Uniaxial Ratcheting Behaviors of Metals with Different Crystal Structures or Values of Fault Energy: Macroscopic Experiments

Transcription

1 J. Mater. Sci. Technol., 11, 7(5), 5-5. Uniaxial Ratcheting Behaviors of Metals with Different Crystal Structures or Values of Fault Energy: Macroscopic Experiments Guozheng Kang 1), Yujie Liu ), Yawei Dong ) and Qing Gao ) 1) State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 11, China ) School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 11, China [Manuscript received October 1,, in revised form January, 1] The uniaxial ratcheting behaviors of several metals with different crystal structures or values of fault energy were observed by the stress-controlled cyclic tests at room temperature. The prescribed metals included 1L stainless steel, pure copper, pure aluminum, and ordinary # carbon steel. The effects of applied mean stress, stress amplitude and stress ratio on the uniaxial ratcheting were also investigated. The observations show that different crystal structures or values of fault energy result in more or less different ratcheting behaviors for the prescribed metals. The different ratcheting behaviors are partially caused by the variation of dislocation mobility. KEY WORDS: Ratcheting; Uniaxial cyclic loading; Crystal structure; Fault energy 1. Introduction Ratcheting was extensively studied in the last two decades as reviewed by Ohno [1] and Kang [], and more recently done by researchers [ 17] and so on. The referable work did not pay more attention to compare the ratcheting behaviors of different materials, even if the existed results showed that the ratcheting depends greatly on the types of materials. Since the experimental observations on the ratcheting behaviors of the metals with different crystal structures or values of fault energy are not sufficient, and the deformation mechanism of ratcheting has not been realized clearly yet, various constitutive models have been developed to describe the ratcheting behaviors of different materials, which restrain the engineering application of such constitutive models. Thus, it urges us to provide a micro-mechanism-based constitutive model to describe the ratcheting behaviors of certain class of metals, such as the metals with the same crystal structure. However, a generalized constitutive model can be constructed only after the micro-mechanism Corresponding author. Prof., Ph.D.; Tel.: + 77; Fax: + 777; address: guozhengkang@yahoo.com.cn (G.Z. Kang). of ratcheting is revealed by detailed microscopic observation. Since the ratcheting deformation is microscopically related to the mobility of dislocation during the cyclic loading [1,1], it is supposed that the metals with different crystal structures or values of fault energy shall present more or less different ratcheting behaviors. Before the micro-mechanism of ratcheting is discussed, it is necessary to investigate the ratcheting behaviors of the metals with different crystal structures or values of faulty energy by macroscopic experimental observations. Therefore, in this paper, the ratcheting behaviors of the metals with different crystal structures or values of fault energy are observed by the uniaxial stresscontrolled cyclic tension-compression tests with nonzero mean tensile stress. Four kinds of metals are employed in the tests. The effects of crystal structure and value of fault energy, as well as applied stress level on the ratcheting are investigated. Some significant conclusions are obtained.. Experimental The experimental materials used in this work were 1L stainless steel, face-centered cubic (FCC) crys-

2 5 G.Z. Kang et al.: J. Mater. Sci. Technol., 11, 7(5), 5 5 Stress, / MPa Normalized stress, / y L stainless steel # carbon steel Copper Pure aluminium 1 5 Strain,..5 Copper L stainless steel Pure aluminium # carbon steel Normalized strain, / b Fig. 1 Monotonic tensile stress-strain curves for four prescribed metals: original ones; normalized ones tal structure with low fault energy; pure copper, facecentered cubic (FCC) crystal structure with moderate fault energy; pure aluminum, face-centered cubic (FCC) crystal structure with high fault energy; and ordinary # carbon steel, body-centered cubic (BCC) crystal structure. Their chemical compositions (in wt%) were listed as follows, respectively: (1) Solution-heat-treated 1L stainless steel (kept at C for 1 h and then cooled in water): C,.; Mn, 1.1; Si,.5; P,.; S,.; Cr, 1.; Ni, 1.; Mo,.1; Fe, remained; () Annealed pure copper (kept at 55 C for 1.5 h and then cooled in air): Cu,.; Bi,.; Sb,.; As,.; Fe,.; Pb,.; S,.; () Annealed pure aluminum 1 (i.e. 1-F): Al.; Fe+Si.; () Hot-rolled ordinary # carbon steel: C,.1; Si,.; Mn,.; P,.1; S,.7; Cr,.; Ni,.1; Cu,.; Fe, remained. The as-received or heat-treated bars were machined to be solid bar specimens (with gauge length of mm and diameter of 1 mm) for the monotonic tension and cyclic tension-compression tests. The test machine was MTS; the loading process was controlled and the data were collected by Teststar control system attached to the machine. The axial strain was measured by uniaxial extensometer. The extensometer was mounted within the gauge length of specimen. No heat-treatment was performed after the specimens were machined, since the machining process influenced the dislocation density in uniaxial specimen slightly. The specimens were tested under the uniaxial strain- or stress-controlled cyclic loading at room temperature. The maximum number of cycles