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The low-cycle fatigue, deformation and final fracture behaviour of an austenitic stainless steel
Materials Science and Engineering A 415 (2006) 104–117
The low-cycle fatigue, deformation and final fracture behaviour of an austenitic stainless steel Duyi Ye a,b,∗ , Saburo Matsuoka b , Noburo Nagashima b , Naoyuki Suzuki b a
b
Department of Mechanics, Zhejiang University, Hangzhou 310027, China National Institute for Materials Science, 1-2-1, Sengen, Tsukuba-Shi, Ibaraki 305-0047, Japan Received in revised form 31 August 2005; accepted 20 September 2005
Abstract The low-cycle fatigue (LCF) behaviour of SUS304-HP austenitic stainless steel was investigated systematically using tension-compression cycling under fully reversed total strain amplitude control conditions at room temperature in laboratory air. In addition to tests at constant strain amplitudes, incremental step tests (IST) were also carried out. Cyclic stress response, during companion specimen tests (CST), revealed combinations of a variable cyclic hardening, stable behaviour and softening, depending on the applied cyclic strain amplitude, while during incremental step tests it exhibited cyclic hardening character at all strain levels. Microstructure observations using optical and transmission electron microscopy (TEM) revealed that with increasing total strain amplitudes the slip band density increased and the dislocation structure changed from a planar array to a more cellular-like structure. Cyclic deformation-induced austenite/martensite transformation was observed at higher cyclic strain amplitudes. The change in microstructures during cycling is responsible for the fatigue hardening/softening behaviour of the material. The SEM micrographs revealed that at low-strain amplitudes the inclusion-type nucleation occurred near the surface, while at the higher strain amplitudes crack initiation characterized by cleavage cracking occurred not only near the surface but also in the interior of the specimen. Linear or single-slope behaviour was seen both in cyclic stress–strain and Coffin-Mason plots. Masing cyclic stress–strain behaviour was presented only in the IST method but not in the CST method. © 2005 Elsevier B.V. All rights reserved. Keywords: Low-cycle fatigue; Mechanical behaviour; Microstructure; Fracture feature
1. Introduction SUS304-HP is an improved version of type 304 austenitic stainless steel through the addition of nitrogen (N) element in its composition for purpose of enhancing the corrosion resistance and mechanical properties. 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 repeated thermal stresses as a result of temperature gradients, which occur on heating and cooling during startups and shutdowns or during variations in operating conditions. Therefore, resistance to lowcycle fatigue (LCF) is an essential requirement in the design of these structures and components against failure under dynamic loading.
∗
Corresponding author. E-mail address: duyi [email protected] (D. Ye).
0921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2005.09.081
Despite the fact that low-cycle fatigue behaviour of type 304 stainless steel has been investigated for many decades and there exists a considerable literature on this topic at present [1–4], relative limited amount of information on LCF behaviour of SUS304-HP stainless steel is available. In earlier studies [5,6] on the influence of nitrogen on fatigue properties of lower alloyed austenitic stainless steels, it has been indicated that nitrogen as an alloy element is capable of enhancing cyclic softening at low-strain amplitude but causing hardening at the higher strain amplitudes. The addition of nitrogen increased the low-cycle fatigue lifetime of austenitic stainless steels [7,8]. The process behind improved fatigue properties is considered to be an increased planarity in the slip mode, suppressing cross slip and promoting slip reversibility [7]. On the other hand, nitrogen was also found to play an essential role in stability of the austenite. Addition of nitrogen as an interstitial element favours the formation of stacking faults and the formation of martensite during straining, which reduces crack growth and leads to rapid hardening, i.e. it increases the resistance to plastic flow [9–11]. It was also indicated [12] that the effect of martensite formed on
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LCF life depended on the amount of martensite present, strain amplitude, grain size and whether crack initiation or propagation controlled fatigue life at a given strain amplitude. In one study [13], the LCF properties deteriorated on martensite formation, owing to more crack initiating sites becoming available. From earlier studies, it can thus be expected that the low-cycle fatigue behaviour of SUS304-HP stainless steel with a certain content of nitrogen will be different from that of conventional type 304 austenitic stainless steel without containing nitrogen content. In this paper, low-cycle fatigue tests of SUS304-HP stainless steel were carried out at room temperature under total strain control using companion specimen test (CST) and incremental step test (IST) methods, respectively. A detailed examination of deformation microstructures and fracture features of the fatigue specimens cycled to failure at various strain amplitudes was also performed. The low-cycle fatigue characteristics were then discussed by means of competing and mutually interactive influences of cyclic strain amplitude, concomitant mechanical response, intrinsic microstructural effects and dislocationmicrostructure interactions during cyclic straining. The main purpose of the present work is to gain a more complete understanding of the low-cycle fatigue behaviour of SUS304-HP austenitic stainless steel, especially concerning the analytical relationship describing its behaviour, so as to use it more effectively in practical structural designing against fatigue. 2. Experimental details The material used for present investigation was SUS304-HP austenitic stainless steel supplied in the form of a plate, 22 mm in thickness. The plates were hot rolled at 1040 ◦ C for 0.2 h, followed by quenching in water. The nominal chemical composition of the material in percentage weight is listed in Table 1. Specimens used in the low-cycle fatigue tests were cylindrical, 6.0 mm in diameter and 14 mm in the gauge-length section. Fully reversed, push–pull and total strain amplitude controlled fatigue tests were performed at room temperature in an ambient air using a closed-loop servohydraulic testing machine (Shimadzu). A triangular strain waveform with zero mean strain (R = −1) at a constant total strain rate ε˙ of 5 × 10−3 S−1 was used. The tests were continued until fracture, with the strain amplitude limits lying between 0.30 and 2.0%. The test frequency (f) at a certain total strain amplitude could be defined by the following formula, f = ε˙ /(4εa ), where εa is the total strain amplitude. The incremental step test method was also employed Table 1 Chemical composition (wt%) of SUS304-HP austenitic stainless steel C Si Mn S P Cr Ni N Fe
0.06 0.45 0.81 0.006 0.029 18.19 8.64 0.052 Bal.
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to determine the cycle stress–strain curve (CSSC). In this case, a specimen was subjected to repeated strain blocks in which the strain amplitude increased from 0.2% linearly up to 1.2%, and then decreased. The IST was also run until the specimen failed. During testing, the load was continually monitored and hysteresis loops were recorded at appropriate intervals by means of a personal computer with a data-collecting and analyzing software. The microstructures of the alloy after fatigue tests were examined by both optical microscopy (OM) and transmission electron microscopy (TEM). Samples for microstructural analysis were prepared below the fractured surface in fatigue failed specimens by cutting perpendicular to the tensile axils with a wire saw. The samples for OM were ground using emery papers of various grinds from 230 to 600 grit, and then etched for 30 s in a solution of 16 vol% of HNO3 , 32 vol% of HCl and 50 vol% of glycerol at 313 K. Samples for TEM obtained from thin slice with 0.3 mm thickness were mechanically thinned to 30 m, and then electropolished in a solution containing 5 vol% of perchloric acid and 55 vol% acetic acid, using a twin jet apparatus at a potential of 20 V and a temperature of 798 K. TEM examinations were performed on a HITACH H9000NA transmission electron microscope, operating at 300 kV. The fractured surfaces of the fatigue failed specimens were ultrasonically cleaned in trichloroethylene, and then observed using a low-magnification binocular microscope to locate relevant feature, which were subsequently examined at higher magnification with a JEOL JSM-T20 scanning electron microscope (SEM) to determine the predominant fracture mode and to characterize the fine-scale topography of the fatigue fracture surface. 3. Results 3.1. Initial microstructure and tensile properties The microstructure of the SUS304-HP stainless steel in the as-heat treated conditions, as shown in Fig. 1, consisted of randomly oriented grains with a few annealing twins. Both the grain and twin boundary were covered with discrete carbide particles. The heat-treatment conditions mentioned previously result in an equiaxed grain size, measured by the conventional linear intercept method, of approximate 88 m (twins not taken into account). Fig. 2 shows a transmission electron microscopy micrograph of the material in the same condition, which reveals that the dislocation structure in the initial condition consists of pinned dislocation lines and small loops with low-dislocation density. Both optical microscopy and transmission electron microscopy observations indicate that, in the undeformed condition, there was no metallographic evidence of austenite/martesitic transformation in the material. The tensile properties of the present material are summarized in Table 2. The results reported are the mean values based on multiple (three) tests. The yield strength (σ ys ) defined as the stress corresponding to a plastic strain of 0.2% is 275 MPa.
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Fig. 3. Cyclic stress response curves. Fig. 1. Optical micrograph of SUS304-HP stainless in the as-heat treated conditions.
Fig. 2. Dislocation structure of SUS304-HP stainless steel in the as-heat treated conditions.
The ultimate strength (σ ult ) is 618 MPa. The large difference between the yield strength and ultimate strength indicates that this material exhibits a significant amount of work hardening during monotonic deformation. The elongation to failure and reduction in area were 68 and 82%, respectively. These tensile properties reveal that SUS304-HP stainless steel has medium strength and high ductility.
