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Effect of mean stress and ratcheting strain on the low cycle fatigue behavior of a wrought 316LN stainless steel
Materials Science & Engineering A 677 (2016) 193–202
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Effect of mean stress and ratcheting strain on the low cycle fatigue behavior of a wrought 316LN stainless steel Xuyang Yuan a, Weiwei Yu a,b, Sichao Fu a, Dunji Yu a,n, Xu Chen a a b
School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China Suzhou Nuclear Power Research Institute, Suzhou 215004, China
art ic l e i nf o
a b s t r a c t
Article history: Received 10 July 2016 Received in revised form 11 September 2016 Accepted 14 September 2016 Available online 15 September 2016
This work reports the low cycle fatigue behavior of a wrought 316LN stainless steel under different control modes at room temperature. Under symmetrical strain and stress cycling, the steel exhibits consistent loading-amplitude-dependent cyclic hardening/softening and fatigue life characteristics. Under asymmetrical stress cycling, the steel is significantly hardened due to mean stress, and the fatigue life at the same strain amplitude is significantly reduced due to ratcheting strain. With the increase of mean stress, though the ratcheting strain level is increased, the fatigue life is prolonged. The effect of meanstress hardening and ratcheting strain on fatigue life is discussed in terms of strain amplitude and microcrack initiation and propagation. The Smith-Walker-Topper (SWT) model and a newly proposed fatigue life model based on the Coffin-Manson equation were used to predict the fatigue life under mean stress, and the proposed model yields more robust predictions. & 2016 Elsevier B.V. All rights reserved.
Keywords: Low cycle fatigue Mean stress Ratcheting strain Fatigue life prediction Cyclic hardening
1. Introduction Engineering components and structures are often subjected to a cyclic stressing with a mean stress, which may significantly affect their fatigue lives. It is mostly recognized for a variety of materials that a tensile mean stress leads to a reduced fatigue life [1–11]. One reasonable explanation for the detrimental effect of tensile mean stress on fatigue life is that tensile mean stress facilitates the crack opening [2]. Meanwhile, the mean stress induced progressive accumulation of inelastic deformation, known as ratcheting strain [12], may also play an important role by causing additional fatigue damage for various materials such as SAE 1045 steel [1], AZ31B magnesium alloy [3], CP-Ti [6], Zircaloy-2 [7], 42CrMo steel [10] and 45 carbon steel [11]. For example, Yang [11] found that the failure mode for carbon steel 45 under cyclic stressing depended on the loading level: large ratcheting strain was the main cause of failure as characterized by apparent necking if the loading level was relatively higher, while low-cycle fatigue was the main cause of failure as featured by brittle fracture if the loading level was relatively lower. However, some recent research results showed beneficial effect of tensile mean stress on fatigue life of some stainless steels [13–17]. Such beneficial effect was found mainly associated with the reduced strain amplitude due to the mean stress induced hardening. Thus it seems that the effect of n
Corresponding author. E-mail address: [email protected] (D. Yu).
http://dx.doi.org/10.1016/j.msea.2016.09.053 0921-5093/& 2016 Elsevier B.V. All rights reserved.
mean stress on fatigue life depends on the materials, which requires further investigation. A great deal of efforts has been made to correct the effect of mean stress on stress-life diagram used for the engineering design [18–20]. The well-known Goodman equation, Morrow equation, Smith equation [21], and Walker equation [22], all describe the detrimental effect of tensile mean stress on fatigue life by introducing an effective stress amplitude higher than the actual stress amplitude. However, for the cases where tensile mean stress extends fatigue life as mentioned previously, these equations show their deficiencies. Liu et al. [23] developed a stress-based fatigue (SBF) model by addressing the maximum stress and stress ratio to consider the effect of mean stress and ratcheting strain, which yielded satisfactory predictions for 304 stainless steel; however, the SBF model requires substantial fitting to determine its stress ratio dependent parameter c. A relatively concise and feasible solution is to combine the mean stress, stress amplitude and strain amplitude as in the well-known Smith-Watson-Topper (SWT) model [21] or energy-based fatigue life models [2,19]. Especially, more life-prediction models have been developed based on the SWT model [18,24,25], which yield higher accuracy of life prediction for specific materials. In this study, fatigue tests were conducted on a wrought 316LN stainless steel under different control modes, i.e. symmetrical strain-control mode, symmetrical stress-control mode and asymmetrical stress-control mode, to explore the effect of mean stress and ratcheting strain on the low cycle fatigue behavior. The SWT model was evaluated for the prediction of fatigue life under
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Table 1 Chemical composition of the wrought 316LN stainless steel (in wt%). C
Si
Mn
P
S
Ni
Cr
Mo
Cu
N
Fe
0.016
0.270
0.810
0.008
0.008
12.12
17.52
2.39
0.08
0.065
balance
different control modes. A modified fatigue life model based on the Coffin-Manson equation was proposed and validated.
2. Material and experiments The material tested in this study is a nuclear grade wrought 316LN austenitic stainless steel which is used for primary circuit piping in the AP1000 PWR nuclear power plants designed by Westinghouse Inc. Its chemical composition (in wt%) is given in Table 1. The average grain size of the steel is about 100 mm, as shown in Fig. 1. Dumbbell-like solid specimens of 27 mm gauge length and 10 mm gauge diameter were machined following the suggested configuration in ASTM Standard E606. The gauge section was polished down to 0.2 mm surface finish prior to testing. All the experiments were carried on a 100-kN closed-loop servo-hydraulic tension–compression fatigue testing machine with a digital controller. The controller can collect about 200 data points per cycle for further analyses. During the tests, the uniaxial strain was measured by a clip-on extensometer attached to the gauge section of the tested specimen with a gauge length of 12.5 mm. A total of 15 tests were carried out in air at room temperature. One tensile test was conducted under displacement control at the equivalent strain rate of 1 10 3 s 1 (the equivalent strain rate is calculated as the ratio of the displacement rate to the gauge length of the specimen) to obtain the basic mechanical properties of the steel. Five fatigue tests were conducted under reversed strain control with the strain amplitude varying from 0.2% to 0.8% at a constant strain rate of 5 10 3 s 1. Three fatigue tests were conducted under reversed stress control with the stress amplitude varying from 250 to 300 MPa at a constant stress rate of 200 MPa/ s. Six fatigue tests were conducted under asymmetrical stress control with the mean stress varying from 50 to 100 MPa and the stress amplitude varying from 200 to 275 MPa. All the test conditions are given in Table 2. Post-test surface characterization of fatigued specimens, including the fracture surface and the outside surface near the fractured area (about 3–5 mm from the fracture cross-section) was carried out using scanning electron microscopy (SEM).
Fig. 1. Metallographic structure of as-received 316LN stainless steel.
