- Email: [email protected]
Random loading fatigue life assessments for notched plates
International Journal of Fatigue 21 (1999) 941–946 www.elsevier.com/locate/ijfatigue
Random loading fatigue life assessments for notched plates Dimitar S. Tchankov b
a,*
, Akihiko Ohta b, Naoyuki Suzuki b, Yoshio Maeda
b
a Department of Strength of Materials, Technical University of Sofia, 1000 Sofia, Bulgaria Frontier Research Center for Structural Materials, National Research Institute for Metals, (NRIM), 1-2-1 Sengen, Tsukuba-shi, Ibaraki 305, Japan
Received 10 March 1999; received in revised form 5 May 1999; accepted 12 May 1999
Abstract Fatigue tests were performed on double edge notched specimens made of JIS SM570Q steel. Four types of notched specimens were used and stress concentration factors were 1, 2, 3 and 4. Cyclic and random loading was applied to the specimens. Random loading was corresponding to Rayleigh distribution of stress ranges, and it was applied as randomized loading blocks. During the loading the maximum stress was kept constant and equal to yield strength while the minimum stress is changed randomly. This test condition is considered to avoid the complex residual stresses at the notch root during variation of stresses. It is believed that by these tests it is possible to simulate the fatigue behavior of welded joints. Suggested equivalent stress was used to correlate the fatigue lives for the variable amplitude histories. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Random loading fatigue; Notched steel plates; High cycle fatigue; Life prediction; Rayleigh distribution
1. Introduction Most fatigue analyses of engineering structures are carried out using a constant amplitude S–N curve, usually for completely reversed loading or for a low stress ratio, e.g. R=0 for the welded structures. Under random loading with a low stress ratio, cycles with small stress ranges can be more damaging than under constant amplitude loading [1–4]. This problem is usually solved by an artificially shifting of the S–N curve to the left or by using a damage sum, D, less than unity, e.g. D=0.5. Also, residual stresses may play an important role in the random fatigue of welded structures, and it is very important to take these stresses properly into account. It is shown that random loading with a large mean stress value [5] or load sequences for which the maximum stress was kept constant [6] gives good correlation with high mean stress constant amplitude loading. A reason for high mean stresses can be the presence of residual stresses in the welded joints. Heller et al. [7] investigated the effect of residual stresses on random loading fatigue. The authors observed an increase in the
* Corresponding author. Tel.: +359 2 6362242; fax: +359 2 683215. E-mail address: [email protected] (D.S. Tchankov)
fatigue life with compressive residual stress and a reduction due to tensile residual stress. The latter has been observed in welded joints and similar results can be found in the literature [8,9]. Most welded structures contain geometrical discontinuities such as weld toe, geometric misalignment, etc. These are commonly referred as notches or stress raisers. In these hot spots the local stresses and strains are higher and usually the fatigue cracks initiate from there. To improve the simulation of different structures and their geometry, mainly notched test specimens are used. High tensile residual stresses in welded joints can be simulated in small specimens by keeping the maximum stress constant and equal to the yield stress [8,10]. As shown in the previous works of Ohta et al. [4,10], such loading results in lower fatigue lives than a loading with constant lower stress ratio. In this condition it is expected that the effect of compressive residual stress induced by a higher stress at notch disappears, as well as in the welded structures, because of the high tensile residual stresses around the stress raiser. Therefore, it is desirable to verify this behavior on fatigue specimens under similar loading conditions as a welded joint and to compare the results. There are many papers on fatigue strength of welded joints. The problem in the prediction of their fatigue life
0142-1123/99/$ - see front matter. 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 1 1 2 3 ( 9 9 ) 0 0 0 7 8 - X
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D.S. Tchankov et al. / International Journal of Fatigue 21 (1999) 941–946