Table 2 Mechanical properties of SUS304-HP stainless steel 0.2% proof stress, σ ys (MPa) Ultimate tensile strength, σ ult (MPa) Elongation, δ (%) Reduction of area, ϕf (%)
275 618 68 82
3.2. Low-cycle fatigue behaviour 3.2.1. Cyclic stress response curve The cyclic stress response curve obtained by plotting the cyclic stress amplitudes, determined by averaging the maximum tensile and compressive stress in a hysteresis loop versus the number of cycles in a total strain-controlled fatigue test, illustrates the path by which the material arrives at the final cyclic flow stress level [14]. Fig. 3 shows the cyclic stress response curves of the SUS304-HP steel at five different total strain amplitudes. As can be seen, the cyclic stress response is dependent on strain level and can be generally characterized as the following three circumstances, i.e. (1) at strain amplitudes less than 0.6%, the material displayed very small initial hardening followed by a progressive softening, and then a saturation up to the final failure, (2) at strain amplitude of 0.9%, the initial mild hardening was followed by a region of nearly stable stress response, and then a pronounced secondary hardening, which persisted until fracture and (3) at strain amplitudes larger than 1.2%, the material exhibited very rapid strain hardening almost without reaching its saturated values till final fracture. In order to make comparison of the relative magnitude of the initial hardening, which occurs at the different strain amplitudes, a simple expression for description of the degree of hardening (H) is given by the following equation [15], H=
σasat − σa1 σa1
(1)
where σa1 and σasat are the stress amplitude at first cycle and the saturated stress amplitude, respectively. The degree of cyclic strain hardening (H) plotted as a function of applied strain amplitudes (εa ) is shown in Fig. 4. This figure indicates that with increasing applied strain amplitude the cyclic strain hardening occurring in the material increases linearly. The strong dependence of cyclic strain hardening on imposed strain amplitude was also reported in other austenitic stainless steels, such as types AISI 304L and AISI 316 [11,16].
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Table 3 Cyclic stress response and fatigue life data of the SUS304-HP stainless steel εt /2
0.003 0.004 0.005 0.006 0.009 0.01 0.012 0.015 0.02
Fig. 4. Dependence of the degree of cyclic strain hardening on imposed strain amplitude.
Values at N = 0.5Nf
Nf
εe /2
εp /2
σ/2
0.00121 0.0014 0.00152 0.00168 0.00218 0.00236 0.00272 0.00305 0.0032
0.00178 0.0026 0.00348 0.0043 0.00682 0.00763 0.00927 0.0119 0.0168
235.5 268.8 293 323.8 419.0 455 522.1 583.4 609.1
132400 17960 23400 4680 1249 753 506 260 165
features especially at the lower strain amplitudes. In the case of the IST, the material exhibits cyclic hardening character at all strain amplitudes investigated. The above results suggest that for SUS304-HP austenitic stainless steel, the cyclic stress response depends greatly on the type of loading or the cyclic-strain history applied to the specimen in additional to the imposed strain amplitudes.
To assess the effect of the type of loading on cyclic hardening/softening behaviour of SUS304-HP stainless steel, the cyclic response for the incremental step test method was determined, in which the stress amplitude responses at strain amplitudes of 0.4, 0.6, 0.9 and 1.2% in each strain block are plotted as a function of fraction of block (bn /bf ), as shown in Fig. 5. In this figure, the cyclic stress response determined by the companion specimens test method, shown in Fig. 3, is also presented for comparison purpose, where the stress amplitude during strain cycling is plotted as a function of fraction of life (N/Nf ). It is found from this figure that the cyclic stress response determined by the above two methods exhibit quite different characteristic
3.2.2. Cyclic stress–strain curve and Manson-Coffin plot The results of low-cycle fatigue tests for the present material are reported in Table 3. The elastic strain amplitude (εea ), plastic strain amplitude (εpa ), total strain amplitude (εta ) and saturation stress amplitude (σ a ) in this table are deduced from the hysteresis loops corresponding to half of the total number of cycles to fracture. Fig. 6 shows the cyclic stress–strain curves of the material determined by the CST and IST methods, respectively, where the values of stress and strain amplitudes for the IST method were taken at half of the total number of strain blocks to fracture. As a comparison, the monotonic stress–strain curve (MSSC) of the material is also presented in this figure. It is seen that both the
Fig. 5. Comparison of cyclic stress response curves determined by the CST and the IST methods.
Fig. 6. Cyclic stress–strain curves (CSSCs) determined by the CST and the IST methods and monotonic stress–strain curve (MSSC).
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CSSCs determined by the above two methods and the MSSC exhibit a straight line in the bilogarithmic plot, from which a high-strain-hardening capacity in the CST compared with that in the IST and the monotonic tensile test is inferred. This observation indicates that for the SUS304-HP stainless steel the capacity for the work hardening inherent in the material greatly depends on the type of loading in addition to the imposed strain levels. The incomparability of the CSSCs determined by the CST and the IST methods, as presented in Fig. 6, suggests that for the material chosen there is no possibility of using one specimen to determine the cyclic stress–strain curve. On the other hand, it is also easily deduced from the relative positions between the CSSCs and MSSC, shown in Fig. 6, that in the CST the material exhibits cyclic strain softening at low-plastic strain regions (εpa ≤ 0.2%) but cyclic hardening at the high-plastic strain regions (εpa ≥ 0.2%), while in the IST the material exhibits cyclic hardening over the range of strain amplitudes investigated. This deduction is in accordance with the dependence of cyclic stress response on applied strain amplitude, as shown in Fig. 3, and on the type of loading, as shown in Fig. 4. A cyclic stress–plastic strain relationship of the form [17],
σa = K (εap )n
(2)
where K is the cyclic strength coefficient and n the cyclic strainhardening exponent, was fitted by the least squares technique for the data presented in Table 3. The derived values of K and n for both the CST and IST methods are listed in Table 4, in which the material constants (K and n) obtained in the monotonic tensile test are also given for comparison purpose. It is noted from Table 4 that the cyclic strain-hardening exponent (n ) determined in the CST is higher than that determined in the IST almost by a factor of 2.5 and larger than the strain hardening exponent (n) obtained in the monotonic tensile test. The variation of fatigue life, in terms of number of reversals to failure (2Nf ), with elastic strain amplitude (εea ), plastic strain amplitude (εpa ) and total strain amplitude (εta ) is analyzed on the basis of the strain-life relationship proposed by Basquin and Coffin-Manson, which can be written in the form [17], εa = εae + εap =
σf (2Nf )b + εf (2Nf )c E
(3)
where σf , b, εf and c are the fatigue strength coefficient, fatigue strength exponent, fatigue ductility coefficient and fatigue ductility exponent, respectively. Table 4 Values of n and K determined by the CST and IST methods Monotonic tensile test n K
0.08 484
CST n K
0.336 3722
IST n K
0.13 933
Fig. 7. Strain amplitude-life plot.
The test data of εea , εpa , εta and 2Nf listed in Table 3 are plotted on a bilogarithmic scale in Fig. 7. The data of both elastic and plastic strain components showing a linear relationship on a log–log plot suggests that Eq. (3) can be used to determine the fatigue behaviour. The values of low-cycle fatigue empirical parameters that satisfy Eq. (3), determined using least-square analysis are summarized in Table 5. It is seen from this table that the value of fatigue parameter (b) is −0.17. This value is more negative than that for the stable materials in which b ranges from −0.05 to −0.15 [18]. The fatigue ductility exponent (c) is −0.346, which is within the generally observed range (−0.7 to −0.2) for a large number of monolithic alloys and their composite counterparts [19,20]. The fatigue ductility coefficient (εf ) is 0.105, which does not accord with the monotonic ductility as measured by the elongation to failure (εf ) of 1.71. It has been indicated that εf was lower than εf by a factor of 2–20, depending on the material condition and the testing parameters employed [1]. Such an unsatisfactory correlation between εf and εf has also been reported by Hennessy et al. [21] and by Landgraf [18]. The inferior cyclic ductility for the present material is ascribed to local stress (and strain) concentrations and deformation characteristics of the microstructure features during fully reversed cyclic straining. As shown by Morrow and Tuler [22] through energy arguments, the fatigue strength exponent (b) and fatigue ductility exponents (c) can also be determined from the cyclic
Table 5 Values of σf , b, εf and c σf (MPa) b b = −n /(1 + 5n ) εf c c = −1/(1 + 5n )
1415.1 −0.17 −0.125 0.105 −0.346 −0.37
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Fig. 8. Stress–strain hysteresis loops plotted with matched lower tips: (a) the CST method; (b) the IST method.
strain-hardening exponent (n ), b≈
−n , 1 + 5n
c≈
−1 1 + 5n
(4)
These calculated values are listed in Table 5 and exhibit agreement with those found from the test. This indicates that, as a first approximation, the empirical relationship (4) is applicable for the case of the SUS304-HP stainless steel. 3.2.3. Masing-type behaviour and cyclic plastic strain energy Tests were also carried out to determine whether SUS304HP stainless steel exhibits Masing cyclic stress–strain behaviour (or Masing-type behaviour) at room temperature. This property is important for description of the hysteresis loop during cycling. Fig. 8a and b shows the superimposed loops plotted with matched lower tips for both the CST and IST methods. It is seen that the material exhibits Masing-type behaviour in the IST but does not follow an ideal Masing-type behaviour in the CST. According to Abdel-Raouf et al. [23], Masing-type behaviour could be determined using the Bauschinger strain (β), defined as the plastic strain in the reverse direction at 75% of the prestress in the forward direction. The Bauschinger strain (β) plotted against plastic strain range (εp ) is shown in Fig. 9. It follows from this figure that for the case of IST the material exhibits Masing-type behaviour, since Bauschinger strain (β) increased linearly with cyclic plastic strain range (εp ), while in the case of the CST non-Masing-type behaviour could be inferred owing to the fact that Bauschinger strain (β) increased with plastic strain range (εp ) in a parabolic manner after an initial linear region at lowstrain levels. The above two methods made the same predictions of Masing-type behaviour for the material investigated. It is known that for the material exhibiting a Masing-type behaviour, the cyclic hysteresis energy per cycle Wp can be calculated directly in terms of the cyclic stress–strain curve Eq. (2), and can thus be expressed as [24], 1 − n σεp (5) Wp = 1 + n where σ (=2σ a ) is the total stress range and εp (=εap ) the plastic strain range.
