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Effects of pre-strain on uniaxial ratcheting and fatigue failure of Z2CN18.10 austenitic stainless steel
International Journal of Fatigue 52 (2013) 106–113
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Effects of pre-strain on uniaxial ratcheting and fatigue failure of Z2CN18.10 austenitic stainless steel Yong Wang, Dunji Yu, Gang Chen, Xu Chen ⇑ School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China
a r t i c l e
i n f o
Article history: Received 7 January 2013 Received in revised form 10 March 2013 Accepted 12 March 2013 Available online 21 March 2013 Keywords: Pre-strain Ratcheting Cyclic deformation Fatigue life prediction Z2CN18.10 steel
a b s t r a c t Effects of both tensile and compressive pre-strain on cyclic deformation of Z2CN18.10 austenitic stainless steel under stress cycling with mean stress are studied. As compared to as-received material, ratcheting strain of subsequent stress cycling decreases with increasing tensile pre-strain (TP) level. Lower level of compressive pre-strain (CP) is found to accelerate ratcheting strain accumulation while higher level of CP retards the accumulation. Tensile pre-straining is beneficial to ratcheting–fatigue life while compressive pre-straining is detrimental. A modified fatigue model to address the effect of pre-straining is proposed to predict the fatigue lives of the stress cycling tests with mean stress. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction The primary auxiliary piping in a nuclear power plant could be subjected to cyclic loading emanating from start-up and shutdown of the plant or variation in operating conditions or seismic events. Cyclic plastic deformation of piping thus becomes inevitable. One of the phenomena in cyclic plasticity is ratcheting, that is defined as a strain accumulation under stress controlled cyclic loading with non-zero mean stress. The development and accumulation of such strain over a number of applied cycles can cause premature damage to the component and adversely affect its fatigue performance. Therefore, for efficient designing purposes and maintaining structural integrity, detailed knowledge of cyclic plastic deformation response is necessary. Many factors have been reported to greatly influence the ratcheting behavior of piping components, such as internal pressure, loading types, and environment temperature [1–6], and among them preload is of much interest and significance because those piping components may be subjected to significant amounts of pre-strain during manufacture and setting-up. Recently, extensive research on the subsequent deformations of materials subjected to preloading has been carried out [7–18]. Yang and Wang [7] studied the effect of two different tensile pre-strain (TP) conditions on the cyclic creep deformation and fracture behavior of a high strength spring steel. A dependence of cyclic hardening or softening behavior on pre-straining was found. ⇑ Corresponding author. Tel.: +86 22 27408399; fax: +86 22 27403389. E-mail address: [email protected] (X. Chen). 0142-1123/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2013.03.007
Taheri et al. [8] found a detrimental effect of pre-hardening in strain control and a beneficial one in stress control by carrying fatigue tests on pre-hardened 304L steel. Kim et al. [9] investigated the effect of pre-strain on mechanical characteristics by carrying out low-temperature tensile tests on different levels of prestrained AISI 304L specimens. Their results suggested that TP increased the yield strength and ultimate tensile strength at the cost of losing ductility at low temperature. Moreover, many literatures focused on the influence of pre-straining on fatigue limit. It has been found that the benefit or detriment of pre-straining on fatigue limit may be a function of material, strain rate during pre-straining, tensile versus compressive pre-straining, re-machining of the pre-strained specimen before cycling, type of fatigue loading (torsional, axial, or bending), stress ratio and loading frequency [19]. It is generally observed that mild steels which have the ability to work hardening significantly, experience a beneficial increase in fatigue limit for a wide range of pre-strains [20]. A detriment in the fatigue limit has been reported for small pre-strains in some steels [21], while larger pre-strains often lead to significant increase in the fatigue limit [22]. Although investigators have studied the impact of pre-strain on material properties in many aspects, the effects of pre-strain on ratcheting and fatigue failure under stress cycling with mean stress are still unclear. In the present study, we will try to characterize the effects of both TP (tensile pre-strain) and CP (compressive pre-strain) on ratcheting behavior and fatigue failure of an austenitic stainless steel Z2CN18.10 that is used as piping material in nuclear power plants. Further, two stress-based fatigue failure models (the SWT parameter and the ratcheting-modified SWT
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Y. Wang et al. / International Journal of Fatigue 52 (2013) 106–113 Table 1 Chemical composition of Z2CN18.10 (in wt.%). Material
C
Si
Mn
P
S
Ni
Cr
Cu
Co
Z2CN18.10
0.016
0.306
1.908
0.022
0.004
9.308
18.085
0.095
0.037
Table 2 Monotonic tensile properties of Z2CN18.10 steel. Material
Proof stress r0.2 (MPa)
Tensile strength rb (MPa)
Strain at failure ef
Reduction of area u (%)
Z2CN18.10
315
560
0.61
70
parameter by Park et al. [23]) will be evaluated for their ability to predict fatigue lives with pre-strain effect.
Table 3 Loading conditions of uniaxial ratcheting tests. Specimen no.
Preload
Pre-strain level (%)
Un1
As-received
0
TP1 TP2 TP3
Tensile pre-strain
1 1.8 3.2
CP1 CP2 CP3 CP4 CP5 CP6
Compressive pre-strain
0.5 0.8 1 1.8 2.5 3.2
2. Experimental procedure Z2CN18.10 austenitic stainless steel was available in the form of pipe with 76 mm outer diameter and 4.5 mm thickness. Its chemical composition (in wt.%) is given in Table 1. Sheet specimens of 10 mm width, 4.5 mm thickness and 25 mm gauge length were machined from the pipe in such a way that the loading axes of the specimens were parallel to the pipe axis. The mechanical properties are given in Table 2. All the experiments were conducted at room temperature by using a 100-kN closed-loop servo-hydraulic tension–compression testing machine with a digital controller. Approximately 200 data points per cycle were collected for further analyses. Uniaxial strains were measured by an extensometer with gauge length of 12.5 mm. All pre-strain and ratcheting experiments were conducted using a triangular waveform at a constant stress rate of 200 MPa/s with the stress amplitude of 260 MPa and mean stress of 60 MPa. In order to elucidate the effect of pre-strain on the cyclic behaviors of Z2CN18.10 austenitic stainless steel, three TP levels and six CP levels were employed. Specimens were first monotonically tensioned or compressed to a predetermined pre-strain level and unloaded under stress control mode. Then the pre-strained specimens directly were cycled under stress control mode till fatigue failure occurred. Experiments of as-received material were also conducted at the same stress amplitude and mean stress for comparison. All the uniaxial ratcheting tests are listed in Table 3.
rm (MPa)
ra (MPa)
60
260
3. Results and discussion Fig. 1. Initial 50 cyclic hysteresis loops for Z2CN18.10 at stress amplitude of 260 MPa and mean stress of 60 MPa.