prescribed was 1. To illustrate the uniaxial ratcheting more clearly, the curves of axial ratcheting strain ε r vs number of cycles N for all load cases were obtained from the experimental data and are shown in figures in Section. In this work, the ratcheting strain ε r is defined as ε r = ε max + ε min (1) where ε max is the maximum axial logarithmic strain in each cycle, and ε min is the minimum one. Also, the ratcheting strain rate is defined as the increment of ratcheting strain after each cycle.. Results and Discussion Before the uniaxial ratcheting behaviors are discussed, some basic performances of the metals are obtained from monotonic tension and shown in Fig. 1, which are helpful to choose the stress levels applied in the cyclic loading tests. Since there is a large difference in the mechanical performances of four prescribed metals, normalized stress σ/σ y and strain ε/ε b are used in Fig. 1 to show the results more clearly, where σ y is the yield stress (σ s for ordinary # carbon steel) or nominal yield stress (σ p. for other prescribed metals) and ε b is the strain corresponding to the ultimate stress σ b. From Fig. 1, it is shown that the metals with different crystal structures or values of fault energy present different mechanical performances: (1) The prescribed FCC metals present better ductility than the BCC # carbon steel, since the dislocation can move more easily in the FCC metals, especially for 1L stainless steel, whose fault energy is low ( MJ/m [] ). It also shows that the elongation ratios of the FCC metals decrease with increasing value of fault energy. with the highest value of fault energy (1 MJ/m [] ) possesses the lowest elongation ratio among three prescribed FCC metals since the movement of dislocation in pure aluminum is restrained by its highest value of faulty energy. Pure copper is the moderate one (its fault energy is 5 MJ/m [] ). The BCC # carbon steel presents the lowest elongation ratio among four prescribed metals, since the dislocation slipping in the BCC # carbon steel is more difficult than that in the FCC metals. () The extent of strain hardening is also different in the prescribed metals, and the FCC metals with low and moderate values of fault energy, i.e., 1L stainless steel and pure copper possess a relatively higher extent of strain hardening and their ratios of yield stress to ultimate stress (σ y /σ b ) are

3 G.Z. Kang et al.: J. Mater. Sci. Technol., 11, 7(5), low (about.5 and., respectively). However, the strain hardening of the BCC # carbon steel is the lowest but its ratio of yield stress to ultimate stress (σ y /σ b ) is the highest (nearly.) among the prescribed metals in this work. The extent of strain hardening also depends upon the mobility of dislocation, and the generation and movement of the dislocation in the FCC metals with low and moderate values of fault energy are much easier than that in other metals, which results in an increased dislocation density and then a stronger strain hardening. It should be noted that although the hot-rolled bars of # carbon steel are directly used to obtain the specimens in the experimental observations, the dislocation density in the specimens is initially low, since the hot-rolled bars are cooled in the air to room temperature after hot-rolling, which is the same as the normalized treatment of such metals. It means that the initial dislocation density in all the prescribed metals is low, and the different responses presented in the monotonic and cyclic deformations of the metals are mainly caused by different crystal structures and values of faulty energy, as well as the different microstructures. Surely, more direct proof should be provided by the detailed dislocation observation of transmission electronic microscopy (TEM), which is beyond the topic of this work, and will be discussed in the future..1 Cyclic softening/hardening features The cyclic softening/hardening features of four prescribed metals were observed by the symmetrical uniaxial strain-controlled cyclic tension-compression tests with various strain amplitudes (e.g.,.%,.%,.5% and.7%), and the results are shown in Fig.. To illustrate the degree of cyclic hardening or cyclic softening more clearly, normalized stress amplitude σ a /σ a is employed in the figures, where the σ a is the responded stress amplitude in the first cycle. It is concluded from Fig. as follows: (1) Three kinds of FCC metals, i.e., 1L stainless steel, pure copper and pure aluminum present cyclic hardening obviously; however, the observed cyclic hardening differs more or less from the metals with different values of faulty energy and also depends greatly on the applied strain amplitude. For 1L stainless steel, when the applied strain amplitude is small, e.g.,.5%, an initial cyclic hardening occurs in the beginning of cyclic loading, but after certain cycles, the responded stress amplitude decreases slightly with increasing number of cycles. After about cycles, a stable cyclic response is reached. However, when the applied strain amplitude is relatively high, e.g.,.7%, it presents apparent cyclic hardening during the cyclic loading, and the responded stress amplitude increases continuously with increasing number of cycles. No saturation of cyclic hardening is reached in Norm. stress amplitude, a / a Norm. stress amplitude, a / a Strain amplitudes 1L.5% 1L.7% #.5% #.7% Strain amplitudes Copper.% Copper.5% Aluminium.% Aluminium.