya Laboraroriya 46, 660462 (1980). [3] H. Sakamoto and S. Takczono, Dependence of stress frequency on fatigue crack initiation in orthotropic material. Fngng Fracture Mech. 36(3), 495-506 (1990). [S] H. Sakamoto, Strain rate dependence of fatigue crack propagation and initiation. Proc. hd ht. Conf. on Computer Aided Assessment and Control Localized Damage 92, Vol. I, pp. 121440 (1992). (51 P. Petzyna, Fundamental program in viscoplasticity, Aduances in Appkd Mechanics, Vol. 9, pp. 243-377. Academic Press, London (1976). (Received 14 June 1993)
001~7!Wl(94)Eo110-3
1994 Ekvicr
scicna
Ltd
Printed in Great Britain. All ri%ts mserved 0013-7944j94 87.00+ 0.00
SURFACE CRACK INITIATION IN PURE TITANIUM UNDER VARIOUS STRESS FREQUENCIES HIDETOSHI
SAKAMOTO
and HIROYUKI
SAIKI
Department of Mechanical Engineering, Kumamoto University, 2-39-l Kurokami Kumamoto 860, Japan and KIYOTAKA TAKANO Yamaha Motor Co. Ltd. 2500 Shinkai Iwata 438, Japan Abatrac-The effect of stress frequency on fatigue surface crack initiation in 99.5% pure titanium, which has remarkable strain rate dependence in the plastic region, was studied by experiment and FE analysis. Surface crack initiation teats were carried out under three different stress frequencies. In this analysis, 3D elasto-v&o-plastic FEM-code was used. A comparison between the surface crack initiation life and the behaviors of the stress concentration part by analysis was made.
1. INTRODUCTION MANY MACHINE and structure materials have strain rate dependence at room temperature. In such materials fatigue strength, that is, fatigue crack initiation and propagation rate more or less depend upon stress frequency [l-4]. However, in many cases, the effect of stress frequency was almost ignored except for the case of consideration of chemical effects and elevated temperature, and fatigue strength was evaluated by the results of fatigue tests under a constant stress frequency. This conventional evaluation is likely to over/underestimate fatigue strength, and it is very important from a practical point of view (fatigue design, precise prediction of fatigue life, etc.) to make clear the effect on stress frequency on fatigue crack initiation life, because fatigue crack initiation life occupies a large part of fatigue life. So, in strain rate dependent materials, the present study makes clear the effect of stress frequency on surface crack initiation from stress concentration parts by the following experiments and analysis. (1) Evaluation of strain rate dependence of material. (2) Making clear the effect of stress frequency on surface crack initiation life by fatigue tests. (3) 3D_elasto-visco-plastic FEM analysis of the stress concentration part. (4) Comparison of the experimental results with the calculation ones by FEM, and propose an evaluation parameter of effect of stress frequency on surface crack initiation life.
2. SURFACE CRACK INITIATION TESTS 2.1. Material and specimen The material used in this study was 99.5% pure titanium bar, which has remarkable strain rate dependence. The chemical composition is given in Table 1. The geometry and dimensions of the specimen of the surface crack initiation test is shown in Fig. 1. Mean size of the crystal grain of this material is about 50 pm. A circular hole of 0.5 mm diameter and 0.5 mm depth was made at the center of the specimen surface to serve as a stress concentration part. All specimens were annealed under argon atmosphere at 540°C for 1 h after machining. The surfaces of the specimens were polished with No. 1500 emery paper and 0.3 pm-alumina polishing suspension for microscopic observation. 2.2. Experimental method Before fatigue tests, the strain rate dependence of the material was made clear by monotonic and cyclic tensile tests under different constant tensile speeds. An Instron-type universal testing machine was used. EFM 49n--Y
317
318
H. SAKAMOTO et al. Table I. Chemcial composition Fe
N
0
H
0.08
0.01
0.12
0.0028
Fatigue tests were performed in a hydraulic servo-type fatigue testing machine. In order to observe the effect of stress frequency on surface fatigue crack initiation life, pulsating loads in tension (Aa = 157, 176 MPa) with three different constant frequencies cf = 0.2, 1, 20 Hz), were applied. Crack initiation from the circular hole was observed with a travelling microscope (x 50). In the case of 20 Hz, the crack lengths were measured by synchronizing a stroboscope. After crack initiation on a surface of the specimen was recognized, crack length was measured at constant interval cycles. The ratio of crack depth and surface crack length was calculated by a bench mark on the fracture surface. 2.3. Experimental results The stress strain relations obtained by monotonic and cyclic tensile tests were shown in Figs 2 and 3. It is found that the stress level increased with higher strain rate in the plastic region both monotonic and cyclic ones and both of the ratio of strain rate dependence were approximately same. Figure 4 shows relation between surface crack initiation life Ni and stress frequency J Crack initiation life was defined as the number of cycles when the crack grew to 0.1 mm under consideration of detectable crack length by travelling microscope ( x 50). This defined length corresponds to about two grain sizes. From this figure, it is observed that crack initiation life depends upon stress frequency. For a low value of frequencyf, a short crack initiation life Ni was obtained. 4. 3D-ELASTO-VISCO-PLASTIC
ANALYSIS OF STRESS CONCENTRATION
PART
For the purpose of introducing strain rate dependence, the Baushinger effect in the plastic region, 3D-elasto-v&o-plastic FEM-code was employed. The elasto-viscoplastic constitutive relation is as follows [5]: {E} = {EC>+ {EV} {E’}= [o’]-‘(u) (.p}
= y(@(F))
J 31aJ;) 2
JJ;
aa
(1)
where the dot denotes partial differentiation with respect of time, and y, E, v are coefficient of viscosity, Young’s modulus and Poisson’s ratio, respectively. The function (G(F)) is defined as follows: (@(F)) = 0 (Q(F))
(F G 0)
= @(F)
(F > 0)
F= (a - d*)/Q*,
Fig. 1. Geometry and dimensions of fatigue specimen.