3.1. Stress cyclic behaviors of as-received materials Before the pre-strain and uniaxial ratcheting experiments, some basic properties of the metal are obtained from monotonic tension at the strain rate of 5 104 s1 as listed in Table 2, which are helpful to choose the stress levels applied in the cyclic loading tests. Fig. 1 shows the initial 50 hysteresis loops of the stress cycling. To illustrate the ratcheting behavior more clearly, the variation of ratcheting strain with the number of cycles for each loading case of cyclic stressing was obtained from the experimental data. In this study, ratcheting strain is defined as:
er ¼
ðemax þ emin Þ 2
ð1Þ
where emax is the maximum axial nominal strain in each cycle measured by the extensometer, and emin is the minimum. Ratcheting strain rate is defined as the increment of ratcheting strain in each cycle and denoted as e_ r . The evolution curve of ratcheting strain defined by Eq. (1) during the stress cycling with respect to the life ratio (N/Nf) is shown in Fig. 2. The ratcheting strain rate with cycles is
Fig. 2. Ratcheting strain and ratcheting strain rate curves for as-received Z2CN18.10 steel with three distinct zones.
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Fig. 3. Stress–strain response of different tensile pre-strains and the first hysteresis loops of subsequent cycling in which 0%, 1%, 1.8%, 3.2% mean pre-strain level.
Fig. 4. Stress–strain response of different compressive pre-strains and the first hysteresis loop of subsequent cycling.
fitted by ratcheting strain curve. Life ratio represents the degree of fatigue damage of a material upon cycling and is defined as the ratio of cyclic numbers and fatigue lives. The curve of ratcheting strain is similar to a conventional creep strain and can be divided into three stages in term of the ratcheting strain rate [24,25]. Primary stage: the ratcheting strain increases rapidly and the ratcheting strain rate decreases gradually with the increase of cyclic number. Secondary stage: the ratcheting strain increases steadily and the ratcheting strain rate keeps almost unchanged. Tertiary stage: the ratcheting strain increases rapidly and the ratcheting strain rate increases quickly with the increasing cyclic number because of the initiation of crack induced from fatigue and ratcheting interaction, and results in a large ratcheting strain in a limited number of cycles. Finally, the specimen fails due to crack propagation. 3.2. Effect of pre-strain on cyclic plastic deformation Fig. 3 gives stress–strain responses of different TPs and first hysteresis loops of subsequent stress cycling. As shown by dash lines in Fig. 3, the initial tension responses are almost same for the specimens with different pre-strain levels. It is obvious that elastic region of loading (denoted as AB) of first cycle is extremely enlarged by prior tensile pre-straining. The expansion of elastic region for TP upon loading can be explained as that the center of yield surface is shifted to tensile direction due to TP. Consequently, tensile prestraining greatly narrows the area encircled by loading (AB) and unloading (BC). Upon reversed loading (CD), the tensile pre-strained material yields quickly which results in enlarged area covered by reversed loading (CD) and unloading (DE). Stress–strain response of CPs and the first subsequent cycles are presented in Fig. 4. As shown in Fig. 4, compressive pre-straining shortens elastic region of loading (AB) which is opposite to the effect of tensile pre-straining. Moreover, plastic deformation take place at the very beginning of the first cycle if CP level is high enough (e.g. 3.2% pre-strain). Compressive pre-straining drags the center of yield surface towards compressive direction and leads to the earlier appearance of yield upon subsequent loading (AB in Fig. 4). The higher the level of CP, the lower the stress upon yielding and the larger the area is covered by loading (AB) and unloading (BC). Ni and Wang [16] found that Bauschinger effect due to pre-straining showed significant influence on hysteresis loop of first cycle under symmetrical stress cycling and the effect of pre-straining on hysteresis loop eventually diminished upon cycling. Fig. 5 reveals cyclic stress–strain hysteresis loops change at the first cycle and the 50th cycle where the beginning of each cycle is translated to a same point for 3.2% TP, 3.2% CP and no pre-strain. As can be seen clearly, the 50th hysteresis loop nearly coincides with each other for three cases. This observation indicates that the Bauschinger
Fig. 5. Hysteresis loops change at the first cycle and the 50th cycle.
Fig. 6. First 50 hysteresis loops for 3.2% tensile pre-strain.
effect due to pre-straining almost diminished after 50 cycles. Furthermore, one should note that the 50th hysteresis loops of prestrained specimens are slightly thinner than that of as-received one, which is the result of pre-hardening due to pre-straining. Fig. 6 shows the initial 50 hysteresis loops for 3.2% TP. Obviously, it shows that the hysteresis loop first shifted towards negative direction and then slowly accumulated in positive direction. The initial 50 hysteresis loops for 3.2% CP are plotted in Fig. 7. Contrary to those with TP, hysteresis loops in CP tests always accumulated in positive direction. In addition, compressive pre-strained material accumulated much more strain than that of tensile pre-strained one with the same magnitude of pre-strain and cyclic numbers as shown in Figs. 6 and 7. To specify the fact more clearly, quantitative data of rat-
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Fig. 7. First 50 hysteresis loops for 3.2% compressive pre-strain.
Fig. 9. Ratcheting strain vs. life ratio for 3.2% tensile pre-strain.
Fig. 8. Accumulated strain at 90% fatigue life for various pre-strain levels.
cheting strain at 90% fatigue life is given in Fig. 8 in terms of various pre-strain levels. The deformation mechanism at tertiary stage is mostly related to the linkup of micro-cracks and growth of the major crack rather than steady accumulation of the plastic strain. Therefore, the ratcheting strain at 0.9 Nf was used as an approximation for the ratcheting strain at failure [23]. Tensile pre-strained sample for each pre-strain level always accumulated less strain than the compressive pre-strained one did. Ratcheting behavior of material can be explained by formation, annihilation, rearrangement and multiplication of dislocations. Investigations have been carried out to study uniaxial ratcheting process in terms of dislocation patterns in different steels: 20 carbon steel [23], 304LN [26] and 316L stainless steel [27,28]. Kang et al. [28] studied dislocation patterns and their evolution in 316L stainless steel subjected to uniaxial stresscontrolled cyclic loading. They observed that most of the dislocation patterns formed in the tensile plastic strain history were dissolved at the reverse loading. However, some original dislocation structures still remained unchanged for the existence of mean stress and thus resulted in ratcheting strain accumulation. It should be noted that the stress (400 MPa) corresponded to pre-straining is much higher than the peak stress (320 MPa) of stress cycling. The complicated dislocation structures formed in the high level of TP history are hard to dissolve at the subsequent cycling. As a result, strain accumulation for tensile pre-strained material is strongly restrained. However, for CP, it is relatively easier for dislocation pairs with opposite signs to annihilate for its opposite pre-hardening direction with mean stress though high level of CP still has some retardation on strain accumulation. It is obvious to say that strain hardening on the same direction of mean stress results in much stronger resistant to strain accumulation than the effect of strain hardening on the opposite direction of mean stress.