% Fig. Curves of normalized stress amplitude, σ a/σ a (σ a, responded stress amplitude in the first cycle) vs number of cycles, N in the strain-controlled cyclic loading tests with different strain amplitudes: for 1L stainless steel and # carbon steel; for pure copper and aluminum the prescribed number of cycles, as shown in Fig.. This is similar to that of stainless steel observed by Kang et al [1]. As shown in Fig., pure copper presents most significant cyclic hardening, and both the extent of cyclic hardening and its evolution rate increase with increasing applied strain amplitude. Different from that of 1L stainless steel, the saturation of cyclic hardening occurs after certain cycles in two prescribed tests with different applied strain amplitudes, and the saturation is reached more quickly when the applied strain amplitude is higher. For pure aluminum, its cyclic hardening just occurs within the first ten cycles; the saturation is reached very quickly and the extent of cyclic hardening is lower than that of 1L stainless steel and pure copper. It is concluded that for the FCC metals, the cyclic hardening also depends on the generation and movement of dislocation. If its value of fault energy is lower and the dislocation can be generated more easily during the cyclic deformation, stronger cyclic hardening occurs in the metal. The saturation of cyclic hardening will be reached when a stable structure of dislocation is formed after certain number of cycles. However, although the 1L stainless steel possesses the lowest value of faulty energy among the prescribed FCC metals, its extent of cyclic hardening is lower than that of

4 5 G.Z. Kang et al.: J. Mater. Sci. Technol., 11, 7(5), Mean stress =. p. 1. p. 1. p. 1. p..55 p. 1 Stress amplitude = 1. p. 1. p..17 p..1 p..5 p. 1 1 (c) Peak stress = 1. p Fig. Uniaxial ratcheting results of 1L stainless steel: constant mean stress and various stress amplitudes; constant stress amplitude and various mean stresses; (c) constant maximum stress and various stress ratios pure copper, whose faulty energy is higher than that of 1L stainless steel. It should be caused by the solid solution microstructure of 1L stainless steel. The interaction of its solute atoms and dislocations has a latent effect on the cyclic deformation of the steel. Thus, its cyclic hardening feature cannot be explained only by the movement of dislocation, which is different from the pure metals such as pure copper and aluminum, whose cyclic hardening behaviors are directly dependent on the values of fault energy. () For the BCC # carbon steel, its cyclic softening/hardening feature depends greatly on the applied strain amplitude. When the strain amplitude is small, e.g.,.5%, as shown in Fig., apparent cyclic softening occurs. The responded stress amplitude decreases with increasing number of cycles and reaches its saturation after about 1 cycles. However, when the strain amplitude is relatively high, e.g.,.7%, the steel presents somewhat cyclic hardening and the stress amplitude increases slightly with increasing number of cycles. Comparison shows that the cyclic softening/hardening feature of # carbon steel is much weaker than that of prescribed FCC metals. Therefore, it can be simplified as a kind of cyclic stable material. It should be noted from Fig. 1 that the applied maximum strains in the prescribed strain-controlled cyclic load cases, i.e.,.5% and.7% are located in the yielding plateau of the steel, and its changeable cyclic softening/hardening feature is straightforward, since the stress-strain response of the steel in the yielding plateau is unstable.. Uniaxial ratcheting behaviors..1 FCC metals with different values of fault energy At first, the uniaxial ratcheting behaviors of the prescribed FCC metals with different values of fault energy, i.e., 1L stainless steel, pure copper and pure aluminum were investigated by the single-stepped uniaxial stress-controlled cyclic tension-compression tests with non-zero mean stress. The results obtained from the cyclic tests with different loading conditions are shown in Figs.. To show the results more clearly, the applied mean stress, stress amplitude and peak stress are expressed in term of material s yield stress (σ p. or σ s ), respectively. For example, in Fig., the applied mean stress is expressed as.σ p. and one of applied stress amplitudes is 1.σ p.. It is seen from Figs. 5 that significant ratcheting occurs in all prescribed FCC metals, and the ratcheting depends greatly upon the applied mean stress, stress amplitude and stress ratio, R. The ratcheting strain increases progressively with increasing number of cycles, but the ratcheting strain rate (defined as the increment of ratcheting strain after each cycle) continuously decreases due to the cyclic hardening features of the metals. In some cases with lower stress levels, a quasi-shakedown of ratcheting (i.e., the ratcheting strain rate here is very close to zero, but not equal to zero) will be reached after a certain number of cycles. The ratcheting strain and its rate increase with increasing stress amplitude and mean stress, but with decreasing stress ratio, as shown in the figures, except for the case of 1L stainless steel with regard to the variation of mean stress. For 1L stainless steel, its ratcheting behavior does not depend monotonically upon the applied mean stress, and the ratcheting strain produced in the case with the mean stress of.1σ p. is higher than that with the mean stress of.17σ p.. This phenomenon is similar to that of stainless steel observed by Kang et al [1].

