Low cycle fatigue data evaluation for a highstrength
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In the present investigation, low cycle fatigue (LCF) behavior is studied using the cylindrical smooth specimens under strain-controlled fully-reversed pull-push conditions for a high-strength spring steel heat-treated to different strength levels. During strain cycling the steel exhibits continuous softening independent of the applied strain levels and heat-treatments. Under the circumstances the saturation of the plastic strain energy density per cycle proves to be a valid criterion to determine the stable hysteresis loops for the cyclic stress-strain (CSS) curve formation. The strain-life curve calculated on the basis of the CSS relationship is in good agreement with the experimental counterpart, indicating a fine consistency between data from the CSS approach and from the strain-life approach. Then the LCF properties are discussed with regard to their dependence on the heat-treatments or strength levels of the steel. © 1997 Elsevier Science Ltd.
ELSEVIER
Int. J. Fatigue Vol. 19, Nos 8-9, pp. 607-612, 1997 © 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0142 1123/97/$17.00+.00
0",, = K ' ( E p a ) n'
(1)
where oa and %. are stress amplitude and plastic strain amplitude, respectively, and K' and n' are constants for the best-fit of data, and are considered the cyclic deformation properties of a material. While obtaining the monotonic stress-strain curve is quite straightforward by tensile tests, the experimental determination of the CSS curve is largely dependent on experiences as well as assumptions. The most frequently adopted methods are the single-step or companion samples method, the multiple-step method and the incremental step method2-% Common to these methods is that the tips of the stable hysteresis loops are connected to form the CSS curve. Then the criterion for the stable hysteresis loop becomes a crucial issue while there is
not a unified definition for the 'stable' state. For instance, with the single-step method, a 'half-life' criterion is conventionally adopted in which the hysteresis loop at 50% life cycles is assumed as the stable oneL For a material that does not reach a (stress or strain) saturation state before specimen failure, however, this criterion becomes arbitrary and hence, has little physical implication. Moreover, different methods usually result in divergent ~CSS curves for a definite material 26. On the other hand, the strain-life relationship is one of the major issues to study, either for the LCF damage analysis or for engineering design. Simply combining Basquin's formula v for the elastic component with Coffin-Manson's formula s,9 for the plastic component, the total strain amplitude, Eta, can be expressed in correlation with the strain reversals to failure, 2Nr, as E,a = ~O-r'(2N/)h + Er,(2Nr)" (2)
PIh S014ຫໍສະໝຸດ Baidu-1123(97)00074-1
Low cycle fatigue data evaluation for a highstrength spring steel
D. M. Li*, K. W. Kim and C. S. Lee
Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang, 790-784 Korea (Received 11 May 1997; accepted 28 May 1997)
*Author for correspondence at: c/o Professor W. Bleck, Institut ftir Eisenhtittenkunde, RWTH Aachen, Intzestral3e 1, 52072 Aachen, Germany.
in which E is Young's modulus, and the four constants, of', ~f', b and c are termed fatigue strength coefficient, fatigue ductility coefficient, fatigue strength exponent and fatigue ductility exponent, respectively, and are also considered fatigue properties of a material. A theoretical consistency between properties obtained from the strain-life data and from the CSS data should be maintained ~,m because they represent the cyclic properties of one single material. However, since the CSS relationship and the strain-life relationship are experimentally determined individually via different approaches, this consistency cannot always be maintained adequately in practice.
