Investigation on hot deformation of 20Cr–25Ni superaustenitic stainless steel with starting columnar dendritic microstructure based on kinetic analysis and processing map

Abstract

The deformation behaviour of a 20Cr–25Ni superaustenitic stainless steel (SASS) with initial microstructure of columnar dendrites was investigated using the hot compression method at temperatures of 1000–1200°C and strain rates of 0·01–10 s⁻¹. It was found that the flow stress was strongly dependent on the applied temperature and strain rate. The constitutive equation relating to the flow stress, temperature and stain rate was proposed for hot deformation of this material, and the apparent activation energy of deformation was calculated to be 516·7 kJ mol⁻¹. Based on the dynamic materials model and the Murty's instability criterion, the variations of dissipation efficiency and instability factor with processing parameters were studied. The processing map, combined with the instability map and the dissipation map, was constructed to demonstrate the relationship between hot workability and microstructural evolution. The stability region for hot processing was inferred accurately from the map. The optimum hot working domains were identified in the respective ranges of the temperature and the strain rate of 1025–1120°C and 0·01–0·03 s⁻¹ or 1140–1200°C and 0·08–1 s⁻¹, where the material produced many more equiaxed recrystallised grains. Moreover, instability regimes that should be avoided in the actual working were also identified by the processing map. The corresponding instability was associated with localised flow, adiabatic shear band, microcracking and free surface cracks.

Keywords

High alloyed austenitic stainless steel Columnar dendrites microstructure Hot compression Processing map Constitutive analysis

Introduction

In recent years, superaustenitic stainless steels (SASSs) have attracted great attention in engineering applications owing to their unique combination of high strength, good toughness and superior corrosion resistance.1^–3 Such excellent properties mainly rely on the features of composition, the high addition of chromium, nickel, molybdenum, copper and other alloying elements in austenite along with low carbon content, which generally causes the balance amount of iron to be less than 50 wt-% of the total in the alloy.4 Therefore, SASSs have been extensively used in several aggressive fields, such as chemical, petrochemical, military, oceanic and nuclear industries.5,6

Generally, in order to obtain a well developed microstructure, such as uniform and fine equiaxed grains, as cast SASSs are always processed at high temperature by radial forging or rough rolling directly. The dynamic recrystallisation (DRX) in as cast structure during the primary stage of ingot breakdown is a main choice to complete the microstructural reconstitution and to improve the hot workability by reducing the propensity for slivering and crack formation. Thus, controlled hot deformation is an important technique employed to optimise the microstructure and mechanical properties of the as cast alloys.

Compared with traditional austenitic stainless steels such as type 304 and type 316, it is not surprising that the hot workability of SASSs will be greatly affected due to many more alloying additions in the austenitic matrix. High alloying in austenitic stainless steel causes an increase of stacking fault energy, which will make the steel exhibit progressively more sluggish recrystallisation because of accelerated recovery processes.7 Actually, during commercial hot processing, the as cast SASSs easily confront with severe problems, such as laminated or surface cracking, which leads to high production costs and low efficiency. The occurrence of defects is strongly associated with complex chemical composition, initial microstructure and also operating conditions used by workers. Hence, in order to evaluate the best hot forming operations and further improve the properties and producing rate, it is necessary to investigate dynamic responses of as cast SASSs at elevated temperatures.

In the previous reports, great efforts have been mainly concentrated on the hot deformation behaviour of wrought, fully recrystallised or fine grain superalloys due to the small ingot size and the absence of accurate microstructural characterisation. For example, Asli and Zarei-Hanzaki8 studied the effect of temperature and strain rate on microstructural evolution of as forged 37Cr–31Ni–3·1Mo SASS and analysed its DRX characteristics. Momeni et al.9 investigated the competition behaviour between strain induced precipitation and DRX for an as forged 28Cr–33Ni–3·1Mo SASS at the temperature range of 950–1050°C and found that the precipitates nucleated at low temperatures and low strain rates were complex carbides with the composition of (Cr, Fe, Mo)₂₃C₆. In addition, Ebrahimi et al.10 also investigated the hot deformation behaviour of another as forged SASS containing 16%Cr and 25%Ni in a wide working condition and pointed out the interaction of DRX with solute dragging effect. Regrettably, little literature is available on the theories about hot working technology of as cast SASSs.

