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Effects of low-cycle fatigue on static mechanical properties, microstructures and fracture behavior of 304 stainless steel
Materials Science and Engineering A 527 (2010) 4092–4102
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Effects of low-cycle fatigue on static mechanical properties, microstructures and fracture behavior of 304 stainless steel Duyi Ye ∗ , Yuandong Xu, Lei Xiao, Haibo Cha Institute for Process Equipments, Zhejiang University, Hangzhou 310027, China
a r t i c l e
i n f o
Article history: Received 27 September 2009 Received in revised form 3 March 2010 Accepted 8 March 2010
Keywords: Static mechanical properties Low-cycle fatigue Microstructures Fracture behavior Martensitic transformation
a b s t r a c t A series of experiments, including constant amplitude low-cycle fatigue tests, post-fatigue tension to failure tests, LOM (TEM) observations, and SEM examinations, were performed at room-temperature to investigate the effects of low-cycle fatigue damage on the static mechanical properties, microstructures and fracture behavior of 304 austenitic stainless steel. The changing characteristics of various static mechanical property parameters, including the strength parameters ( ys and ult ), stiffness parameter (E), ductility parameters (ı and ϕf ) and strain hardening exponent (n) during fatigue damage process of the stainless steel were obtained experimentally and their micromechanisms were discussed by analyzing both the deformation microstructures and the fracture features of cyclically pre-deformed specimens. It was shown that the austenite/martensite transformation resulting from the accumulation of cyclic plastic strain was mostly responsible for the variation in the strength, ductility and strain hardening ability of the stainless steel during fatigue damage process. The depletion of the inherent ductility in the material due to fatigue damage evolution led to the ductile-to-brittle transition (DBT) in the fracture modes. Based on the macro/micro-experiments regarding the exhaustion of the ductility during fatigue damage, the ductility parameter was suggested as a damage indicating parameter for the present stainless steel in further studying the fatigue damage mechanics model as well as the residual fatigue life prediction method. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Static mechanical properties of a material, such as the elastic modulus, yield strength, ultimate tensile strength, elongation and reduction in area provide the most fundamental parameters for the structural design, particularly in the stress calculation and strength analysis of structural components and elements. It has been indicated [1,2] that these material properties not only depend on various metallurgical factors, such as grain size, alloying element, quenching, aging, and annealing, but also are intensively influenced by service conditions including the loading history, state of stress imposed, environment, temperature, etc. In the case of engineering structures operating under dynamic or alternating loading conditions, a notable character is that their service properties, especially the mechanical properties, deteriorates progressively with the service times. This degradation in material properties due to alternating loading, also called fatigue damage, seriously affects the service safety of engineering structures or components and thus is an important consideration in their designing against fatigue fail-
∗ Corresponding author at: Institute for Process Equipments, 38 Zheda Road, Hangzhou 310027, Zhejiang, China. Tel.: +86 571 88869213; fax: +86 571 88869213. E-mail address: duyi [email protected] (D. Ye). 0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2010.03.027
ure. On the other hand, the residual fatigue life studies of existing engineering structures in service conditions, generally, involve the evaluation of fatigue damage. Such evaluation is frequently performed by quantitatively measuring the mechanical deterioration of a material, such as the elastic modulus, ultimate tensile strength, hardness, reduction in area and toughness [3–6], in the framework of continuous damage mechanics (CDM). It is accordingly of great practical meaning to investigate the effects of fatigue damage on the static mechanical properties of structural materials as well as the damage evaluation method based on the degradation of material mechanical properties during fatigue damage process. Austenitic stainless steel 304 is an extremely important commercial alloy in engineering applications due to its excellent corrosion resistance, high strength, good ductility and toughness. This alloy is currently being used in industrial installations, such as petrochemical plants, electric-power generating stations and process plants as piping and structural material. In these applications, the components of the structures are often subjected to dynamic or alternating stresses as a result of temperature gradients, which occur on heating and cooling during startups and shutdowns, or during variations in operating conditions. For this reason, evaluation of fatigue damage and the residual fatigue life becomes an important content in their safe designing against fatigue failure. Despite the fact that fatigue mechanical behavior of type 304
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austenitic stainless steel, such as the cyclic stress response, cyclic stress–strain curves (CSSCs) and Coffin–Manson curves have been investigated extensively in the past decades [7–14], relatively few studies, however, have focused on the changing characteristics of the static mechanical properties of this steel during fatigue damage process. As it has been pointed out, the latter would be of great importance for the safe designing against fatigue failure, especially for the prediction of the residual fatigue life of existing structures or components operating under alternating service conditions. This is the motivation of the present study to investigate the effects of low-cycle fatigue damage on the static mechanical properties, deformation microstructures and fractural behavior of type 304 stainless steel. The main purpose of this study, on the one hand, is to gain a more complete understanding of fatigue mechanical properties of this stainless steel so as to use it more effectively in engineering practical applications, on the other hand, to provide an experimental basis for further study of the reliable residual fatigue life prediction method. 2. Experimental details The material used in this investigation is an austenitic 304 stainless steel supplied in the form of a plate, 18 mm in thickness. The plates were hot rolled at 1040 ◦ C for 0.2 h, followed by quenching in water. The chemical composition of the steel in percentage weight is listed in Table 1. The 18 mm plates were then machined into conventional push–pull cylindrical specimens with the tensile axis parallel to the final rolling direction. The nominal dimensions of the specimen in the gauge section were 14.0 mm (length) × 6.0 mm (diameter). Prior to testing, the surface of each specimen was mechanically polished to a final roughness of ∼0.4 m. Tests for the present investigation purpose consist mainly of (i) constant amplitude low-cycle fatigue tests to produce specimens with various amounts of cyclic pre-deformation or fatigue damage, and (ii) uniaxial tension to fracture tests to measure the post-fatigue static mechanical property parameters. Details of testing procedures are described as follows. Fully reversed, push–pull, total strain amplitude controlled fatigue tests were performed at room temperature in an ambient air using a 250 kN closed-loop servohydraulic testing system. A triangular strain waveform with zero mean strain (R = −1) at a ˙ of 5 × 10−3 S−1 was used. The strain constant total strain rate (ε) amplitudes (εa ) chosen for the present fatigue testing were 0.6% and 1.0%, resulting in the fatigue life (Nf5 ) 184 and 2280, respectively. In this study, the fatigue life (Nf5 ) was defined as the cycles corresponding to 5% drop in the maximum stress amplitude, which was related to the growth of the macro cracks. Cyclic tests were interrupted at various chosen fatigue life fractions (N/Nf5 ) at each of strain amplitudes before fracture to produce specimens with various amounts of cyclic pre-deformation. At each strain amplitude, fatigue tests were conducted at least with 15–20 different cyclic fractions. During testing, the load was continuously monitored and hysteresis loops were recorded at appropriate intervals. After the cycling, the specimens were returned to the state of zero stress and zero strain and then loaded in monotonic tension to fracture with a strain rate of 3.0 × 10−5 S−1 . Cyclically pre-deformed specimens were first pulled to a certain strain level in a strain control mode to measure the modulus of elasticity (E) and 0.2 pct proof stress ( ys ), and then tensioned up to fracture in a dis-
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placement control mode to measure the ultimate tensile strength ( ult ), the elongation (ı) and the reduction in area (ϕf ), respectively. The strain hardening exponent (n) was determined from the power-law that relates stress and plastic strain [15], = Kεnp , where K is the strength coefficient, together with the measured data. During tension, the load–displacement plots were recorded continuously. Microstructural changes during low-cycle fatigue process were examined using a light optical microscopy (LOM) and a transmission electron microscopy (TEM). In the case of LOM, the deformation microstructures formed at various stages of the fatigue damage process were examined, while in the case of TEM only the fatigue fracture microstructures were observed. Samples for the microstructural examinations were prepared below the fractured surface in the fatigue failure specimens and taken from the gauge portions in the cyclically pre-deformed specimens by cutting perpendicular to the tensile axils. LOM samples were first mechanically polished using emery papers of various grinds from 230 to 600 grit and then using 1.5 m diamond paste to a final roughness of ∼0.1 m. To reveal the grains, etching for 30 s was used in a mixed solution of 16 vol% of HNO3 , 32 vol% of HCl and 50 vol% of glycerol at 313 K. TEM samples were mechanically thinned to 30 m or less from the initial thickness of about 0.3 mm, and then thinned to perforation by a twin-jet electrochemical polisher. The TEM foils were examined in a HITACH H9000NA transmission electron microscope. Fracture surfaces of both the fatigue failure specimens and the post-fatigue tension to fracture specimens were observed using a scanning electron microscope (SEM). SEM examinations were performed with a SIRION-100 scanning electron microscopy operating at 25 kV. 3. Experimental results 3.1. Initial microstructures and tensile properties The optical microscopy of 304 stainless steel in the as-received condition, as shown in Fig. 1, reveals that the initial grain structure consists of equiaxed austenitic grains with a few straight annealing twins and small elongated delta-ferrite. Fig. 2 shows a TEM micrograph of the virgin material, indicating that the initial dislocation structures have in general low density and consist of primary dislocations having predominantly screw character (either completely straight or with bowed segments) and small loops. Both
Table 1 Chemical composition of 304 stainless steel in wt.%. C
Si
Mn
S
P
Cr
Ni
Mo
N
0.015
0.53
1.64
0.0048
0.03
18.27
8.16
0.02
0.049
Fig. 1. Optical micrograph of 304 austenitic stainless steel in the as-received condition.
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Fig. 2. TEM micrograph of 304 austenitic stainless steel in the as-received condition. Fig. 4. Typical cyclic stress response of 304 stainless steel.