Fig. 10. Ratcheting strain vs. life ratio for 3.2% compressive pre-strain.
In order to realize the pre-strain effects on the accumulated strain more clearly, evolution curves of ratcheting strain with respect to life ratio (N/Nf) are obtained for both TP and CP cases. Ratcheting strain for 3.2% TP is plotted as a function of life ratio in Fig. 9. The up-left curve in Fig. 9 is ratcheting strain evolution of initial 100 cycles. Unlike a conventional ratcheting strain curve, a sharp drop is observed in ratcheting strain of initial few cycles for TP. Furthermore, ratcheting strain of primary stage accumulates in a much lower rate as compared with secondary and tertiary stage which is also different from a traditional one. As for CP, an enlarged steady stage (secondary stage) and a shortened primary stage are observed in Fig. 10 as compared to ratcheting strain curve of as-received sample (Fig. 2). Fig. 11 presents the results of ratcheting strain for different levels of TP. Residual strains induced by prior pre-straining are included in Fig. 11a while residual strains are eliminated in Fig. 11b. As shown in Fig. 11, TP restrains strain accumulation of subsequent stress cycling. A clear trend can be found that the accumulated strain of subsequent cycling decreases with the increase of TP level as shown in Fig. 11b. Surprisingly, a discernible trend can be observed in Fig. 11a that the ratcheting strain of 1% and 1.8% prestrained specimens gradually approach the ratcheting strain of un-pre-strained material. Namely, the influence of pre-straining on ratcheting strain become negligible after a certain small number of cycles in subsequent cyclic deformation for lower level of prestrain. Moreover, the lower the pre-strain level, the earlier the influence of pre-straining on ratcheting strain vanishes. However, this is
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Fig. 11. Ratcheting strain vs. number of cycles for various TPs: (a) with pre-strains; and (b): without pre-strains.
not true for 3.2% pre-strained specimen where the material is extremely hardened by pre-straining and the ratcheting strain grow slowly upon cycling. Ratcheting strains for various levels of CP are plotted as a function of cyclic number in Fig. 12. Residual strains induced by prior pre-straining are included in Fig. 12a while residual strains are eliminated in Fig. 12b. Although initial strains of compressive pre-strained specimens are smaller than that of un-prestrained one (Fig. 12a), specimens of three lower levels of pre-strain accumulate much larger ratcheting strain than as-received material within a limited number of cycles while ratcheting strains for three higher levels of pre-strain are always smaller than that of as-received one within 6000 cycles. Concurrently, it is found that ratcheting strain of steady state increases with increasing CP until a maximum is reached, following which, further increase of CP level results in smaller ratcheting strain. The maximum ratcheting strain is found around pre-strain level of 0.8%. Figs. 13 and 14 show ratcheting strain rates of the first cycles and half-life as a function of pre-strain levels, respectively. It is clear from Fig. 13 that ratcheting strain rate of the first cycle is sensitive to low level of pre-strain but insensitive to high level of prestrain and the relation between ratcheting strain rate of the first cycle and pre-strain level can be fitted by a Boltzmann curve:
e_ ri ¼
A1 A2 epre x0
1þe
þ A2
ð2Þ
x1
where e_ ri is ratcheting strain rate of the first cycle and epre is prestrain level. A1 and A2 are upper and lower limits of ratcheting strain rate, respectively. In other words, ratcheting strain rates of the first cycles are always limited in this bound as far as our test conditions are considered. x0 is the center of curve. Slope of curve center is expressed as (A2 A1)/4x1. Value of each parameter is listed in Table 4. In spite of the domination of Bauschinger effect, the higher level of
Fig. 12. Ratcheting strain vs. number of cycles for various CPs: (a) with pre-strains; and (b): without pre-strains.
Fig. 13. Ratcheting strain rate of the first cycle for various pre-strains.
pre-strain creates a more pronounced pre-hardening which enhances resistance to plastic strain accumulation and is manifested as insensitivity of ratcheting strain rate on high level of pre-strain. Besides, it is noteworthy that Bauschinger effect caused by TP results in plastic strain accumulation of initial few cycles in negative direction as shown in Fig. 9. However, ratcheting strain rate for TP eventually become positive upon cycling with the effect of positive mean stress. Ratcheting strain rates for higher level of TP drop much faster upon cycling for its remarkable pre-hardening and this explains the fact that ratcheting strain rate of half-life decreases with increasing TP as shown by open square in Fig. 14. Contrary to TP, ratcheting strain rates for CP are always positive and the ratcheting
Y. Wang et al. / International Journal of Fatigue 52 (2013) 106–113
Fig. 14. Ratcheting strain rate of half-life for various pre-strains.
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Fig. 15. Correlation of ratcheting–fatigue lives with pre-strain levels.
Table 4 Values of Boltzmann parameters. Parameter
A1
A2
x0
x1
Value
0.065
0.042
0.29
0.433
strain rate of the first cycle increases as pre-strain increased as shown by open circle in Fig. 13, whereas ratcheting strain rate of half-life increases with the increase of pre-strain until a critical pre-strain is reached, and then, it decreases with increasing prestrain as indicated by open circle in Fig. 14. This behavior could be explained by the following facts that, ratcheting strain rate drops much faster upon cycling for higher level of CP for the influence of pre-hardening while the pre-hardening effect is weak and Bauschinger effect dominates upon cycling for lower level of CP. Fig. 16. Correlation of ratcheting–fatigue lives with Park–Kim–Kim model.