The SASS with composition of Fe–20Cr–25Ni–4Mo–Cu shows wide application potential due to its high yield strength and good corrosion resistance. For example, it has been broadly employed as the candidate material for the desalination equipment in China. In actual industry production, rough rolling locates the first processing stage for the homogenised continuous casting billets. However, there is still lack of basic understanding of microstructural evolution during hot deformation and designing suitable hot working parameters for this steel until now. The as cast microstructure in the billet is composed of columnar dendrites in the border and equiaxial grains in the central area. It has been recognised that the deformation and recrystallisation of ingot material during primary breakdown are sensitive to the starting as cast microstructure.11 Therefore, the purpose of the present work was to systematically investigate the hot workability of Cr₂₀Ni₂₅Mo₄Cu SASS with starting columnar dendritic microstructure, and precise deformation mechanism and desired processing parameters will be revealed by processing map and associated microstructural observation.

Materials and methods

Materials and samples

The Cr₂₀Ni₂₅Mo₄Cu SASS used in the present investigation was commercially produced by TISCO (China) and supplied as continuous casting billets that are 200 mm thick, which had been suffered from high temperature annealing at 1230°C for 3 h in order to eliminate the segregation of alloying elements and to make the microstructure homogeneous. Its chemical composition is as follows: Fe–25·5Ni–20·0Cr–4·4Mo–1·3Cu–0·4Si–1·5Mn–0·015C–0·07N (in wt-%).

The columnar grain region in as received casting billet was identified by macroetching a transverse section and cut from the billet. Cylindrical samples of Ø10×15 mm were directly machined from the region with the sample axis parallel to the axes of the columnar grains. Figure 1a shows the starting microstructure of the studied steel. The compressed direction is parallel to the major axes of the columnar grains. The austenitic columnar dendrites are uniformly distributed, and no ferrites are observed. The phase diagram analyses using the Thermo-Calc software confirm that the steel exhibits complete austenite microstructure at high temperatures from 1000 to 1330°C, as shown in Fig. 1b.

Hot compression tests

Hot compression tests were conducted on a Gleeble 1500D thermomechanical simulator over the ranges of temperatures from 1000 to 1200°C at 50°C intervals and of strain rates from 0·01 to 10 s⁻¹ at intervals of an order of magnitude. A tantalum foil that is 0·05 mm thick is placed between the anvil and the specimen to reduce the friction. The heating method involved first heating to 1250°C and holding for 5 min and then cooling to the deformation temperature at ∼5°C s⁻¹ was adopted to simulate the practical industrial process (shown schematically in Fig. 2). Before each testing, the specimen was soaked at the deformation temperature for 10 s to eliminate thermal gradients before deformation. All the specimens were deformed to a true strain of ∼0·7 and then quenched into water within 2 s to preserve the microstructure after the high temperature deformation. Samples for optical microscopy were sectioned at midplane parallel to the compression axis, and the cut sections were mounted, mechanically polished according to the standard procedure and then electrolytically etched with a solution of 10% hydrochloric acid.

Method of processing map

It is well recognised that the processing map coupled the processing conditions such as deformation rate and temperature with a desired microstructure is a valuable tool for the optimisation of working parameters and for controlling the microstructure and property of the product. Based on the dynamic materials model developed by Prasad and Sasidhara,12 the processing map is constituted by a superimposition of a power dissipation map and an instability map. Two regions of stability and instability deformation are then identified. What's more, the thermal deformation mechanisms can be revealed by the processing map within different regions, such as dynamic recovery (DRV), DRX, superplastic deformation, etc. Until now, the processing maps have been successfully applied in alloys of magnesium, aluminium, titanium and Ni based superalloys, as well as stainless steels, such as austenitic, martensitic and duplex stainless steel.13^–19

Briefly, in this model, the workpiece deformed during hot compression is assumed to be a non-linear dissipater of power supplied by a particular source. The instantaneous dissipated power P is thought to be divided into two complementary parts: G content and J cocontent, which represent the power dissipated by temperature rise and microstructural changes respectively. Their relationship is given by equation (1) (1) where σ and denote the flow stress (MPa) and the strain rate (s⁻¹) respectively. Generally, the power dissipation capacity of workpiece is represented by the efficiency of power dissipation η (%), indicating how efficiently the material dissipates energy by the microstructural changes, which is defined as follows (2) where m is the strain rate sensitivity and J_max is the maximum when an ideal linear dissipater (m = 1) is achieved. However, the m value varies with the strain rate especially at high strain rates and high stress levels. Therefore, it is not a constant in fact. The calculation of η value using the equation (2) may be incorrect.20 In this case, Murty and Rao21,22 proposed a modified model in which m was regarded as a variable to calculate the η value, which can be expressed as follows (3) The variation of the η value with deformation temperature and strain rate at a given strain constitutes a map called power dissipation map, which may exhibit different domains directly correlated with specific microstructural mechanisms.