The expression for calculating the plastic stain energy for a non-Masing-type material was developed by Jhansale and Topper [25] and can be written as, 1−n 2n (6) (σεp ) + (δσ0 εp ) Wp = 1+n 1+n where n is the exponent of the equation of the skeleton curve, εp = (σ/2E0 )1/n , and δσ 0 represents the increase in the proportional stress range due to non-Masing behaviour of the material. From the tests data of SU304-HP stainless steel, the coefficient n of Eq. (6), evaluated by a least squares technique, is 0.21. Note that the value of n is quite different from the cyclic strain-hardening exponent n (see Table 4). The increase in the proportional stress range, δσ 0 , can be obtained from the cyclic stress–strain curve and is given by δσ 0 = (σ/2) − 60. The plastic strain energy per cycle at half-life, determined by measuring the area of the hysteresis loop and calculated from Eqs. (5) and (6), are reported in Table 6. It easily follows from this table that the prediction precision of the plastic strain energy based on Eq. (6) has been improved greatly due to reckoning into the effect of non-Masing-type behaviour.
Fig. 9. Bauschinger strain vs. plastic strain range.
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Table 6 Comparison of experimental and theoretical values of plastic strain energy per cycle εa (%)
Wp (MPa) measured experimentally
Wp (MPa) calculated according to Eq. (5)
Wp (MPa) calculated according to Eq. (6)
0.40 0.60 0.90 1.2 2.0
2.03 4.2 8.8 14.8 30.8
1.42 2.84 5.83 9.91 21.12
1.88 4.08 8.44 13.84 29.05
3.3. Deformation microstructure The investigation of deformation microstructures was focused on examining and understanding their physical correlation to low-cycle fatigue behaviour of the material presented in the previous section. Thus, the slip band and dislocation structure developed in the fatigued specimens tested at three strain amplitudes (εa ≤ 0.6%, εa = 0.9% and εa ≥ 1.2%) that correspond to the three circumstances of the cyclic stress response curves shown in Fig. 3 and from now on referred to as low, intermediate and high-strain amplitudes are examined. Figs. 10–12 show typical optical micrographes taken from a deformed region of the specimens cycled to failure at three strain amplitudes mentioned above. At the low-strain amplitude (εa = 0.4%) the grains generally contained a few slip bands and slip was restricted to one system of parallel {1 1 1} planes (Fig. 10). At an intermediate strain amplitude (εa = 0.9%) increasing imposed strain amplitude results in the activation of new slip systems, a higher density and more uniform distribution, from grain to grain, of the slip bands (Fig. 11a). Meanwhile, the martensitic phase appeared as thin parallel individual striations in the austenitic grains, as shown by arrows in
Fig. 11b. In agreement with the observations of Bayerlein et al. [11] during cyclic deformation of AISI 304L stainless steel, a direct austenite/martensite transformation must have occurred in the austenitic matrix of the material within this strain amplitude. At the high-strain amplitude (εa = 2.0%), most of grains in the specimen contained two or more activated slip systems and the interband spacing becomes smaller (see Fig. 12a). The high-magnification micrograph (Fig. 12b) reveals the presence of spatially distributed bands with different contrast. As suggested by Botshekan et al. [16], these bands can be ascribed to the presence of microtwins and martensite platelets. The amount of austenite/martensite transformation in the austenitic matrix further increases with strain amplitude (see Fig. 12c), where martensite with an irregular blocky shape extended completely across grains or as platelets arranged in bands was visible. The dislocation structures observed in specimens cycled to failure at three strain amplitudes are summarized in Figs. 13–15. At a lower strain amplitude (εa = 0.6%), the austenitic grains show a progressive accumulation of dislocation arrays and pileups of planar character, mainly correlated to a unique slip plane within individual grains (Fig. 13a). These planar arrays are formed by dissociated dislocations, clearly identified for showing stacking fault contrast as observed in Fig. 13b. At the intermediate strain amplitude (εa = 0.9%), the dislocation structure was characterized by elongated and not fully developed cells (see Fig. 14). Both within and outside the cells, a number of dislocation loops and debris were observed. The poorly developed cells must be the result of dislocations from different slip systems interacting and trapping each other at intersecting regions, as suggested by Jin et al. [26]. At the high-strain amplitude (εa = 2.0%), the cellular dislocation structures or subgrains were fully developed and densely clustered in the majority of grains, as has been observed in Fig. 15a. The regions between the dislocation cells are almost entirely dislocation free. In some grains, the cellular structure is penetrated by individual striations having parallel orientation (Fig. 15b). In analogy with similar striations observed by Botshekan et al. [16], after unidirectional cyclic straining, these striations can be ascribed to the presence of microtwins and/or martensite platelets. 3.4. Cyclic fracture features
Fig. 10. Optical micrograph showing slip band features in the fractured specimen tested in LCF at εa = 0.4%.
Examination of the fracture surface of the low-cycle fatigue specimens was performed: (a) at low magnification to identify the fatigue and final fracture (overload) regions and (b) at higher magnifications to identify regions of crack initiation and early crack growth in the fatigue region, and also to identify the finescale fracture features in the overload region. Figs. 16–18 show representative micrographs of the fracture surfaces features of the specimens cycled to failure at low, intermediate and high-strain amplitudes, respectively. At the lowcyclic total strain amplitude (ε/2 = 0.4%), the crack initiated near the surface and propagated inward, leaving a distinct region of crack propagation, which appeared as alternating furrows and ridges or strips of steps (Figs. 16a and b). High-magnification
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Fig. 11. Optical micrographes in the fractured specimen tested in LCF at εa = 0.9% showing: (a) slip band features; (b) morphologies of martensite.
observations of the crack nucleation or formation region revealed the crack initiation to occur at inclusions near the surface (Fig. 16c). The inclusion-type nucleation can be understood as cyclic slip localization due to stress-concentration at the inclusion, leading to either decohesion of the inclusion–matrix interface or cracking of the inclusion [17]. Observations of the crack
early growth region (Fig. 16d) revealed a crystallographic (stage I) morphology of crack growth characterized by arrangements of wavy striations that have steps intersection at right angles. The arrangements of steps are comparable to brittle striations. The overload region (Fig. 16e) comprised of microscopic voids of a variety of sizes and shallow dimples indicating the highly ductile
Fig. 12. Optical micrographes in the fractured specimen tested in LCF at εa = 2.0% showing: (a and b) slip band features; (c) different morphologies of martensite.
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Fig. 13. TEM micrographs in the fractured specimen tested in LCF at εa = 0.6% showing: (a) a planar array of dislocation structures; (b) stacking faults.
Fig. 14. TEM micrographs showing loose and incomplete dislocation cell structure in the fractured specimen tested in LCF at εa = 0.9%.
nature. At the intermediate strain amplitude (ε/2 = 0.9%) the fracture features on a macroscopic scale were similar to those observed at the lower strain amplitude, as shown in Fig. 17a. Microcracks originated from the specimen surface was also characteristic of fatigue crack nucleation at this strain amplitude (see Fig. 17b). Higher magnification observations of the crack nucle-
ation or formation region revealed the presence of fatigue slip bands and cyclic cleavage facets (Fig. 17c). The region of early crack growth showed distinct evidence of crystallographic (stage I) crack growth prior to propagation of the crack along a plane normal to the stress axis (stage II), as shown in Fig. 17d. In analogy with what was observed at the low-strain amplitude, the sudden fracture region also exhibits high-ductile characteristic (Fig. 17e). At the high-strain amplitudes (εa = 1.2%), the crack initiated not only near the surface but also in the interior of the specimen (Fig. 18a and b). Higher magnification observations of the crack nucleation region revealed that cleavage fracture was characteristic of fatigue crack nucleation at this strain amplitude (see Fig. 18c). An example of deformation twins as nucleation sites of cleavage fracture is shown in Fig. 18d. The crack nucleation of this type is termed “direct cleavage cracking”, in contrast to that initiated by shear, indicates thereby that shear cracking is not the only mechanism for crack nucleation at the higher strain amplitudes. Observations of the regions of transgranular fracture (Fig. 19e) revealed the fatigue striations to be covered with finer striations, which are indicative of repeated plastic deformation occurring in a single cycle and accompanied by local secondary cracks along striations. High magnification observation of the sudden fracture regions (Fig. 19f) revealed microscopic features indicative of classic ductile fracture.
Fig. 15. TEM micrographs in the fractured specimen tested in LCF at εa = 2.0% showing: (a) well-developed dislocation cell structure; (b) cellular structure penetrated by individual striations with parallel orientation.
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Fig. 16. (a–e) Macroscopic fractograph and SEM micrographs of the fracture surface in the specimen tested in LCF at εa = 0.4%.