(2)
Effect of stress frequency on surface crack initiation
319
b
b
0.5
1.0 &
1.5
1
2.0
%
Fig. 2. Monotonic stress-strain
curves.
3
2 &
Fig. 3. Cyclic stressstrain
(%) curves.
where d is equivalent stress and c* is quasi-static stress that was obtained from the cyclic stress-strain relation in the case of smallest strain rate (E = 2.47 x lo-‘). In this analysis, the yield condition used is von Mises’ criterion. Analytical model and crack initiation surface subdivision is shown in Fig. 5. Utilizing symmetry, l/4 of the region was analyzed. An eight-node complex element was used and the shortest side length of an element around the stress concentration part is 0.2 mm. 5. ANALYTICAL
RESULTS
AND DISCUSSION
Figure 6 shows the relation between equivalent visco-plastic strain range At? and stress frequencyfin logarithmic coordinates. It is found that AP has the increasing tendency for a lower value off, and this is approximately in inverse proportion to f”(n > 0). From this figure, plastic work or damage per cycle at the stress concentration part increases with the decrease of stress frequencyf. This relation corresponds well with the trend of the N&curve in Fig. 4 obtained from the surface crack initiation tests. The fact mentioned above suggests that surface crack initiation life can be expressed in terms of equivalent v&o-plastic strain range AI?’ at the stress concentration part. The relation between the number of cycles to crack initiation Ni in Fig. 4 and equivalent v&o-plastic strain range A.P is shown in Fig. 7. If Ni is plotted against in logarithmic coordinates, this relation is approximated by a straight line. Consequently, the dependence of surface crack initiation life is closely related to the equivalent v&o-plastic strain range at stress concentration part based on viscoplasticity of material.
f
cycle
Fig. 4. Relation between surface crack initiation life N, and stress frequency J
320
Ii. SAKAMOTO er al.
I
initial crack tm Fig. 5. Analytical model and subdivision.
6. CONCLUSIONS (I) It was found from fatigue crack initiation tests that the number of cycles to surface crack initiation Ni depended upon stress frequency J (2) The crack initiation life Ni is closely related to equivalent v&co-plastic strain range AP at stress ~n~ntration part by 3D-elasto-visco-plastic analysis. If & is plotted against AP, the relation can be approximately expressed by a straight line in logarithmic coordinates for any stress frequency. This relation is expressed as follows; AE’P(N;)” = c C,n:
(n > 0)
material constants. 0.014
0.014
d;! 0.013
*
e ‘W
a
(3)
0.013
0.012
P 1Q.I _.J 0.012
0.011
0.011
0.010lo-’
10’
1
f
il
102
cycle
Fig. 6. Relation between equivalent visco-plastic strain range Ass and stress frequency I:
0.010 1
5
10
50
* 10’
Ni
Fig. 7. Relation between number of cycles to crack initiation N, and equivalent visco-plastic strain range Aew.
Effect of stress frequency on surface crack initiation
321
REFERENCES [l] K. Yokobori and K. Sate, The effect of frequency on fatigue crack propagation rate and striation spacing in 2024-T3 aluminum alloy and SM-54 steel. Engng Fracfure Me& 8, 81-88 (1976). [2] E. N. Strova, Influence of loading frequency on the rate of fatigue crack growth in aluminum alloys. Zuuo&aya Laboraroriya 46, 660462 (1980). [3] H. Sakamoto and S. Takczono, Dependence of stress frequency on fatigue crack initiation in orthotropic material. Fngng Fracture Mech. 36(3), 495-506 (1990). [S] H. Sakamoto, Strain rate dependence of fatigue crack propagation and initiation. Proc. hd ht. Conf. on Computer Aided Assessment and Control Localized Damage 92, Vol. I, pp. 121440 (1992). (51 P. Petzyna, Fundamental program in viscoplasticity, Aduances in Appkd Mechanics, Vol. 9, pp. 243-377. Academic Press, London (1976). (Received 14 June 1993)