However, during hot deformation, some materials may exhibit some processes like flow localisation, adiabatic shear deformation, formation of new phases, void generation and dynamic strain aging, all of which can make the materials instable and thereby decrease the ductility of the materials.23,24 For the identification of these instabilities during the plastic flow, Murty's instability criterion was used and validated in various alloys. This criterion is defined by25 (4) Consequently, the instability map can be obtained depending on the relationship between the m and the η at different temperatures and strain rates at a given strain, and it is superimposed on the above power dissipation map to constitute a processing map, which can determine the optimal condition for thermomechanical processing.

Results and discussion

Flow behaviour

Figure 3 shows the flow curves obtained at the strain rate of 0·01 s⁻¹ for different temperatures (1000–1200°C) and at the temperature of 1200°C for different strain rates (0·01–10 s⁻¹). As expected, the flow stress is a strong function of the temperature and the strain rate, and it increases and decreases with decreasing the temperature and the strain rate respectively. However, unlike equiaxed materials, most of the flow curves exhibit gradual increase in stress after initial sharp strain hardening without obvious crest or steady state, particularly at higher strain rates or lower temperatures, which indicates that the workhardening is still predominant although the limited restoration has already taken place. This phenomenon has been observed on other materials with columnar dendrites like BFe10-1-1 alloy and 316L steel.7,26 There may be two reasons for this behaviour: one is that the dynamic restoration in the columnar dendrites structure is very slowly and insufficiently. Basically, the hot deformation for metals and alloys is mainly controlled by the mobility of dislocations. The recrystallised grains start to nucleate during the hot deformation once a critical accumulative density of moving dislocation is exceeded. However, the moving dislocations are not easily accumulated for the material containing columnar grains because of low surface fraction of grain boundaries in columnar grains and low resistance to motion for dislocations. Hence, it can be concluded that the critical dislocation density for the DRX is hard to reach, leading to the insufficient softening and sluggish recrystallisation, which will not offset timely the effect of workhardening. In addition, the inhomogeneous deformation within the internal microstructure due to non-uniformity in chemical composition is probably another reason for such increase in the flow stress at high strain level.

It should be noted that a slight decrease in stress at large strain can be observed on the flow curve at the high strain rate of 10 s⁻¹, which is usually considered as an indication of flow instability such as cracking. In view of the characteristics of the above flow curves, it is concluded that further analysis on hot deformation behaviour ought to be carried out using the kinetic analysis, processing map and associated microstructure observation.

Kinetic analysis

During hot plastic deformation, the flow stress in a wider range can be related to deformation temperature and strain rate in the form of an Arrhenius kinetic rate equation proposed by Sellars and Mctegart27 (5) where is the strain rate (s⁻¹), A and α are the material constants (s⁻¹ and MPa⁻¹), σ is the flow stress for any strain (MPa), n is the stress exponent (n = 1/m, here m is the strain rate sensitivity), Q is the activation energy for deformation (J mol⁻¹), R is the gas constant (J mol⁻¹ K⁻¹) and T is the deformation temperature (K). Generally, the above formula also can be expressed by (6) In the above equation, the value of constant α must be firstly estimated before describing the relationship between flow stress, strain rate and temperature under a particular strain. In this case (ϵ = 0·7), the value of α is calculated to be 0·0072 MPa⁻¹ by means of the statistical regression methods.28 Then, the variation of the flow stress in a hyperbolic sine type with strain rate at different temperatures is plotted in Fig. 4a. Each slope of the line represents the n value at different deformation temperatures. It is easy to find that the n value ranges from 5·89 to 6·82, and the average one is calculated to be ∼6·32 with a mean linearly dependent coefficient of 0·985.