LOM and TEM observations display no metallographic evidence of martensitic transformation in the initial state of the stainless steel. According to Schaeffler diagram [16], steels with compositions in the range where austenite, delta-ferrite and martensite are in equilibrium can be expected to become unstable during plastic deformation by nucleation of martensite. The susceptibility to martensitc transformation for the present stainless steel was estimated using Schaeffler diagram by calculating its chromium and nickel equivalents, as illustrated in Fig. 3. It appears in this figure that the stabilized grade of 304 stainless steel is located in the twophase region of martensite + austenite, indicating thereby that the martensitic transformation may take place in the present material when the other factors, such as temperature, strain, strain rate and stress state are satisfied. Table 2 lists the monotonic tensile properties of the virgin 304 stainless steel at room-temperature. The results reported are the mean values based on multiple (three) tests. The yield strength ( ys ) defined as the stress corresponding to a plastic strain of 0.2% is 259.8 MPa. The ultimate tensile strength ( ult ) is 750.3 MPa. The large difference between the yield strength and the ultimate tensile strength indicates a significant amount of work hardening in
Fig. 3. Position of 304 austenitic stainless steel grade in the Schaeffler diagram.
the virgin material during monotonic deformation. The elongation to failure and reduction in area were 69.1% and 65.1%, respectively, indicative of a high ductility in the initial state of the austenitic stainless steel. 3.2. Stress response during low-cycle fatigue The stress response curves of 304 stainless steel, cycled at two strain amplitudes investigated, are shown in Fig. 4. It is visible in this figure that during fatigue damage process, the material exhibits an initial small hardening followed by a great hardening up to final failure. The period of the second great hardening leads even to an inflexion on the stress response curves. This inflexion occurs later with a small applied strain amplitude. The above-present two-stage cyclic hardening characters provide useful information pertaining to the mechanical stability of the stainless steel during low-cycle fatigue and will help to understand the micromechanisms responsible for the variation of the static mechanical properties during fatigue damage process, which will be present subsequently.
Fig. 5. Typical post-fatigue tensile plots of stress vs. strain of 304 stainless steel.
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Table 2 Mechanical properties of the virgin 304 stainless steel. 0.2% proof stress, ys (MPa)
Ultimate tensile strength, ult (MPa)
Elongation, ı (%)
Reduction of area, ϕf (%)
259.8
750.3
69.1
65.1
3.3. Static mechanical properties at various fatigue damage stages Typical post-fatigue tensile plots of stress vs. strain, obtained from 304 stainless steel specimens subjected to various numbers of precycles at the constant strain amplitude εa = 1.0%, followed by monotonic tension to fracture, are shown in Fig. 5, where the tensile plot of the virgin specimen is also present for comparative purposes. Fig. 6 gives out a set of these tension to fracture specimens.
It is obvious in Fig. 5 that for the present austenitic stainless steel the prior cyclic straining history remarkably influences its subsequent tensile stress–strain behavior. The applied previous straining cycles results in an intensive increase in the tensile stress response, but a distinct decrease in the total elongations to failure. As the precycles increased, the slope in the rising portion of the tensile plots that is a measure of the strain hardening appears progressive decrease and the tensile plots become relative flat beyond the yield strength. The reduction in the total elongation to failure resulting from cyclic pre-deformation can also be inferred from the observation of the tension to fracture specimens shown in Fig. 6, where the final length of the fractured specimens tends to decrease and the necking phenomenon of the specimens becomes unapparent as the precycles increased. The variation of the various static mechanical property parameters of 304 stainless steel during fatigue damage process at two strain amplitudes investigated, is exhibited in Figs. 7–10, where the solid and dashed lines present, respectively, the changing trends of the individual mechanical property at each strain amplitude. Table 3 summarizes a set of typical post-fatigue static mechanical property parameters of the stainless steel specimens, in which the monotonic tensile properties of the virgin specimen were also listed for comparison purpose. Table 3 Typical measured data of post-fatigue static mechanical property parameters of 304 stainless steel specimens (εa = 1.0%).
Fig. 6. Post-fatigue tensile fracture specimens: (1) N = 0; (2) N = 10; (3) N = 20; (4) N = 30; (5) N = 50; (6) N = 100; (7) N = 150; (8) N = 184.
N (cycles)
E (GPa)
0.2 (MPa)
ult (MPa)
n
ı (%)
ϕf (%)
0 3 10 20 30 50 70 100 120 150 184
200.3 196.7 192.4 191.6 175.1 188.1 161.0 177.3 174.8 180.1 156.9
259.8 276.2 326.8 366.4 451.5 550.8 617.7 685.2 721.3 749.9 740.8
750.3 764.5 791.1 791.1 819.9 856.5 894.0 933.2 970.1 957.2 935.9
0.23 0.22 0.23 0.2 0.19 0.18 0.15 0.14 0.13 0.08 0.007
69.1 68.3 69.1 60.3 57 55.8 52.5 47.1 45.8 42.1 15.3
65.1 61.9 61.7 59.5 61.0 59.2 53.4 46.7 41.0 40.2 16.2
Fig. 7. Variation of the strength parameters ( ys and ult ) with straining cycles. (a) 0.2 pct proof stress ( ys ) and (b) Ultimate tensile strength ( ult ).
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Fig. 8. Variation of the modulus of elasticity (E) with straining cycles.
Note in Fig. 7 that under cyclic straining both ys and ult exhibit initial slight increase followed by strong increase almost without reaching their saturated values. This changing character in the strength parameters well corresponds to the two-stage cyclic hardening behavior in Fig. 4. Data analyse, in Table 3, further indicates that the straining cycles to failure enhance ys and ult by around 3 and 1.2 times, respectively, as compared to those of the virgin specimen. This means that for 304 austenitic stainless steel the strength is a sensitive mechanical property to the cyclic straining history. The modulus of elasticity (E) that is a measure of the stiffness property of a material appears a progressive decrease, as a whole, with the increase of straining cycles (Fig. 8). In contrast to the two-stage increasing character in the strength parameters, the ductile parameters (ı and ϕf ) exhibit two-stage descending behavior in the course of fatigue failure, as shown in Fig. 9. In this figure an initial slight decrease followed by a drastic decrease up to final exhaustion in both ı and ϕf is clearly visible. Such inverse correlation between the strength parameters and the ductility parameters observed in the present stainless steel has also been reported for other metastable steels subjected to fatigue loading [17–20]. It is also obtained in Fig. 9 that the ductility parameters are sensi-
Fig. 10. Variation of the strain hardening exponent (n) with straining cycles.
tive to the fatigue damage evolution process. As shown in Fig. 10, the strain hardening exponent (n) displays a two-stage descending character as well during fatigue damage process. Thus the cyclic pre-deformation can deplete significantly the ability to strain hardening of the stainless steel. The above-present changing characteristics of the static mechanical properties of 304 stainless steel during low-cycle fatigue were also obtained in studies of the effects of cyclic pre-deformation on tensile properties of other metallic materials, such as structural steels and nickel-based superalloys [21–24]. 3.4. Microstructures at various fatigue damage stages The microstructure formed in 304 stainless steel at various stages of fatigue damage process has been examined using LOM. Figs. 11–13 show typical optical micrographs of the stainless steel specimens subjected to 5%, 25% and 100% of the fatigue fracture life, respectively, at a total strain amplitude of 1.0%. It is obvious in Fig. 11a that, after 5% of the fatigue fracture life, the grains generally contained a few slip bands and slip is
Fig. 9. Variation of the ductility parameters (ı and ϕf ) with straining cycles. (a) elongation (ı) and (b) reduction in area (ϕf ).
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Fig. 11. Optical micrograph of the specimen subjected to 5% of the fatigue life at εa = 1.0%: (a) slip band features and (b) different morphologies of martensite.
Fig. 12. Optical micrograph of the specimen subjected to 50% of the fatigue life at εa = 1.0%: (a) slip band features and (b) different morphologies of martensite.
Fig. 13. Optical micrograph of the specimen cycled to the end of fatigue life at εa = 1.0%: (a) slip band features and (b) different morphologies of martensite.
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Fig. 14. TEM micrograph of the specimen cycled to the end of fatigue life at εa = 1.0%.