3.3. Effect of pre-strain on the fatigue life As mentioned by many researchers, pre-straining may affect fatigue behavior of material under fully reversed stress or strain cycling [7,10,13,18]. However, the effect of pre-strain on fatigue life of stress cycling with mean stress is unclear. Therefore, cycle numbers to failure in terms of various pre-strain levels is given in Fig. 15 on a semi-log coordinate. As depicted in Fig. 15, ratcheting–fatigue life increased with increasing TP level and decreasing CP level, respectively. Therefore, it can be concluded that the TP improves ratcheting life while CP is detrimental to ratcheting life for Z2CN18.10 stainless steel under stress cycling with positive mean stress. 4. Fatigue life predictions Generally, life prediction models of high-cycle fatigue are established in the framework of stress-based approach while failure models for low-cycle fatigue favor strain-based approach. However, some researches show that the stress-based approach is also capable of correlating the data of stress controlled low-cycle fatigue [29–31]. Therefore, stress-based approaches are considered in this study. Basquin [32] observed that stress-life (S–N) data of fully reversed uniaxial stress cycling could be plotted linearly on a log– log scale by:
ra ¼ r0f ð2Nf Þb
ð3Þ
where ra is the stress amplitude, Nf is the fatigue life, r0f and b are fatigue strength coefficient and exponent, respectively. As far as
stress cycling with mean stress is considered, the stress amplitude is replaced by the equivalent stress amplitude, req a , which accounts for the mean stress effect. Several expressions of req a were proposed in literatures [23,33–35]. Two representative mean stress models are considered in this work: Smith–Watson–Topper (SWT) model [34] and its modification by Park et al. [23]. The Smith–Watson– Topper (SWT) parameter is:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
req rmax ra a ¼
ð4Þ
where rmax is the maximum stress. The SWT parameter cannot predict ratcheting–fatigue life with pre-straining since the effect of pre-strain on the ratcheting–fatigue interaction is not included in the model and it predicts the same fatigue life for various prestrains under the same stress amplitude and maximum stress [23]. Park et al. [23] modified the SWT parameter by incorporating the ratcheting strain in the equation: eq a
r
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ffi 1 f ¼ rm er þ ra ra 2
ð5Þ
where rm is the mean stress, efr is the ratcheting strain at 90% of fatigue life. The fatigue data correlated with the Park–Kim–Kim parameter is given in Fig. 16 with fatigue properties listed in Table 5. The correlation appears to be satisfactory if the life factor 2 is considered. It’s worth noting that the range of fatigue life in this study narrows from 8000 to 20,000 cycles. The choose of life factor 1.1 rather than 2 seems more reasonable by analyzing the experimental data distribution. However, if life factor 1.1 is considered, the correlation of fatigue lives with Eq. (5) seems much unconservative. The
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Table 5 Fatigue properties of Z2CN18.10 steel. Model
Fatigue strength coefficient, r0f (MPa)
Fatigue strength exponent, b
Park–Kim–Kim Modified SWT
37,103 657
0.467 0.082
Fig. 17. Comparison of predicted and experimental lives for the modified model.
Park–Kim–Kim model failed to predict fatigue life for three higher levels of CP due to the fact that the fatigue life does not decrease monotonically with the increase of ratcheting strain for CP. Fatigue life and ratcheting strain both decrease with increasing pre-strain for higher level of CP. The experimental results performed on two structural steels by Rider et al. [36] showed that, subjected to cyclic plastic torsion in combination with axial loads, fatigue life of a lowcarbon steel (En3) was not governed by the degree of ratcheting strain accumulation. Considering the monotonical relation between pre-strain and fatigue life, a pre-strain related factor Cpre is incorporated in the SWT parameter to address the effect of pre-straining. The modified equation is given by:
C pre ¼ 1
req a ¼
epre ef
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C pre rmax ra
ð6Þ
ð7Þ
where Cpre is a dimensionless quantity and denoted as pre-strain coefficient, ef is strain at failure in monotonic tension test and epre is the pre-strain level. It is noted that the modified model reduces to the SWT parameter if the pre-strain level is 0% (no pre-straining) and Cpre is simplified to unity. Cpre is less than unity for TP and a longer fatigue life is predicted whilst CP gives a Cpre greater than unity and a shortened fatigue life is obtained. The correlation for this modified SWT parameter defined by Eq. (7) is shown in Fig. 17. The modified SWT parameter yielded fairly good correlation with no experiment point outside the band of factor 1.1. It should be noted that pre-strain effects on ratcheting–fatigue interaction with only constant stress amplitude and mean stress are examined in this study. Further tests would be necessary to determine whether this is true at various stresses amplitude or mean stresses under pre-strain conditions. 5. Conclusions The stress cyclic behavior of Z2CN18.10 austenitic stainless steel has been studied in terms of various tensile pre-strain (TP)
and compressive pre-strain (CP) levels. Based on the experimental observation, the effect of TP and CP on ratcheting behavior and fatigue life are carefully discussed and the following conclusions are drawn: (1) TP restrains ratcheting strain accumulation. The specimen with higher level of TP responds to the same applied subsequent stress cycling with smaller ratcheting strain. Moreover, influence of lower level of pre-strain on ratcheting strain gradually vanishes after a certain number of cycles. (2) Low-level CP accelerates the ratcheting strain accumulation while high-level CP retards the ratcheting strain accumulation. CP shortens the primary stage and enlarges the secondary stage of ratcheting strain curve. (3) Retardation of TP on strain accumulation is more remarkable than that of CP since the direction of strain hardening induced by TP is consistent with the direction of ratcheting strain accumulation but CP is quite opposite. (4) A Boltzmann relationship is found between ratcheting strain rate of first cycle and pre-strain level. Namely, strain rate of first cycle is sensitive to low level of pre-strain but insensitive to high level of tensile or compressive pre-strain. (5) Tensile pre-straining improves ratcheting–fatigue life while compressive pre-straining is detrimental to ratcheting– fatigue life. A modified SWT parameter incorporated with pre-strain effect is found to yield fairly good prediction of ratcheting life for present test conditions.