LCF results. Principal properties obtained from these tests are listed in Table 1. RESULTS AND DISCUSSION In the present study, the single-step method was adopted for the determination of the CSS curve since enough specimens were available as they were tested for the strain-life correlation. In order to use this method, the state of the stable hysteresis loop has to be decided. Under the strain-controlled condition, the variation of stress amplitude during cycling has to be examined to check if the material is cyclically softening, hardening, stable or exhibits mixed behavior. It is observed that, for each applied strain amplitude (Ea), the stress amplitude oa decreases continuously as the strain cycling proceeds. All the five groups of specimens exhibit the same trend of this variation, with Figure 1 showing representative examples. Therefore the steels behave as cyclically softening independent of their specific microstructures. This is in agreement with the cyclically softening behavior reported for some other high-strength steels ~2. As is noted earlier, in the case where no stable stress is reached during cycling, defining the stable hysteresis loop by the 'half-life' criterion is somewhat artificial or is not physically based. On the other hand, from a viewpoint of damage accumulation, the strain energy-based criterion has been proved to be more consistent in describing the LCF behavior ~3. Then, the variation of the plastic strain energy density, as measured by the area of the hysteresis loop in the true stress-true strain plot, has to be checked. Figure 2 shows the plastic energy density per cycle, AW~,, as a function of cycle N for specimens with different strain amplitude Ea. It provides data for the steels tempered at 300 and 500°C but is representative of all groups of steels studied. As is seen from Figure 2, the value of AWe first increases with increasing N and then saturates to a stable value when N reaches a critical value. For the present case, this critical value of N ranges between 10 and 20 cycles. In view of this experimental trend, the stable hysteresis loop for the determination of the CSS curve is chosen as the one at the critical cycle when AWp reaches a stable value. For each specimen group, the stable hysteresis loops were selected according to the above criterion, and the tips of these loops were connected, to form the CSS curve. All the CSS curves determined by this procedure are given in Figure 3, in comparison with their counterparts obtained in monotonic tension. It is indicated that, for all groups of specimens, the CSS curve lies beneath the corresponding monotonic stress-strain curve, confirming the cyclic softening behavior as is reflected in the variation of the stress amplitude
607
608
D . M . Li et al.
In the present investigation, the LCF behavior of a high-strength spring steel is approached both experimentally and analytically. It is aimed at establishing an appropriate criterion for the determination of the stable state of the LCF deformation and at examining the consistency between data of the CSS and the strainlife approaches.
(Keywords: low cycle fatigue; high-strength steel; cyclic stress-strain correlation; strain-life correlation)
Despite the fact that low cycle fatigue (LCF) behavior has been studied for many decades and become a rather classic topic, some of its fundamentals still need to be clarified systematically in order to have a better understanding of the LCF mechanism. Just as in the monotonic loading condition, an appropriate determination of the cyclic stress-strain (CSS) relationship is also of key importance in the description of basic cyclic deformation behavior. As a conventional practice, the cyclic stress-plastic strain relationship is generally expressed in a power-law equation as l
ELSEVIER
Int. J. Fatigue Vol. 19, Nos 8-9, pp. 607-612, 1997 © 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0142 1123/97/$17.00+.00
0",, = K ' ( E p a ) n'
(1)
where oa and %. are stress amplitude and plastic strain amplitude, respectively, and K' and n' are constants for the best-fit of data, and are considered the cyclic deformation properties of a material. While obtaining the monotonic stress-strain curve is quite straightforward by tensile tests, the experimental determination of the CSS curve is largely dependent on experiences as well as assumptions. The most frequently adopted methods are the single-step or companion samples method, the multiple-step method and the incremental step method2-% Common to these methods is that the tips of the stable hysteresis loops are connected to form the CSS curve. Then the criterion for the stable hysteresis loop becomes a crucial issue while there is
not a unified definition for the 'stable' state. For instance, with the single-step method, a 'half-life' criterion is conventionally adopted in which the hysteresis loop at 50% life cycles is assumed as the stable oneL For a material that does not reach a (stress or strain) saturation state before specimen failure, however, this criterion becomes arbitrary and hence, has little physical implication. Moreover, different methods usually result in divergent ~CSS curves for a definite material 26. On the other hand, the strain-life relationship is one of the major issues to study, either for the LCF damage analysis or for engineering design. Simply combining Basquin's formula v for the elastic component with Coffin-Manson's formula s,9 for the plastic component, the total strain amplitude, Eta, can be expressed in correlation with the strain reversals to failure, 2Nr, as E,a = ~O-r'(2N/)h + Er,(2Nr)" (2)
PIh S014ຫໍສະໝຸດ Baidu-1123(97)00074-1
Low cycle fatigue data evaluation for a highstrength spring steel
D. M. Li*, K. W. Kim and C. S. Lee
Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang, 790-784 Korea (Received 11 May 1997; accepted 28 May 1997)
*Author for correspondence at: c/o Professor W. Bleck, Institut ftir Eisenhtittenkunde, RWTH Aachen, Intzestral3e 1, 52072 Aachen, Germany.