mostly restricted to one system. In some austenitic grains, martensitic phase with different morphologies has already been observed, as shown in Fig. 11b. It is also visible in this figure that at the initial stages of cyclic deformation the distribution of martensitic phase is highly inhomogeneous in austenitic matrix. The above microstructural observation indicates that for the present investigated stainless steel even a small number of straining cycles or a small amount of cumulative plastic strain has resulted in a phase transformation from austenite to martensite. When the specimen subjected to 50% of the fatigue life, in addition to the localized single slip bands, multiple slip modes with intersecting bands on different planes, penetrating the whole austenitic grains, are found commonly in the cyclically deformed specimen (Fig. 12a). Meanwhile, the nucleation of martensite has frequently been observed over several austenitic grains, as seen in Fig. 12b. From this microstructural observation, it can be recognized that with increasing number of straining cycles, not only the density of slip band, but also the volume fraction of the strain-induced martensite increases considerably in the cycled specimen. Similar microstructural features with those presented in Fig. 12 are also observed in the fatigue failure specimen, as shown in Fig. 13, in which the further increase in the slip band density characterized by more activated slip systems and smaller interband spacing of the slip band and the further increase in the amount of the strain-induced martensite are, more or less, visible. The substructure formed in the fatigue failure specimens of 304 stainless steel has also been characterized by TEM in this study. Fig. 14 shows the representative dislocation structure presented in the specimens cycled to the end of fatigue life at a strain amplitude of 1.0%. In this figure, in addition to some dislocation pile-ups and microtwins observed, a well-developed cellular dislocation network is found to be dominant in the austenite matrix. As suggested by Jin et al. [25], these well-developed cells must be the result of dislocations from different slip systems interacting and trapping each other at intersecting regions. The cellular structure penetrated by individual striations with parallel orientation in the austenite matrix indicates the strain-induced martensite transformation from grain to grain. 3.5. Fracture features at various fatigue damage stages Fig. 15 shows typical SEM observations on the fracture surface of 304 stainless steel specimens subjected to various numbers of
precycles followed by monotonic tension to fracture, where the fractography of uncycled specimen was also presented as a comparison. It is seen in Fig. 15a that in the case of the uncycled specimen the tension fracture surface comprises a high population of micro-voids with wide range of sizes and large and deep dimples, indicative of a high-ductile nature in the virgin material. When the specimen undergone 25% of the fatigue fracture life, an embryonic cleavage-like feature characterized by the formation of crystallographic facets connected with ductile bridge is, more or less, visible on the fracture surface, although the dimpled or microvoid coalescence appearance is still dominant (see Fig. 15b). For the specimen subjected to 50% of the fatigue fracture life, a multitude of quasi-cleavage facets with isolated steps in grain interior and small amount of ductile dimples at grain boundaries, are clearly observed on the fracture surface (Fig. 15c). These features basically indicate occurrence of brittle modes of fracture at local regions probably originating from presence of brittle phase in the cyclically pre-deformed specimen [19]. Such mixed brittle/ductile fracture feature becomes more pronounced for the specimen undergone 80% of the total number of cycles to fracture, as seen in Fig. 15d. The fatigue fracture surface exhibits extensive micro-cracks with a typical transgranular appearance on well-defined striations, as seen in Fig. 15e. Some isolated planar facets are also observed in the crack propagation region (Fig. 15f). Crack propagation occurred by a striation-forming mechanism indicates some cyclic cleavage fracture feature. The above microscopic fracture observations thus indicate that, with increasing number of precycles, the fracture mode in 304 stainless steel specimens takes place distinct ductile-to-brittle transition (DBT), which well accords with the progressive loss in the ductility during fatigue damage process of the stainless steel presented in the previous section.
4. Discussions The variation in the static mechanical property parameters of 304 stainless steel during low-cycle fatigue, as presented in the previous section, essentially comes from the complex submicroscopic and microscopic evolution in the structure in the course of fatigue failure. In the initial state of the stainless steel, the grain structure displays complete austenite without martensitic transformation product (Fig. 1), and the dislocation substructures exhibit a low-dislocation density (Fig. 2). While the specimen is subjected to cyclic straining, the unpinning and multiplication of dislocations as well as the mutual interactions of dislocations and the interactions of dislocations with grain and twin boundaries increases the resistance to plastic deformation, which may be responsible for the initial increase in the strength parameters ( ys and ult ), as shown in Fig. 7. The nucleation of the localized slip bands (see Fig. 11a) can be considered as an indication of this early evolution of the deformation microstructures. The repeated plastic straining also results in the depletion of the inherent ductility in the material that gives rise to the decrease in the ductile parameters (ı and ϕf ), as shown in Fig. 9. According to the Schaeffler diagram in Fig. 3, the stainless steel under investigation is structurally metastable at room-temperature and may undergo a partial phase transformation from austenite to martensite during cyclic deformation. It has been indicated by numerous investigations [8–12] that, during cycling of metastable steels, the deformation-induced phase transformation not only depends on the plastic strain amplitude, but also relies on its accumulative value. For a given strain amplitude, there exists a critical value of the cumulative plastic strain necessary to initiate the martensitic transformation in the austenitic matrix [11,12]. Investigation of the influence of the martensitic transformation on the fatigue mechanical behavior of metastable
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Fig. 15. Fractographies of specimens subjected to various cyclic fractions (N/Nf5 ) at 1.0% strain amplitude followed by tensioning to fracture: (a) N/Nf5 = 0; (b) N/Nf5 = 25%; (c) N/Nf5 = 50%; (d) N/Nf5 = 80%; (e) and (f) N/Nf5 = 1.0.
stainless steels also revealed that the formation of the martensite led to a substantial cyclic hardening in the materials [10,11,17]. A direct correlation between the martensitic transformation and hardening was established by measurements of the volume fraction of the martensite during fatigue tests of 300 series stainless steels [10,11,19,20]. In the present study, a well-defined martensitic structure has been observed in austenitic grains after the specimen undergone 5% of the fatigue fracture life (see Fig. 11b).
This microstructural observation thus suggests that for 304 stainless steel investigated, only a small amount of cumulative plastic strain might induce the martensitic transformation during cyclic deformation. To verify this suggestion, the degree of cyclic hardening defined by ( a − ys ) is plotted as a function of the accumulated plastic strain (4 εpa ) in Fig. 16, where a is the stress amplitude, and ys is the yield stress. It is visible in this figure that when the accumulated plastic strain reaches a value found to be
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Fig. 16. Dependence of the degree of cyclic hardening on the accumulated plastic strain.
Fig. 17. Typical indentation load–penetration depth (P–h) curves for austenitic and martensitic phases.
about 0.5 for 1.0% strain amplitude and 1.0 for 0.6% strain amplitude, the secondary strong hardening takes place. These values of the cumulative plastic strain, dependent on the applied strain amplitude, mostly correspond to the formation of the martensite in the present stainless steel in accordance with the investigation by Smaga et al. [12]. In order to discern the relative differences of the local mechanical properties between austenite and martensite, the depth-sensing indentation (DSI) testing has been performed in this study. In doing so, an instrumented indentation with a Vickers indenter was utilized under a load of 500 mN to measure the indentation hardness (HV) as well as the residual depth of penetration after complete unloading (hr ) for each constitutive phase. The DSI tests were carried out according to ISO 14577-1. The indentation hardness (HV) is defined as the ratio between the maximum force (Pmax ) and the surface area of indentation (A) in accordance with ISO 6507-1. As it is indicated [26], HV represents the resistance to plastic deformation and hr characterizes the ability of plasticity in a material. Table 4 summarizes the measured values of HV and hr as well as their mean values of two constitutive phases. Fig. 17 shows typical indentation load–penetration depth (P–h) curves for both austenitic and martensitic structures. For the sake of clarity, only one curve for each phase is presented in this figure. It follows from Table 4 that the deformation resistance of the martensite is almost two times greater than that of the austenite, while the plasticity of the martensite is obviously less than that of the austenite. From the indentation load–penetration depth (P–h) curves, the strain hardening exponent (n) of two constitutive phases can also be estimated approximately by using the approach suggested by Dao et al. [27], which has also been listed in Table 4. The estimated values of n in Table 4 indicate that the martensitic phase possesses a less strain hardening ability in comparison with the austenitic
phase. From the above investigations, it can thus be deduced that for the present stainless steel, accompanied by the formation of the martensite in austenitic matrix, the strength parameters ( ys and ult ) will increase considerably due to the strengthening effect of the martensite, while the ductility parameters (ı and ϕf ) as well as the strain hardening exponent (n) will decrease substantially as a result of fact that the martensitic phase possess a less plasticity and strain hardening ability compared to the austenitic phase. This behavior is expected to further develop with increasing amount of martensite in the austenitic matrix by increasing the number of straining cycles. Therefore, in accordance with the numerous investigation conclusions [10,11,19,20], the formation of the martensite will be responsible for the two-stage changing behavior observed in the strength, ductility and strain hardening ability of the present austenitic stainless steel (Figs. 7, 9 and 10). In addition to the strengthening effect of the martensitic transformation, the increase of the slip band density with straining cycles, as seen in Figs.11a through 13a, will also contribute to the increasing behavior of the strength property during cyclic deformation according to Ashby’s model [28], f = y0 + (1 − /d)(K1 /d) + (/d)(K2 −1/2 ), where f is the flow stress, y0 the friction stress, the slip length, d the grain diameter, and K1 and K2 are constants. From this model an inverse proportional relation between the flow stress ( f ) and slip length () can be deduced when the slip band density become very large and the slip length approaches zero. Since the martensitic phase possesses a high strength, when the initiated micro-cracks encounter the hard martensitic phase, it is liable to progress in a brittle manner exhibiting the quasi-cleavage facets as observed on the fracture surface of the cyclically pre-deformed specimens (see Fig. 15c and d). In other words, brittle behavior is promoted due to the formation of the martensite in the austenitic stainless steel. Therefore, the tension fracture of the cyclically pre-deformed specimens tends to occurring ductile-to-brittle transition (DBT) features with increasing number of precycles and hence greater deformation-induced martensite, as shown in Fig. 15. The physics of metals [2] points out that the modulus of elasticity (E) is only determined by the binding force between atoms and cannot be changed without changing the basic nature of the material. The progressive decrease in E during cycling, as shown in Fig. 8, is thus attributed to the destruction of local ordered atomic arrangement in the material as well as the formation of point defects such as vacancies and interstices, and the formation of new free surface such as voids and cracks internal and external the specimens in the
Table 4 Summary of the measured values from the DSI tests. Measurement
Austenite
Martensite
HV 0.05
hr (m)
n
HV 0.05
hr (m)
n
1 2 3 4 5
261.2 226.1 244.2 269.7 253.9
2.7 2.72 2.47 2.39 2.48
0.365 0.364 0.366 0.366 0.366
430.8 443.1 430.2 442.7 456.4
1.91 1.87 2.11 1.96 1.88
0.321 0.321 0.322 0.321 0.32
Mean value
253.9
2.48
0.366
456.4
1.88
0.321
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Fig. 18. Variation of the static toughness (Ut ) with straining cycles.