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[26] Dutta K, Sivaprasad S, Tarafder S, Ray KK. Influence of asymmetric cyclic loading on substructure formation and ratcheting fatigue behaviour of AISI 304LN stainless steel. Mater Sci Eng A 2010;527:7571–9. [27] Gaudin C, Feaugas X. Cyclic creep process in AISI 316L stainless steel in terms of dislocation patterns and internal stresses. Acta Mater 2004;52:3097–110. [28] Kang G, Dong Y, Wang H, Liu Y, Cheng X. Dislocation evolution in 316L stainless steel subjected to uniaxial ratcheting deformation. Mater Sci Eng A 2010;527:5952–61. [29] Kwofie S, Chandler H. Fatigue life prediction under conditions where cyclic creep-fatigue interaction occurs. Int J Fatigue 2007;29:2117–24. [30] Liu Y, Kang G, Gao Q. Stress-based fatigue failure models for uniaxial ratcheting–fatigue interaction. Int J Fatigue 2008;30:1065–73. [31] Lin Y, Chen XM, Liu ZH, Chen J. Investigation of uniaxial low-cycle fatigue failure behavior of hot-rolled AZ91 magnesium alloy. Int J Fatigue 2012;48:122–32. [32] Basquin OH. The exponential law of endurance tests. Proc ASTM 1910;10:625–30. [33] Smith JO. Effect of range of stress on fatigue strength of metals. Univ Illinois, Eng Exp Station, Bull No. 334 1942. [34] Smith KN, Watson P, Topper TH. A stress–strain function for the fatigue of metals. J Mater 1970;5:767–78. [35] Walker EK. The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7076-T6 aluminum. In: Effect of environment and complex load history on fatigue life, ASTM STP 462. Philadelphia: American Society for Testing and Materials; 1970. p. 1–14. [36] Rider R, Harvey S, Chandler H. Fatigue and ratcheting interactions. Int J Fatigue 1995;17:507–11.
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Effects of pre-strain on uniaxial ratcheting and fatigue failure of Z2CN18.10 austenitic stainless steel Yong Wang, Dunji Yu, Gang Chen, Xu Chen ⇑ School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China
a r t i c l e
i n f o
Article history: Received 7 January 2013 Received in revised form 10 March 2013 Accepted 12 March 2013 Available online 21 March 2013 Keywords: Pre-strain Ratcheting Cyclic deformation Fatigue life prediction Z2CN18.10 steel
a b s t r a c t Effects of both tensile and compressive pre-strain on cyclic deformation of Z2CN18.10 austenitic stainless steel under stress cycling with mean stress are studied. As compared to as-received material, ratcheting strain of subsequent stress cycling decreases with increasing tensile pre-strain (TP) level. Lower level of compressive pre-strain (CP) is found to accelerate ratcheting strain accumulation while higher level of CP retards the accumulation. Tensile pre-straining is beneficial to ratcheting–fatigue life while compressive pre-straining is detrimental. A modified fatigue model to address the effect of pre-straining is proposed to predict the fatigue lives of the stress cycling tests with mean stress. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction The primary auxiliary piping in a nuclear power plant could be subjected to cyclic loading emanating from start-up and shutdown of the plant or variation in operating conditions or seismic events. Cyclic plastic deformation of piping thus becomes inevitable. One of the phenomena in cyclic plasticity is ratcheting, that is defined as a strain accumulation under stress controlled cyclic loading with non-zero mean stress. The development and accumulation of such strain over a number of applied cycles can cause premature damage to the component and adversely affect its fatigue performance. Therefore, for efficient designing purposes and maintaining structural integrity, detailed knowledge of cyclic plastic deformation response is necessary. Many factors have been reported to greatly influence the ratcheting behavior of piping components, such as internal pressure, loading types, and environment temperature [1–6], and among them preload is of much interest and significance because those piping components may be subjected to significant amounts of pre-strain during manufacture and setting-up. Recently, extensive research on the subsequent deformations of materials subjected to preloading has been carried out [7–18]. Yang and Wang [7] studied the effect of two different tensile pre-strain (TP) conditions on the cyclic creep deformation and fracture behavior of a high strength spring steel. A dependence of cyclic hardening or softening behavior on pre-straining was found. ⇑ Corresponding author. Tel.: +86 22 27408399; fax: +86 22 27403389. E-mail address: [email protected] (X. Chen). 0142-1123/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2013.03.007
Taheri et al. [8] found a detrimental effect of pre-hardening in strain control and a beneficial one in stress control by carrying fatigue tests on pre-hardened 304L steel. Kim et al. [9] investigated the effect of pre-strain on mechanical characteristics by carrying out low-temperature tensile tests on different levels of prestrained AISI 304L specimens. Their results suggested that TP increased the yield strength and ultimate tensile strength at the cost of losing ductility at low temperature. Moreover, many literatures focused on the influence of pre-straining on fatigue limit. It has been found that the benefit or detriment of pre-straining on fatigue limit may be a function of material, strain rate during pre-straining, tensile versus compressive pre-straining, re-machining of the pre-strained specimen before cycling, type of fatigue loading (torsional, axial, or bending), stress ratio and loading frequency [19]. It is generally observed that mild steels which have the ability to work hardening significantly, experience a beneficial increase in fatigue limit for a wide range of pre-strains [20]. A detriment in the fatigue limit has been reported for small pre-strains in some steels [21], while larger pre-strains often lead to significant increase in the fatigue limit [22]. Although investigators have studied the impact of pre-strain on material properties in many aspects, the effects of pre-strain on ratcheting and fatigue failure under stress cycling with mean stress are still unclear. In the present study, we will try to characterize the effects of both TP (tensile pre-strain) and CP (compressive pre-strain) on ratcheting behavior and fatigue failure of an austenitic stainless steel Z2CN18.10 that is used as piping material in nuclear power plants. Further, two stress-based fatigue failure models (the SWT parameter and the ratcheting-modified SWT
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Y. Wang et al. / International Journal of Fatigue 52 (2013) 106–113 Table 1 Chemical composition of Z2CN18.10 (in wt.%). Material
C
Si
Mn
P
S
Ni
Cr
Cu
Co
Z2CN18.10
0.016
0.306
1.908
0.022
0.004
9.308
18.085
0.095
0.037
Table 2 Monotonic tensile properties of Z2CN18.10 steel. Material
Proof stress r0.2 (MPa)
Tensile strength rb (MPa)
Strain at failure ef
Reduction of area u (%)
Z2CN18.10
315
560
0.61
70
parameter by Park et al. [23]) will be evaluated for their ability to predict fatigue lives with pre-strain effect.
Table 3 Loading conditions of uniaxial ratcheting tests. Specimen no.