is very important and accounts for the continuing interest in this area. Usually, fatigue tests are carried out on welded specimens [4–6,8–11] and the loading pattern is with low stress ratio (0 or 0.1). Ohta et al. [11] showed that by applying variable loading but keeping the maximum nominal stress constant, it is possible to simulate the high tensile residual stresses on small welded specimens. To investigate the applicability of Miner’s rule, Ohta [6] carried out fatigue tests under random loading and the stress condition smax=sy, and Niemi [5] carried out random loading tests with high mean stress. Both observed that Miner’s rule for damage accumulation gives very good fatigue life prediction. The aim of this paper is to present the results of a large fatigue testing program of random loading of notched specimens and to discuss the applicability of Miner’s damage accumulation rule, equivalent stress and effective number of cycles. 1.1. Theory Fatigue life predictions under random loading are mostly based on Miner’s damage accumulation rule [2,12]. According to this rule, failure is expected when the sum of the accumulated fatigue damage reaches unity
冘 k
ni ⫽1 N i⫽1 i
D⫽
(1)
where D is the damage sum, ni is the number of cycles applied at a stress range level ⌬si and corresponding number of cycles to failure Ni under constant amplitude tests. Ni is estimated according to the constant amplitude S–N curve ⌬smN⫽C
(2)
where C and m are material constants. The damage summation is performed for all stress range levels above the fatigue limit. Predicted fatigue life Npr is estimated as Npr⫽1/D
(3)
When using the modified Miner’s rule, which neglects the existence of fatigue limit ⌬sw, the equivalent stress is given as
冉
⌬sM eq⫽
冊
⌺⌬smini ntotal
1/m
(4)
where ⌬sM eq is the equivalent stress, ni is the number of cycles in step number i, and ⌬si is the stress range in step number i. ntotal is the total number of cycles for a block. Ohta et al. [6] show that an equivalent stress can be used to correlate the fatigue lives under random loading and the equivalent stress ⌬seq and the effective number of cycles to failure Neff can be estimated as
⌬seq⫽
冉
冊
⌺⌬smini Neff
1/m
Neff⫽⌺ni
(5) (6)
where ni=ni for ⌬si⬎⌬sw, and ni=0 for ⌬siⱕ⌬sw.
2. Experimental procedure The specimens were made of steel JIS SM570Q, which is widely used in welded structures. The chemical composition and material properties are listed in Table 1, as supplied by the manufacturer. The steel plate was quenched at 910°C and tempered at 620°C. The specimens were double-edge notched plates with rectangular cross section (Fig. 1). Commercially available 12-mm-thick plate was used. Four different specimens were used, with elastic stress concentration factor Kt=1.0 (unnotched), 2.0, 3.0 and 4.0. The final treatment of the notched surfaces of the specimens was fine milling, but the flat surface was as received, with an oxide layer on it. The tests were carried out on a MTS-810, 500 kN servo-hydraulic machine with computer control. The loading frequency was between 15 and 45 Hz, depending on the stress range applied. The tests were carried out under load control at room temperature. During the tests the stress and strain histories were recorded on a personal computer for further analysis. Constant amplitude tests were carried out in order to obtain the S–N curve for the material. Later, random loading, which consists of randomized blocks with different stress ranges, was applied. For all tests the maximum nominal stress was kept constant and equal to yield strength (Fig. 2a) as it is believed that such a pattern avoids the complex residual stresses at the notch root during variation of stresses and it gives the lower bound of the S–N curve for the material [4,6]. It is believed that by use of these tests it is possible to simulate the fatigue behavior of welded joints. The stress histories were generated by randomizing the cyclic blocks of stress ranges according to a random number table (Fig. 2b). The same order of sequence was used for all tests. The number of steps used was 16 for the majority of tests, but in some tests 12 or eight stress range levels were used in order to keep the difference between the levels not less than 10 MPa. Each block consists of 10 000 cycles. An example of loading history applied to the specimen is shown in Fig. 2b. The blocks were repeated until failure of the specimen. To achieve a better reproduction of the command signal, each loading sequence was initially applied to a specimen and output load was measured and recorded. Then the output and command signals were compared and the command signal was changed in order
D.S. Tchankov et al. / International Journal of Fatigue 21 (1999) 941–946
943
Table 1 Chemical composition (wt%) and mechanical properties of SM 570Q steel C
Si
Mn
P
S
Ni
Cr
Yield strength (MPa)
UTS (MPa)
Elongation (%)
0.14
0.26
1.53
0.013
0.002
0.01
0.02
611
662
31
ined by breaking a thin (0.05 mm) enameled wire bonded onto the notch of the specimen.
3. Experimental results and discussion 3.1. Fatigue life under constant amplitude loading
Fig. 1.