4. Analysis and discussion The micromechanisms responsible for the cyclic stress response during low-cycle fatigue are dependent on the microstructure and strain amplitude [17]. In the as-heat treated conditions of SUS304-HP stainless steel, the initial microstructure comprises pinned dislocation lines and loops with lowdislocation density (Fig. 2). During cyclic straining, the unpinning and multiplication of dislocations as well as the mutual interactions of dislocations and the interactions of dislocations with grain boundaries increases the resistance to plastic deformation, which is responsible for the observed initial hardening in the cyclically deformed material. According to Lerch and Gerod
[27], an increase in slip band density is responsible for the hardening in austenitic steels. To verify this suggestion, specimens tested at different total strain amplitudes were also examined for the present material. The number of slip bands per grain was divided by the grain diameter in a direction perpendicular to the slip bands to estimate the average slip band spacing. About 50–75 grains were counted for each specimen. Fig. 19 shows the dependence of slip band spacing on imposed strain amplitudes, in which a decrease in slip band spacing with an increase in the applied strain amplitude was observed. Thus, consistent with earlier studies [27,28], it can be inferred that an increase in the degree of cyclic strain hardening with strain amplitude for the present material, as shown in Fig. 4, can be
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Fig. 17. (a–e) Macroscopic fractograph and SEM micrographs of the fracture surface in the specimen tested in LCF at εa = 0.9%.
related to the number of slip bands and slip systems activated in the cyclically deformed specimens. Since the material studied here is quasi-stable at room temperature due to addition of nitrogen, it underwent a deformation-induced austenitic/martensitic transformation during cyclic straining. Numerous investigations [9–13] have shown that the formation of martensites during cyclic loading strongly affects the fatigue mechanical behaviour of various types of steels. Magnetic measurements on the fracture surface of fractured specimens after the LCF deformation showed that the martensite content had increased with the applied total strain amplitude [10]. The measurement of the volume fraction of martensite during fatigue tests also documented that a direct relation exists between hardening and martensitic
transformation [16,21]. Therefore, after initial cyclic hardening, the stress response of the present material is governed by two competitive processes, namely dynamic recovery (i.e. formation of cells and subgrains) and defomation-induced martenstic transformation. The formation of cells and subgrains due to recovery mechanisms leads to an increase in the mean path for dislocations, which favours cyclic softening [1], whereas the formation of martensite by strain-induced processes drastically increases the resistance to plastic flow that promotes cyclic hardening of the material [11]. According to TEM observations at low-strain amplitudes, the saturation dislocation structures in the deformed specimen displayed a planar-array dislocation configuration (Fig. 13a). Both OM and TEM examinations revealed no marten-
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Fig. 18. (a–f) Macroscopic fractograph and SEM micrographs of the fracture surface in the specimen tested in LCF at εa = 1.2%.
site formation in austenitic grains tested at this strain amplitude. This agrees with the findings of Baudy and Pineau [10] concerning the critical total or plastic strain amplitude, which must be achieved in order to induce martensite formation in cyclic straining. Consequently, at low-strain amplitude, the progressive softening process after initial cyclic hardening is attributed to the formation of a dislocation configuration that bears the plastic strain more easily [17]. At the intermediate strain amplitude austenite/martensite transformation takes place and the amount of this transformation increases with an increasing number of cycles, as shown in Fig. 11b. Meanwhile, the tendency to form a dislocation substructure characterized by a developing cell structure containing low-dislocation density/ill-defined cell walls (Fig. 14) suggests localization of deformation in the material, which results in less stress for sustaining a given strain amplitude, namely softening. Thus, when an increase of the resistance to plastic deformation resulting from formation of martensite can
compensate for the softening effect associated with dislocation cellular structure, the material exhibits a saturation character as has been observed in the cyclic stress response curves (Fig. 3), which is followed by secondary hardening as a result of the fact that the volume fraction of strain-induced martensite transformation further increased with the increasing number of straining cycles. At high-strain amplitudes, the cumulation of the cyclic plastic strain leads to a continuous increase in the density of shear bands, and thus in the density of sites for strain-induced nucleation of martensite (see Figs. 12c and 15b). In other words, more martensite is formed with a less number of cycles in this case. As a result, the material displayed continuous strain hardening up to failure without displaying an intermediate stage of stress saturation at the higher strain amplitudes (see Fig. 3). On the other hand, the formation of more martensite also leads to more crack initiating sites in the fatigued specimen at high-strain amplitude, which has been exhibited in the fatigue fracture (see Fig. 18a–d).
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5. Conclusions The experimental results on the room-temperature low-cycle fatigue behaviour, deformation microstructures and fracture features of the austenitic stainless steel SUS304-HP reported in this paper support the following conclusions:
Fig. 19. Variation of slip band spacing with strain amplitude.
The sensitivity of the cyclic stress response to the type of loading or the imposed strain history, as shown in Fig. 5, was also reported in other austenitic stainless steels, such as AISI 316L and AISI 446 [29], and was explained as a result of the strong evolution of dislocation structures and nucleation of the deformation-induced martensitic transformation during fatigue testing. Since the dislocation structure built up in the IST was mostly characteristic of the highest strain amplitude in the strain block and remained practically that of the highest strain amplitude throughout the block [12], both the saturation dislocation structure and the martensite transformation in the present material can be expected to be formed at early stages of strain blocks due to the fact that the highest strain amplitude occurred in each strain block. In other words, the material remained practically similar regardless of stress amplitudes in the IST. As a result, the material exhibits cyclic hardening in the IST even when the strain amplitude decreased within a block, as has been observed in Fig. 5. In the CST, however, the dislocation structure was different at different strain amplitudes and more martensite formed at the high-strain amplitudes, which is responsible for the observed hardening/softening behaviour in the cyclic stress response curves. The lower slope for the CSSC obtained by the IST as compared to that determined by the CST, as shown in Fig. 6, is in agreement with observations by Nystrom et al. [30] and Zhong et al. [31] in AISI 316L and AISI 310 types of stainless steel. It is likely that this general difference in slope between the two methods is caused by differences in the developing dislocation structure during the IST and CST. This difference of the microstructure induced by the two methods can be used to explain why Masing-type behaviour was seen in the IST but not in the CST, for Masing-type behaviour is expected to be present only for the cases where the microstructure does not change appreciably [12]. In other words, the difference of the microstructures during the CST is responsible for the observed non-Masing-type behaviour of the SUS304-HP stainless steel in this loading condition.
(1) Cyclic stress response, during companion specimen tests, revealed combinations of a variable cyclic hardening, stable behaviour and softening, depending on the applied cyclic strain amplitude, while, during incremental step tests, exhibited hardening character at all strain levels. In the case of the CST, the degree of cyclic strain hardening increases almost linearly with increasing strain amplitude. (2) The CSS curves obtained by the CST and IST methods exhibits different characteristic features. The CST, compared to the IST, gives a higher slope of the CSSC or a higher strain hardening capacity at all strain amplitudes. Therefore, in the case of the present material, there is no possibility of using one specimen to determine the cyclic stress–strain curve. (3) The fatigue lifetime shows single-slope behaviour in both Basquin and Cofffin-Manson diagrams. (4) Masing cyclic stress–strain behaviour was presented only in the IST method but not in the CST method. The prediction precision of the cyclic plastic strain energy was improved greatly due to reckoning into the effect of non-Masing-type behaviour in terms of the modified equation developed by Jhansale and Topper [25]. (5) Observations of fatigue-related microstructures revealed that with increasing total strain amplitude the slip band density increased and the dislocation structure changed from a planar dislocation array to a more cellular-like structure. A strong tendency of the cyclic deformation-induced austenitic/martensitic transformation was observed in the austenitic matrix at higher cyclic strain amplitudes. (6) The SEM examinations revealed that at low-strain amplitudes the inclusion-type nucleation occurred near the surface, while at high-strain amplitudes the crack initiation characterized by cleavage cracking occurred not only near the surface but also in the interior of the specimen. Acknowledgements The first author would like to express his sincere thanks to Dr. Akihiko OHTA, the former host researcher of the first author, who provided financial assistance through 2001Y JSPS Postdoctoral Fellowship under Grant PB01021. He also wishes to acknowledge the National Institute for Materials Science (NIMS), Japan, for his appointment as a visiting researcher in Materials Information Technology Center during February 1st, 2002 through January 31st, 2004. References [1] K. Bhanu Sankara Rao, M. Valsan, S.L. Mannan, Mater. Sci. Eng. A130 (1990) 67.
D. Ye et al. / Materials Science and Engineering A 415 (2006) 104–117 [2] K. Bhanu Sankara Rao, M. Valsan, R. Sandhya, S.L. Mannan, P. Rodrignez, Metall. Trans. A 24 (1993) 913. [3] M.R. Bayoumi, A.K. Abd Ellatif, J. Mater. Sci. 30 (1995) 3944. [4] G.C. Kaschner, J.C. Gibeling, Mater. Sci. Eng. A336 (2002) 170. [5] M.L.G. Byrnes, M. Grujicic, W.S. Owen, Acta Metall. 35 (1987) 1853. [6] Y. Li, C. Laid, Mater. Sci. Eng. A186 (1994) 87. [7] J.-O. Nilsson, Scr. Metall. 17 (1983) 593. [8] J.B. Vogt, S. Degallaix, J. Foct, Int. J. Fatigue 6 (1984) 211. [9] L.D. Murr, K.P. Stand Hammer, S.S. Hecker, Metall. Trans. A13 (1982) 627. [10] G. Baudry, A. Pineau, Mater. Sci. Eng. 28 (1977) 229. [11] M. Bayerlein, H.–J. Christ, H. Mughrabi, Mater. Sci. Eng. A114 (1989) L11. [12] S. Ganesh Sundara Raman, K.A. Padmanabhan, Int. J. Fatigue 17 (1995) 271. [13] G.R. Chanani, S.D. Antolovich, Metall. Trans 5 (1974) 217. [14] T.S. Srivatsan, S. Anand, J.D. Troxell, Int. J. Fatigue 15 (1993) 355. [15] R.P. Skelton, High Temperature Fatigue (Properties and Prediction), Elsevier, London/New York, 1987. [16] M. Botshekan, S. Degallaix, Y. Desplanques, J. Polak, Fatigue Fract. Eng. Mater. Struct. 21 (1998) 651.