LCF tests under symmetrical strain and stress control, which are in terms of stress amplitude and strain amplitude, respectively. Note
Table 2 LCF results of 316LN stainless steel under different control modes. sm
(%)
εap (%)
sa
Control mode
(MPa)
(MPa)
Symmetrical strain cycling Symmetrical strain cycling Symmetrical strain cycling Symmetrical strain cycling Symmetrical strain cycling Symmetrical stress cycling Symmetrical stress cycling Symmetrical stress cycling Asymmetrical stress cycling Asymmetrical stress cycling Asymmetrical stress cycling Asymmetrical stress cycling Asymmetrical stress cycling Asymmetrical stress cycling
0.2 0.3 0.4 0.6 0.8 0.3799 0.4639 0.5330 0.3603 0.2495 0.2054 0.1236 0.1554 0.1667
0.1026 0.2044 0.2980 0.4775 0.6513 0.2571 0.3292 0.3821 0.2233 0.1231 0.0783 0.0237 0.0413 0.0525
218 237 252 308 341 250 275 300 275 250 250 200 225 250
3.6 1.3 0.2 0.5 1.7 0 0 0 25 50 75 100 100 100
εa
2Nf
135340 28164 15364 5900 3240 21938 14138 7132 13888 23702 32640 193476 89084 48912
3. Experimental results and discussion 3.1. Monotonic tensile behavior The monotonic tensile stress-strain curve of the steel is shown in Fig. 2. The steel displays the feature of significant and continuous nonlinear strain hardening from the yielding strength of 249.6 MPa to the ultimate tensile strength of 560.1 MPa. The fracture strain of 73.2% and the percent reduction in area of 82% indicate the excellent ductility of the steel. 3.2. Cyclic stress/strain response The fatigue testing results including the cyclic stress/strain response and fatigue life under different control modes are presented in Table 2 and Figs. 3–6. Fig. 3(a) and (b) shows the cyclic stress and strain response in
Fig. 2. Engineering stress–strain curve of the steel at room temperature.
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Fig. 3. Cyclic stress/strain response: (a) evolution of stress amplitude under symmetrical strain cycling; (b) evolution of strain amplitude under symmetrical stress cycling.
Fig. 4. Cyclic strain response to different stress amplitudes under asymmetrical stress cycling: (a) stress-strain hysteresis loops in the first two cycles and the midlife cycle, (b) evolution of ratcheting strain, and (c) evolution of strain amplitude.
that an increase in the stress amplitude under cyclic straining or a decrease in the strain amplitude under cyclic stressing indicates cyclic hardening; cyclic softening otherwise. Under reversed cyclic straining as shown in Fig. 3(a), the steel exhibits the strain amplitude dependent feature of cyclic hardening/softening: one stage at low strain amplitude (0.2%) characterized as continuous gradual softening to failure; two stages at intermediate strain amplitude (0.3% and 0.4%) characterized as rapid initial hardening for the first 20 cycles and gradual softening until failure; three stages at high strain amplitude (0.6% and 0.8%) characterized as rapid initial hardening, gradual softening and stabilization to failure. Under reversed cyclic stressing as shown in Fig. 3(b), for the first 20
cycles the steel experiences subtle cyclic hardening at relatively low stress amplitude of 250 and 275 MPa and significant cyclic hardening at relatively high stress amplitude of 300 MPa, after which the steel exhibits continuous gradual softening at all stress amplitudes. Compared to the cyclic feature under strain control, no stabilization stage is observed under stress control. But the loading amplitude dependent cyclic hardening and softening feature seems consistent under both control modes. Fig. 4 shows the cyclic strain response to different stress amplitudes under asymmetrical stress cycling. As shown in Fig. 4(a), the stress-strain hysteresis loops are seen with an evident strain gap in the first two cycles but become almost closed in the midlife
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Fig. 5. Cyclic strain response to different mean stresses under asymmetrical stress cycling: (a) stress-strain hysteresis loop in the first two cycles and the midlife cycle, (b) evolution of ratcheting strain, and (c) evolution of strain amplitude.
Fig. 6. Histograms showing variations of fatigue life with (a) strain amplitude under symmetrical strain cycling, (b) stress amplitude under symmetrical stress cycling.
cycle. The strain gap in the first two cycles is apparently larger at higher amplitude. As a matter of fact, the non-closure of hysteresis loops directly results in the position translation of hysteresis loops, which consequently leads to the accumulation of inelastic strain, known as ratcheting strain. By defining the ratcheting strain εr as the average strain during one cycle, i.e. εr ¼(εmax þ εmin)/2, where εmax and εmin are respectively the maximum strain and minimum strain in one cycle, the evolution of ratcheting strain with stress cycling can be obtained as shown in Fig. 4(b). It is seen that the ratcheting strain increases rapidly for the first 100 cycles under all stress amplitudes, and then enters a stage characterized as gradual increasing at high stress amplitude (250 MPa) or saturation at low stress amplitude (225 and 200 MPa), and finally shows an abrupt
increase due to the fracturing failure (except for the case at the stress amplitude of 200 MPa where the specimen didn’t fail and the test was manually stopped). Meanwhile, the ratcheting strain level is seen higher at higher stress amplitude. Comparing Fig. 4 (a) with 4(b), it can be inferred that the evolution of ratcheting strain actually corresponds to the diminishing process of strain gap in the stress-strain hysteresis loop. A larger strain gap leads to a more rapid increase of ratcheting strain. When the strain gap diminishes, the hysteresis loop becomes closed, and the ratcheting strain achieves saturation, i.e. the so-called “shakedown of ratcheting”. While ratcheting strain indicates the position translation of hysteresis loop, strain amplitude can reflect the shape evolution