5 G.Z. Kang et al.: J. Mater. Sci. Technol., 11, 7(5), Mean stress =. p. 1.1 p. 1.5 p. 1. p.. p. Mean stress =.1 p. 1.7 p. 1.1 p.. p. 1 Stress amplitude = 1. p p.. p.. p. 1 (c) Peak stress =. p Fig. Uniaxial ratcheting results of pure copper: constant mean stress and various stress amplitudes; constant stress amplitude and various mean stresses; (c) constant maximum stress and various stress ratios From Fig., with the same stress level, a direct comparison shows that the ratcheting behaviors of three prescribed FCC metals do not increase monotonically with decreasing value of faulty energy, but decrease with increasing extent of cyclic hardening the metals presented. The ratcheting of pure aluminum is the most significant one among three prescribed FCC metals, since its extent of cyclic hardening is the lowest one as shown in Fig.. On the other hand, pure copper presents the weakest ratcheting behavior due to its strongest cyclic hardening among three prescribed FCC metals. It means that the quicker the stable 1 7 Stress amplitude =. p p.. p..1 p. 1 (c) Peak stress = 1.55 p Fig. 5 Uniaxial ratcheting results of pure aluminum: constant mean stress and various stress amplitudes; constant stress amplitude and various mean stresses; (c) constant maximum stress and various stress ratios dislocation structures, such as dislocation cell formed, the weaker the ratcheting in the metals... Metals with different crystal structures In this section, the ratcheting behaviors of the metals with different crystal structures are investigated, i.e., for the FCC pure aluminum and BCC # carbon steel. Figure 7 provides the results of # carbon steel obtained in the uniaxial stress-controlled cyclic tension-compression tests with different applied mean stresses, stress amplitudes and stress ratios. It is shown that significant ratcheting also occurs in the BCC # carbon steel and the ratcheting also de-

6 5 G.Z. Kang et al.: J. Mater. Sci. Technol., 11, 7(5), Mean stress=. p. 1 Mean stress=. p. 1 Stress amplitude=1 p. SS1L Pure copper Stress amplitude=1.1 p. 1L stainless steel Pure copper 1 1 Fig. Comparison of uniaxial ratcheting results for the prescribed FCC metals with different values of fault energy 1 Mean stress =.17 s 1. s.17 s. s 1 1 Stress amplitude =. s.5 s. s.17 s 1 1 (c) Peak stress = 1.17 s Fig. 7 Uniaxial ratcheting results of # carbon steel: constant mean stress and various stress amplitudes; constant stress amplitude and various mean stresses; (c) constant maximum stress and various stress ratios Mean stress=. p. Stress amplitude=1. p. # carbon steel 1 Mean stress=. p. Stress amplitude=1.1 p. # carbon steel 1 1 Fig. Comparison of uniaxial ratcheting results for the prescribed metals with different crystal structures:.±1.σ p.;.±1.1σ p. pends greatly upon the applied stress level. The ratcheting strain increases monotonically with increasing stress amplitude and mean stress, but with decreasing stress ratio. However, different from those of the prescribed FCC metals, for the BCC # carbon steel, a constant ratcheting strain rate (the constant rate is much higher than zero) is reached after a certain number of cycles due to its cyclic stable feature and no quasi-shakedown of ratcheting occurs within the prescribed number of cycles, as shown in Fig. 7. Direct comparison in Fig. shows that the ratcheting behavior of BCC # carbon steel is more significant than that of pure aluminum. It means that the ratcheting behaviors of polycrystalline materials mainly depend upon their cyclic softening/hardening features presented in the cyclic loading in macroscopic scale. The macroscopic observations show that different ratcheting behaviors occur in the prescribed metals with different crystal structures or values of faulty energy. Although the elongation ratios of the prescribed metals are directly relative to the generation and mobility of dislocation, which is corresponding to the crystal structure and value of faulty energy, their ratcheting behaviors do not depend only upon the crystal structure or value of faulty energy, because