Preload
Pre-strain level (%)
Un1
As-received
0
TP1 TP2 TP3
Tensile pre-strain
1 1.8 3.2
CP1 CP2 CP3 CP4 CP5 CP6
Compressive pre-strain
0.5 0.8 1 1.8 2.5 3.2
2. Experimental procedure Z2CN18.10 austenitic stainless steel was available in the form of pipe with 76 mm outer diameter and 4.5 mm thickness. Its chemical composition (in wt.%) is given in Table 1. Sheet specimens of 10 mm width, 4.5 mm thickness and 25 mm gauge length were machined from the pipe in such a way that the loading axes of the specimens were parallel to the pipe axis. The mechanical properties are given in Table 2. All the experiments were conducted at room temperature by using a 100-kN closed-loop servo-hydraulic tension–compression testing machine with a digital controller. Approximately 200 data points per cycle were collected for further analyses. Uniaxial strains were measured by an extensometer with gauge length of 12.5 mm. All pre-strain and ratcheting experiments were conducted using a triangular waveform at a constant stress rate of 200 MPa/s with the stress amplitude of 260 MPa and mean stress of 60 MPa. In order to elucidate the effect of pre-strain on the cyclic behaviors of Z2CN18.10 austenitic stainless steel, three TP levels and six CP levels were employed. Specimens were first monotonically tensioned or compressed to a predetermined pre-strain level and unloaded under stress control mode. Then the pre-strained specimens directly were cycled under stress control mode till fatigue failure occurred. Experiments of as-received material were also conducted at the same stress amplitude and mean stress for comparison. All the uniaxial ratcheting tests are listed in Table 3.
rm (MPa)
ra (MPa)
60
260
3. Results and discussion Fig. 1. Initial 50 cyclic hysteresis loops for Z2CN18.10 at stress amplitude of 260 MPa and mean stress of 60 MPa.
3.1. Stress cyclic behaviors of as-received materials Before the pre-strain and uniaxial ratcheting experiments, some basic properties of the metal are obtained from monotonic tension at the strain rate of 5 104 s1 as listed in Table 2, which are helpful to choose the stress levels applied in the cyclic loading tests. Fig. 1 shows the initial 50 hysteresis loops of the stress cycling. To illustrate the ratcheting behavior more clearly, the variation of ratcheting strain with the number of cycles for each loading case of cyclic stressing was obtained from the experimental data. In this study, ratcheting strain is defined as:
er ¼
ðemax þ emin Þ 2
ð1Þ
where emax is the maximum axial nominal strain in each cycle measured by the extensometer, and emin is the minimum. Ratcheting strain rate is defined as the increment of ratcheting strain in each cycle and denoted as e_ r . The evolution curve of ratcheting strain defined by Eq. (1) during the stress cycling with respect to the life ratio (N/Nf) is shown in Fig. 2. The ratcheting strain rate with cycles is
Fig. 2. Ratcheting strain and ratcheting strain rate curves for as-received Z2CN18.10 steel with three distinct zones.
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Fig. 3. Stress–strain response of different tensile pre-strains and the first hysteresis loops of subsequent cycling in which 0%, 1%, 1.8%, 3.2% mean pre-strain level.
Fig. 4. Stress–strain response of different compressive pre-strains and the first hysteresis loop of subsequent cycling.
fitted by ratcheting strain curve. Life ratio represents the degree of fatigue damage of a material upon cycling and is defined as the ratio of cyclic numbers and fatigue lives. The curve of ratcheting strain is similar to a conventional creep strain and can be divided into three stages in term of the ratcheting strain rate [24,25]. Primary stage: the ratcheting strain increases rapidly and the ratcheting strain rate decreases gradually with the increase of cyclic number. Secondary stage: the ratcheting strain increases steadily and the ratcheting strain rate keeps almost unchanged. Tertiary stage: the ratcheting strain increases rapidly and the ratcheting strain rate increases quickly with the increasing cyclic number because of the initiation of crack induced from fatigue and ratcheting interaction, and results in a large ratcheting strain in a limited number of cycles. Finally, the specimen fails due to crack propagation. 3.2. Effect of pre-strain on cyclic plastic deformation Fig. 3 gives stress–strain responses of different TPs and first hysteresis loops of subsequent stress cycling. As shown by dash lines in Fig. 3, the initial tension responses are almost same for the specimens with different pre-strain levels. It is obvious that elastic region of loading (denoted as AB) of first cycle is extremely enlarged by prior tensile pre-straining. The expansion of elastic region for TP upon loading can be explained as that the center of yield surface is shifted to tensile direction due to TP. Consequently, tensile prestraining greatly narrows the area encircled by loading (AB) and unloading (BC). Upon reversed loading (CD), the tensile pre-strained material yields quickly which results in enlarged area covered by reversed loading (CD) and unloading (DE). Stress–strain response of CPs and the first subsequent cycles are presented in Fig. 4. As shown in Fig. 4, compressive pre-straining shortens elastic region of loading (AB) which is opposite to the effect of tensile pre-straining. Moreover, plastic deformation take place at the very beginning of the first cycle if CP level is high enough (e.g. 3.2% pre-strain). Compressive pre-straining drags the center of yield surface towards compressive direction and leads to the earlier appearance of yield upon subsequent loading (AB in Fig. 4). The higher the level of CP, the lower the stress upon yielding and the larger the area is covered by loading (AB) and unloading (BC). Ni and Wang [16] found that Bauschinger effect due to pre-straining showed significant influence on hysteresis loop of first cycle under symmetrical stress cycling and the effect of pre-straining on hysteresis loop eventually diminished upon cycling. Fig. 5 reveals cyclic stress–strain hysteresis loops change at the first cycle and the 50th cycle where the beginning of each cycle is translated to a same point for 3.2% TP, 3.2% CP and no pre-strain. As can be seen clearly, the 50th hysteresis loop nearly coincides with each other for three cases. This observation indicates that the Bauschinger
Fig. 5. Hysteresis loops change at the first cycle and the 50th cycle.
Fig. 6. First 50 hysteresis loops for 3.2% tensile pre-strain.
effect due to pre-straining almost diminished after 50 cycles. Furthermore, one should note that the 50th hysteresis loops of prestrained specimens are slightly thinner than that of as-received one, which is the result of pre-hardening due to pre-straining. Fig. 6 shows the initial 50 hysteresis loops for 3.2% TP. Obviously, it shows that the hysteresis loop first shifted towards negative direction and then slowly accumulated in positive direction. The initial 50 hysteresis loops for 3.2% CP are plotted in Fig. 7. Contrary to those with TP, hysteresis loops in CP tests always accumulated in positive direction. In addition, compressive pre-strained material accumulated much more strain than that of tensile pre-strained one with the same magnitude of pre-strain and cyclic numbers as shown in Figs. 6 and 7. To specify the fact more clearly, quantitative data of rat-
Y. Wang et al. / International Journal of Fatigue 52 (2013) 106–113
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Fig. 7. First 50 hysteresis loops for 3.2% compressive pre-strain.
Fig. 9. Ratcheting strain vs. life ratio for 3.2% tensile pre-strain.