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with stress cycling, as shown in Fig. 4(c) and (d), respectively. The rapid decrease of strain amplitude in the first 100 cycles under all stress amplitudes corresponds to the shape change from a “fat” non-closed style to a “thin” almost closed style as shown in Fig. 4 (a), which indicates significant hardening. However, after the rapid decrease, unlike the data under symmetrical stress control showing continuous increasing [Fig. 3(b)], the strain amplitude under mean stress exhibits the trend of gradual decreasing, which indicates continuous hardening under mean stress. It seems that the mean stress poses great influence on the cyclic hardening/softening characterization of the steel, which will be discussed later. Meanwhile, higher stress amplitude leads to larger strain amplitude. Fig. 5 shows the cyclic strain response to different mean stresses under asymmetrical stress cycling. As shown in Fig. 5(a), the strain gap of the hysteresis loops in the first two cycles increases with the increase of mean stress. The ratcheting strain level also increases with mean stress as seen from Fig. 5(b). The shape evolution of hysteresis loops under all mean stresses, as indicated by the strain amplitude in Fig. 5(c), shows a consistent tendency: a rapid decrease followed by gradual decreasing. One interesting feature is that the rapid decrease under a higher mean stress is so dramatic that the strain amplitude in the gradual decreasing stage becomes lower than that under a lower mean stress. 3.3. Fatigue life Fig. 6 shows the comparison of fatigue lives under symmetrical loading, which indicates that fatigue life decreases with increasing load amplitude under both strain and stress control. This tendency stays true when a mean stress of 100 MPa is introduced under stress cycling, as shown in the lower set of Fig. 7(a). Meanwhile, the total accumulated ratcheting strain increases with increasing
197
stress amplitude, as seen in the upper inset of Fig. 7(a). Thus it appears that high load level leads to high ratcheting strain level, both of which may jointly contribute to the reduction of fatigue life under mean stress. However, when the mean stress is increased under a constant stress amplitude as shown in Fig. 7(b), though the total ratcheting strain is increased accordingly, the fatigue life is extended. Therefore, it can be inferred that the tensile mean stress is beneficial to the fatigue life, while the role of ratcheting strain is not clear from Fig. 7, which will be further discussed in the next section. 3.4. Microstructure observation The morphology of outside surface near the fracture crosssection of fatigued specimen under symmetrical loading, as shown in Fig. 8(a)–(d), indicates that high loading amplitude leads to more micro-cracks under both symmetrical strain and stress control. Unlike the relatively smooth surface under symmetrical loading, wrinkle-like morphology prevails under asymmetrical stress cycling, as seen from Fig. 8(e) and (f), which indicates significant plastic deformation as a result of ratcheting. By comparing Fig. 8(a) and (b), more micro-cracks are observed under the lower mean stress of 50 MPa than under the higher mean stress of 100 MPa. Moreover, the micro-cracks seem pulled open under asymmetrical stress cycling, compared with those under symmetrical loading. Hence, it can be inferred that cracks may initiate more easily under high loading amplitude and low mean stress. Meanwhile, the fatigue striations shown in Fig. 9 indicate the similar effect of loading amplitude and mean stress on the propagation of fatigue cracks. After cracks initiation, the opening and closing of cracks occur alternatively during each fatigue cycle, thus leading to the cumulative propagation of fatigue cracks, manifested by the fatigue striations shown in Fig. 9. Each striation corresponds to one fatigue cycle period and the width of the
Fig. 7. Histograms showing variations of total accumulated ratcheting strain (εrf) and fatigue life with (a) stress amplitude under the mean stress of 100 MPa and (b) mean stress under the stress amplitude of 250 MPa.
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Fig. 8. SEM observation on the outside surface near the fracture cross-section of fatigued specimen: under symmetrical strain cycling at the strain amplitude of (a) 0.4% and (b) 0.8%; under symmetrical stress cycling at the stress amplitude of (c) 250 and (d) 300 MPa; under asymmetrical stress cycling at the stress amplitude of 250 MPa and the mean stress of (e) 50 and (f) 100 MPa.
striation represent the crack length increment in that cycle. Thus the density of striations can reflect the fatigue crack propagation rate. It is evident from Fig. 9 that the striations are sparser at higher strain amplitude or stress amplitude whereas denser at high mean stress. This fact indicates that cracks may propagate more easily under high loading amplitude and low mean stress. Collectively, it is safe to conclude that high loading amplitude and low mean stress facilitate fatigue crack initiation and propagation. 3.5. Discussion 3.5.1. Effect of mean stress on cyclic behavior As observed from Fig. 3 and discussed previously, the steel exhibits rapid cyclic hardening followed by gradual cyclic softening under symmetrical loading. With the introduction of mean stress under stress cycling, the steel shows rapid cyclic hardening followed by gradual cyclic hardening, as seen from Figs. 4(c) and 5 (c). Moreover, the degree of cyclic hardening seems to increase with increasing mean stress, which can be seen from Fig. 10 as evidenced by the reduced plastic strain amplitude (hysteresis loop
width) with increased mean stress. Such great influence of mean stress on cyclic behavior of the steel, as referred to as “mean-stress hardening” in the present study, can be associated with the accumulation of ratcheting strain. Krempl and Ruggles [26] found that ratcheting strain caused similar strain hardening as in monotonic tension based on the post-ratcheting tensile testing of a 304 austenitic stainless steel. Dutta and Ray [27] observed increase of post-ratcheting tensile strength in an aluminum alloy, and attributed such increase to the cyclic hardening during ratcheting. Thus it is possible that the mean-stress hardening is the superimposed result of cyclic hardening and monotonic hardening. Based on this assumption, the rapid decrease in strain amplitude for the first tens of cycles as seen from Figs. 4(c) and 5 (c) can be mainly attributed to the monotonic hardening because a great amount of ratcheting strain is accumulated during that period. Meanwhile, as can be seen from Figs. 4(c), 5(c) and 10(b), the strain amplitudes under asymmetrical stress cycling are all below 0.25% during a large fraction of the fatigue life, which should correspond to cyclic softening in accordance with the strain amplitude dependent trend of cyclic hardening/softening shown
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Fig. 9. Crack propagation on the fracture cross-section of fatigued specimen: under symmetrical strain cycling at the strain amplitude of (a) 0.4% and (b) 0.8%; under symmetrical stress cycling at the stress amplitude of (c) 250 and (d) 300 MPa; under asymmetrical stress cycling at the stress amplitude of 250 MPa and the mean stress of (e) 50 and (f) 100 MPa.
Fig. 10. Comparison of midlife-cycle (a) stress-strain hysteresis loops and (b) strain amplitude under different mean stresses.