Fig. 19. Synthetical comparison of the normalized static mechanical property parameters (εa = 1.0%; Nf5 = 184).
course of fatigue failure [4–6]. The above fatigue damage evolution process reduces the load-carrying area of the cyclically deformed specimen that results in the reduction in the stiffness property of the stainless steel. The inverse correlation between the strength parameters ( ys and ult ) and ductility parameters (ı and ϕf ) during fatigue damage process, as observed in the present study, has also been reported to be characteristic for the metastable stainless steels subjected to cyclic loading [17–20]. The austenitic/martensitic transformation during cyclic deformation would be responsible for this inverse performance [19,20]. In the case of engineering structures operating under alternating loading, the increase in the strength is beneficial due to its strengthening the material and hence reducing the plastic deformation, while the progressive loss in the ductility is detrimental due to its promoting the brittle behavior in the material. This synthetical effect of the strength and ductility on the material property can also be represented by a single parameter, static toughness (Ut ) defined as the total area under the tensile stress–strain plot [2]. This parameter characterizes the ability of a material to absorb energy in the process of deformation and fracture and is an important property of a material in the resistance to fracture. Generally, Ut can be determined directly by integrating the area of the tensile stress–strain plot. For the purpose of engineering approximative calculation, it can also be determined by the following simplified expression [1]: Ut =
ys + ult ·ı 2
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(1)
It follows from the above equation that the static toughness is a composite mechanical property relating both the strength and ductility. Fig. 18 shows Ut , determined by integrating the tensile stress–strain plots, as a function of the number of straining cycles. It is seen in this figure that for the majority of fatigue life Ut exhibits an insignificant decreasing behavior, and only by the end of fatigue failure, it displays sharp decrease up to final exhaustion. This result indicates that for 304 stainless steel investigated, although both the strength and ductility parameters are sensitive to the cyclic straining history, their composite parameter, the static toughness, is an insensitive mechanical property to the fatigue damage evolution process. The mechanical properties of a material in monotonic loading are of interest in fatigue damage analysis and evaluation as they can be measured in relatively simple, fast and cheap ways
[29]. According to the continuum damage mechanics (CDM) based on the thermodynamics [4], any physical parameter developing monotonously from initial state to the expiration of fatigue life can be used as a scale for the degree of fatigue damage. This physical parameter is called ‘damage indicating parameter’. In terms of the CDM, for the present investigated stainless steel, the stiffness parameter (E), ductility parameters (ı and ϕf ) and strain hardening exponent (n) as well as the composite mechanical parameter, the static toughness (Ut ), can be chosen as the damage indicating parameters, since they decrease monotonously with straining cycles, as obtained experimentally in this study. Generally, an appropriate damage indicator parameter should further satisfy the following features, i.e., it is consistent with the fatigue damage mechanisms, sensitive to fatigue damage process, and can be measured by a simple experimental procedure [4]. In order to compare the sensitivity of the above-mentioned damage indicating parameters to the fatigue damage evolution process, the static mechanical property parameters (E, ı, ϕf , n and Ut ) were expressed by dimensionless ratios with respect to their original values and then plotted against the cyclic fraction in Fig. 19. It follows in this figure that as the cyclic fractions (N/Nf5 ) increase, the ductility parameters (ı, ϕf ) and strain hardening exponent (n) display more sensitive changing characteristics than the stiffness parameter (E) and the composite mechanical parameter, the static toughness (Ut ). Since the depletion of the ductility during fatigue failure process reveals the deterioration of the inherent material property due to fatigue damage evolution, and according to the ‘exhaustion of ductility’ model [29], the depletion of the ductility can be further related to the summation of cyclic plastic strain that is ultimately responsible for fatigue damage [29], it is then suggested from the present investigation that for 304 stainless steel, it would be a promising way to study the fatigue damage mechanics model as well as the residual fatigue life prediction method on the basis of the depletion of the ductility during fatigue damage process. Such investigation is being carried out and will be presented elsewhere. 5. Conclusions The investigation regarding the effects of low-cycle fatigue damage on the static mechanical properties, deformation microstructures and fracture behavior of 304 austenitic stainless steel at room-temperature leads to the following conclusions:
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1. During low-cycle fatigue process, the strength parameters ( ys and ult ) exhibit initial slight increase followed by strong increase without reaching their saturated values, which well corresponds to the two-stage cyclic hardening behavior, while the ductile parameters (ı and ϕf ) as well as the strain hardening exponent (n) present two-stage descending characteristic features. The modulus of elasticity (E) displays a progressive decrease, as a whole, with the increase of precycles. 2. The synthetical effect of the strength and ductility on the material property can be represented by a single parameter, static toughness (Ut ). It is shown that during fatigue damage process Ut exhibits an insignificant decrease for the majority of fatigue life, and only by the end of fatigue failure it displays a sharp decrease up to exhaustion. This means that the composite parameter of the strength and ductility, the static toughness, is an insensitive mechanical property to the fatigue damage evolution process. 3. With increasing number of straining cycles, both the number of grains containing slip bands and the slip band density within the grains tend to increase, and the amount of the deformationinduced austenisite/martensite transformation also exhibits increase. The critical value of the cumulative plastic strain to initiate the martensite in austenitic matrix is found to be about 0.5 for 1.0% strain amplitude and 1.0 for 0.6% strain amplitude. It is shown by the depth-sensing indentation (DSI) tests that the deformation resistance of the martensite is almost two times greater than that of the austenite, while the plasticity of the martensite is obviously less than that of the austenite. The strain hardening exponent (n) estimated from the indentation load–penetration depth (P–h) curves also indicates that the martensitic phase possesses a less strain hardening ability in comparison with the austenitic phase. 4. As the number of precycles increases, the tension fracture exhibits distinct ductile-to-brittle transition (DBT) feature. This change in the fracture mode is mostly attributed to the evolution of deformation microstructures, especially the deformationinduced martensitic transformation, during low-cycle fatigue process. 5. It is shown that the ductility parameters exhibit a sensitive changing character to the fatigue damage evolution process and can thus be chosen as the damage indicating parameter. Based on the macro/micro-experimental results of the present investigation, it is suggested that for 304 stainless steel it would be a promising way to study the fatigue damage mechanics model as well as the residual fatigue life prediction method on the
basis of the depletion of the ductility during fatigue damage process. Acknowledgements The authors would like to express their sincere thanks for the financial support of ‘National Natural Science Foundation of China (NSFC)’ under Grant 50975254 and 10572126 as well as ‘National High-Tech Research Development Project (863) of China’ under Grant 2006AA04Z419 and 2009AA044801 in completion of this research work. The first author also wishes to thank Dr. Zhiying He for her valuable discussions in preparing this manuscript. References [1] H.E. Boyer, Atlas of Stress–Strain Curves, ASM International, Metal Park, Ohio, 1987. [2] S. Wole, Mechanical Properties of Engineered Materials, Marcel Dekker, Inc., 2003. [3] J. Lemaitre, J. Dufailly, Eng. Fract. Mech. 28 (1987) 643. [4] J. Lemaitre, J. Dufailly, Engineering Damage Mechanics, Springer, Berlin/Heidelberg/New York, 2004. [5] D. Ye, Z. Wang, Int. J. Fatigue 23 (2001) 85. [6] D. Ye, Z. Wang, Int. J. Fatigue 23 (2001) 679. [7] R.C. Covind, D.A. Stephen, Metall. Trans. 5 (1974) 217. [8] G. Baudry, A. Pineau, Mater. Sci. Eng. 28 (1977) 229. [9] H.-J. Bassler, D. Eifler, Low Cycle Fatigue and Elasto-Plastic Behavior of Materials, Elsevier Science Ltd., 1998, 285. [10] R.G. Teteruk, H.J. Maier, H.-J. Christ, Low Cycle Fatigue and Elasto-Plastic Behavior of Materials, Elsevier Science Ltd., 1998, 321. [11] K. Bhanu, S. Rao, M. Valsan, R. Sandlya, S.L. Mannan, P. Rodrignez, Metall. Trans. A 24 (1993) 913. [12] M. Smaga, F. Rao, Walther, D. Eifler, Mater. Sci. Eng. A 483–484 (2008) 394. [13] M.R. Bayoumi, A.K. Abd Ellatif, J. Mater. Sci. 30 (1995) 3944. [14] D. Ye, S. Matsuoka, N. Nagashima, N. Suzuki, Mater. Sci. Eng. A 445 (2006) 104. [15] M. Klesnil, P. Lukáˇs, Fatigue of Metallic Materials, Elsevier, Amstardam/Oxford/New York, 1980. [16] H.J. Leber, M. Niffenegger, B. Tirbonod, Mater. Charact. 58 (2007) 1006. [17] D. Hennessy, G. Steckel, C. Altstetter, Metall. Trans. A 7 (1976) 415. [18] M. Topic, R.B. Tait, C. Allen, Int. J. Fatigue 29 (2007) 656. [19] S. Biswas, S. Sivaprasad, N. Narasaish, S. Tarafder, P.C. Chakraborti, Int. J. Fatigue 29 (2007) 786. [20] M. Bayerlein, H.J. Christ, H. Mughrabi, Mater. Sci. Eng. A 114 (1989) L11. [21] D.P. Harvey, R.J. Bonenberger, J.M. Wolla, Int. J. Fatigue 20 (1998) 291. [22] T. Arahori, M. Ninomi, K. Fukunaga, Metall. Trans. 31A (2000) 1937. [23] D. Ye, Z. Wang, Mater. Sci. Eng. A 297 (2001) 54. [24] D. Ye, Int. J. Fatigue 27 (2005) 1102. [25] N.Y. Jin, C. Zhong, X. Chen, Metall. Mater. 38 (1990) 2141. [26] D. Ye, S. Matsuoka, N. Nagashima, Mater. Sci. Eng. A 456 (2007) 120. [27] M. Dao, N. Chollacoop, K.J. Van Vliet, T.A. Venkatesh, S. Suresh, Acta Mater. 49 (2001) 3899. [28] M.F. Ashby, Philos. Mag. 21 (1970) 299. [29] B.I. Sandor, Fundamentals of Cyclic Stainless and Strain, The University of Wisconsin Press, Ltd., 1972.