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[17] M. Klesnil, P. Lukas, Fatigue of Metallic Materials, Elsevier, Amsterdam/Oxford/New York, 1980. [18] R.W. Landgraf, Am. Soc. Test. Mater. Spec. Tech. Publ. 467 (1970) 3. [19] B. Tomkins, Philos. Magn. 18 (1968) 1041. [20] T.S. Srivatsan, R. Auradkar, Int. J. Fatigue 14 (1992) 355. [21] D. Hennessy, G. Steckel, C. Altstetter, Metall. Trans. 7A (1976) 415. [22] J.D. Morrow, F.R. Tuler, J. Basic Eng. 87 (1965) 275. [23] H. Abdel-Raouf, T.H. Topper, A. Plumtree, Proceeding of the Fourth International Conference on Fracture, Waterloo, 1977, p. 1107. [24] D. Lefebvre, F. Ellyin, Int. J. Fatigue 6 (1984) 9. [25] H.R. Jhansale, T.H. Topper, ASTM STP 519, American Society of Testing and Materials, 1973, p. 246. [26] N.Y. Jin, C. Zhong, X. Chen, Acta Metall. Mater. 38 (1990) 2141. [27] B.A. Lerch, A. Gerold, Acta Metall. 33 (1985) 1709. [28] S. Ganesh Sundara Raman, K.A. Padmanabhan, Fatigue 16 (1994) 209. [29] E. Mousavi-Torshizi, S. Degallaix, Proceeding of the Fourth International Conference on Fracture, Waterloo, 1977, p. 75. [30] M. Nystrom, U. Lindstedt, B. Karlsson, J.-O. Nilsson, Mater. Sci. Technol. 13 (1997) 560. [31] C. Zhong, N.-Y. Jin, X. Zhou, E. Meng, X. Chen, Acta Metall. Mater. 38 (1990) 2135.
The low-cycle fatigue, deformation and final fracture behaviour of an austenitic stainless steel Duyi Ye a,b,∗ , Saburo Matsuoka b , Noburo Nagashima b , Naoyuki Suzuki b a
b
Department of Mechanics, Zhejiang University, Hangzhou 310027, China National Institute for Materials Science, 1-2-1, Sengen, Tsukuba-Shi, Ibaraki 305-0047, Japan Received in revised form 31 August 2005; accepted 20 September 2005
Abstract The low-cycle fatigue (LCF) behaviour of SUS304-HP austenitic stainless steel was investigated systematically using tension-compression cycling under fully reversed total strain amplitude control conditions at room temperature in laboratory air. In addition to tests at constant strain amplitudes, incremental step tests (IST) were also carried out. Cyclic stress response, during companion specimen tests (CST), revealed combinations of a variable cyclic hardening, stable behaviour and softening, depending on the applied cyclic strain amplitude, while during incremental step tests it exhibited cyclic hardening character at all strain levels. Microstructure observations using optical and transmission electron microscopy (TEM) revealed that with increasing total strain amplitudes the slip band density increased and the dislocation structure changed from a planar array to a more cellular-like structure. Cyclic deformation-induced austenite/martensite transformation was observed at higher cyclic strain amplitudes. The change in microstructures during cycling is responsible for the fatigue hardening/softening behaviour of the material. The SEM micrographs revealed that at low-strain amplitudes the inclusion-type nucleation occurred near the surface, while at the higher strain amplitudes crack initiation characterized by cleavage cracking occurred not only near the surface but also in the interior of the specimen. Linear or single-slope behaviour was seen both in cyclic stress–strain and Coffin-Mason plots. Masing cyclic stress–strain behaviour was presented only in the IST method but not in the CST method. © 2005 Elsevier B.V. All rights reserved. Keywords: Low-cycle fatigue; Mechanical behaviour; Microstructure; Fracture feature
1. Introduction SUS304-HP is an improved version of type 304 austenitic stainless steel through the addition of nitrogen (N) element in its composition for purpose of enhancing the corrosion resistance and mechanical properties. 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 repeated thermal stresses as a result of temperature gradients, which occur on heating and cooling during startups and shutdowns or during variations in operating conditions. Therefore, resistance to lowcycle fatigue (LCF) is an essential requirement in the design of these structures and components against failure under dynamic loading.
∗
Corresponding author. E-mail address: duyi [email protected] (D. Ye).
0921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2005.09.081
Despite the fact that low-cycle fatigue behaviour of type 304 stainless steel has been investigated for many decades and there exists a considerable literature on this topic at present [1–4], relative limited amount of information on LCF behaviour of SUS304-HP stainless steel is available. In earlier studies [5,6] on the influence of nitrogen on fatigue properties of lower alloyed austenitic stainless steels, it has been indicated that nitrogen as an alloy element is capable of enhancing cyclic softening at low-strain amplitude but causing hardening at the higher strain amplitudes. The addition of nitrogen increased the low-cycle fatigue lifetime of austenitic stainless steels [7,8]. The process behind improved fatigue properties is considered to be an increased planarity in the slip mode, suppressing cross slip and promoting slip reversibility [7]. On the other hand, nitrogen was also found to play an essential role in stability of the austenite. Addition of nitrogen as an interstitial element favours the formation of stacking faults and the formation of martensite during straining, which reduces crack growth and leads to rapid hardening, i.e. it increases the resistance to plastic flow [9–11]. It was also indicated [12] that the effect of martensite formed on
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LCF life depended on the amount of martensite present, strain amplitude, grain size and whether crack initiation or propagation controlled fatigue life at a given strain amplitude. In one study [13], the LCF properties deteriorated on martensite formation, owing to more crack initiating sites becoming available. From earlier studies, it can thus be expected that the low-cycle fatigue behaviour of SUS304-HP stainless steel with a certain content of nitrogen will be different from that of conventional type 304 austenitic stainless steel without containing nitrogen content. In this paper, low-cycle fatigue tests of SUS304-HP stainless steel were carried out at room temperature under total strain control using companion specimen test (CST) and incremental step test (IST) methods, respectively. A detailed examination of deformation microstructures and fracture features of the fatigue specimens cycled to failure at various strain amplitudes was also performed. The low-cycle fatigue characteristics were then discussed by means of competing and mutually interactive influences of cyclic strain amplitude, concomitant mechanical response, intrinsic microstructural effects and dislocationmicrostructure interactions during cyclic straining. The main purpose of the present work is to gain a more complete understanding of the low-cycle fatigue behaviour of SUS304-HP austenitic stainless steel, especially concerning the analytical relationship describing its behaviour, so as to use it more effectively in practical structural designing against fatigue. 2. Experimental details The material used for present investigation was SUS304-HP austenitic stainless steel supplied in the form of a plate, 22 mm in thickness. The plates were hot rolled at 1040 ◦ C for 0.2 h, followed by quenching in water. The nominal chemical composition of the material in percentage weight is listed in Table 1. Specimens used in the low-cycle fatigue tests were cylindrical, 6.0 mm in diameter and 14 mm in the gauge-length section. Fully reversed, push–pull and total strain amplitude controlled fatigue tests were performed at room temperature in an ambient air using a closed-loop servohydraulic testing machine (Shimadzu). A triangular strain waveform with zero mean strain (R = −1) at a constant total strain rate ε˙ of 5 × 10−3 S−1 was used. The tests were continued until fracture, with the strain amplitude limits lying between 0.30 and 2.0%. The test frequency (f) at a certain total strain amplitude could be defined by the following formula, f = ε˙ /(4εa ), where εa is the total strain amplitude. The incremental step test method was also employed Table 1 Chemical composition (wt%) of SUS304-HP austenitic stainless steel C Si Mn S P Cr Ni N Fe
0.06 0.45 0.81 0.006 0.029 18.19 8.64 0.052 Bal.
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to determine the cycle stress–strain curve (CSSC). In this case, a specimen was subjected to repeated strain blocks in which the strain amplitude increased from 0.2% linearly up to 1.2%, and then decreased. The IST was also run until the specimen failed. During testing, the load was continually monitored and hysteresis loops were recorded at appropriate intervals by means of a personal computer with a data-collecting and analyzing software. The microstructures of the alloy after fatigue tests were examined by both optical microscopy (OM) and transmission electron microscopy (TEM). Samples for microstructural analysis were prepared below the fractured surface in fatigue failed specimens by cutting perpendicular to the tensile axils with a wire saw. The samples for OM were ground using emery papers of various grinds from 230 to 600 grit, and then etched for 30 s in a solution of 16 vol% of HNO3 , 32 vol% of HCl and 50 vol% of glycerol at 313 K. Samples for TEM obtained from thin slice with 0.3 mm thickness were mechanically thinned to 30 m, and then electropolished in a solution containing 5 vol% of perchloric acid and 55 vol% acetic acid, using a twin jet apparatus at a potential of 20 V and a temperature of 798 K. TEM examinations were performed on a HITACH H9000NA transmission electron microscope, operating at 300 kV. The fractured surfaces of the fatigue failed specimens were ultrasonically cleaned in trichloroethylene, and then observed using a low-magnification binocular microscope to locate relevant feature, which were subsequently examined at higher magnification with a JEOL JSM-T20 scanning electron microscope (SEM) to determine the predominant fracture mode and to characterize the fine-scale topography of the fatigue fracture surface. 3. Results 3.1. Initial microstructure and tensile properties The microstructure of the SUS304-HP stainless steel in the as-heat treated conditions, as shown in Fig. 1, consisted of randomly oriented grains with a few annealing twins. Both the grain and twin boundary were covered with discrete carbide particles. The heat-treatment conditions mentioned previously result in an equiaxed grain size, measured by the conventional linear intercept method, of approximate 88 m (twins not taken into account). Fig. 2 shows a transmission electron microscopy micrograph of the material in the same condition, which reveals that the dislocation structure in the initial condition consists of pinned dislocation lines and small loops with low-dislocation density. Both optical microscopy and transmission electron microscopy observations indicate that, in the undeformed condition, there was no metallographic evidence of austenite/martesitic transformation in the material. The tensile properties of the present material are summarized in Table 2. The results reported are the mean values based on multiple (three) tests. The yield strength (σ ys ) defined as the stress corresponding to a plastic strain of 0.2% is 275 MPa.