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in Fig. 3(a). However, no significant softening is observed under asymmetrical cyclic loading in the present study. This fact is probably because that the ratcheting strain induced monotonic hardening covers or refrains the strain amplitude induced cyclic softening. The hardening in metallic materials has been known to result from the increased level of immobile dislocation density [28], and the softening is associated with formation of persistent slip bands, cross-slip and other complex dislocation processes that promote the mobility of pinned dislocations or the annihilation of dislocations [29–31]. Under symmetrical cyclic loading, the deformation of material is back and forth to a limited extent, thus plastic deformation of each point of the material is confined to a local range. Consequently, the generation and movement of dislocations are constrained in a local range. During the initial symmetrical cyclic loading, the generation of dislocations is much faster than the annihilation of dislocations, resulting in a rapid increase in dislocation density, consequently a rapid cyclic hardening as observed from Fig. 3. Due to the limited deformation range, when the dislocation density is high enough, the movement of dislocations facilitate the annihilation of dislocations that prevails over the generation of dislocations, thus leading to a gradual decrease in dislocation density, consequently a gradual cyclic softening. In contrary, the plastic deformation range is evolving under asymmetrical stress cycling due to the accumulation of ratcheting strain. Thus the generation of dislocations is less restrained to a limited range, leading to a continuous increase of dislocation density as revealed by some XRD results [32,33], consequently a continuous cyclic hardening. In brief, the mean-stress hardening is probably the superimposed result of ratcheting strain induced monotonic hardening and stress cycling induced cyclic hardening. 3.5.2. Effect of mean stress on fatigue life Normally one would expect a shorter fatigue life under a higher loading level. However, in the present study the fatigue life was found extended with the increase of mean stress as shown in Table 2 and Fig. 7(b). Moreover, low mean stress seems to facilitate crack initiation and propagation as inferred from Figs. 8 and 9. These facts, though appearing “abnormal” or “surprising”, are understandable if strain amplitude is considered as the fatigue damage parameter. It can be inferred from Fig. 10 that the fatigue specimen tested under a high mean stress is in fact experiencing a low strain amplitude fatigue test as a result of mean-stress hardening. As observed from Figs. 6(a), 8(a) and (b) and 9(a) and (b) and discussed previously, low strain amplitude corresponds to long fatigue life, few crack initiation and slow crack propagation. Thus it seems that the mean-stress hardening induced decrease of strain amplitude is beneficial to the reduction of crack initiation and crack propagation rate as well as the extension of fatigue life. However, the detrimental effect of ratcheting strain on fatigue life should not be neglected. Kang et al. [17] observed two kinds of failure modes for 304 type stainless steel under asymmetrical stress cycling, i.e., ratcheting failure with obvious necking due to large ratcheting strain and fatigue failure due to low-cycle fatigue with nearly constant responded strain amplitude. Paul et al. [14] concluded that the tensile ratcheting strain accumulation can lead to further enhancement of fatigue damage by continuous thinning out of the components cross-sectional area, and their combine effect can lead to premature failure of a 304LN stainless steel. In the present study, at the same strain amplitude, as shown in Fig. 11, the fatigue life under mean stress is much shorter than that under symmetrical loading. One possible reason is that the ratcheting strain may cause local stress concentration, such as the wrinkle-like morphology shown in Fig. 8(e) and (f), facilitating the crack initiations. Collectively, the effect of mean stress on fatigue
Fig. 11. Relation of strain amplitude with fatigue life under all control modes.
life depends on the competition of mean-stress hardening and ratcheting strain. In the present study, the beneficial effect of mean-stress hardening on fatigue life seems overweighing the detrimental effect of ratcheting strain.
4. Fatigue life modeling For fully-reversed (strain and stress control) tests, BasquinCoffin-Manson Eq. (1) can be employed to predict the fatigue life. Fig. 12 shows the relationship of the elastic, plastic and total strain amplitude with reversals to failure. The equation parameters for fully-reversed tests are presented in Table 3.
εa = εae + εap =
σ ′f b c ( 2Nf ) + ε′f ( 2Nf ) E
(1) εae
where εa is the total strain amplitude, is the elastic strain amplitude, and εap is plastic strain amplitude, E is the elastic modulus, σ′f is the fatigue strength coefficient, b is the fatigue strength exponent, ε′f is the fatigue ductility coefficient, c is the fatigue ductility exponent and 2Nf is the number of reversals to failure. As noticed from Fig. 11, the correlation between strain amplitude and fatigue life under mean stress does not follow the track of that under symmetrical loading. Thus strain amplitude is not a proper fatigue parameter to correlate with fatigue life under all control modes. In order to predict the fatigue life under mean stress, the SWT model as given in Eq. (2) was employed. σmaxεa is the fatigue parameter that takes mean stress into account ( σmax = σm + σa ). Parameters of the SWT model are the same as in
Fig. 12. Elastic, plastic and total strain amplitude versus reversals to failure for fully-reversed strain control (εC) and stress control (LC).
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Table 3 Parameters of Basquin-Coffin-Manson equation for the wrought 316LN steel.
σ ′f
b
ε′f
c
851.5
0.1207
0.3261
0.4884
Fig. 15. Correlation of the tests results with the proposed fatigue parameters.
Fig. 13. The SWT parameter versus reversals to failure under all control modes.
Fig. 16. Comparison between observed life and predicted life using the proposed model.
which is better than the predicted results by the SWT model.
⎛σ ⎞ c f ⎜ m ⎟εap = ε′f ( 2Nf ) ⎝ σa ⎠ Fig. 14. Comparison between observed life and predicted life using the SWT model.
the Basquin-Coffin-Manson equation as given in Table 3. The predicted results are shown in Fig. 13, and it can be seen that all points with mean stress are close to a best-fit solid line. The comparison between observed life and predicted life is presented in Fig. 14. The fatigue life points under all control modes are all located in the twice error band.
(3)
where
⎛σ ⎞ σ f⎜ m⎟ = 1 + β m σa ⎝ σa ⎠
(4)
⎛ σ ⎞ −0.4884 ⎜ 1 + 4.670 m ⎟εap = 0.3261( 2Nf ) σa ⎠ ⎝
(5)
2
σmaxεa =
( σ′f ) E
b
( 2Nf )2
b+ c
+ σ ′f ε′f ( 2Nf )
(2)
By introducing a mean stress function as in Ref. [2,20] into the Coffin-Manson equation, a new fatigue life model is proposed as given in Eq. (3). In this model, the plastic strain amplitude is corrected by the function given in Eq. (4) to account for the effect of mean stress. The parameters in the right side of Eq. (3) are the same as in the Coffin-Manson equation as given in Table 3. Then the parameter of Eq. (4) can been calculated through one loading condition of mean stress tests (the test under sm ¼50 MPa and sa ¼250 MPa was used here). Finally, the proposed fatigue model for the present study is obtained as Eq. (5). Fig. 15 shows the correlation of the proposed fatigue parameter with fatigue life under all control modes, and compared with the SWT model, the data points are closer to the solid line. As can be seen from Fig. 16, the fatigue life points are all located in the 1.5 times error band,
5. Conclusion Low cycle fatigue experiments under different control modes, i.e. symmetrical strain cycling, symmetrical stress cycling and asymmetrical stress cycling, were performed on a wrought 316LN stainless steel at room temperature. The effect of mean stress and ratcheting strain on the low cycle fatigue behavior of the steel were explored. The main observations and conclusions are as follows: (1) Under symmetrical strain and stress cycling, the steel exhibits consistent cyclic hardening/softening characteristics: rapid cyclic hardening followed by gradual cyclic softening, while under asymmetrical stress cycling, the steel exhibits significant and continuous cyclic hardening due to mean stress.
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(2) Fatigue life decreases with the increase of loading amplitude under all control modes, but increases with increasing mean stress under asymmetrical stress cycling. If compared under the same strain amplitude, the fatigue life is found significantly reduced due to ratcheting strain that may facilitate the crack initiation and propagation. The extension of fatigue life with increasing mean stress is mainly attributed to the reduced strain amplitude by mean stress hardening. (3) The SWT model and a newly proposed fatigue life model based on the Coffin-Manson equation were employed to predict the fatigue life under asymmetrical stress cycling. Both models were found yielding robust predictions, while the proposed model is superior to the SWT model in the predicting accuracy.
Acknowledgements The authors gratefully acknowledge financial support for this work from the National Natural Science Foundation of China (Nos. 51435012 and 51505325) and Ph.D. Programs Foundation of Ministry of Education of China (No. 20130032110018).