Figure 4b shows the linear relationship between 1/T and ln [sinh (ασ)]. Thus, the deformation activation energy Q for the hot compression can be calculated by (7) After averaging the Q values at different strain rates, the Q value in the present study is found to be 516·7 kJ mol⁻¹. This value is much greater than that for self-diffusion in γ iron (Q = 280 kJ mol⁻¹),29 implying that the deformation mechanism of the superalloy is dominated by the DRX instead of diffusion. In fact, the hot deformation is a thermal activation course. The Q value describes the activation barrier that atoms need to overcome to follow the deformation procedure30 and thus reflects the deformation difficulty degree during the hot working. Compared with the reported values of other SASSs, for example Cr₁₆Ni₂₅Mo₆ (Q = 484 kJ mol⁻¹)10 and Cr₂₈Ni₃₃Mo₃ (Q = 406 kJ mol⁻¹),31 the Q value obtained here is also much higher. Such high Q value for the studied steel indicates that the flow stress in this steel is highly temperature dependent and that the condition for the occurrence of the DRX is quite high.

Figure 5 illustrates the relationship between flow stress and ln Z [Z is the Zener–Hollomon parameter, ]. It is found that the data of the flow stress functioned by hyperbolic sine in the given test conditions are very well fitted to the ln Z values. The smaller the flow stress, the lower the Z parameter.

Finally, substituting the values of material constants, such as a, n, A and Q, into equation (5), the flow stress constitutive equation of the hot deformation for the studied steel with the initial microstructure of columnar grains is extracted as follows (8)

Processing map and microstructural analysis

According to the principles of dynamic materials model introduced in the section on ‘Method of processing map’, the three-dimensional maps of power dissipation at the strains of 0·5 and 0·7 are gained and shown in Fig. 6, in which the colour of the grid denotes the value of efficiency of power dissipation (shown as a percentage). It reveals that there is no significant effect of strain on the distribution and change of power dissipation efficiency. In both maps, there exhibit two saffron yellow domains with high efficiency, strongly suggesting that the significant microstructural changes during the hot deformation occur due to more energy dissipation. Additionally, the instability map identified by Murty's criterion is presented in Fig. 7. It can be seen that the instability regimes slightly expand with increasing the strain. When the strain reaches to 0·7, a new flow instability regime is located at higher temperature and lower strain rate, where the η value is negative.

The two-dimensional processing map with strain of 0·7 can be generated by superimposing the instability map on the power dissipation map, as shown in Fig. 8. Two areas of instability (grey tone region) and stability (white region) are easily found in this map. Contour numbers indicate constant efficiency of power dissipation marked as per cent. Obviously, the variation of power dissipation efficiency is very complicated over the entire range of testing parameters. Every region represents a specific microstructural process that leads to different power dissipation. It is observed from Fig. 8 that the processing map exhibits two domains with high power dissipation efficiency: domain 1 occurs at 1025–1120°C and 0·01–0·03 s⁻¹ with a peak efficiency of ∼39%, while domain 2 occurs at 1140–1200°C and 0·08–1 s⁻¹ with a peak efficiency of ∼36%. It is widely recognised that the higher the value of efficiency, the better workability at this deformation domain, which implies that it may be the optimum condition for hot processing. Meanwhile, the processing map at the present strain exhibits three instability regimes: the first one (regime 1) is located at the upper left corner and extends with the temperature increasing and the strain rate decreasing; the second one (regime 2) lies in the ranges of 1125–1200°C and 2–10 s⁻¹; and the third one (regime 3) is emerged at 1160–1180°C and strain rate <0·03 s⁻¹. Consequently, these instability regimes and the corresponding processing parameters obtained from the processing map should be kept away during practical application. In order to investigate and validate the microstructural evolutions during the hot working, detailed metallographic analysis will be performed in the following parts based on the typical areas on the processing map.