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Effects of low-cycle fatigue on static mechanical properties, microstructures and fracture behavior of 304 stainless steel Duyi Ye ∗ , Yuandong Xu, Lei Xiao, Haibo Cha Institute for Process Equipments, Zhejiang University, Hangzhou 310027, China
a r t i c l e
i n f o
Article history: Received 27 September 2009 Received in revised form 3 March 2010 Accepted 8 March 2010
Keywords: Static mechanical properties Low-cycle fatigue Microstructures Fracture behavior Martensitic transformation
a b s t r a c t A series of experiments, including constant amplitude low-cycle fatigue tests, post-fatigue tension to failure tests, LOM (TEM) observations, and SEM examinations, were performed at room-temperature to investigate the effects of low-cycle fatigue damage on the static mechanical properties, microstructures and fracture behavior of 304 austenitic stainless steel. The changing characteristics of various static mechanical property parameters, including the strength parameters ( ys and ult ), stiffness parameter (E), ductility parameters (ı and ϕf ) and strain hardening exponent (n) during fatigue damage process of the stainless steel were obtained experimentally and their micromechanisms were discussed by analyzing both the deformation microstructures and the fracture features of cyclically pre-deformed specimens. It was shown that the austenite/martensite transformation resulting from the accumulation of cyclic plastic strain was mostly responsible for the variation in the strength, ductility and strain hardening ability of the stainless steel during fatigue damage process. The depletion of the inherent ductility in the material due to fatigue damage evolution led to the ductile-to-brittle transition (DBT) in the fracture modes. Based on the macro/micro-experiments regarding the exhaustion of the ductility during fatigue damage, the ductility parameter was suggested as a damage indicating parameter for the present stainless steel in further studying the fatigue damage mechanics model as well as the residual fatigue life prediction method. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Static mechanical properties of a material, such as the elastic modulus, yield strength, ultimate tensile strength, elongation and reduction in area provide the most fundamental parameters for the structural design, particularly in the stress calculation and strength analysis of structural components and elements. It has been indicated [1,2] that these material properties not only depend on various metallurgical factors, such as grain size, alloying element, quenching, aging, and annealing, but also are intensively influenced by service conditions including the loading history, state of stress imposed, environment, temperature, etc. In the case of engineering structures operating under dynamic or alternating loading conditions, a notable character is that their service properties, especially the mechanical properties, deteriorates progressively with the service times. This degradation in material properties due to alternating loading, also called fatigue damage, seriously affects the service safety of engineering structures or components and thus is an important consideration in their designing against fatigue fail-
∗ Corresponding author at: Institute for Process Equipments, 38 Zheda Road, Hangzhou 310027, Zhejiang, China. Tel.: +86 571 88869213; fax: +86 571 88869213. E-mail address: duyi [email protected] (D. Ye). 0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2010.03.027
ure. On the other hand, the residual fatigue life studies of existing engineering structures in service conditions, generally, involve the evaluation of fatigue damage. Such evaluation is frequently performed by quantitatively measuring the mechanical deterioration of a material, such as the elastic modulus, ultimate tensile strength, hardness, reduction in area and toughness [3–6], in the framework of continuous damage mechanics (CDM). It is accordingly of great practical meaning to investigate the effects of fatigue damage on the static mechanical properties of structural materials as well as the damage evaluation method based on the degradation of material mechanical properties during fatigue damage process. Austenitic stainless steel 304 is an extremely important commercial alloy in engineering applications due to its excellent corrosion resistance, high strength, good ductility and toughness. This alloy is currently being used in industrial installations, such as petrochemical plants, electric-power generating stations and process plants as piping and structural material. In these applications, the components of the structures are often subjected to dynamic or alternating stresses as a result of temperature gradients, which occur on heating and cooling during startups and shutdowns, or during variations in operating conditions. For this reason, evaluation of fatigue damage and the residual fatigue life becomes an important content in their safe designing against fatigue failure. Despite the fact that fatigue mechanical behavior of type 304
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austenitic stainless steel, such as the cyclic stress response, cyclic stress–strain curves (CSSCs) and Coffin–Manson curves have been investigated extensively in the past decades [7–14], relatively few studies, however, have focused on the changing characteristics of the static mechanical properties of this steel during fatigue damage process. As it has been pointed out, the latter would be of great importance for the safe designing against fatigue failure, especially for the prediction of the residual fatigue life of existing structures or components operating under alternating service conditions. This is the motivation of the present study to investigate the effects of low-cycle fatigue damage on the static mechanical properties, deformation microstructures and fractural behavior of type 304 stainless steel. The main purpose of this study, on the one hand, is to gain a more complete understanding of fatigue mechanical properties of this stainless steel so as to use it more effectively in engineering practical applications, on the other hand, to provide an experimental basis for further study of the reliable residual fatigue life prediction method. 2. Experimental details The material used in this investigation is an austenitic 304 stainless steel supplied in the form of a plate, 18 mm in thickness. The plates were hot rolled at 1040 ◦ C for 0.2 h, followed by quenching in water. The chemical composition of the steel in percentage weight is listed in Table 1. The 18 mm plates were then machined into conventional push–pull cylindrical specimens with the tensile axis parallel to the final rolling direction. The nominal dimensions of the specimen in the gauge section were 14.0 mm (length) × 6.0 mm (diameter). Prior to testing, the surface of each specimen was mechanically polished to a final roughness of ∼0.4 m. Tests for the present investigation purpose consist mainly of (i) constant amplitude low-cycle fatigue tests to produce specimens with various amounts of cyclic pre-deformation or fatigue damage, and (ii) uniaxial tension to fracture tests to measure the post-fatigue static mechanical property parameters. Details of testing procedures are described as follows. Fully reversed, push–pull, total strain amplitude controlled fatigue tests were performed at room temperature in an ambient air using a 250 kN closed-loop servohydraulic testing system. A triangular strain waveform with zero mean strain (R = −1) at a ˙ of 5 × 10−3 S−1 was used. The strain constant total strain rate (ε) amplitudes (εa ) chosen for the present fatigue testing were 0.6% and 1.0%, resulting in the fatigue life (Nf5 ) 184 and 2280, respectively. In this study, the fatigue life (Nf5 ) was defined as the cycles corresponding to 5% drop in the maximum stress amplitude, which was related to the growth of the macro cracks. Cyclic tests were interrupted at various chosen fatigue life fractions (N/Nf5 ) at each of strain amplitudes before fracture to produce specimens with various amounts of cyclic pre-deformation. At each strain amplitude, fatigue tests were conducted at least with 15–20 different cyclic fractions. During testing, the load was continuously monitored and hysteresis loops were recorded at appropriate intervals. After the cycling, the specimens were returned to the state of zero stress and zero strain and then loaded in monotonic tension to fracture with a strain rate of 3.0 × 10−5 S−1 . Cyclically pre-deformed specimens were first pulled to a certain strain level in a strain control mode to measure the modulus of elasticity (E) and 0.2 pct proof stress ( ys ), and then tensioned up to fracture in a dis-
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placement control mode to measure the ultimate tensile strength ( ult ), the elongation (ı) and the reduction in area (ϕf ), respectively. The strain hardening exponent (n) was determined from the power-law that relates stress and plastic strain [15], = Kεnp , where K is the strength coefficient, together with the measured data. During tension, the load–displacement plots were recorded continuously. Microstructural changes during low-cycle fatigue process were examined using a light optical microscopy (LOM) and a transmission electron microscopy (TEM). In the case of LOM, the deformation microstructures formed at various stages of the fatigue damage process were examined, while in the case of TEM only the fatigue fracture microstructures were observed. Samples for the microstructural examinations were prepared below the fractured surface in the fatigue failure specimens and taken from the gauge portions in the cyclically pre-deformed specimens by cutting perpendicular to the tensile axils. LOM samples were first mechanically polished using emery papers of various grinds from 230 to 600 grit and then using 1.5 m diamond paste to a final roughness of ∼0.1 m. To reveal the grains, etching for 30 s was used in a mixed solution of 16 vol% of HNO3 , 32 vol% of HCl and 50 vol% of glycerol at 313 K. TEM samples were mechanically thinned to 30 m or less from the initial thickness of about 0.3 mm, and then thinned to perforation by a twin-jet electrochemical polisher. The TEM foils were examined in a HITACH H9000NA transmission electron microscope. Fracture surfaces of both the fatigue failure specimens and the post-fatigue tension to fracture specimens were observed using a scanning electron microscope (SEM). SEM examinations were performed with a SIRION-100 scanning electron microscopy operating at 25 kV. 3. Experimental results 3.1. Initial microstructures and tensile properties The optical microscopy of 304 stainless steel in the as-received condition, as shown in Fig. 1, reveals that the initial grain structure consists of equiaxed austenitic grains with a few straight annealing twins and small elongated delta-ferrite. Fig. 2 shows a TEM micrograph of the virgin material, indicating that the initial dislocation structures have in general low density and consist of primary dislocations having predominantly screw character (either completely straight or with bowed segments) and small loops. Both
Table 1 Chemical composition of 304 stainless steel in wt.%. C
Si
Mn
S
P
Cr
Ni
Mo
N
0.015
0.53
1.64
0.0048
0.03
18.27
8.16
0.02
0.049
Fig. 1. Optical micrograph of 304 austenitic stainless steel in the as-received condition.
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Fig. 2. TEM micrograph of 304 austenitic stainless steel in the as-received condition. Fig. 4. Typical cyclic stress response of 304 stainless steel.