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Effect of mean stress and ratcheting strain on the low cycle fatigue behavior of a wrought 316LN stainless steel Xuyang Yuan a, Weiwei Yu a,b, Sichao Fu a, Dunji Yu a,n, Xu Chen a a b
School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China Suzhou Nuclear Power Research Institute, Suzhou 215004, China
art ic l e i nf o
a b s t r a c t
Article history: Received 10 July 2016 Received in revised form 11 September 2016 Accepted 14 September 2016 Available online 15 September 2016
This work reports the low cycle fatigue behavior of a wrought 316LN stainless steel under different control modes at room temperature. Under symmetrical strain and stress cycling, the steel exhibits consistent loading-amplitude-dependent cyclic hardening/softening and fatigue life characteristics. Under asymmetrical stress cycling, the steel is significantly hardened due to mean stress, and the fatigue life at the same strain amplitude is significantly reduced due to ratcheting strain. With the increase of mean stress, though the ratcheting strain level is increased, the fatigue life is prolonged. The effect of meanstress hardening and ratcheting strain on fatigue life is discussed in terms of strain amplitude and microcrack initiation and propagation. The Smith-Walker-Topper (SWT) model and a newly proposed fatigue life model based on the Coffin-Manson equation were used to predict the fatigue life under mean stress, and the proposed model yields more robust predictions. & 2016 Elsevier B.V. All rights reserved.
Keywords: Low cycle fatigue Mean stress Ratcheting strain Fatigue life prediction Cyclic hardening
1. Introduction Engineering components and structures are often subjected to a cyclic stressing with a mean stress, which may significantly affect their fatigue lives. It is mostly recognized for a variety of materials that a tensile mean stress leads to a reduced fatigue life [1–11]. One reasonable explanation for the detrimental effect of tensile mean stress on fatigue life is that tensile mean stress facilitates the crack opening [2]. Meanwhile, the mean stress induced progressive accumulation of inelastic deformation, known as ratcheting strain [12], may also play an important role by causing additional fatigue damage for various materials such as SAE 1045 steel [1], AZ31B magnesium alloy [3], CP-Ti [6], Zircaloy-2 [7], 42CrMo steel [10] and 45 carbon steel [11]. For example, Yang [11] found that the failure mode for carbon steel 45 under cyclic stressing depended on the loading level: large ratcheting strain was the main cause of failure as characterized by apparent necking if the loading level was relatively higher, while low-cycle fatigue was the main cause of failure as featured by brittle fracture if the loading level was relatively lower. However, some recent research results showed beneficial effect of tensile mean stress on fatigue life of some stainless steels [13–17]. Such beneficial effect was found mainly associated with the reduced strain amplitude due to the mean stress induced hardening. Thus it seems that the effect of n
Corresponding author. E-mail address: [email protected] (D. Yu).
http://dx.doi.org/10.1016/j.msea.2016.09.053 0921-5093/& 2016 Elsevier B.V. All rights reserved.
mean stress on fatigue life depends on the materials, which requires further investigation. A great deal of efforts has been made to correct the effect of mean stress on stress-life diagram used for the engineering design [18–20]. The well-known Goodman equation, Morrow equation, Smith equation [21], and Walker equation [22], all describe the detrimental effect of tensile mean stress on fatigue life by introducing an effective stress amplitude higher than the actual stress amplitude. However, for the cases where tensile mean stress extends fatigue life as mentioned previously, these equations show their deficiencies. Liu et al. [23] developed a stress-based fatigue (SBF) model by addressing the maximum stress and stress ratio to consider the effect of mean stress and ratcheting strain, which yielded satisfactory predictions for 304 stainless steel; however, the SBF model requires substantial fitting to determine its stress ratio dependent parameter c. A relatively concise and feasible solution is to combine the mean stress, stress amplitude and strain amplitude as in the well-known Smith-Watson-Topper (SWT) model [21] or energy-based fatigue life models [2,19]. Especially, more life-prediction models have been developed based on the SWT model [18,24,25], which yield higher accuracy of life prediction for specific materials. In this study, fatigue tests were conducted on a wrought 316LN stainless steel under different control modes, i.e. symmetrical strain-control mode, symmetrical stress-control mode and asymmetrical stress-control mode, to explore the effect of mean stress and ratcheting strain on the low cycle fatigue behavior. The SWT model was evaluated for the prediction of fatigue life under
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Table 1 Chemical composition of the wrought 316LN stainless steel (in wt%). C
Si
Mn
P
S
Ni
Cr
Mo
Cu
N
Fe
0.016
0.270
0.810
0.008
0.008
12.12
17.52
2.39
0.08
0.065
balance
different control modes. A modified fatigue life model based on the Coffin-Manson equation was proposed and validated.
2. Material and experiments The material tested in this study is a nuclear grade wrought 316LN austenitic stainless steel which is used for primary circuit piping in the AP1000 PWR nuclear power plants designed by Westinghouse Inc. Its chemical composition (in wt%) is given in Table 1. The average grain size of the steel is about 100 mm, as shown in Fig. 1. Dumbbell-like solid specimens of 27 mm gauge length and 10 mm gauge diameter were machined following the suggested configuration in ASTM Standard E606. The gauge section was polished down to 0.2 mm surface finish prior to testing. All the experiments were carried on a 100-kN closed-loop servo-hydraulic tension–compression fatigue testing machine with a digital controller. The controller can collect about 200 data points per cycle for further analyses. During the tests, the uniaxial strain was measured by a clip-on extensometer attached to the gauge section of the tested specimen with a gauge length of 12.5 mm. A total of 15 tests were carried out in air at room temperature. One tensile test was conducted under displacement control at the equivalent strain rate of 1 10 3 s 1 (the equivalent strain rate is calculated as the ratio of the displacement rate to the gauge length of the specimen) to obtain the basic mechanical properties of the steel. Five fatigue tests were conducted under reversed strain control with the strain amplitude varying from 0.2% to 0.8% at a constant strain rate of 5 10 3 s 1. Three fatigue tests were conducted under reversed stress control with the stress amplitude varying from 250 to 300 MPa at a constant stress rate of 200 MPa/ s. Six fatigue tests were conducted under asymmetrical stress control with the mean stress varying from 50 to 100 MPa and the stress amplitude varying from 200 to 275 MPa. All the test conditions are given in Table 2. Post-test surface characterization of fatigued specimens, including the fracture surface and the outside surface near the fractured area (about 3–5 mm from the fracture cross-section) was carried out using scanning electron microscopy (SEM).
Fig. 1. Metallographic structure of as-received 316LN stainless steel.