Fig. 8. Accumulated strain at 90% fatigue life for various pre-strain levels.
cheting strain at 90% fatigue life is given in Fig. 8 in terms of various pre-strain levels. The deformation mechanism at tertiary stage is mostly related to the linkup of micro-cracks and growth of the major crack rather than steady accumulation of the plastic strain. Therefore, the ratcheting strain at 0.9 Nf was used as an approximation for the ratcheting strain at failure [23]. Tensile pre-strained sample for each pre-strain level always accumulated less strain than the compressive pre-strained one did. Ratcheting behavior of material can be explained by formation, annihilation, rearrangement and multiplication of dislocations. Investigations have been carried out to study uniaxial ratcheting process in terms of dislocation patterns in different steels: 20 carbon steel [23], 304LN [26] and 316L stainless steel [27,28]. Kang et al. [28] studied dislocation patterns and their evolution in 316L stainless steel subjected to uniaxial stresscontrolled cyclic loading. They observed that most of the dislocation patterns formed in the tensile plastic strain history were dissolved at the reverse loading. However, some original dislocation structures still remained unchanged for the existence of mean stress and thus resulted in ratcheting strain accumulation. It should be noted that the stress (400 MPa) corresponded to pre-straining is much higher than the peak stress (320 MPa) of stress cycling. The complicated dislocation structures formed in the high level of TP history are hard to dissolve at the subsequent cycling. As a result, strain accumulation for tensile pre-strained material is strongly restrained. However, for CP, it is relatively easier for dislocation pairs with opposite signs to annihilate for its opposite pre-hardening direction with mean stress though high level of CP still has some retardation on strain accumulation. It is obvious to say that strain hardening on the same direction of mean stress results in much stronger resistant to strain accumulation than the effect of strain hardening on the opposite direction of mean stress.
Fig. 10. Ratcheting strain vs. life ratio for 3.2% compressive pre-strain.
In order to realize the pre-strain effects on the accumulated strain more clearly, evolution curves of ratcheting strain with respect to life ratio (N/Nf) are obtained for both TP and CP cases. Ratcheting strain for 3.2% TP is plotted as a function of life ratio in Fig. 9. The up-left curve in Fig. 9 is ratcheting strain evolution of initial 100 cycles. Unlike a conventional ratcheting strain curve, a sharp drop is observed in ratcheting strain of initial few cycles for TP. Furthermore, ratcheting strain of primary stage accumulates in a much lower rate as compared with secondary and tertiary stage which is also different from a traditional one. As for CP, an enlarged steady stage (secondary stage) and a shortened primary stage are observed in Fig. 10 as compared to ratcheting strain curve of as-received sample (Fig. 2). Fig. 11 presents the results of ratcheting strain for different levels of TP. Residual strains induced by prior pre-straining are included in Fig. 11a while residual strains are eliminated in Fig. 11b. As shown in Fig. 11, TP restrains strain accumulation of subsequent stress cycling. A clear trend can be found that the accumulated strain of subsequent cycling decreases with the increase of TP level as shown in Fig. 11b. Surprisingly, a discernible trend can be observed in Fig. 11a that the ratcheting strain of 1% and 1.8% prestrained specimens gradually approach the ratcheting strain of un-pre-strained material. Namely, the influence of pre-straining on ratcheting strain become negligible after a certain small number of cycles in subsequent cyclic deformation for lower level of prestrain. Moreover, the lower the pre-strain level, the earlier the influence of pre-straining on ratcheting strain vanishes. However, this is
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Fig. 11. Ratcheting strain vs. number of cycles for various TPs: (a) with pre-strains; and (b): without pre-strains.
not true for 3.2% pre-strained specimen where the material is extremely hardened by pre-straining and the ratcheting strain grow slowly upon cycling. Ratcheting strains for various levels of CP are plotted as a function of cyclic number in Fig. 12. Residual strains induced by prior pre-straining are included in Fig. 12a while residual strains are eliminated in Fig. 12b. Although initial strains of compressive pre-strained specimens are smaller than that of un-prestrained one (Fig. 12a), specimens of three lower levels of pre-strain accumulate much larger ratcheting strain than as-received material within a limited number of cycles while ratcheting strains for three higher levels of pre-strain are always smaller than that of as-received one within 6000 cycles. Concurrently, it is found that ratcheting strain of steady state increases with increasing CP until a maximum is reached, following which, further increase of CP level results in smaller ratcheting strain. The maximum ratcheting strain is found around pre-strain level of 0.8%. Figs. 13 and 14 show ratcheting strain rates of the first cycles and half-life as a function of pre-strain levels, respectively. It is clear from Fig. 13 that ratcheting strain rate of the first cycle is sensitive to low level of pre-strain but insensitive to high level of prestrain and the relation between ratcheting strain rate of the first cycle and pre-strain level can be fitted by a Boltzmann curve:
e_ ri ¼
A1 A2 epre x0
1þe
þ A2
ð2Þ
x1
where e_ ri is ratcheting strain rate of the first cycle and epre is prestrain level. A1 and A2 are upper and lower limits of ratcheting strain rate, respectively. In other words, ratcheting strain rates of the first cycles are always limited in this bound as far as our test conditions are considered. x0 is the center of curve. Slope of curve center is expressed as (A2 A1)/4x1. Value of each parameter is listed in Table 4. In spite of the domination of Bauschinger effect, the higher level of
Fig. 12. Ratcheting strain vs. number of cycles for various CPs: (a) with pre-strains; and (b): without pre-strains.
Fig. 13. Ratcheting strain rate of the first cycle for various pre-strains.
pre-strain creates a more pronounced pre-hardening which enhances resistance to plastic strain accumulation and is manifested as insensitivity of ratcheting strain rate on high level of pre-strain. Besides, it is noteworthy that Bauschinger effect caused by TP results in plastic strain accumulation of initial few cycles in negative direction as shown in Fig. 9. However, ratcheting strain rate for TP eventually become positive upon cycling with the effect of positive mean stress. Ratcheting strain rates for higher level of TP drop much faster upon cycling for its remarkable pre-hardening and this explains the fact that ratcheting strain rate of half-life decreases with increasing TP as shown by open square in Fig. 14. Contrary to TP, ratcheting strain rates for CP are always positive and the ratcheting
Y. Wang et al. / International Journal of Fatigue 52 (2013) 106–113
Fig. 14. Ratcheting strain rate of half-life for various pre-strains.
111
Fig. 15. Correlation of ratcheting–fatigue lives with pre-strain levels.