Shape and dimensions of the tested specimens.
to receive the expected output signal. This procedure was applied several times. The statistical properties of the random loading correspond to Rayleigh distribution [13] p⫽1.011X exp(⫺X2/2); X⫽(⌬s⫺⌬smin)/sd; s⫽⌬sd/⌬sm
(7)
where 0ⱕXⱕ3. The parameters of Rayleigh distribution ⌬sm, ⌬sd are shown in Fig. 3a. The random loading was generated as randomized block loading with Rayleigh distribution of stress ranges. The cycles with stress ranges above the fatigue limit were dominant in a block. Some of the applied stress range distributions are shown in Fig. 3b. The number of cycles to crack initiation were determ-
Fig. 2.
Fig. 4 correlates the fatigue lives with stress ranges under constant amplitude cyclic loading. The parameters of S–N curves (Eq. (2)), and the fatigue limit, ⌬sw, are given in Fig. 4. It is observed that fatigue strength becomes smaller with increasing stress concentration factor. Such behavior is confirmed for other steels under constant amplitude cyclic tests with R=0 [6], and smax=sy=const condition [8]. In Fig. 5 the variation of the fatigue limit with the stress concentration factor is presented. Almost linear dependence can be observed for Kt=2, 3 and 4. The relatively low fatigue strength and fatigue limit for Kt=1 may be explained by the oxide surface of the material. It has to be pointed out, in the case of the notched specimen, that the stress concentration factor is larger than that of the oxide layer and therefore the notched specimen fractured from the notch. However, the weakest point is on the oxide layer for specimens of Kt=1. Therefore, this stress concentration factor can be considered only as theoretical but not effective due to the rough oxide surface. The comparison between the fatigue crack initiation life, as detected by breaking the wire, and the total
Example of smax=sy condition test and random loading pattern.
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D.S. Tchankov et al. / International Journal of Fatigue 21 (1999) 941–946
Fig. 3.
(a) Variation of the Rayleigh stress ranges distribution pattern. (b) Examples of some applied loading patterns.
Fig. 4. Relationship between fatigue life and applied stress range under constant amplitude loading.
Fig. 5. factor.
fatigue life shows that the crack initiation life shared more than 80% of failure life for both constant amplitude and random loading.
be obtained. The fatigue life data for constant amplitude loading are plotted as open symbols, and data for random loading are plotted as solid ones. The details of fatigue life results are given in [14]. For fatigue life predictions, the best fitted S–N curve parameters C and m (Eq. (2)), are used, as shown in Fig. 4. In Fig. 6 the solid and dashed lines represent the 50% prediction line and 95% confidence intervals for constant amplitude tests, respectively. It can be seen that the fatigue lives for random loading test results are within the 95% confidence interval. Knowing that the stress concentration factor Kt in the weld toe is between 1.5 and 4 [15], it could be concluded that Miner’s damage accumulation rule is a good one for welded joints under random loading.
3.2. Fatigue life predictions under random loading The stress range ⌬s for constant amplitude loading is plotted against the total number of cycles to failure N and the equivalent stress range ⌬seq, (Eq. (5)), for random loading is plotted against the effective number of cycles to failure Nf, Fig. 6, for Kt=1, 2, 3 and 4. These axes are considered important because if the figure has the axis of the equivalent stress range and the total number of cycles, the coincidence between the constant amplitude results and the random loading results cannot
Dependence of the fatigue strength on stress concentration
D.S. Tchankov et al. / International Journal of Fatigue 21 (1999) 941–946
Fig. 6.
945
Correlation of the stress range with fatigue life: (a) Kt=1; (b) Kt=2; (c) Kt=3; (d) Kt=4.
It was observed in Fig. 4 that the slopes m of the S– N curves for each Kt value are very close each to other; therefore, slope m=3 could be used as a common value for such fatigue random loading tests, which could be very useful at the design stage.
4. Conclusions The smax=sy condition tests under constant amplitude and random loading were performed on notched JIS SM570Q steel plates. The following conclusions were reached.
laboratory conditions using notched specimens under constant and variable amplitude loading. 3. Using the equivalent stress range (5) and effective number of cycles to failure gives good predicted fatigue live values. From an engineering point of view, it is concluded that Miner’s damage rule is valid to represent the fatigue data under random loading. 4. For these tests the slope m of S–N curves for different Kt was close to 3, a value commonly used in the study of welded joint fatigue.