LCF tests under symmetrical strain and stress control, which are in terms of stress amplitude and strain amplitude, respectively. Note
Table 2 LCF results of 316LN stainless steel under different control modes. sm
(%)
εap (%)
sa
Control mode
(MPa)
(MPa)
Symmetrical strain cycling Symmetrical strain cycling Symmetrical strain cycling Symmetrical strain cycling Symmetrical strain cycling Symmetrical stress cycling Symmetrical stress cycling Symmetrical stress cycling Asymmetrical stress cycling Asymmetrical stress cycling Asymmetrical stress cycling Asymmetrical stress cycling Asymmetrical stress cycling Asymmetrical stress cycling
0.2 0.3 0.4 0.6 0.8 0.3799 0.4639 0.5330 0.3603 0.2495 0.2054 0.1236 0.1554 0.1667
0.1026 0.2044 0.2980 0.4775 0.6513 0.2571 0.3292 0.3821 0.2233 0.1231 0.0783 0.0237 0.0413 0.0525
218 237 252 308 341 250 275 300 275 250 250 200 225 250
3.6 1.3 0.2 0.5 1.7 0 0 0 25 50 75 100 100 100
εa
2Nf
135340 28164 15364 5900 3240 21938 14138 7132 13888 23702 32640 193476 89084 48912
3. Experimental results and discussion 3.1. Monotonic tensile behavior The monotonic tensile stress-strain curve of the steel is shown in Fig. 2. The steel displays the feature of significant and continuous nonlinear strain hardening from the yielding strength of 249.6 MPa to the ultimate tensile strength of 560.1 MPa. The fracture strain of 73.2% and the percent reduction in area of 82% indicate the excellent ductility of the steel. 3.2. Cyclic stress/strain response The fatigue testing results including the cyclic stress/strain response and fatigue life under different control modes are presented in Table 2 and Figs. 3–6. Fig. 3(a) and (b) shows the cyclic stress and strain response in
Fig. 2. Engineering stress–strain curve of the steel at room temperature.
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Fig. 3. Cyclic stress/strain response: (a) evolution of stress amplitude under symmetrical strain cycling; (b) evolution of strain amplitude under symmetrical stress cycling.
Fig. 4. Cyclic strain response to different stress amplitudes under asymmetrical stress cycling: (a) stress-strain hysteresis loops in the first two cycles and the midlife cycle, (b) evolution of ratcheting strain, and (c) evolution of strain amplitude.
that an increase in the stress amplitude under cyclic straining or a decrease in the strain amplitude under cyclic stressing indicates cyclic hardening; cyclic softening otherwise. Under reversed cyclic straining as shown in Fig. 3(a), the steel exhibits the strain amplitude dependent feature of cyclic hardening/softening: one stage at low strain amplitude (0.2%) characterized as continuous gradual softening to failure; two stages at intermediate strain amplitude (0.3% and 0.4%) characterized as rapid initial hardening for the first 20 cycles and gradual softening until failure; three stages at high strain amplitude (0.6% and 0.8%) characterized as rapid initial hardening, gradual softening and stabilization to failure. Under reversed cyclic stressing as shown in Fig. 3(b), for the first 20
cycles the steel experiences subtle cyclic hardening at relatively low stress amplitude of 250 and 275 MPa and significant cyclic hardening at relatively high stress amplitude of 300 MPa, after which the steel exhibits continuous gradual softening at all stress amplitudes. Compared to the cyclic feature under strain control, no stabilization stage is observed under stress control. But the loading amplitude dependent cyclic hardening and softening feature seems consistent under both control modes. Fig. 4 shows the cyclic strain response to different stress amplitudes under asymmetrical stress cycling. As shown in Fig. 4(a), the stress-strain hysteresis loops are seen with an evident strain gap in the first two cycles but become almost closed in the midlife
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Fig. 5. Cyclic strain response to different mean stresses under asymmetrical stress cycling: (a) stress-strain hysteresis loop in the first two cycles and the midlife cycle, (b) evolution of ratcheting strain, and (c) evolution of strain amplitude.
Fig. 6. Histograms showing variations of fatigue life with (a) strain amplitude under symmetrical strain cycling, (b) stress amplitude under symmetrical stress cycling.
cycle. The strain gap in the first two cycles is apparently larger at higher amplitude. As a matter of fact, the non-closure of hysteresis loops directly results in the position translation of hysteresis loops, which consequently leads to the accumulation of inelastic strain, known as ratcheting strain. By defining the ratcheting strain εr as the average strain during one cycle, i.e. εr ¼(εmax þ εmin)/2, where εmax and εmin are respectively the maximum strain and minimum strain in one cycle, the evolution of ratcheting strain with stress cycling can be obtained as shown in Fig. 4(b). It is seen that the ratcheting strain increases rapidly for the first 100 cycles under all stress amplitudes, and then enters a stage characterized as gradual increasing at high stress amplitude (250 MPa) or saturation at low stress amplitude (225 and 200 MPa), and finally shows an abrupt
increase due to the fracturing failure (except for the case at the stress amplitude of 200 MPa where the specimen didn’t fail and the test was manually stopped). Meanwhile, the ratcheting strain level is seen higher at higher stress amplitude. Comparing Fig. 4 (a) with 4(b), it can be inferred that the evolution of ratcheting strain actually corresponds to the diminishing process of strain gap in the stress-strain hysteresis loop. A larger strain gap leads to a more rapid increase of ratcheting strain. When the strain gap diminishes, the hysteresis loop becomes closed, and the ratcheting strain achieves saturation, i.e. the so-called “shakedown of ratcheting”. While ratcheting strain indicates the position translation of hysteresis loop, strain amplitude can reflect the shape evolution