Stability domain

As stated above, the domain 1 with high power dissipation efficiency of 30–39% occurs at 1025–1120°C and 0·01–0·03 s⁻¹. Basically, the domain with maximum efficiency may be interpreted to correspond with the DRX.16 Complete DRX is beneficial to the hot deformation since it provides stable flow and ideal workability to the material by simultaneously softening and reconstituting the microstructure. Figure 9a shows the microstructure of the specimen after the hot deformation at 1100°C/0·01 s⁻¹, which is marked as point A in the processing map. It is clearly seen that a large number of recrystallised grains have occurred in the matrix with an average grain size of ∼18 μm. In addition, some grain boundaries exhibit serrate characteristics indicated by the arrows, implying that the DRX process is continuing at this working condition. It is thus clear that the greater the applied deformation, the more the extent of DRX. In this case, the original as cast columnar structure is gradually replaced by a relatively fine recrystallised microstructure. This is because the low strain rate provides enough time for the nucleation and growth of new recrystallised grains at the adequate deformation temperature. Thus, it can be deduced that the DRX is the main softening mechanism when deformed at 1100°C/0·01 s⁻¹, with a peak efficiency of 39%.

The domain 2 is another stability domain with high power dissipation efficiency of 30–36% that occurs at 1140–1200°C and 0·08–1 s⁻¹. The microstructure of the specimen deformed at 1150°C/0·1 s⁻¹, which is marked as point B in the map, is shown in Fig. 9b. Numerous DRX grains have indeed developed, indicating that the imparted mechanical energy during deformation is sufficient enough to promote the initiation of DRX, and thereby, the DRX is the dominant power dissipation mechanism. Therefore, the corresponding working parameters may result in the enhanced ductility of the steel during the hot deformation. Moreover, from the appearance of the deformed specimen (Fig. 9b inset), the smooth surface without any shear bands and cracks can also support the above interpretation.

In addition, the rest of the stability domain with relatively low efficiency obtained from the processing map is also analysed by the microstructural examination. Figure 10a shows the typical microstructure after the hot deformation at 1000°C/0·1 s⁻¹, which is marked as point C in the map. As seen from Fig. 10a, there is no obvious DRX occurring during deforming at the present condition, though the dissipation efficiency reaches to 25%. A lot of banded dislocation substructures (indicated by arrows) exhibiting the same crystallographic orientation are formed in the areas between the undulations. The similar phenomenon has been observed in as cast 317L steel.11 This indicates that the DRV characterised by substructure occurring has taken place. It is established that the migration and entanglement of substructures will promote the initiation DRX when the strain is further increased. The microstructure of the specimen deformed at 1100°C/1 s⁻¹ is shown in Fig. 10b, which is marked as point D in the map. It is easily found that the new recrystallised grains nucleate on the foot of the undulations and gradually extend to the austenitic matrix. Then, the necklace structure has formed. Meanwhile, the serrated wavy structures together with local bulges are also observed on the new formed grain boundaries. Such wavy structures or bulges imply the early stages of the DRX.9 Thus, it can be conducted that the DRX in this state is insufficient and incomplete, and partial DRX or DRV is the main deformation mechanism. Figure 10c shows the microstructure of the specimen deformed at 1150°C/0·01 s⁻¹, which is marked as point E in the map, located near the instability regime 3. It represents the obvious DRX accompanied with locally abnormal grain coarsening. So, the power dissipation by microstructure changes in this region is lower.32 Therefore, these non-peak areas (except domains 1 and 2) are not feasible processing zones even though they are not in the instability regimes.

Combined with the above analysis from the processing map and the microstructures, the optimum hot working parameters for Cr₂₀Ni₂₅Mo₄Cu steel with the initial microstructure of columnar dendrites should be chosen in the temperature and strain rate ranges of 1025–1120°C and 0·01–0·03 s^−-1, or 1140–1200°C and 0·08–1 s⁻¹, where the material will receive much more recrystallisation and keep the stability of the microstructure, which lead to good intrinsic workability.

Instability regimes on map

It is obviously seen from Fig. 8 that the three instability regimes are identified by the processing map. The instability mechanism is probably associated with the flow localisation, adiabatic shear deformation, cracking, void generation, etc. These predictions need to be validated by the microstructural observations on the deformed specimens.

The instability regime 1 is displayed in the position of top left corner and extends with increasing the temperature and decreasing the strain rate. The typical microstructure characterisation of instability in this region is shown in Fig. 11, corresponding to the specimen deformed at 1000°C/10 s⁻¹ and 1050°C/1 s⁻¹ (marked as the cross a and b in the map). It can be seen that the microstructures exhibit intense, localised deformation zones caused by non-uniform deformation during the hot working. The localised deformation zones can easily lead to crack initiation and propagation by further deformation. Moreover, the low power dissipation efficiency in this region also suggests that most of the plastic power input converts to heat and dissipates in the form of temperature rise in the material. Hence, the flow localisation is disadvantageous to obtaining good mechanical properties and thus should be kept away during practical processing.