LOM and TEM observations display no metallographic evidence of martensitic transformation in the initial state of the stainless steel. According to Schaeffler diagram [16], steels with compositions in the range where austenite, delta-ferrite and martensite are in equilibrium can be expected to become unstable during plastic deformation by nucleation of martensite. The susceptibility to martensitc transformation for the present stainless steel was estimated using Schaeffler diagram by calculating its chromium and nickel equivalents, as illustrated in Fig. 3. It appears in this figure that the stabilized grade of 304 stainless steel is located in the twophase region of martensite + austenite, indicating thereby that the martensitic transformation may take place in the present material when the other factors, such as temperature, strain, strain rate and stress state are satisfied. Table 2 lists the monotonic tensile properties of the virgin 304 stainless steel at room-temperature. The results reported are the mean values based on multiple (three) tests. The yield strength ( ys ) defined as the stress corresponding to a plastic strain of 0.2% is 259.8 MPa. The ultimate tensile strength ( ult ) is 750.3 MPa. The large difference between the yield strength and the ultimate tensile strength indicates a significant amount of work hardening in
Fig. 3. Position of 304 austenitic stainless steel grade in the Schaeffler diagram.
the virgin material during monotonic deformation. The elongation to failure and reduction in area were 69.1% and 65.1%, respectively, indicative of a high ductility in the initial state of the austenitic stainless steel. 3.2. Stress response during low-cycle fatigue The stress response curves of 304 stainless steel, cycled at two strain amplitudes investigated, are shown in Fig. 4. It is visible in this figure that during fatigue damage process, the material exhibits an initial small hardening followed by a great hardening up to final failure. The period of the second great hardening leads even to an inflexion on the stress response curves. This inflexion occurs later with a small applied strain amplitude. The above-present two-stage cyclic hardening characters provide useful information pertaining to the mechanical stability of the stainless steel during low-cycle fatigue and will help to understand the micromechanisms responsible for the variation of the static mechanical properties during fatigue damage process, which will be present subsequently.
Fig. 5. Typical post-fatigue tensile plots of stress vs. strain of 304 stainless steel.
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Table 2 Mechanical properties of the virgin 304 stainless steel. 0.2% proof stress, ys (MPa)
Ultimate tensile strength, ult (MPa)
Elongation, ı (%)
Reduction of area, ϕf (%)
259.8
750.3
69.1
65.1
3.3. Static mechanical properties at various fatigue damage stages Typical post-fatigue tensile plots of stress vs. strain, obtained from 304 stainless steel specimens subjected to various numbers of precycles at the constant strain amplitude εa = 1.0%, followed by monotonic tension to fracture, are shown in Fig. 5, where the tensile plot of the virgin specimen is also present for comparative purposes. Fig. 6 gives out a set of these tension to fracture specimens.
It is obvious in Fig. 5 that for the present austenitic stainless steel the prior cyclic straining history remarkably influences its subsequent tensile stress–strain behavior. The applied previous straining cycles results in an intensive increase in the tensile stress response, but a distinct decrease in the total elongations to failure. As the precycles increased, the slope in the rising portion of the tensile plots that is a measure of the strain hardening appears progressive decrease and the tensile plots become relative flat beyond the yield strength. The reduction in the total elongation to failure resulting from cyclic pre-deformation can also be inferred from the observation of the tension to fracture specimens shown in Fig. 6, where the final length of the fractured specimens tends to decrease and the necking phenomenon of the specimens becomes unapparent as the precycles increased. The variation of the various static mechanical property parameters of 304 stainless steel during fatigue damage process at two strain amplitudes investigated, is exhibited in Figs. 7–10, where the solid and dashed lines present, respectively, the changing trends of the individual mechanical property at each strain amplitude. Table 3 summarizes a set of typical post-fatigue static mechanical property parameters of the stainless steel specimens, in which the monotonic tensile properties of the virgin specimen were also listed for comparison purpose. Table 3 Typical measured data of post-fatigue static mechanical property parameters of 304 stainless steel specimens (εa = 1.0%).
Fig. 6. Post-fatigue tensile fracture specimens: (1) N = 0; (2) N = 10; (3) N = 20; (4) N = 30; (5) N = 50; (6) N = 100; (7) N = 150; (8) N = 184.
N (cycles)
E (GPa)
0.2 (MPa)
ult (MPa)
n
ı (%)
ϕf (%)
0 3 10 20 30 50 70 100 120 150 184
200.3 196.7 192.4 191.6 175.1 188.1 161.0 177.3 174.8 180.1 156.9
259.8 276.2 326.8 366.4 451.5 550.8 617.7 685.2 721.3 749.9 740.8
750.3 764.5 791.1 791.1 819.9 856.5 894.0 933.2 970.1 957.2 935.9
0.23 0.22 0.23 0.2 0.19 0.18 0.15 0.14 0.13 0.08 0.007
69.1 68.3 69.1 60.3 57 55.8 52.5 47.1 45.8 42.1 15.3
65.1 61.9 61.7 59.5 61.0 59.2 53.4 46.7 41.0 40.2 16.2
Fig. 7. Variation of the strength parameters ( ys and ult ) with straining cycles. (a) 0.2 pct proof stress ( ys ) and (b) Ultimate tensile strength ( ult ).
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Fig. 8. Variation of the modulus of elasticity (E) with straining cycles.
Note in Fig. 7 that under cyclic straining both ys and ult exhibit initial slight increase followed by strong increase almost without reaching their saturated values. This changing character in the strength parameters well corresponds to the two-stage cyclic hardening behavior in Fig. 4. Data analyse, in Table 3, further indicates that the straining cycles to failure enhance ys and ult by around 3 and 1.2 times, respectively, as compared to those of the virgin specimen. This means that for 304 austenitic stainless steel the strength is a sensitive mechanical property to the cyclic straining history. The modulus of elasticity (E) that is a measure of the stiffness property of a material appears a progressive decrease, as a whole, with the increase of straining cycles (Fig. 8). In contrast to the two-stage increasing character in the strength parameters, the ductile parameters (ı and ϕf ) exhibit two-stage descending behavior in the course of fatigue failure, as shown in Fig. 9. In this figure an initial slight decrease followed by a drastic decrease up to final exhaustion in both ı and ϕf is clearly visible. Such inverse correlation between the strength parameters and the ductility parameters observed in the present stainless steel has also been reported for other metastable steels subjected to fatigue loading [17–20]. It is also obtained in Fig. 9 that the ductility parameters are sensi-
Fig. 10. Variation of the strain hardening exponent (n) with straining cycles.
tive to the fatigue damage evolution process. As shown in Fig. 10, the strain hardening exponent (n) displays a two-stage descending character as well during fatigue damage process. Thus the cyclic pre-deformation can deplete significantly the ability to strain hardening of the stainless steel. The above-present changing characteristics of the static mechanical properties of 304 stainless steel during low-cycle fatigue were also obtained in studies of the effects of cyclic pre-deformation on tensile properties of other metallic materials, such as structural steels and nickel-based superalloys [21–24]. 3.4. Microstructures at various fatigue damage stages The microstructure formed in 304 stainless steel at various stages of fatigue damage process has been examined using LOM. Figs. 11–13 show typical optical micrographs of the stainless steel specimens subjected to 5%, 25% and 100% of the fatigue fracture life, respectively, at a total strain amplitude of 1.0%. It is obvious in Fig. 11a that, after 5% of the fatigue fracture life, the grains generally contained a few slip bands and slip is
Fig. 9. Variation of the ductility parameters (ı and ϕf ) with straining cycles. (a) elongation (ı) and (b) reduction in area (ϕf ).
D. Ye et al. / Materials Science and Engineering A 527 (2010) 4092–4102
Fig. 11. Optical micrograph of the specimen subjected to 5% of the fatigue life at εa = 1.0%: (a) slip band features and (b) different morphologies of martensite.
Fig. 12. Optical micrograph of the specimen subjected to 50% of the fatigue life at εa = 1.0%: (a) slip band features and (b) different morphologies of martensite.
Fig. 13. Optical micrograph of the specimen cycled to the end of fatigue life at εa = 1.0%: (a) slip band features and (b) different morphologies of martensite.
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Fig. 14. TEM micrograph of the specimen cycled to the end of fatigue life at εa = 1.0%.
mostly restricted to one system. In some austenitic grains, martensitic phase with different morphologies has already been observed, as shown in Fig. 11b. It is also visible in this figure that at the initial stages of cyclic deformation the distribution of martensitic phase is highly inhomogeneous in austenitic matrix. The above microstructural observation indicates that for the present investigated stainless steel even a small number of straining cycles or a small amount of cumulative plastic strain has resulted in a phase transformation from austenite to martensite. When the specimen subjected to 50% of the fatigue life, in addition to the localized single slip bands, multiple slip modes with intersecting bands on different planes, penetrating the whole austenitic grains, are found commonly in the cyclically deformed specimen (Fig. 12a). Meanwhile, the nucleation of martensite has frequently been observed over several austenitic grains, as seen in Fig. 12b. From this microstructural observation, it can be recognized that with increasing number of straining cycles, not only the density of slip band, but also the volume fraction of the strain-induced martensite increases considerably in the cycled specimen. Similar microstructural features with those presented in Fig. 12 are also observed in the fatigue failure specimen, as shown in Fig. 13, in which the further increase in the slip band density characterized by more activated slip systems and smaller interband spacing of the slip band and the further increase in the amount of the strain-induced martensite are, more or less, visible. The substructure formed in the fatigue failure specimens of 304 stainless steel has also been characterized by TEM in this study. Fig. 14 shows the representative dislocation structure presented in the specimens cycled to the end of fatigue life at a strain amplitude of 1.0%. In this figure, in addition to some dislocation pile-ups and microtwins observed, a well-developed cellular dislocation network is found to be dominant in the austenite matrix. As suggested by Jin et al. [25], these well-developed cells must be the result of dislocations from different slip systems interacting and trapping each other at intersecting regions. The cellular structure penetrated by individual striations with parallel orientation in the austenite matrix indicates the strain-induced martensite transformation from grain to grain. 3.5. Fracture features at various fatigue damage stages Fig. 15 shows typical SEM observations on the fracture surface of 304 stainless steel specimens subjected to various numbers of
precycles followed by monotonic tension to fracture, where the fractography of uncycled specimen was also presented as a comparison. It is seen in Fig. 15a that in the case of the uncycled specimen the tension fracture surface comprises a high population of micro-voids with wide range of sizes and large and deep dimples, indicative of a high-ductile nature in the virgin material. When the specimen undergone 25% of the fatigue fracture life, an embryonic cleavage-like feature characterized by the formation of crystallographic facets connected with ductile bridge is, more or less, visible on the fracture surface, although the dimpled or microvoid coalescence appearance is still dominant (see Fig. 15b). For the specimen subjected to 50% of the fatigue fracture life, a multitude of quasi-cleavage facets with isolated steps in grain interior and small amount of ductile dimples at grain boundaries, are clearly observed on the fracture surface (Fig. 15c). These features basically indicate occurrence of brittle modes of fracture at local regions probably originating from presence of brittle phase in the cyclically pre-deformed specimen [19]. Such mixed brittle/ductile fracture feature becomes more pronounced for the specimen undergone 80% of the total number of cycles to fracture, as seen in Fig. 15d. The fatigue fracture surface exhibits extensive micro-cracks with a typical transgranular appearance on well-defined striations, as seen in Fig. 15e. Some isolated planar facets are also observed in the crack propagation region (Fig. 15f). Crack propagation occurred by a striation-forming mechanism indicates some cyclic cleavage fracture feature. The above microscopic fracture observations thus indicate that, with increasing number of precycles, the fracture mode in 304 stainless steel specimens takes place distinct ductile-to-brittle transition (DBT), which well accords with the progressive loss in the ductility during fatigue damage process of the stainless steel presented in the previous section.