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with stress cycling, as shown in Fig. 4(c) and (d), respectively. The rapid decrease of strain amplitude in the first 100 cycles under all stress amplitudes corresponds to the shape change from a “fat” non-closed style to a “thin” almost closed style as shown in Fig. 4 (a), which indicates significant hardening. However, after the rapid decrease, unlike the data under symmetrical stress control showing continuous increasing [Fig. 3(b)], the strain amplitude under mean stress exhibits the trend of gradual decreasing, which indicates continuous hardening under mean stress. It seems that the mean stress poses great influence on the cyclic hardening/softening characterization of the steel, which will be discussed later. Meanwhile, higher stress amplitude leads to larger strain amplitude. Fig. 5 shows the cyclic strain response to different mean stresses under asymmetrical stress cycling. As shown in Fig. 5(a), the strain gap of the hysteresis loops in the first two cycles increases with the increase of mean stress. The ratcheting strain level also increases with mean stress as seen from Fig. 5(b). The shape evolution of hysteresis loops under all mean stresses, as indicated by the strain amplitude in Fig. 5(c), shows a consistent tendency: a rapid decrease followed by gradual decreasing. One interesting feature is that the rapid decrease under a higher mean stress is so dramatic that the strain amplitude in the gradual decreasing stage becomes lower than that under a lower mean stress. 3.3. Fatigue life Fig. 6 shows the comparison of fatigue lives under symmetrical loading, which indicates that fatigue life decreases with increasing load amplitude under both strain and stress control. This tendency stays true when a mean stress of 100 MPa is introduced under stress cycling, as shown in the lower set of Fig. 7(a). Meanwhile, the total accumulated ratcheting strain increases with increasing
197
stress amplitude, as seen in the upper inset of Fig. 7(a). Thus it appears that high load level leads to high ratcheting strain level, both of which may jointly contribute to the reduction of fatigue life under mean stress. However, when the mean stress is increased under a constant stress amplitude as shown in Fig. 7(b), though the total ratcheting strain is increased accordingly, the fatigue life is extended. Therefore, it can be inferred that the tensile mean stress is beneficial to the fatigue life, while the role of ratcheting strain is not clear from Fig. 7, which will be further discussed in the next section. 3.4. Microstructure observation The morphology of outside surface near the fracture crosssection of fatigued specimen under symmetrical loading, as shown in Fig. 8(a)–(d), indicates that high loading amplitude leads to more micro-cracks under both symmetrical strain and stress control. Unlike the relatively smooth surface under symmetrical loading, wrinkle-like morphology prevails under asymmetrical stress cycling, as seen from Fig. 8(e) and (f), which indicates significant plastic deformation as a result of ratcheting. By comparing Fig. 8(a) and (b), more micro-cracks are observed under the lower mean stress of 50 MPa than under the higher mean stress of 100 MPa. Moreover, the micro-cracks seem pulled open under asymmetrical stress cycling, compared with those under symmetrical loading. Hence, it can be inferred that cracks may initiate more easily under high loading amplitude and low mean stress. Meanwhile, the fatigue striations shown in Fig. 9 indicate the similar effect of loading amplitude and mean stress on the propagation of fatigue cracks. After cracks initiation, the opening and closing of cracks occur alternatively during each fatigue cycle, thus leading to the cumulative propagation of fatigue cracks, manifested by the fatigue striations shown in Fig. 9. Each striation corresponds to one fatigue cycle period and the width of the
Fig. 7. Histograms showing variations of total accumulated ratcheting strain (εrf) and fatigue life with (a) stress amplitude under the mean stress of 100 MPa and (b) mean stress under the stress amplitude of 250 MPa.
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Fig. 8. SEM observation on the outside surface near the fracture cross-section of fatigued specimen: under symmetrical strain cycling at the strain amplitude of (a) 0.4% and (b) 0.8%; under symmetrical stress cycling at the stress amplitude of (c) 250 and (d) 300 MPa; under asymmetrical stress cycling at the stress amplitude of 250 MPa and the mean stress of (e) 50 and (f) 100 MPa.
striation represent the crack length increment in that cycle. Thus the density of striations can reflect the fatigue crack propagation rate. It is evident from Fig. 9 that the striations are sparser at higher strain amplitude or stress amplitude whereas denser at high mean stress. This fact indicates that cracks may propagate more easily under high loading amplitude and low mean stress. Collectively, it is safe to conclude that high loading amplitude and low mean stress facilitate fatigue crack initiation and propagation. 3.5. Discussion 3.5.1. Effect of mean stress on cyclic behavior As observed from Fig. 3 and discussed previously, the steel exhibits rapid cyclic hardening followed by gradual cyclic softening under symmetrical loading. With the introduction of mean stress under stress cycling, the steel shows rapid cyclic hardening followed by gradual cyclic hardening, as seen from Figs. 4(c) and 5 (c). Moreover, the degree of cyclic hardening seems to increase with increasing mean stress, which can be seen from Fig. 10 as evidenced by the reduced plastic strain amplitude (hysteresis loop
width) with increased mean stress. Such great influence of mean stress on cyclic behavior of the steel, as referred to as “mean-stress hardening” in the present study, can be associated with the accumulation of ratcheting strain. Krempl and Ruggles [26] found that ratcheting strain caused similar strain hardening as in monotonic tension based on the post-ratcheting tensile testing of a 304 austenitic stainless steel. Dutta and Ray [27] observed increase of post-ratcheting tensile strength in an aluminum alloy, and attributed such increase to the cyclic hardening during ratcheting. Thus it is possible that the mean-stress hardening is the superimposed result of cyclic hardening and monotonic hardening. Based on this assumption, the rapid decrease in strain amplitude for the first tens of cycles as seen from Figs. 4(c) and 5 (c) can be mainly attributed to the monotonic hardening because a great amount of ratcheting strain is accumulated during that period. Meanwhile, as can be seen from Figs. 4(c), 5(c) and 10(b), the strain amplitudes under asymmetrical stress cycling are all below 0.25% during a large fraction of the fatigue life, which should correspond to cyclic softening in accordance with the strain amplitude dependent trend of cyclic hardening/softening shown
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Fig. 9. Crack propagation on the fracture cross-section of fatigued specimen: under symmetrical strain cycling at the strain amplitude of (a) 0.4% and (b) 0.8%; under symmetrical stress cycling at the stress amplitude of (c) 250 and (d) 300 MPa; under asymmetrical stress cycling at the stress amplitude of 250 MPa and the mean stress of (e) 50 and (f) 100 MPa.
Fig. 10. Comparison of midlife-cycle (a) stress-strain hysteresis loops and (b) strain amplitude under different mean stresses.
