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The blocking effects of interphase precipitation on dislocations’ movement in Ti-bearing micro-alloyed steels
Materials Letters 139 (2015) 177–181
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
The blocking effects of interphase precipitation on dislocations’ movement in Ti-bearing micro-alloyed steels Yang Xu, Weina Zhang, Mingxue Sun, Hailong Yi, Zhenyu Liu n State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110819, China
art ic l e i nf o
a b s t r a c t
Article history: Received 25 May 2014 Accepted 19 July 2014 Available online 30 July 2014
The effects of interphase precipitation and random dispersive precipitation on dislocations’ movement in ferrite grains and nano-mechanical properties have been investigated by using an in-situ nanomechanical tester. Through the analyses of load–depth curves, nano-hardness was measured to be 4.19 GPa for interphase precipitation and 3.90 GPa for random dispersive precipitation, respectively. Plateaus are formed in the early stages of load–depth curves for specimens with interphase precipitates, while no plateaus can be observed for specimens with random dispersive precipitates. Mechanism for the interaction between dislocations and precipitates has been established by using Ashby–Orowan theory, which is believed to have been caused by the blockage of parallel precipitates on dislocations, resulting in the drop of applied stress to generate plateaus in load–depth curves. & 2014 Elsevier B.V. All rights reserved.
Keywords: Metals and alloys Interphase precipitation Indentation and hardness Load–depth curve Plateaus
1. Introduction Interphase precipitation can be formed during the advance of austenite/ferrite interface by the ledge, quasi-ledge or bowing mechanisms [1], and is recognized as an effective way to strengthening micro-alloyed steels with Ti, Nb, V, and Mo because these nano-sized precipitates in ferrite grains can provide sufficient precipitation strengthening effects [1–4]. Titanium is a strong carbide forming element from supersaturated austenite and ferrite solid solutions to form random precipitation or during austenite to ferrite transformation to form interphase precipitation. These carbides, which exhibit the NaCl type crystal structure, have the Baker–Nutting (B–N) or Nishiyama–Wassermann (NW) orientation relationship with the ferrite [5]. Most of previous studies have estimated the precipitation strengthening effects by micro hardness testing [4,6], in which the strengthening effects by grain boundaries had inevitably been included. Nano-indentation has been proved an effective method to precisely assessing mechanical behavior such as the hardening effects by grain boundaries and precipitates for metals, and new mechanical phenomenon can usually be discovered when it gets down to micro or nano-scales [7–11]. In order to further clarify the strengthening effects by interphase precipitation and understand the influence of precipitate's spatial arrangement on dislocations’ nucleation and movement, nano-indentations on ferrite grains with
n
Corresponding author. E-mail address: [email protected] (Z. Liu).
http://dx.doi.org/10.1016/j.matlet.2014.07.135 0167-577X/& 2014 Elsevier B.V. All rights reserved.
interphase precipitates and random dispersive precipitates were performed, and their nano-scale mechanical behaviors were investigated.
2. Experimental procedures In present work, composition of the experimental steel has been chosen to be C-0.08, Mn-1.76, Si-0.21, Ti-0.11, Nb-0.058 and Fe-balance (wt%). Cylindrical specimens were prepared from hot rolled plates for thermo-mechanical simulation tests, during which the specimens were reheated to 1523 K with a heating rate of 10 K/s, held for 5 min in order to dissolve niobium and titanium carbonitrides, and cooled at 5 K/s to 1323 K and 1113 K to be hot deformed by the reduction of 30% at the strain rate of 5/s, respectively. After deformation, specimens were cooled to 873 K and 913 K at the rate of 10 K/s, respectively, and then cooled to room temperature at the rate of 0.1 K/s. The samples for OM (optical metallography), EBSD (electron backscattered diffraction) and TEM (transmission electron microscopy) observations were prepared in standard ways. Specimens for nanoindentation were mechanically ground and polished by using SiC papers, followed by electrolytic polishing with the reagent of 12.5% perchloric acid, 81.25% ethanol and 6.25% water under the potential of 45 V for 45 s. For each specimen, 25 indentations with the load of 2000 μN were performed by using triboindenter in-situ nanomechanical testing system with a three-sided pyramidal Berkovich tip.