4. Discussions The variation in the static mechanical property parameters of 304 stainless steel during low-cycle fatigue, as presented in the previous section, essentially comes from the complex submicroscopic and microscopic evolution in the structure in the course of fatigue failure. In the initial state of the stainless steel, the grain structure displays complete austenite without martensitic transformation product (Fig. 1), and the dislocation substructures exhibit a low-dislocation density (Fig. 2). While the specimen is subjected to cyclic straining, the unpinning and multiplication of dislocations as well as the mutual interactions of dislocations and the interactions of dislocations with grain and twin boundaries increases the resistance to plastic deformation, which may be responsible for the initial increase in the strength parameters ( ys and ult ), as shown in Fig. 7. The nucleation of the localized slip bands (see Fig. 11a) can be considered as an indication of this early evolution of the deformation microstructures. The repeated plastic straining also results in the depletion of the inherent ductility in the material that gives rise to the decrease in the ductile parameters (ı and ϕf ), as shown in Fig. 9. According to the Schaeffler diagram in Fig. 3, the stainless steel under investigation is structurally metastable at room-temperature and may undergo a partial phase transformation from austenite to martensite during cyclic deformation. It has been indicated by numerous investigations [8–12] that, during cycling of metastable steels, the deformation-induced phase transformation not only depends on the plastic strain amplitude, but also relies on its accumulative value. For a given strain amplitude, there exists a critical value of the cumulative plastic strain necessary to initiate the martensitic transformation in the austenitic matrix [11,12]. Investigation of the influence of the martensitic transformation on the fatigue mechanical behavior of metastable
D. Ye et al. / Materials Science and Engineering A 527 (2010) 4092–4102
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Fig. 15. Fractographies of specimens subjected to various cyclic fractions (N/Nf5 ) at 1.0% strain amplitude followed by tensioning to fracture: (a) N/Nf5 = 0; (b) N/Nf5 = 25%; (c) N/Nf5 = 50%; (d) N/Nf5 = 80%; (e) and (f) N/Nf5 = 1.0.
stainless steels also revealed that the formation of the martensite led to a substantial cyclic hardening in the materials [10,11,17]. A direct correlation between the martensitic transformation and hardening was established by measurements of the volume fraction of the martensite during fatigue tests of 300 series stainless steels [10,11,19,20]. In the present study, a well-defined martensitic structure has been observed in austenitic grains after the specimen undergone 5% of the fatigue fracture life (see Fig. 11b).
This microstructural observation thus suggests that for 304 stainless steel investigated, only a small amount of cumulative plastic strain might induce the martensitic transformation during cyclic deformation. To verify this suggestion, the degree of cyclic hardening defined by ( a − ys ) is plotted as a function of the accumulated plastic strain (4 εpa ) in Fig. 16, where a is the stress amplitude, and ys is the yield stress. It is visible in this figure that when the accumulated plastic strain reaches a value found to be
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Fig. 16. Dependence of the degree of cyclic hardening on the accumulated plastic strain.
Fig. 17. Typical indentation load–penetration depth (P–h) curves for austenitic and martensitic phases.
about 0.5 for 1.0% strain amplitude and 1.0 for 0.6% strain amplitude, the secondary strong hardening takes place. These values of the cumulative plastic strain, dependent on the applied strain amplitude, mostly correspond to the formation of the martensite in the present stainless steel in accordance with the investigation by Smaga et al. [12]. In order to discern the relative differences of the local mechanical properties between austenite and martensite, the depth-sensing indentation (DSI) testing has been performed in this study. In doing so, an instrumented indentation with a Vickers indenter was utilized under a load of 500 mN to measure the indentation hardness (HV) as well as the residual depth of penetration after complete unloading (hr ) for each constitutive phase. The DSI tests were carried out according to ISO 14577-1. The indentation hardness (HV) is defined as the ratio between the maximum force (Pmax ) and the surface area of indentation (A) in accordance with ISO 6507-1. As it is indicated [26], HV represents the resistance to plastic deformation and hr characterizes the ability of plasticity in a material. Table 4 summarizes the measured values of HV and hr as well as their mean values of two constitutive phases. Fig. 17 shows typical indentation load–penetration depth (P–h) curves for both austenitic and martensitic structures. For the sake of clarity, only one curve for each phase is presented in this figure. It follows from Table 4 that the deformation resistance of the martensite is almost two times greater than that of the austenite, while the plasticity of the martensite is obviously less than that of the austenite. From the indentation load–penetration depth (P–h) curves, the strain hardening exponent (n) of two constitutive phases can also be estimated approximately by using the approach suggested by Dao et al. [27], which has also been listed in Table 4. The estimated values of n in Table 4 indicate that the martensitic phase possesses a less strain hardening ability in comparison with the austenitic
phase. From the above investigations, it can thus be deduced that for the present stainless steel, accompanied by the formation of the martensite in austenitic matrix, the strength parameters ( ys and ult ) will increase considerably due to the strengthening effect of the martensite, while the ductility parameters (ı and ϕf ) as well as the strain hardening exponent (n) will decrease substantially as a result of fact that the martensitic phase possess a less plasticity and strain hardening ability compared to the austenitic phase. This behavior is expected to further develop with increasing amount of martensite in the austenitic matrix by increasing the number of straining cycles. Therefore, in accordance with the numerous investigation conclusions [10,11,19,20], the formation of the martensite will be responsible for the two-stage changing behavior observed in the strength, ductility and strain hardening ability of the present austenitic stainless steel (Figs. 7, 9 and 10). In addition to the strengthening effect of the martensitic transformation, the increase of the slip band density with straining cycles, as seen in Figs.11a through 13a, will also contribute to the increasing behavior of the strength property during cyclic deformation according to Ashby’s model [28], f = y0 + (1 − /d)(K1 /d) + (/d)(K2 −1/2 ), where f is the flow stress, y0 the friction stress, the slip length, d the grain diameter, and K1 and K2 are constants. From this model an inverse proportional relation between the flow stress ( f ) and slip length () can be deduced when the slip band density become very large and the slip length approaches zero. Since the martensitic phase possesses a high strength, when the initiated micro-cracks encounter the hard martensitic phase, it is liable to progress in a brittle manner exhibiting the quasi-cleavage facets as observed on the fracture surface of the cyclically pre-deformed specimens (see Fig. 15c and d). In other words, brittle behavior is promoted due to the formation of the martensite in the austenitic stainless steel. Therefore, the tension fracture of the cyclically pre-deformed specimens tends to occurring ductile-to-brittle transition (DBT) features with increasing number of precycles and hence greater deformation-induced martensite, as shown in Fig. 15. The physics of metals [2] points out that the modulus of elasticity (E) is only determined by the binding force between atoms and cannot be changed without changing the basic nature of the material. The progressive decrease in E during cycling, as shown in Fig. 8, is thus attributed to the destruction of local ordered atomic arrangement in the material as well as the formation of point defects such as vacancies and interstices, and the formation of new free surface such as voids and cracks internal and external the specimens in the
Table 4 Summary of the measured values from the DSI tests. Measurement
Austenite
Martensite
HV 0.05
hr (m)
n
HV 0.05
hr (m)
n
1 2 3 4 5
261.2 226.1 244.2 269.7 253.9
2.7 2.72 2.47 2.39 2.48
0.365 0.364 0.366 0.366 0.366
430.8 443.1 430.2 442.7 456.4
1.91 1.87 2.11 1.96 1.88
0.321 0.321 0.322 0.321 0.32
Mean value
253.9
2.48
0.366
456.4
1.88
0.321
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Fig. 18. Variation of the static toughness (Ut ) with straining cycles.