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Fig. 3. Cyclic stress response curves. Fig. 1. Optical micrograph of SUS304-HP stainless in the as-heat treated conditions.
Fig. 2. Dislocation structure of SUS304-HP stainless steel in the as-heat treated conditions.
The ultimate strength (σ ult ) is 618 MPa. The large difference between the yield strength and ultimate strength indicates that this material exhibits a significant amount of work hardening during monotonic deformation. The elongation to failure and reduction in area were 68 and 82%, respectively. These tensile properties reveal that SUS304-HP stainless steel has medium strength and high ductility.
Table 2 Mechanical properties of SUS304-HP stainless steel 0.2% proof stress, σ ys (MPa) Ultimate tensile strength, σ ult (MPa) Elongation, δ (%) Reduction of area, ϕf (%)
275 618 68 82
3.2. Low-cycle fatigue behaviour 3.2.1. Cyclic stress response curve The cyclic stress response curve obtained by plotting the cyclic stress amplitudes, determined by averaging the maximum tensile and compressive stress in a hysteresis loop versus the number of cycles in a total strain-controlled fatigue test, illustrates the path by which the material arrives at the final cyclic flow stress level [14]. Fig. 3 shows the cyclic stress response curves of the SUS304-HP steel at five different total strain amplitudes. As can be seen, the cyclic stress response is dependent on strain level and can be generally characterized as the following three circumstances, i.e. (1) at strain amplitudes less than 0.6%, the material displayed very small initial hardening followed by a progressive softening, and then a saturation up to the final failure, (2) at strain amplitude of 0.9%, the initial mild hardening was followed by a region of nearly stable stress response, and then a pronounced secondary hardening, which persisted until fracture and (3) at strain amplitudes larger than 1.2%, the material exhibited very rapid strain hardening almost without reaching its saturated values till final fracture. In order to make comparison of the relative magnitude of the initial hardening, which occurs at the different strain amplitudes, a simple expression for description of the degree of hardening (H) is given by the following equation [15], H=
σasat − σa1 σa1
(1)
where σa1 and σasat are the stress amplitude at first cycle and the saturated stress amplitude, respectively. The degree of cyclic strain hardening (H) plotted as a function of applied strain amplitudes (εa ) is shown in Fig. 4. This figure indicates that with increasing applied strain amplitude the cyclic strain hardening occurring in the material increases linearly. The strong dependence of cyclic strain hardening on imposed strain amplitude was also reported in other austenitic stainless steels, such as types AISI 304L and AISI 316 [11,16].
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Table 3 Cyclic stress response and fatigue life data of the SUS304-HP stainless steel εt /2
0.003 0.004 0.005 0.006 0.009 0.01 0.012 0.015 0.02
Fig. 4. Dependence of the degree of cyclic strain hardening on imposed strain amplitude.
Values at N = 0.5Nf
Nf
εe /2
εp /2
σ/2
0.00121 0.0014 0.00152 0.00168 0.00218 0.00236 0.00272 0.00305 0.0032
0.00178 0.0026 0.00348 0.0043 0.00682 0.00763 0.00927 0.0119 0.0168
235.5 268.8 293 323.8 419.0 455 522.1 583.4 609.1
132400 17960 23400 4680 1249 753 506 260 165
features especially at the lower strain amplitudes. In the case of the IST, the material exhibits cyclic hardening character at all strain amplitudes investigated. The above results suggest that for SUS304-HP austenitic stainless steel, the cyclic stress response depends greatly on the type of loading or the cyclic-strain history applied to the specimen in additional to the imposed strain amplitudes.
To assess the effect of the type of loading on cyclic hardening/softening behaviour of SUS304-HP stainless steel, the cyclic response for the incremental step test method was determined, in which the stress amplitude responses at strain amplitudes of 0.4, 0.6, 0.9 and 1.2% in each strain block are plotted as a function of fraction of block (bn /bf ), as shown in Fig. 5. In this figure, the cyclic stress response determined by the companion specimens test method, shown in Fig. 3, is also presented for comparison purpose, where the stress amplitude during strain cycling is plotted as a function of fraction of life (N/Nf ). It is found from this figure that the cyclic stress response determined by the above two methods exhibit quite different characteristic
3.2.2. Cyclic stress–strain curve and Manson-Coffin plot The results of low-cycle fatigue tests for the present material are reported in Table 3. The elastic strain amplitude (εea ), plastic strain amplitude (εpa ), total strain amplitude (εta ) and saturation stress amplitude (σ a ) in this table are deduced from the hysteresis loops corresponding to half of the total number of cycles to fracture. Fig. 6 shows the cyclic stress–strain curves of the material determined by the CST and IST methods, respectively, where the values of stress and strain amplitudes for the IST method were taken at half of the total number of strain blocks to fracture. As a comparison, the monotonic stress–strain curve (MSSC) of the material is also presented in this figure. It is seen that both the
Fig. 5. Comparison of cyclic stress response curves determined by the CST and the IST methods.
Fig. 6. Cyclic stress–strain curves (CSSCs) determined by the CST and the IST methods and monotonic stress–strain curve (MSSC).
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CSSCs determined by the above two methods and the MSSC exhibit a straight line in the bilogarithmic plot, from which a high-strain-hardening capacity in the CST compared with that in the IST and the monotonic tensile test is inferred. This observation indicates that for the SUS304-HP stainless steel the capacity for the work hardening inherent in the material greatly depends on the type of loading in addition to the imposed strain levels. The incomparability of the CSSCs determined by the CST and the IST methods, as presented in Fig. 6, suggests that for the material chosen there is no possibility of using one specimen to determine the cyclic stress–strain curve. On the other hand, it is also easily deduced from the relative positions between the CSSCs and MSSC, shown in Fig. 6, that in the CST the material exhibits cyclic strain softening at low-plastic strain regions (εpa ≤ 0.2%) but cyclic hardening at the high-plastic strain regions (εpa ≥ 0.2%), while in the IST the material exhibits cyclic hardening over the range of strain amplitudes investigated. This deduction is in accordance with the dependence of cyclic stress response on applied strain amplitude, as shown in Fig. 3, and on the type of loading, as shown in Fig. 4. A cyclic stress–plastic strain relationship of the form [17],
σa = K (εap )n
(2)
where K is the cyclic strength coefficient and n the cyclic strainhardening exponent, was fitted by the least squares technique for the data presented in Table 3. The derived values of K and n for both the CST and IST methods are listed in Table 4, in which the material constants (K and n) obtained in the monotonic tensile test are also given for comparison purpose. It is noted from Table 4 that the cyclic strain-hardening exponent (n ) determined in the CST is higher than that determined in the IST almost by a factor of 2.5 and larger than the strain hardening exponent (n) obtained in the monotonic tensile test. The variation of fatigue life, in terms of number of reversals to failure (2Nf ), with elastic strain amplitude (εea ), plastic strain amplitude (εpa ) and total strain amplitude (εta ) is analyzed on the basis of the strain-life relationship proposed by Basquin and Coffin-Manson, which can be written in the form [17], εa = εae + εap =
σf (2Nf )b + εf (2Nf )c E
(3)
where σf , b, εf and c are the fatigue strength coefficient, fatigue strength exponent, fatigue ductility coefficient and fatigue ductility exponent, respectively. Table 4 Values of n and K determined by the CST and IST methods Monotonic tensile test n K
0.08 484
CST n K
0.336 3722
IST n K
0.13 933
Fig. 7. Strain amplitude-life plot.
The test data of εea , εpa , εta and 2Nf listed in Table 3 are plotted on a bilogarithmic scale in Fig. 7. The data of both elastic and plastic strain components showing a linear relationship on a log–log plot suggests that Eq. (3) can be used to determine the fatigue behaviour. The values of low-cycle fatigue empirical parameters that satisfy Eq. (3), determined using least-square analysis are summarized in Table 5. It is seen from this table that the value of fatigue parameter (b) is −0.17. This value is more negative than that for the stable materials in which b ranges from −0.05 to −0.15 [18]. The fatigue ductility exponent (c) is −0.346, which is within the generally observed range (−0.7 to −0.2) for a large number of monolithic alloys and their composite counterparts [19,20]. The fatigue ductility coefficient (εf ) is 0.105, which does not accord with the monotonic ductility as measured by the elongation to failure (εf ) of 1.71. It has been indicated that εf was lower than εf by a factor of 2–20, depending on the material condition and the testing parameters employed [1]. Such an unsatisfactory correlation between εf and εf has also been reported by Hennessy et al. [21] and by Landgraf [18]. The inferior cyclic ductility for the present material is ascribed to local stress (and strain) concentrations and deformation characteristics of the microstructure features during fully reversed cyclic straining. As shown by Morrow and Tuler [22] through energy arguments, the fatigue strength exponent (b) and fatigue ductility exponents (c) can also be determined from the cyclic
Table 5 Values of σf , b, εf and c σf (MPa) b b = −n /(1 + 5n ) εf c c = −1/(1 + 5n )
1415.1 −0.17 −0.125 0.105 −0.346 −0.37
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Fig. 8. Stress–strain hysteresis loops plotted with matched lower tips: (a) the CST method; (b) the IST method.