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Y. Xu et al. / Materials Letters 139 (2015) 177–181
Fig. 1. Optical metallographs, EBSD orientation imaging maps, TEM and selection area diffraction pattern in ferrite for the experimental steel, (a), (c) and (e) 873 K, (b), (d) and (f) 913 K.
Y. Xu et al. / Materials Letters 139 (2015) 177–181
3. Results and discussion Fig. 1(a) and (b) show the typical metallographs under the coiling temperatures of 873 K and 913 K, which clearly indicate that the microstructure in the specimen coiled at 873 K is comprised of ferrite, bainite and small amount of pearlite, while the microstructure in the specimen coiled at 913 K is comprised of only ferrite and pearlite. High resolution EBSD scans of the microstructure at 873 K and 913 K where nano-indentation was performed are shown in Fig. 1(c) and (d). There are several preferred orientations for ferrite around {1 1 1} and {1 0 1} at 913 K while the orientation of ferrite is random at 873 K. Fig. 1(e) and (f) show the TEM micrographs and the corresponding selected area diffraction patterns (SADP) for the specimens coiled at 873 K and 913 K, which clearly show that random precipitates have been formed in ferrite grains at the coiling temperature of 873 K, while precipitates regularly arranged in parallel rows have been formed in ferrite grains at the coiling temperature of 913 K. The SADP along the zone axis ½0 1 1ferrite ==½1 1 1carbide for interphase precipitation, Fig. 1 (f) shows that the precipitates obey the N–W orientation relationship of ð0 1 1Þferrite ==ð1 1 1Þcarbide , ½1 0 0ferrite ==½1 1 0carbide with respect to the ferrite matrix [12,13]. Fig. 2(a) shows the typical indentation morphologies by nanoindenter and the elastic load–depth curve calculated by Hertzian elastic contact solution [14], where the radius of curvature for the Berkovich indenter is approximately 150 nm and the reduced modulus is 215 GPa. Fig. 2(b) and (c) show the typical load–depth curves for specimens coiled at 913 K and 873 K, from which the
179
average nano-hardness values were measured to be 4.19 GPa and 3.90 GPa by using the Oliver–Pharr method [11]. It is well known that the hardness of ferrite grains depends upon the carbon content, density of dislocations and precipitation. In present work, the specimens were slowly cooled at 0.1 K/s during the coiling processes, so that carbon content should be close to the equilibrium concentration with low dislocation density. Therefore, the most possible strengthening effect is believed to have been resulted from the precipitates in ferrite grains. It has been consistently noted that plateaus occurred in the early stages of the load–depth curves for the specimen coiled at 913 K, while no plateaus can be observed at all for the specimens coiled at 873 K. Fig. 2(d) shows the converted nanohardness-depth curves, which clearly indicates that the nanohardness for the specimen coiled at 913 K drastically decreased after the peak. For the indentations at 913 K, the average depth for the onset of plateaus has been measured to be about 7 nm with the load of about 90 μN, and the plateaus may last for about 9 nm. Previous studies concluded that the plateaus in load–depth curves had been caused by the blocking effects by oxide layers, grain boundaries on dislocations’ movements, dislocation nucleation and dislocation source activation [10,15–18]. In present work, since all of the specimens had undergone the same electrolytic polishing process and the indentations were kept away from ferrite grain boundaries, the influences of oxide layers and grain boundaries, therefore, could be excluded. The effect of interphase precipitation on plateau phenomenon may like grain boundary studied in Soer's research [9], and implying that the interaction between dislocations and precipitates may also lead to the plateau
Fig. 2. Indentation response of ferrite grain: (a) indents in the microstructure, (b) representative load–depth curves, (c) image of the plateau area, (d) nanohardness-depth curves.