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in Fig. 3(a). However, no significant softening is observed under asymmetrical cyclic loading in the present study. This fact is probably because that the ratcheting strain induced monotonic hardening covers or refrains the strain amplitude induced cyclic softening. The hardening in metallic materials has been known to result from the increased level of immobile dislocation density [28], and the softening is associated with formation of persistent slip bands, cross-slip and other complex dislocation processes that promote the mobility of pinned dislocations or the annihilation of dislocations [29–31]. Under symmetrical cyclic loading, the deformation of material is back and forth to a limited extent, thus plastic deformation of each point of the material is confined to a local range. Consequently, the generation and movement of dislocations are constrained in a local range. During the initial symmetrical cyclic loading, the generation of dislocations is much faster than the annihilation of dislocations, resulting in a rapid increase in dislocation density, consequently a rapid cyclic hardening as observed from Fig. 3. Due to the limited deformation range, when the dislocation density is high enough, the movement of dislocations facilitate the annihilation of dislocations that prevails over the generation of dislocations, thus leading to a gradual decrease in dislocation density, consequently a gradual cyclic softening. In contrary, the plastic deformation range is evolving under asymmetrical stress cycling due to the accumulation of ratcheting strain. Thus the generation of dislocations is less restrained to a limited range, leading to a continuous increase of dislocation density as revealed by some XRD results [32,33], consequently a continuous cyclic hardening. In brief, the mean-stress hardening is probably the superimposed result of ratcheting strain induced monotonic hardening and stress cycling induced cyclic hardening. 3.5.2. Effect of mean stress on fatigue life Normally one would expect a shorter fatigue life under a higher loading level. However, in the present study the fatigue life was found extended with the increase of mean stress as shown in Table 2 and Fig. 7(b). Moreover, low mean stress seems to facilitate crack initiation and propagation as inferred from Figs. 8 and 9. These facts, though appearing “abnormal” or “surprising”, are understandable if strain amplitude is considered as the fatigue damage parameter. It can be inferred from Fig. 10 that the fatigue specimen tested under a high mean stress is in fact experiencing a low strain amplitude fatigue test as a result of mean-stress hardening. As observed from Figs. 6(a), 8(a) and (b) and 9(a) and (b) and discussed previously, low strain amplitude corresponds to long fatigue life, few crack initiation and slow crack propagation. Thus it seems that the mean-stress hardening induced decrease of strain amplitude is beneficial to the reduction of crack initiation and crack propagation rate as well as the extension of fatigue life. However, the detrimental effect of ratcheting strain on fatigue life should not be neglected. Kang et al. [17] observed two kinds of failure modes for 304 type stainless steel under asymmetrical stress cycling, i.e., ratcheting failure with obvious necking due to large ratcheting strain and fatigue failure due to low-cycle fatigue with nearly constant responded strain amplitude. Paul et al. [14] concluded that the tensile ratcheting strain accumulation can lead to further enhancement of fatigue damage by continuous thinning out of the components cross-sectional area, and their combine effect can lead to premature failure of a 304LN stainless steel. In the present study, at the same strain amplitude, as shown in Fig. 11, the fatigue life under mean stress is much shorter than that under symmetrical loading. One possible reason is that the ratcheting strain may cause local stress concentration, such as the wrinkle-like morphology shown in Fig. 8(e) and (f), facilitating the crack initiations. Collectively, the effect of mean stress on fatigue
Fig. 11. Relation of strain amplitude with fatigue life under all control modes.
life depends on the competition of mean-stress hardening and ratcheting strain. In the present study, the beneficial effect of mean-stress hardening on fatigue life seems overweighing the detrimental effect of ratcheting strain.
4. Fatigue life modeling For fully-reversed (strain and stress control) tests, BasquinCoffin-Manson Eq. (1) can be employed to predict the fatigue life. Fig. 12 shows the relationship of the elastic, plastic and total strain amplitude with reversals to failure. The equation parameters for fully-reversed tests are presented in Table 3.
εa = εae + εap =
σ ′f b c ( 2Nf ) + ε′f ( 2Nf ) E
(1) εae
where εa is the total strain amplitude, is the elastic strain amplitude, and εap is plastic strain amplitude, E is the elastic modulus, σ′f is the fatigue strength coefficient, b is the fatigue strength exponent, ε′f is the fatigue ductility coefficient, c is the fatigue ductility exponent and 2Nf is the number of reversals to failure. As noticed from Fig. 11, the correlation between strain amplitude and fatigue life under mean stress does not follow the track of that under symmetrical loading. Thus strain amplitude is not a proper fatigue parameter to correlate with fatigue life under all control modes. In order to predict the fatigue life under mean stress, the SWT model as given in Eq. (2) was employed. σmaxεa is the fatigue parameter that takes mean stress into account ( σmax = σm + σa ). Parameters of the SWT model are the same as in
Fig. 12. Elastic, plastic and total strain amplitude versus reversals to failure for fully-reversed strain control (εC) and stress control (LC).
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Table 3 Parameters of Basquin-Coffin-Manson equation for the wrought 316LN steel.
σ ′f
b
ε′f
c
851.5
0.1207
0.3261
0.4884
Fig. 15. Correlation of the tests results with the proposed fatigue parameters.
Fig. 13. The SWT parameter versus reversals to failure under all control modes.
Fig. 16. Comparison between observed life and predicted life using the proposed model.
which is better than the predicted results by the SWT model.
⎛σ ⎞ c f ⎜ m ⎟εap = ε′f ( 2Nf ) ⎝ σa ⎠ Fig. 14. Comparison between observed life and predicted life using the SWT model.
the Basquin-Coffin-Manson equation as given in Table 3. The predicted results are shown in Fig. 13, and it can be seen that all points with mean stress are close to a best-fit solid line. The comparison between observed life and predicted life is presented in Fig. 14. The fatigue life points under all control modes are all located in the twice error band.
(3)
where
⎛σ ⎞ σ f⎜ m⎟ = 1 + β m σa ⎝ σa ⎠
(4)
⎛ σ ⎞ −0.4884 ⎜ 1 + 4.670 m ⎟εap = 0.3261( 2Nf ) σa ⎠ ⎝
(5)
2
σmaxεa =
( σ′f ) E
b
( 2Nf )2
b+ c
+ σ ′f ε′f ( 2Nf )
(2)
By introducing a mean stress function as in Ref. [2,20] into the Coffin-Manson equation, a new fatigue life model is proposed as given in Eq. (3). In this model, the plastic strain amplitude is corrected by the function given in Eq. (4) to account for the effect of mean stress. The parameters in the right side of Eq. (3) are the same as in the Coffin-Manson equation as given in Table 3. Then the parameter of Eq. (4) can been calculated through one loading condition of mean stress tests (the test under sm ¼50 MPa and sa ¼250 MPa was used here). Finally, the proposed fatigue model for the present study is obtained as Eq. (5). Fig. 15 shows the correlation of the proposed fatigue parameter with fatigue life under all control modes, and compared with the SWT model, the data points are closer to the solid line. As can be seen from Fig. 16, the fatigue life points are all located in the 1.5 times error band,
5. Conclusion Low cycle fatigue experiments under different control modes, i.e. symmetrical strain cycling, symmetrical stress cycling and asymmetrical stress cycling, were performed on a wrought 316LN stainless steel at room temperature. The effect of mean stress and ratcheting strain on the low cycle fatigue behavior of the steel were explored. The main observations and conclusions are as follows: (1) Under symmetrical strain and stress cycling, the steel exhibits consistent cyclic hardening/softening characteristics: rapid cyclic hardening followed by gradual cyclic softening, while under asymmetrical stress cycling, the steel exhibits significant and continuous cyclic hardening due to mean stress.
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(2) Fatigue life decreases with the increase of loading amplitude under all control modes, but increases with increasing mean stress under asymmetrical stress cycling. If compared under the same strain amplitude, the fatigue life is found significantly reduced due to ratcheting strain that may facilitate the crack initiation and propagation. The extension of fatigue life with increasing mean stress is mainly attributed to the reduced strain amplitude by mean stress hardening. (3) The SWT model and a newly proposed fatigue life model based on the Coffin-Manson equation were employed to predict the fatigue life under asymmetrical stress cycling. Both models were found yielding robust predictions, while the proposed model is superior to the SWT model in the predicting accuracy.
Acknowledgements The authors gratefully acknowledge financial support for this work from the National Natural Science Foundation of China (Nos. 51435012 and 51505325) and Ph.D. Programs Foundation of Ministry of Education of China (No. 20130032110018).
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