Acknowledgements 1. The fatigue crack initiation life shared more than 80% of the failure life. 2. Welded joints can be simulated successfully under
The STA Research Fellowship for Dr. D.S. Tchankov at NRIM, Japan is gratefully acknowledged.
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D.S. Tchankov et al. / International Journal of Fatigue 21 (1999) 941–946
References [1] Leibold HA, Naumann EC. A study of fatigue life under random loading. Proc ASTM 1963;63:717–33. [2] Schu¨tz W. The prediction of fatigue life in the crack initiation and propagation stages — a state of the art survey. Eng Fract Mech 1979;11:405–21. [3] Tchankov DS, Giunti T. On multiaxial fatigue testing time reduction. In: Marquis G, Solin J, editors. Fatigue design of structures. Elsevier, 1997:157–68. [4] Suzuki N, Takeda H, Ohta A, Ohuchida H. Evaluation of fatigue crack properties under random loading avoiding crack closure. Fatigue Fract Eng Mater Struct 1991;14(8):815–21. [5] Niemi EJ. Fatigue tests on butt and fillet welded joints under variable amplitude loading. In: Proceedings of the Welding Institute International Conference. The Welding Institut, 1987:8.1–10. [6] Ohta A, Maeda Y, Suzuki N. Fatigue strength of butt-welded joints under constant maximum stress and random minimum stress conditions. Fatigue Fract Eng Mater Struct 1996;19(2/3):265–75. [7] Heller RA, Seki M. Freudenthal AM, the effect of residual stress on random fatigue life. Proc ASTM 1964;64:516–36.
[8] Ohta A et al. Fatigue strength evaluation of welded joints containing high tensile residual stresses. Int J Fatigue 1986;July:146–50. [9] Gurney TR, Maddox SJ. A re-analysis of fatigue data for welded joints in steel. Welding Res Int 1973;3:1–54. [10] Ohta A, Kosuge M, Sasaki E. Fatigue crack closure over the range of stress ratios from ⫺1 to 0.8 down to stress intensity threshold level in HT80 and SUS304 stainless steel. Int J Fracture 1978;14:251–64. [11] Ohta A, Kosuge M, Nishijima S. Conservative data for fatigue crack propagation analysis. Int J Pressure Vessels Piping 1988;33:251–68. [12] Miner AM. Cumulative damage in fatigue. J Appl Mech 1945;September:151–64. [13] Albrecht P, Yamada K. Simulation of service fatigue loads for short-span highway bridges. In: Abelkis PR, Potter JM, editors. Service fatigue loads monitoring, simulation and analysis, ASTM STP 671. ASTM, 1979:255–77. [14] Tchankov DS, Ohta A, Suzuki N, Maeda Y. Fatigue life assessments for variable loaded notched plates. In: Proceedings of Fatigue Design ’98 Symposium, VTT, Espoo (Finland), 1998:415–26. [15] NRIM Fatigue Data Sheet, Technical Document No. 2, NRIM, 1983:74.
Random loading fatigue life assessments for notched plates Dimitar S. Tchankov b
a,*
, Akihiko Ohta b, Naoyuki Suzuki b, Yoshio Maeda
b
a Department of Strength of Materials, Technical University of Sofia, 1000 Sofia, Bulgaria Frontier Research Center for Structural Materials, National Research Institute for Metals, (NRIM), 1-2-1 Sengen, Tsukuba-shi, Ibaraki 305, Japan
Received 10 March 1999; received in revised form 5 May 1999; accepted 12 May 1999
Abstract Fatigue tests were performed on double edge notched specimens made of JIS SM570Q steel. Four types of notched specimens were used and stress concentration factors were 1, 2, 3 and 4. Cyclic and random loading was applied to the specimens. Random loading was corresponding to Rayleigh distribution of stress ranges, and it was applied as randomized loading blocks. During the loading the maximum stress was kept constant and equal to yield strength while the minimum stress is changed randomly. This test condition is considered to avoid the complex residual stresses at the notch root during variation of stresses. It is believed that by these tests it is possible to simulate the fatigue behavior of welded joints. Suggested equivalent stress was used to correlate the fatigue lives for the variable amplitude histories. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Random loading fatigue; Notched steel plates; High cycle fatigue; Life prediction; Rayleigh distribution