strain-hardening exponent (n ), b≈
−n , 1 + 5n
c≈
−1 1 + 5n
(4)
These calculated values are listed in Table 5 and exhibit agreement with those found from the test. This indicates that, as a first approximation, the empirical relationship (4) is applicable for the case of the SUS304-HP stainless steel. 3.2.3. Masing-type behaviour and cyclic plastic strain energy Tests were also carried out to determine whether SUS304HP stainless steel exhibits Masing cyclic stress–strain behaviour (or Masing-type behaviour) at room temperature. This property is important for description of the hysteresis loop during cycling. Fig. 8a and b shows the superimposed loops plotted with matched lower tips for both the CST and IST methods. It is seen that the material exhibits Masing-type behaviour in the IST but does not follow an ideal Masing-type behaviour in the CST. According to Abdel-Raouf et al. [23], Masing-type behaviour could be determined using the Bauschinger strain (β), defined as the plastic strain in the reverse direction at 75% of the prestress in the forward direction. The Bauschinger strain (β) plotted against plastic strain range (εp ) is shown in Fig. 9. It follows from this figure that for the case of IST the material exhibits Masing-type behaviour, since Bauschinger strain (β) increased linearly with cyclic plastic strain range (εp ), while in the case of the CST non-Masing-type behaviour could be inferred owing to the fact that Bauschinger strain (β) increased with plastic strain range (εp ) in a parabolic manner after an initial linear region at lowstrain levels. The above two methods made the same predictions of Masing-type behaviour for the material investigated. It is known that for the material exhibiting a Masing-type behaviour, the cyclic hysteresis energy per cycle Wp can be calculated directly in terms of the cyclic stress–strain curve Eq. (2), and can thus be expressed as [24], 1 − n σεp (5) Wp = 1 + n where σ (=2σ a ) is the total stress range and εp (=εap ) the plastic strain range.
The expression for calculating the plastic stain energy for a non-Masing-type material was developed by Jhansale and Topper [25] and can be written as, 1−n 2n (6) (σεp ) + (δσ0 εp ) Wp = 1+n 1+n where n is the exponent of the equation of the skeleton curve, εp = (σ/2E0 )1/n , and δσ 0 represents the increase in the proportional stress range due to non-Masing behaviour of the material. From the tests data of SU304-HP stainless steel, the coefficient n of Eq. (6), evaluated by a least squares technique, is 0.21. Note that the value of n is quite different from the cyclic strain-hardening exponent n (see Table 4). The increase in the proportional stress range, δσ 0 , can be obtained from the cyclic stress–strain curve and is given by δσ 0 = (σ/2) − 60. The plastic strain energy per cycle at half-life, determined by measuring the area of the hysteresis loop and calculated from Eqs. (5) and (6), are reported in Table 6. It easily follows from this table that the prediction precision of the plastic strain energy based on Eq. (6) has been improved greatly due to reckoning into the effect of non-Masing-type behaviour.
Fig. 9. Bauschinger strain vs. plastic strain range.
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Table 6 Comparison of experimental and theoretical values of plastic strain energy per cycle εa (%)
Wp (MPa) measured experimentally
Wp (MPa) calculated according to Eq. (5)
Wp (MPa) calculated according to Eq. (6)
0.40 0.60 0.90 1.2 2.0
2.03 4.2 8.8 14.8 30.8
1.42 2.84 5.83 9.91 21.12
1.88 4.08 8.44 13.84 29.05
3.3. Deformation microstructure The investigation of deformation microstructures was focused on examining and understanding their physical correlation to low-cycle fatigue behaviour of the material presented in the previous section. Thus, the slip band and dislocation structure developed in the fatigued specimens tested at three strain amplitudes (εa ≤ 0.6%, εa = 0.9% and εa ≥ 1.2%) that correspond to the three circumstances of the cyclic stress response curves shown in Fig. 3 and from now on referred to as low, intermediate and high-strain amplitudes are examined. Figs. 10–12 show typical optical micrographes taken from a deformed region of the specimens cycled to failure at three strain amplitudes mentioned above. At the low-strain amplitude (εa = 0.4%) the grains generally contained a few slip bands and slip was restricted to one system of parallel {1 1 1} planes (Fig. 10). At an intermediate strain amplitude (εa = 0.9%) increasing imposed strain amplitude results in the activation of new slip systems, a higher density and more uniform distribution, from grain to grain, of the slip bands (Fig. 11a). Meanwhile, the martensitic phase appeared as thin parallel individual striations in the austenitic grains, as shown by arrows in
Fig. 11b. In agreement with the observations of Bayerlein et al. [11] during cyclic deformation of AISI 304L stainless steel, a direct austenite/martensite transformation must have occurred in the austenitic matrix of the material within this strain amplitude. At the high-strain amplitude (εa = 2.0%), most of grains in the specimen contained two or more activated slip systems and the interband spacing becomes smaller (see Fig. 12a). The high-magnification micrograph (Fig. 12b) reveals the presence of spatially distributed bands with different contrast. As suggested by Botshekan et al. [16], these bands can be ascribed to the presence of microtwins and martensite platelets. The amount of austenite/martensite transformation in the austenitic matrix further increases with strain amplitude (see Fig. 12c), where martensite with an irregular blocky shape extended completely across grains or as platelets arranged in bands was visible. The dislocation structures observed in specimens cycled to failure at three strain amplitudes are summarized in Figs. 13–15. At a lower strain amplitude (εa = 0.6%), the austenitic grains show a progressive accumulation of dislocation arrays and pileups of planar character, mainly correlated to a unique slip plane within individual grains (Fig. 13a). These planar arrays are formed by dissociated dislocations, clearly identified for showing stacking fault contrast as observed in Fig. 13b. At the intermediate strain amplitude (εa = 0.9%), the dislocation structure was characterized by elongated and not fully developed cells (see Fig. 14). Both within and outside the cells, a number of dislocation loops and debris were observed. The poorly developed cells must be the result of dislocations from different slip systems interacting and trapping each other at intersecting regions, as suggested by Jin et al. [26]. At the high-strain amplitude (εa = 2.0%), the cellular dislocation structures or subgrains were fully developed and densely clustered in the majority of grains, as has been observed in Fig. 15a. The regions between the dislocation cells are almost entirely dislocation free. In some grains, the cellular structure is penetrated by individual striations having parallel orientation (Fig. 15b). In analogy with similar striations observed by Botshekan et al. [16], after unidirectional cyclic straining, these striations can be ascribed to the presence of microtwins and/or martensite platelets. 3.4. Cyclic fracture features
Fig. 10. Optical micrograph showing slip band features in the fractured specimen tested in LCF at εa = 0.4%.
Examination of the fracture surface of the low-cycle fatigue specimens was performed: (a) at low magnification to identify the fatigue and final fracture (overload) regions and (b) at higher magnifications to identify regions of crack initiation and early crack growth in the fatigue region, and also to identify the finescale fracture features in the overload region. Figs. 16–18 show representative micrographs of the fracture surfaces features of the specimens cycled to failure at low, intermediate and high-strain amplitudes, respectively. At the lowcyclic total strain amplitude (ε/2 = 0.4%), the crack initiated near the surface and propagated inward, leaving a distinct region of crack propagation, which appeared as alternating furrows and ridges or strips of steps (Figs. 16a and b). High-magnification
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Fig. 11. Optical micrographes in the fractured specimen tested in LCF at εa = 0.9% showing: (a) slip band features; (b) morphologies of martensite.
observations of the crack nucleation or formation region revealed the crack initiation to occur at inclusions near the surface (Fig. 16c). The inclusion-type nucleation can be understood as cyclic slip localization due to stress-concentration at the inclusion, leading to either decohesion of the inclusion–matrix interface or cracking of the inclusion [17]. Observations of the crack
early growth region (Fig. 16d) revealed a crystallographic (stage I) morphology of crack growth characterized by arrangements of wavy striations that have steps intersection at right angles. The arrangements of steps are comparable to brittle striations. The overload region (Fig. 16e) comprised of microscopic voids of a variety of sizes and shallow dimples indicating the highly ductile
Fig. 12. Optical micrographes in the fractured specimen tested in LCF at εa = 2.0% showing: (a and b) slip band features; (c) different morphologies of martensite.
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Fig. 13. TEM micrographs in the fractured specimen tested in LCF at εa = 0.6% showing: (a) a planar array of dislocation structures; (b) stacking faults.
Fig. 14. TEM micrographs showing loose and incomplete dislocation cell structure in the fractured specimen tested in LCF at εa = 0.9%.
nature. At the intermediate strain amplitude (ε/2 = 0.9%) the fracture features on a macroscopic scale were similar to those observed at the lower strain amplitude, as shown in Fig. 17a. Microcracks originated from the specimen surface was also characteristic of fatigue crack nucleation at this strain amplitude (see Fig. 17b). Higher magnification observations of the crack nucle-
ation or formation region revealed the presence of fatigue slip bands and cyclic cleavage facets (Fig. 17c). The region of early crack growth showed distinct evidence of crystallographic (stage I) crack growth prior to propagation of the crack along a plane normal to the stress axis (stage II), as shown in Fig. 17d. In analogy with what was observed at the low-strain amplitude, the sudden fracture region also exhibits high-ductile characteristic (Fig. 17e). At the high-strain amplitudes (εa = 1.2%), the crack initiated not only near the surface but also in the interior of the specimen (Fig. 18a and b). Higher magnification observations of the crack nucleation region revealed that cleavage fracture was characteristic of fatigue crack nucleation at this strain amplitude (see Fig. 18c). An example of deformation twins as nucleation sites of cleavage fracture is shown in Fig. 18d. The crack nucleation of this type is termed “direct cleavage cracking”, in contrast to that initiated by shear, indicates thereby that shear cracking is not the only mechanism for crack nucleation at the higher strain amplitudes. Observations of the regions of transgranular fracture (Fig. 19e) revealed the fatigue striations to be covered with finer striations, which are indicative of repeated plastic deformation occurring in a single cycle and accompanied by local secondary cracks along striations. High magnification observation of the sudden fracture regions (Fig. 19f) revealed microscopic features indicative of classic ductile fracture.