Table 4 Values of Boltzmann parameters. Parameter
A1
A2
x0
x1
Value
0.065
0.042
0.29
0.433
strain rate of the first cycle increases as pre-strain increased as shown by open circle in Fig. 13, whereas ratcheting strain rate of half-life increases with the increase of pre-strain until a critical pre-strain is reached, and then, it decreases with increasing prestrain as indicated by open circle in Fig. 14. This behavior could be explained by the following facts that, ratcheting strain rate drops much faster upon cycling for higher level of CP for the influence of pre-hardening while the pre-hardening effect is weak and Bauschinger effect dominates upon cycling for lower level of CP. Fig. 16. Correlation of ratcheting–fatigue lives with Park–Kim–Kim model.
3.3. Effect of pre-strain on the fatigue life As mentioned by many researchers, pre-straining may affect fatigue behavior of material under fully reversed stress or strain cycling [7,10,13,18]. However, the effect of pre-strain on fatigue life of stress cycling with mean stress is unclear. Therefore, cycle numbers to failure in terms of various pre-strain levels is given in Fig. 15 on a semi-log coordinate. As depicted in Fig. 15, ratcheting–fatigue life increased with increasing TP level and decreasing CP level, respectively. Therefore, it can be concluded that the TP improves ratcheting life while CP is detrimental to ratcheting life for Z2CN18.10 stainless steel under stress cycling with positive mean stress. 4. Fatigue life predictions Generally, life prediction models of high-cycle fatigue are established in the framework of stress-based approach while failure models for low-cycle fatigue favor strain-based approach. However, some researches show that the stress-based approach is also capable of correlating the data of stress controlled low-cycle fatigue [29–31]. Therefore, stress-based approaches are considered in this study. Basquin [32] observed that stress-life (S–N) data of fully reversed uniaxial stress cycling could be plotted linearly on a log– log scale by:
ra ¼ r0f ð2Nf Þb
ð3Þ
where ra is the stress amplitude, Nf is the fatigue life, r0f and b are fatigue strength coefficient and exponent, respectively. As far as
stress cycling with mean stress is considered, the stress amplitude is replaced by the equivalent stress amplitude, req a , which accounts for the mean stress effect. Several expressions of req a were proposed in literatures [23,33–35]. Two representative mean stress models are considered in this work: Smith–Watson–Topper (SWT) model [34] and its modification by Park et al. [23]. The Smith–Watson– Topper (SWT) parameter is:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
req rmax ra a ¼
ð4Þ
where rmax is the maximum stress. The SWT parameter cannot predict ratcheting–fatigue life with pre-straining since the effect of pre-strain on the ratcheting–fatigue interaction is not included in the model and it predicts the same fatigue life for various prestrains under the same stress amplitude and maximum stress [23]. Park et al. [23] modified the SWT parameter by incorporating the ratcheting strain in the equation: eq a
r
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ffi 1 f ¼ rm er þ ra ra 2
ð5Þ
where rm is the mean stress, efr is the ratcheting strain at 90% of fatigue life. The fatigue data correlated with the Park–Kim–Kim parameter is given in Fig. 16 with fatigue properties listed in Table 5. The correlation appears to be satisfactory if the life factor 2 is considered. It’s worth noting that the range of fatigue life in this study narrows from 8000 to 20,000 cycles. The choose of life factor 1.1 rather than 2 seems more reasonable by analyzing the experimental data distribution. However, if life factor 1.1 is considered, the correlation of fatigue lives with Eq. (5) seems much unconservative. The
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Table 5 Fatigue properties of Z2CN18.10 steel. Model
Fatigue strength coefficient, r0f (MPa)
Fatigue strength exponent, b
Park–Kim–Kim Modified SWT
37,103 657
0.467 0.082
Fig. 17. Comparison of predicted and experimental lives for the modified model.
Park–Kim–Kim model failed to predict fatigue life for three higher levels of CP due to the fact that the fatigue life does not decrease monotonically with the increase of ratcheting strain for CP. Fatigue life and ratcheting strain both decrease with increasing pre-strain for higher level of CP. The experimental results performed on two structural steels by Rider et al. [36] showed that, subjected to cyclic plastic torsion in combination with axial loads, fatigue life of a lowcarbon steel (En3) was not governed by the degree of ratcheting strain accumulation. Considering the monotonical relation between pre-strain and fatigue life, a pre-strain related factor Cpre is incorporated in the SWT parameter to address the effect of pre-straining. The modified equation is given by:
C pre ¼ 1
req a ¼
epre ef
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C pre rmax ra
ð6Þ
ð7Þ
where Cpre is a dimensionless quantity and denoted as pre-strain coefficient, ef is strain at failure in monotonic tension test and epre is the pre-strain level. It is noted that the modified model reduces to the SWT parameter if the pre-strain level is 0% (no pre-straining) and Cpre is simplified to unity. Cpre is less than unity for TP and a longer fatigue life is predicted whilst CP gives a Cpre greater than unity and a shortened fatigue life is obtained. The correlation for this modified SWT parameter defined by Eq. (7) is shown in Fig. 17. The modified SWT parameter yielded fairly good correlation with no experiment point outside the band of factor 1.1. It should be noted that pre-strain effects on ratcheting–fatigue interaction with only constant stress amplitude and mean stress are examined in this study. Further tests would be necessary to determine whether this is true at various stresses amplitude or mean stresses under pre-strain conditions. 5. Conclusions The stress cyclic behavior of Z2CN18.10 austenitic stainless steel has been studied in terms of various tensile pre-strain (TP)
and compressive pre-strain (CP) levels. Based on the experimental observation, the effect of TP and CP on ratcheting behavior and fatigue life are carefully discussed and the following conclusions are drawn: (1) TP restrains ratcheting strain accumulation. The specimen with higher level of TP responds to the same applied subsequent stress cycling with smaller ratcheting strain. Moreover, influence of lower level of pre-strain on ratcheting strain gradually vanishes after a certain number of cycles. (2) Low-level CP accelerates the ratcheting strain accumulation while high-level CP retards the ratcheting strain accumulation. CP shortens the primary stage and enlarges the secondary stage of ratcheting strain curve. (3) Retardation of TP on strain accumulation is more remarkable than that of CP since the direction of strain hardening induced by TP is consistent with the direction of ratcheting strain accumulation but CP is quite opposite. (4) A Boltzmann relationship is found between ratcheting strain rate of first cycle and pre-strain level. Namely, strain rate of first cycle is sensitive to low level of pre-strain but insensitive to high level of tensile or compressive pre-strain. (5) Tensile pre-straining improves ratcheting–fatigue life while compressive pre-straining is detrimental to ratcheting– fatigue life. A modified SWT parameter incorporated with pre-strain effect is found to yield fairly good prediction of ratcheting life for present test conditions.
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