in which E is Young's modulus, and the four constants, of', ~f', b and c are termed fatigue strength coefficient, fatigue ductility coefficient, fatigue strength exponent and fatigue ductility exponent, respectively, and are also considered fatigue properties of a material. A theoretical consistency between properties obtained from the strain-life data and from the CSS data should be maintained ~,m because they represent the cyclic properties of one single material. However, since the CSS relationship and the strain-life relationship are experimentally determined individually via different approaches, this consistency cannot always be maintained adequately in practice.
LCF results. Principal properties obtained from these tests are listed in Table 1. RESULTS AND DISCUSSION In the present study, the single-step method was adopted for the determination of the CSS curve since enough specimens were available as they were tested for the strain-life correlation. In order to use this method, the state of the stable hysteresis loop has to be decided. Under the strain-controlled condition, the variation of stress amplitude during cycling has to be examined to check if the material is cyclically softening, hardening, stable or exhibits mixed behavior. It is observed that, for each applied strain amplitude (Ea), the stress amplitude oa decreases continuously as the strain cycling proceeds. All the five groups of specimens exhibit the same trend of this variation, with Figure 1 showing representative examples. Therefore the steels behave as cyclically softening independent of their specific microstructures. This is in agreement with the cyclically softening behavior reported for some other high-strength steels ~2. As is noted earlier, in the case where no stable stress is reached during cycling, defining the stable hysteresis loop by the 'half-life' criterion is somewhat artificial or is not physically based. On the other hand, from a viewpoint of damage accumulation, the strain energy-based criterion has been proved to be more consistent in describing the LCF behavior ~3. Then, the variation of the plastic strain energy density, as measured by the area of the hysteresis loop in the true stress-true strain plot, has to be checked. Figure 2 shows the plastic energy density per cycle, AW~,, as a function of cycle N for specimens with different strain amplitude Ea. It provides data for the steels tempered at 300 and 500°C but is representative of all groups of steels studied. As is seen from Figure 2, the value of AWe first increases with increasing N and then saturates to a stable value when N reaches a critical value. For the present case, this critical value of N ranges between 10 and 20 cycles. In view of this experimental trend, the stable hysteresis loop for the determination of the CSS curve is chosen as the one at the critical cycle when AWp reaches a stable value. For each specimen group, the stable hysteresis loops were selected according to the above criterion, and the tips of these loops were connected, to form the CSS curve. All the CSS curves determined by this procedure are given in Figure 3, in comparison with their counterparts obtained in monotonic tension. It is indicated that, for all groups of specimens, the CSS curve lies beneath the corresponding monotonic stress-strain curve, confirming the cyclic softening behavior as is reflected in the variation of the stress amplitude
607
608
D . M . Li et al.
In the present investigation, the LCF behavior of a high-strength spring steel is approached both experimentally and analytically. It is aimed at establishing an appropriate criterion for the determination of the stable state of the LCF deformation and at examining the consistency between data of the CSS and the strainlife approaches.
(Keywords: low cycle fatigue; high-strength steel; cyclic stress-strain correlation; strain-life correlation)
Despite the fact that low cycle fatigue (LCF) behavior has been studied for many decades and become a rather classic topic, some of its fundamentals still need to be clarified systematically in order to have a better understanding of the LCF mechanism. Just as in the monotonic loading condition, an appropriate determination of the cyclic stress-strain (CSS) relationship is also of key importance in the description of basic cyclic deformation behavior. As a conventional practice, the cyclic stress-plastic strain relationship is generally expressed in a power-law equation as l