1. Introduction Most fatigue analyses of engineering structures are carried out using a constant amplitude S–N curve, usually for completely reversed loading or for a low stress ratio, e.g. R=0 for the welded structures. Under random loading with a low stress ratio, cycles with small stress ranges can be more damaging than under constant amplitude loading [1–4]. This problem is usually solved by an artificially shifting of the S–N curve to the left or by using a damage sum, D, less than unity, e.g. D=0.5. Also, residual stresses may play an important role in the random fatigue of welded structures, and it is very important to take these stresses properly into account. It is shown that random loading with a large mean stress value [5] or load sequences for which the maximum stress was kept constant [6] gives good correlation with high mean stress constant amplitude loading. A reason for high mean stresses can be the presence of residual stresses in the welded joints. Heller et al. [7] investigated the effect of residual stresses on random loading fatigue. The authors observed an increase in the
* Corresponding author. Tel.: +359 2 6362242; fax: +359 2 683215. E-mail address: [email protected] (D.S. Tchankov)
fatigue life with compressive residual stress and a reduction due to tensile residual stress. The latter has been observed in welded joints and similar results can be found in the literature [8,9]. Most welded structures contain geometrical discontinuities such as weld toe, geometric misalignment, etc. These are commonly referred as notches or stress raisers. In these hot spots the local stresses and strains are higher and usually the fatigue cracks initiate from there. To improve the simulation of different structures and their geometry, mainly notched test specimens are used. High tensile residual stresses in welded joints can be simulated in small specimens by keeping the maximum stress constant and equal to the yield stress [8,10]. As shown in the previous works of Ohta et al. [4,10], such loading results in lower fatigue lives than a loading with constant lower stress ratio. In this condition it is expected that the effect of compressive residual stress induced by a higher stress at notch disappears, as well as in the welded structures, because of the high tensile residual stresses around the stress raiser. Therefore, it is desirable to verify this behavior on fatigue specimens under similar loading conditions as a welded joint and to compare the results. There are many papers on fatigue strength of welded joints. The problem in the prediction of their fatigue life
0142-1123/99/$ - see front matter. 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 1 1 2 3 ( 9 9 ) 0 0 0 7 8 - X
942
D.S. Tchankov et al. / International Journal of Fatigue 21 (1999) 941–946
is very important and accounts for the continuing interest in this area. Usually, fatigue tests are carried out on welded specimens [4–6,8–11] and the loading pattern is with low stress ratio (0 or 0.1). Ohta et al. [11] showed that by applying variable loading but keeping the maximum nominal stress constant, it is possible to simulate the high tensile residual stresses on small welded specimens. To investigate the applicability of Miner’s rule, Ohta [6] carried out fatigue tests under random loading and the stress condition smax=sy, and Niemi [5] carried out random loading tests with high mean stress. Both observed that Miner’s rule for damage accumulation gives very good fatigue life prediction. The aim of this paper is to present the results of a large fatigue testing program of random loading of notched specimens and to discuss the applicability of Miner’s damage accumulation rule, equivalent stress and effective number of cycles. 1.1. Theory Fatigue life predictions under random loading are mostly based on Miner’s damage accumulation rule [2,12]. According to this rule, failure is expected when the sum of the accumulated fatigue damage reaches unity
冘 k
ni ⫽1 N i⫽1 i
D⫽
(1)
where D is the damage sum, ni is the number of cycles applied at a stress range level ⌬si and corresponding number of cycles to failure Ni under constant amplitude tests. Ni is estimated according to the constant amplitude S–N curve ⌬smN⫽C
(2)
where C and m are material constants. The damage summation is performed for all stress range levels above the fatigue limit. Predicted fatigue life Npr is estimated as Npr⫽1/D
(3)
When using the modified Miner’s rule, which neglects the existence of fatigue limit ⌬sw, the equivalent stress is given as
冉
⌬sM eq⫽
冊
⌺⌬smini ntotal
1/m
(4)
where ⌬sM eq is the equivalent stress, ni is the number of cycles in step number i, and ⌬si is the stress range in step number i. ntotal is the total number of cycles for a block. Ohta et al. [6] show that an equivalent stress can be used to correlate the fatigue lives under random loading and the equivalent stress ⌬seq and the effective number of cycles to failure Neff can be estimated as
⌬seq⫽
冉
冊
⌺⌬smini Neff
1/m
Neff⫽⌺ni
(5) (6)
where ni=ni for ⌬si⬎⌬sw, and ni=0 for ⌬siⱕ⌬sw.