Fig. 19. Synthetical comparison of the normalized static mechanical property parameters (εa = 1.0%; Nf5 = 184).
course of fatigue failure [4–6]. The above fatigue damage evolution process reduces the load-carrying area of the cyclically deformed specimen that results in the reduction in the stiffness property of the stainless steel. The inverse correlation between the strength parameters ( ys and ult ) and ductility parameters (ı and ϕf ) during fatigue damage process, as observed in the present study, has also been reported to be characteristic for the metastable stainless steels subjected to cyclic loading [17–20]. The austenitic/martensitic transformation during cyclic deformation would be responsible for this inverse performance [19,20]. In the case of engineering structures operating under alternating loading, the increase in the strength is beneficial due to its strengthening the material and hence reducing the plastic deformation, while the progressive loss in the ductility is detrimental due to its promoting the brittle behavior in the material. This synthetical effect of the strength and ductility on the material property can also be represented by a single parameter, static toughness (Ut ) defined as the total area under the tensile stress–strain plot [2]. This parameter characterizes the ability of a material to absorb energy in the process of deformation and fracture and is an important property of a material in the resistance to fracture. Generally, Ut can be determined directly by integrating the area of the tensile stress–strain plot. For the purpose of engineering approximative calculation, it can also be determined by the following simplified expression [1]: Ut =
ys + ult ·ı 2
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(1)
It follows from the above equation that the static toughness is a composite mechanical property relating both the strength and ductility. Fig. 18 shows Ut , determined by integrating the tensile stress–strain plots, as a function of the number of straining cycles. It is seen in this figure that for the majority of fatigue life Ut exhibits an insignificant decreasing behavior, and only by the end of fatigue failure, it displays sharp decrease up to final exhaustion. This result indicates that for 304 stainless steel investigated, although both the strength and ductility parameters are sensitive to the cyclic straining history, their composite parameter, the static toughness, is an insensitive mechanical property to the fatigue damage evolution process. The mechanical properties of a material in monotonic loading are of interest in fatigue damage analysis and evaluation as they can be measured in relatively simple, fast and cheap ways
[29]. According to the continuum damage mechanics (CDM) based on the thermodynamics [4], any physical parameter developing monotonously from initial state to the expiration of fatigue life can be used as a scale for the degree of fatigue damage. This physical parameter is called ‘damage indicating parameter’. In terms of the CDM, for the present investigated stainless steel, the stiffness parameter (E), ductility parameters (ı and ϕf ) and strain hardening exponent (n) as well as the composite mechanical parameter, the static toughness (Ut ), can be chosen as the damage indicating parameters, since they decrease monotonously with straining cycles, as obtained experimentally in this study. Generally, an appropriate damage indicator parameter should further satisfy the following features, i.e., it is consistent with the fatigue damage mechanisms, sensitive to fatigue damage process, and can be measured by a simple experimental procedure [4]. In order to compare the sensitivity of the above-mentioned damage indicating parameters to the fatigue damage evolution process, the static mechanical property parameters (E, ı, ϕf , n and Ut ) were expressed by dimensionless ratios with respect to their original values and then plotted against the cyclic fraction in Fig. 19. It follows in this figure that as the cyclic fractions (N/Nf5 ) increase, the ductility parameters (ı, ϕf ) and strain hardening exponent (n) display more sensitive changing characteristics than the stiffness parameter (E) and the composite mechanical parameter, the static toughness (Ut ). Since the depletion of the ductility during fatigue failure process reveals the deterioration of the inherent material property due to fatigue damage evolution, and according to the ‘exhaustion of ductility’ model [29], the depletion of the ductility can be further related to the summation of cyclic plastic strain that is ultimately responsible for fatigue damage [29], it is then suggested from the present investigation that for 304 stainless steel, it would be a promising way to study the fatigue damage mechanics model as well as the residual fatigue life prediction method on the basis of the depletion of the ductility during fatigue damage process. Such investigation is being carried out and will be presented elsewhere. 5. Conclusions The investigation regarding the effects of low-cycle fatigue damage on the static mechanical properties, deformation microstructures and fracture behavior of 304 austenitic stainless steel at room-temperature leads to the following conclusions:
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1. During low-cycle fatigue process, the strength parameters ( ys and ult ) exhibit initial slight increase followed by strong increase without reaching their saturated values, which well corresponds to the two-stage cyclic hardening behavior, while the ductile parameters (ı and ϕf ) as well as the strain hardening exponent (n) present two-stage descending characteristic features. The modulus of elasticity (E) displays a progressive decrease, as a whole, with the increase of precycles. 2. The synthetical effect of the strength and ductility on the material property can be represented by a single parameter, static toughness (Ut ). It is shown that during fatigue damage process Ut exhibits an insignificant decrease for the majority of fatigue life, and only by the end of fatigue failure it displays a sharp decrease up to exhaustion. This means that the composite parameter of the strength and ductility, the static toughness, is an insensitive mechanical property to the fatigue damage evolution process. 3. With increasing number of straining cycles, both the number of grains containing slip bands and the slip band density within the grains tend to increase, and the amount of the deformationinduced austenisite/martensite transformation also exhibits increase. The critical value of the cumulative plastic strain to initiate the martensite in austenitic matrix is found to be about 0.5 for 1.0% strain amplitude and 1.0 for 0.6% strain amplitude. It is shown by the depth-sensing indentation (DSI) tests that the deformation resistance of the martensite is almost two times greater than that of the austenite, while the plasticity of the martensite is obviously less than that of the austenite. The strain hardening exponent (n) estimated from the indentation load–penetration depth (P–h) curves also indicates that the martensitic phase possesses a less strain hardening ability in comparison with the austenitic phase. 4. As the number of precycles increases, the tension fracture exhibits distinct ductile-to-brittle transition (DBT) feature. This change in the fracture mode is mostly attributed to the evolution of deformation microstructures, especially the deformationinduced martensitic transformation, during low-cycle fatigue process. 5. It is shown that the ductility parameters exhibit a sensitive changing character to the fatigue damage evolution process and can thus be chosen as the damage indicating parameter. Based on the macro/micro-experimental results of the present investigation, it is suggested that for 304 stainless steel it would be a promising way to study the fatigue damage mechanics model as well as the residual fatigue life prediction method on the
basis of the depletion of the ductility during fatigue damage process. Acknowledgements The authors would like to express their sincere thanks for the financial support of ‘National Natural Science Foundation of China (NSFC)’ under Grant 50975254 and 10572126 as well as ‘National High-Tech Research Development Project (863) of China’ under Grant 2006AA04Z419 and 2009AA044801 in completion of this research work. The first author also wishes to thank Dr. Zhiying He for her valuable discussions in preparing this manuscript. References [1] H.E. Boyer, Atlas of Stress–Strain Curves, ASM International, Metal Park, Ohio, 1987. [2] S. Wole, Mechanical Properties of Engineered Materials, Marcel Dekker, Inc., 2003. [3] J. Lemaitre, J. Dufailly, Eng. Fract. Mech. 28 (1987) 643. [4] J. Lemaitre, J. Dufailly, Engineering Damage Mechanics, Springer, Berlin/Heidelberg/New York, 2004. [5] D. Ye, Z. Wang, Int. J. Fatigue 23 (2001) 85. [6] D. Ye, Z. Wang, Int. J. Fatigue 23 (2001) 679. [7] R.C. Covind, D.A. Stephen, Metall. Trans. 5 (1974) 217. [8] G. Baudry, A. Pineau, Mater. Sci. Eng. 28 (1977) 229. [9] H.-J. Bassler, D. Eifler, Low Cycle Fatigue and Elasto-Plastic Behavior of Materials, Elsevier Science Ltd., 1998, 285. [10] R.G. Teteruk, H.J. Maier, H.-J. Christ, Low Cycle Fatigue and Elasto-Plastic Behavior of Materials, Elsevier Science Ltd., 1998, 321. [11] K. Bhanu, S. Rao, M. Valsan, R. Sandlya, S.L. Mannan, P. Rodrignez, Metall. Trans. A 24 (1993) 913. [12] M. Smaga, F. Rao, Walther, D. Eifler, Mater. Sci. Eng. A 483–484 (2008) 394. [13] M.R. Bayoumi, A.K. Abd Ellatif, J. Mater. Sci. 30 (1995) 3944. [14] D. Ye, S. Matsuoka, N. Nagashima, N. Suzuki, Mater. Sci. Eng. A 445 (2006) 104. [15] M. Klesnil, P. Lukáˇs, Fatigue of Metallic Materials, Elsevier, Amstardam/Oxford/New York, 1980. [16] H.J. Leber, M. Niffenegger, B. Tirbonod, Mater. Charact. 58 (2007) 1006. [17] D. Hennessy, G. Steckel, C. Altstetter, Metall. Trans. A 7 (1976) 415. [18] M. Topic, R.B. Tait, C. Allen, Int. J. Fatigue 29 (2007) 656. [19] S. Biswas, S. Sivaprasad, N. Narasaish, S. Tarafder, P.C. Chakraborti, Int. J. Fatigue 29 (2007) 786. [20] M. Bayerlein, H.J. Christ, H. Mughrabi, Mater. Sci. Eng. A 114 (1989) L11. [21] D.P. Harvey, R.J. Bonenberger, J.M. Wolla, Int. J. Fatigue 20 (1998) 291. [22] T. Arahori, M. Ninomi, K. Fukunaga, Metall. Trans. 31A (2000) 1937. [23] D. Ye, Z. Wang, Mater. Sci. Eng. A 297 (2001) 54. [24] D. Ye, Int. J. Fatigue 27 (2005) 1102. [25] N.Y. Jin, C. Zhong, X. Chen, Metall. Mater. 38 (1990) 2141. [26] D. Ye, S. Matsuoka, N. Nagashima, Mater. Sci. Eng. A 456 (2007) 120. [27] M. Dao, N. Chollacoop, K.J. Van Vliet, T.A. Venkatesh, S. Suresh, Acta Mater. 49 (2001) 3899. [28] M.F. Ashby, Philos. Mag. 21 (1970) 299. [29] B.I. Sandor, Fundamentals of Cyclic Stainless and Strain, The University of Wisconsin Press, Ltd., 1972.