The region located at 1125–1200°C and 2–10 s⁻¹ is identified to be another instable hot working regime (instability regime 2). The significant oscillations on the flow curves and the abnormal softening at high strain level can be found at the strain rate of 10 s⁻¹ (Fig. 3b), which is generally interpreted as an indication of flow instability such as flow localisation or cracking.33 The microstructure of the specimen deformed at 1150°C/10 s⁻¹ is shown in Fig. 12a (marked as the cross c in the map). The adiabatic shear bands oriented at an angle of 30° with respect to the compression axis have been developed, and plenty of fine newly nucleated recrystallised grains along macroscopic shear planes are formed. These shear bands in the deformed microstructure is a typical feature of the local flow softening, which may be associated to cracks and cavity. Figure 12b shows the microstructure of the specimen deformed at 1200°C/10 s⁻¹ (marked as the cross d in the map). It is clear that the microcracks indicated by the white arrow have been generated at the severe deformation bands because the shear bands are intensely centralised in the deformation zone. In addition, the specimen deformed in this condition presents the characteristic of free surface cracking (Fig. 12b inset). The occurrence of such free surface cracking is attributed to the secondary tensile stresses caused by bulging of the cylindrical specimen during upsetting.34 The above examinations of microstructure and appearance indicate that the material has poor hot workability in the regime 2, which is in good agreement with the prediction by the processing map.

Moreover, the processing map also predicts a small instability regime 3 located at 1160–1180°C and 0·01–0·03 s⁻¹, where the efficiency is negative. Generally, the grain boundary sliding and wedge cracking caused by long time exposure at high deformation temperature may be responsible for the occurrence of this instability,35 though the well developed microstructure has been obtained. A universally accepted explanation is that at higher deformation temperature and lower strain rate, considerable stress concentration easily occurs at the triple junctions due to the high sliding of grain boundary or grain growth.36^–38 If not relieved by accommodation process, the wedge cracking will be induced. Therefore, this region should also be kept away from hot working.

Conclusions

The hot deformation characteristics of Cr₂₀Ni₂₅Mo₄Cu SASS with the initial microstructure of columnar dendrites have been investigated using processing map method combined with microstructural observations at temperatures of 1000–1200°C and strain rates of 0·01–10 s⁻¹. The following conclusions have been drawn.

The deformation temperature and strain rate significantly affect the flow stress in the hot deformation process. The flow stress increases with increasing strain rate or decreasing deformation temperature. Most of the flow curves exhibit the prolonged workhardening feature after initial sharp strain hardening in the present working conditions, though a limited softening has taken place.

The classical hyperbolic sine equation is adopted to describe the relationship between the flow stress, the strain rate and the deformation temperature, in which the mean apparent activation energy Q and stress exponent n are 516·7 kJ mol⁻¹ and 6·32 respectively. The flow stresses are very well fitted to the lnZ values, and the lower the Z parameter, the smaller the flow stress.

The processing map combined with the instability map and the dissipation map was constructed to demonstrate the relationship between the hot workability and the microstructural evolution. The stability region for the hot working was inferred accurately from the processing map. It is suggested that the optimum processing parameters should be chosen in the respective ranges of temperature and strain rate of 1025–1120°C and 0·01–0·03 s⁻¹, or 1140–1200°C and 0·08–1 s⁻¹, where the material will produce many more equiaxed recrystallised grains and the original columnar dendrites can be replaced.

The instability regimes for the hot working are also estimated from the processing map. The flow localisation, adiabatic shear bands, microcracks and free surface cracking are the main reasons for instability occurring. Such instability regimes should be kept away during practical processing.

Footnotes

Acknowledgements

The authors would like to acknowledge the Program for New Century Excellent Talents in University (grant no. ET-11-0425), the National High-Tech R&D Program of China (863 Program) (grant no. SQ2011AAJY2755), the Natural Science Foundation of Shaanxi Province (grant no. 2012JM6004), the Key Grant Project of Chinese Ministry of Education (grant no. 313046), the Scientific Research Program of Shaanxi Provincial Education Department (grant no. 2011JG14) and the State Key Laboratory for Mechanical Behavior of Materials (grant no. 20111212) for their financial support of this present study.

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