2. Experimental procedure The specimens were made of steel JIS SM570Q, which is widely used in welded structures. The chemical composition and material properties are listed in Table 1, as supplied by the manufacturer. The steel plate was quenched at 910°C and tempered at 620°C. The specimens were double-edge notched plates with rectangular cross section (Fig. 1). Commercially available 12-mm-thick plate was used. Four different specimens were used, with elastic stress concentration factor Kt=1.0 (unnotched), 2.0, 3.0 and 4.0. The final treatment of the notched surfaces of the specimens was fine milling, but the flat surface was as received, with an oxide layer on it. The tests were carried out on a MTS-810, 500 kN servo-hydraulic machine with computer control. The loading frequency was between 15 and 45 Hz, depending on the stress range applied. The tests were carried out under load control at room temperature. During the tests the stress and strain histories were recorded on a personal computer for further analysis. Constant amplitude tests were carried out in order to obtain the S–N curve for the material. Later, random loading, which consists of randomized blocks with different stress ranges, was applied. For all tests the maximum nominal stress was kept constant and equal to yield strength (Fig. 2a) as it is believed that such a pattern avoids the complex residual stresses at the notch root during variation of stresses and it gives the lower bound of the S–N curve for the material [4,6]. It is believed that by use of these tests it is possible to simulate the fatigue behavior of welded joints. The stress histories were generated by randomizing the cyclic blocks of stress ranges according to a random number table (Fig. 2b). The same order of sequence was used for all tests. The number of steps used was 16 for the majority of tests, but in some tests 12 or eight stress range levels were used in order to keep the difference between the levels not less than 10 MPa. Each block consists of 10 000 cycles. An example of loading history applied to the specimen is shown in Fig. 2b. The blocks were repeated until failure of the specimen. To achieve a better reproduction of the command signal, each loading sequence was initially applied to a specimen and output load was measured and recorded. Then the output and command signals were compared and the command signal was changed in order
D.S. Tchankov et al. / International Journal of Fatigue 21 (1999) 941–946
943
Table 1 Chemical composition (wt%) and mechanical properties of SM 570Q steel C
Si
Mn
P
S
Ni
Cr
Yield strength (MPa)
UTS (MPa)
Elongation (%)
0.14
0.26
1.53
0.013
0.002
0.01
0.02
611
662
31
ined by breaking a thin (0.05 mm) enameled wire bonded onto the notch of the specimen.
3. Experimental results and discussion 3.1. Fatigue life under constant amplitude loading
Fig. 1.
Shape and dimensions of the tested specimens.
to receive the expected output signal. This procedure was applied several times. The statistical properties of the random loading correspond to Rayleigh distribution [13] p⫽1.011X exp(⫺X2/2); X⫽(⌬s⫺⌬smin)/sd; s⫽⌬sd/⌬sm
(7)
where 0ⱕXⱕ3. The parameters of Rayleigh distribution ⌬sm, ⌬sd are shown in Fig. 3a. The random loading was generated as randomized block loading with Rayleigh distribution of stress ranges. The cycles with stress ranges above the fatigue limit were dominant in a block. Some of the applied stress range distributions are shown in Fig. 3b. The number of cycles to crack initiation were determ-
Fig. 2.
Fig. 4 correlates the fatigue lives with stress ranges under constant amplitude cyclic loading. The parameters of S–N curves (Eq. (2)), and the fatigue limit, ⌬sw, are given in Fig. 4. It is observed that fatigue strength becomes smaller with increasing stress concentration factor. Such behavior is confirmed for other steels under constant amplitude cyclic tests with R=0 [6], and smax=sy=const condition [8]. In Fig. 5 the variation of the fatigue limit with the stress concentration factor is presented. Almost linear dependence can be observed for Kt=2, 3 and 4. The relatively low fatigue strength and fatigue limit for Kt=1 may be explained by the oxide surface of the material. It has to be pointed out, in the case of the notched specimen, that the stress concentration factor is larger than that of the oxide layer and therefore the notched specimen fractured from the notch. However, the weakest point is on the oxide layer for specimens of Kt=1. Therefore, this stress concentration factor can be considered only as theoretical but not effective due to the rough oxide surface. The comparison between the fatigue crack initiation life, as detected by breaking the wire, and the total
Example of smax=sy condition test and random loading pattern.