7 G.Z. Kang et al.: J. Mater. Sci. Technol., 11, 7(5), the generation and mobility of the dislocation in polycrystalline metals are also influenced by many other microstructure features such as solute atoms, second phase particles, textures and grain boundary. It means that the micro-mechanism of ratcheting for the polycrystalline metals is very complicated. To discuss the effects of crystal structure and value of faulty energy on the ratcheting, the single crystal materials should be employed. Also, a systematic microscopic observation on the dislocation structure and its evolution during the cyclic loading is necessary, which will be discussed in the future work.. Conclusions (1) Significant ratcheting behaviors occur in the prescribed metals under the uniaxial stress-controlled cyclic tension-compression test with non-zero mean stress. The ratcheting behaviors obviously depend on the applied mean stress, stress amplitude and stress ratio. () Different cyclic softening/hardening features are observed in the prescribed metals. The FCC metals, i.e., solution heat-treated 1L stainless steel, annealed pure copper and annealed pure aluminum present obvious cyclic hardening, and the extent of cyclic hardening for 1L stainless steel or pure copper is higher than that for pure aluminum. While the BCC # carbon steel can be taken as a cyclic stable material. () The ratcheting behaviors of the prescribed metals depend phenomenologically upon the cyclic softening/hardening features of the metals presented in macroscopic scale, rather than directly on the crystal structure and value of faulty energy. presents the most significant ratcheting behavior among three prescribed FCC metals due to its highest value of faulty energy and weakest cyclic hardening. The ratcheting of BCC # carbon steel is more significant than those of three prescribed FCC metals due to its cyclic stable feature. () To discuss the effects of crystal structure and value of faulty energy on the ratcheting, good candidates are single crystal materials. Acknowledgement Financial support of the National Natural Science Foundation of China (Grant No. 177) was gratefully acknowledged. REFERENCES [1 ] N. Ohno: Mater. Sci. Res. Int., 17, (1), 1. [ ] G.Z. Kang: Int. J. Fatigue,, (), 1. [ ] G. Cailletaud and K. Sai: Mater. Sci. Eng. A,, (1),. [ ] S.J. Yun and A. Palazotto: Int. J. Fatigue,, (), 7. [5 ] Z. Zhang, X. Chen and T. Wang: Poly. Eng. Sci.,, (1),. [ ] W.W. Yu, X. Chen, Y.P. Wang, L. Yan and N. Bai: Poly. Eng. Sci.,, (), 11. [7 ] Y.J. Liu, G.Z. Kang and Q. Gao: Int. J. Fatigue,, (7),. [ ] O.U. Colak: Mater. Design,, (), 75. [ ] Y.Y. Jiang and J.X. Zhang: Int. J. Plasticity,, (), 11. [1] J.X. Zhang and Y.Y. Jiang: Int. J. Plasticity,, (1), 1. [11] K. Nakane, N. Ohno, M. Tsuda, Y. Yagi, I. Nakagawa and T. Atsumi: Int. J. Plasticity,, (1), 11. [] M. Wolff and L. Taleb: Int. J. Plasticity,, (11), 5. [1] T. Hassan, L. Taleb and S. Krishna: Int. J. Plasticity,, (1), 1. [1] G.Z. Kang, Y.J. Liu and J. Ding: Int. J. Fatigue,, (), 1. [] G.Z. Kang, Q.H. Kan, L.M. Qian and Y.J. Liu: Mech. Mater.,, 1(1), 1. [1] H. Gao and X. Chen: Int. J. Fatigue,, 1(), 7. [17] C.B. Lim, K.S. Kim and J.B. Seong: Int. J. Fatigue,, 1(), 51. [1] C. Gaudin and X. Feaugas: Acta Mater.,, 5(), 7. [1] X. Feaugas and C. Gaudin: Int. J. Plasticity,, (),. [] J.S. Pan, J.M. Tong and M.B. Tian: Fundamentals of Materials Science, Tsinghua University Press, Beijing, 1. (in Chinese) [1] G.Z. Kang, Y.J. Liu and Z. Li: Mater. Sci. Eng. A,, 5-,.