Fig. 15. TEM micrographs in the fractured specimen tested in LCF at εa = 2.0% showing: (a) well-developed dislocation cell structure; (b) cellular structure penetrated by individual striations with parallel orientation.
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Fig. 16. (a–e) Macroscopic fractograph and SEM micrographs of the fracture surface in the specimen tested in LCF at εa = 0.4%.
4. Analysis and discussion The micromechanisms responsible for the cyclic stress response during low-cycle fatigue are dependent on the microstructure and strain amplitude [17]. In the as-heat treated conditions of SUS304-HP stainless steel, the initial microstructure comprises pinned dislocation lines and loops with lowdislocation density (Fig. 2). During cyclic straining, the unpinning and multiplication of dislocations as well as the mutual interactions of dislocations and the interactions of dislocations with grain boundaries increases the resistance to plastic deformation, which is responsible for the observed initial hardening in the cyclically deformed material. According to Lerch and Gerod
[27], an increase in slip band density is responsible for the hardening in austenitic steels. To verify this suggestion, specimens tested at different total strain amplitudes were also examined for the present material. The number of slip bands per grain was divided by the grain diameter in a direction perpendicular to the slip bands to estimate the average slip band spacing. About 50–75 grains were counted for each specimen. Fig. 19 shows the dependence of slip band spacing on imposed strain amplitudes, in which a decrease in slip band spacing with an increase in the applied strain amplitude was observed. Thus, consistent with earlier studies [27,28], it can be inferred that an increase in the degree of cyclic strain hardening with strain amplitude for the present material, as shown in Fig. 4, can be
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Fig. 17. (a–e) Macroscopic fractograph and SEM micrographs of the fracture surface in the specimen tested in LCF at εa = 0.9%.
related to the number of slip bands and slip systems activated in the cyclically deformed specimens. Since the material studied here is quasi-stable at room temperature due to addition of nitrogen, it underwent a deformation-induced austenitic/martensitic transformation during cyclic straining. Numerous investigations [9–13] have shown that the formation of martensites during cyclic loading strongly affects the fatigue mechanical behaviour of various types of steels. Magnetic measurements on the fracture surface of fractured specimens after the LCF deformation showed that the martensite content had increased with the applied total strain amplitude [10]. The measurement of the volume fraction of martensite during fatigue tests also documented that a direct relation exists between hardening and martensitic
transformation [16,21]. Therefore, after initial cyclic hardening, the stress response of the present material is governed by two competitive processes, namely dynamic recovery (i.e. formation of cells and subgrains) and defomation-induced martenstic transformation. The formation of cells and subgrains due to recovery mechanisms leads to an increase in the mean path for dislocations, which favours cyclic softening [1], whereas the formation of martensite by strain-induced processes drastically increases the resistance to plastic flow that promotes cyclic hardening of the material [11]. According to TEM observations at low-strain amplitudes, the saturation dislocation structures in the deformed specimen displayed a planar-array dislocation configuration (Fig. 13a). Both OM and TEM examinations revealed no marten-
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Fig. 18. (a–f) Macroscopic fractograph and SEM micrographs of the fracture surface in the specimen tested in LCF at εa = 1.2%.
site formation in austenitic grains tested at this strain amplitude. This agrees with the findings of Baudy and Pineau [10] concerning the critical total or plastic strain amplitude, which must be achieved in order to induce martensite formation in cyclic straining. Consequently, at low-strain amplitude, the progressive softening process after initial cyclic hardening is attributed to the formation of a dislocation configuration that bears the plastic strain more easily [17]. At the intermediate strain amplitude austenite/martensite transformation takes place and the amount of this transformation increases with an increasing number of cycles, as shown in Fig. 11b. Meanwhile, the tendency to form a dislocation substructure characterized by a developing cell structure containing low-dislocation density/ill-defined cell walls (Fig. 14) suggests localization of deformation in the material, which results in less stress for sustaining a given strain amplitude, namely softening. Thus, when an increase of the resistance to plastic deformation resulting from formation of martensite can
compensate for the softening effect associated with dislocation cellular structure, the material exhibits a saturation character as has been observed in the cyclic stress response curves (Fig. 3), which is followed by secondary hardening as a result of the fact that the volume fraction of strain-induced martensite transformation further increased with the increasing number of straining cycles. At high-strain amplitudes, the cumulation of the cyclic plastic strain leads to a continuous increase in the density of shear bands, and thus in the density of sites for strain-induced nucleation of martensite (see Figs. 12c and 15b). In other words, more martensite is formed with a less number of cycles in this case. As a result, the material displayed continuous strain hardening up to failure without displaying an intermediate stage of stress saturation at the higher strain amplitudes (see Fig. 3). On the other hand, the formation of more martensite also leads to more crack initiating sites in the fatigued specimen at high-strain amplitude, which has been exhibited in the fatigue fracture (see Fig. 18a–d).
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5. Conclusions The experimental results on the room-temperature low-cycle fatigue behaviour, deformation microstructures and fracture features of the austenitic stainless steel SUS304-HP reported in this paper support the following conclusions:
Fig. 19. Variation of slip band spacing with strain amplitude.
The sensitivity of the cyclic stress response to the type of loading or the imposed strain history, as shown in Fig. 5, was also reported in other austenitic stainless steels, such as AISI 316L and AISI 446 [29], and was explained as a result of the strong evolution of dislocation structures and nucleation of the deformation-induced martensitic transformation during fatigue testing. Since the dislocation structure built up in the IST was mostly characteristic of the highest strain amplitude in the strain block and remained practically that of the highest strain amplitude throughout the block [12], both the saturation dislocation structure and the martensite transformation in the present material can be expected to be formed at early stages of strain blocks due to the fact that the highest strain amplitude occurred in each strain block. In other words, the material remained practically similar regardless of stress amplitudes in the IST. As a result, the material exhibits cyclic hardening in the IST even when the strain amplitude decreased within a block, as has been observed in Fig. 5. In the CST, however, the dislocation structure was different at different strain amplitudes and more martensite formed at the high-strain amplitudes, which is responsible for the observed hardening/softening behaviour in the cyclic stress response curves. The lower slope for the CSSC obtained by the IST as compared to that determined by the CST, as shown in Fig. 6, is in agreement with observations by Nystrom et al. [30] and Zhong et al. [31] in AISI 316L and AISI 310 types of stainless steel. It is likely that this general difference in slope between the two methods is caused by differences in the developing dislocation structure during the IST and CST. This difference of the microstructure induced by the two methods can be used to explain why Masing-type behaviour was seen in the IST but not in the CST, for Masing-type behaviour is expected to be present only for the cases where the microstructure does not change appreciably [12]. In other words, the difference of the microstructures during the CST is responsible for the observed non-Masing-type behaviour of the SUS304-HP stainless steel in this loading condition.
(1) Cyclic stress response, during companion specimen tests, revealed combinations of a variable cyclic hardening, stable behaviour and softening, depending on the applied cyclic strain amplitude, while, during incremental step tests, exhibited hardening character at all strain levels. In the case of the CST, the degree of cyclic strain hardening increases almost linearly with increasing strain amplitude. (2) The CSS curves obtained by the CST and IST methods exhibits different characteristic features. The CST, compared to the IST, gives a higher slope of the CSSC or a higher strain hardening capacity at all strain amplitudes. Therefore, in the case of the present material, there is no possibility of using one specimen to determine the cyclic stress–strain curve. (3) The fatigue lifetime shows single-slope behaviour in both Basquin and Cofffin-Manson diagrams. (4) Masing cyclic stress–strain behaviour was presented only in the IST method but not in the CST method. The prediction precision of the cyclic plastic strain energy was improved greatly due to reckoning into the effect of non-Masing-type behaviour in terms of the modified equation developed by Jhansale and Topper [25]. (5) Observations of fatigue-related microstructures revealed that with increasing total strain amplitude the slip band density increased and the dislocation structure changed from a planar dislocation array to a more cellular-like structure. A strong tendency of the cyclic deformation-induced austenitic/martensitic transformation was observed in the austenitic matrix at higher cyclic strain amplitudes. (6) The SEM examinations revealed that at low-strain amplitudes the inclusion-type nucleation occurred near the surface, while at high-strain amplitudes the crack initiation characterized by cleavage cracking occurred not only near the surface but also in the interior of the specimen. Acknowledgements The first author would like to express his sincere thanks to Dr. Akihiko OHTA, the former host researcher of the first author, who provided financial assistance through 2001Y JSPS Postdoctoral Fellowship under Grant PB01021. He also wishes to acknowledge the National Institute for Materials Science (NIMS), Japan, for his appointment as a visiting researcher in Materials Information Technology Center during February 1st, 2002 through January 31st, 2004. References [1] K. Bhanu Sankara Rao, M. Valsan, S.L. Mannan, Mater. Sci. Eng. A130 (1990) 67.
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