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D.S. Tchankov et al. / International Journal of Fatigue 21 (1999) 941–946
Fig. 3.
(a) Variation of the Rayleigh stress ranges distribution pattern. (b) Examples of some applied loading patterns.
Fig. 4. Relationship between fatigue life and applied stress range under constant amplitude loading.
Fig. 5. factor.
fatigue life shows that the crack initiation life shared more than 80% of failure life for both constant amplitude and random loading.
be obtained. The fatigue life data for constant amplitude loading are plotted as open symbols, and data for random loading are plotted as solid ones. The details of fatigue life results are given in [14]. For fatigue life predictions, the best fitted S–N curve parameters C and m (Eq. (2)), are used, as shown in Fig. 4. In Fig. 6 the solid and dashed lines represent the 50% prediction line and 95% confidence intervals for constant amplitude tests, respectively. It can be seen that the fatigue lives for random loading test results are within the 95% confidence interval. Knowing that the stress concentration factor Kt in the weld toe is between 1.5 and 4 [15], it could be concluded that Miner’s damage accumulation rule is a good one for welded joints under random loading.
3.2. Fatigue life predictions under random loading The stress range ⌬s for constant amplitude loading is plotted against the total number of cycles to failure N and the equivalent stress range ⌬seq, (Eq. (5)), for random loading is plotted against the effective number of cycles to failure Nf, Fig. 6, for Kt=1, 2, 3 and 4. These axes are considered important because if the figure has the axis of the equivalent stress range and the total number of cycles, the coincidence between the constant amplitude results and the random loading results cannot
Dependence of the fatigue strength on stress concentration
D.S. Tchankov et al. / International Journal of Fatigue 21 (1999) 941–946
Fig. 6.
945
Correlation of the stress range with fatigue life: (a) Kt=1; (b) Kt=2; (c) Kt=3; (d) Kt=4.
It was observed in Fig. 4 that the slopes m of the S– N curves for each Kt value are very close each to other; therefore, slope m=3 could be used as a common value for such fatigue random loading tests, which could be very useful at the design stage.
4. Conclusions The smax=sy condition tests under constant amplitude and random loading were performed on notched JIS SM570Q steel plates. The following conclusions were reached.
laboratory conditions using notched specimens under constant and variable amplitude loading. 3. Using the equivalent stress range (5) and effective number of cycles to failure gives good predicted fatigue live values. From an engineering point of view, it is concluded that Miner’s damage rule is valid to represent the fatigue data under random loading. 4. For these tests the slope m of S–N curves for different Kt was close to 3, a value commonly used in the study of welded joint fatigue.
Acknowledgements 1. The fatigue crack initiation life shared more than 80% of the failure life. 2. Welded joints can be simulated successfully under
The STA Research Fellowship for Dr. D.S. Tchankov at NRIM, Japan is gratefully acknowledged.
946
D.S. Tchankov et al. / International Journal of Fatigue 21 (1999) 941–946
References [1] Leibold HA, Naumann EC. A study of fatigue life under random loading. Proc ASTM 1963;63:717–33. [2] Schu¨tz W. The prediction of fatigue life in the crack initiation and propagation stages — a state of the art survey. Eng Fract Mech 1979;11:405–21. [3] Tchankov DS, Giunti T. On multiaxial fatigue testing time reduction. In: Marquis G, Solin J, editors. Fatigue design of structures. Elsevier, 1997:157–68. [4] Suzuki N, Takeda H, Ohta A, Ohuchida H. Evaluation of fatigue crack properties under random loading avoiding crack closure. Fatigue Fract Eng Mater Struct 1991;14(8):815–21. [5] Niemi EJ. Fatigue tests on butt and fillet welded joints under variable amplitude loading. In: Proceedings of the Welding Institute International Conference. The Welding Institut, 1987:8.1–10. [6] Ohta A, Maeda Y, Suzuki N. Fatigue strength of butt-welded joints under constant maximum stress and random minimum stress conditions. Fatigue Fract Eng Mater Struct 1996;19(2/3):265–75. [7] Heller RA, Seki M. Freudenthal AM, the effect of residual stress on random fatigue life. Proc ASTM 1964;64:516–36.
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