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Y. Xu et al. / Materials Letters 139 (2015) 177–181
Fig. 3. Schematic drawing for the Ashby–Orowan modeling of the interaction between precipitates and dislocations’ movement; (a) and (g): the slip plane and distribution of particles, (b) and (h): variation of nanohardness-depth curve, (c) and (i), (d) and (j), (e) and (k), (f) and (l): pinning up and bypassing of the dislocations along the slip plane at stage I, II, III and IV shown in (b) and (h).
formation. As shown in Fig. 2(c), sample with random precipitation is easier access into plastic deformation during indention rather than sample with interphase precipitation. It reveals that dislocations, which are considered geometrically necessary dislocation and nucleated around the indenter tip before plateau point, could be hindered effectively by the row of precipitate particles. The blocking effects of precipitates on dislocations’ movements can be explained by the classic Ashby–Orowan theory. Fig. 3 shows the modeling for the influence of random precipitates on dislocations’ movements, with Fig. 3(b) representing different stages in the load–depth curve, and Fig. 3(c)–(f) showing the schematic interactions between dislocations and precipitate particles for random precipitation. In the beginning, Fig. 3(c), the indentation load is monotonously increased with depth when dislocations are generated and approaching the precipitate particles; then, the dislocation is blocked by the particle and started to bend around it, leading the indentation load to reaching the peak; in the later
stage, the dislocation has bypassed the precipitate particle, leaving dislocation loop behind, resulting in decrease of the indentation load; finally, the indentation loading is in a stable process because dislocations are continuously blocked by and have bypassed the random precipitate particles. Fig. 3(g)–(l) shows the Ashby–Orowan model for dislocations moving along the slip plane across interphase precipitate particles, which are aligned in parallel rows, with the sheet plane and slip plane being shown in Fig. 3(g). Fig. 3(h) represents different stages in a typical load–depth curve, and Fig. 3(i)–(l) shows the dislocation's movement along slip plane interacting with interphase precipitates. In the first stage, the load is increased with the indentation depth when dislocations approach a row of precipitate particles; then, dislocations begin to bend around the row of interphase precipitate particles when they are blocked, and the indentation load reaches the peak; after that, the dislocation has to bypass the row of particles simultaneously leaving the dislocation loops behind, resulting in the decrease of indentation load. After
Y. Xu et al. / Materials Letters 139 (2015) 177–181
more and more dislocations have bypassed the rows of precipitate particles, more resistance has to be overcome, leading to the increase of indentation load with depth in the later stages of loading.
181
One of the authors (Yang Xu) thanks the Graduate Research Innovation Program Funded Project (N110607006) for financial supports. The authors would like to thank Ms Wenying Xue and Dr. Yifeng Shen for the analyses of the nano-mechanical tests.
4. Conclusion Interphase precipitation was found in ferrite grains coiled at 913 K while random dispersed precipitates were formed at 873 K. The nano-hardness values for ferrite grains with interphase precipitation and random dispersive precipitation were measured to be 4.19 GPa and 3.90 GPa, respectively. Plateaus can be observed at the initial stage of load–depth curves for the ferrite grains with interphase precipitation. The Ashby–Orowan models for random dispersive precipitates and interphase precipitates have been established to account for the different loading behaviors of ferrite grains with random dispersive and interphase precipitates. It has been worked out that the blocking effect by parallel rows of precipitates can be the reason for the formation of plateaus in the load–depth curves when interphase precipitates are formed in the steel.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
Acknowledgements This work was supported by the Major Innovative Research Project by Education Ministry of China under the contract of N120807001.
[16] [17] [18]
Honeycombe RWK. Metall Trans A 1976;7:915. Brito RM, Kestenbach HJ. J Mater Sci 1981;16:1257. Sakuma T, Honeycombe RWK. Met Sci 1984;18:449. Yen HW, Chen PY, Huang CY, Yang JR. Acta Mater 2011;59:6254. Jang JH, Heo YU, Lee CH, Bhadeshia HDK, Suh. DW. Mater Sci Technol 2013;29:309. Campos SS, Morales EV, Kestenbach HJ. Metall Trans A 2001;32:1245. Arzt E. Acta Mater 1998;46:5611. Joonoh M, Sanghoon K, Jae-il J, Jongbong L, Changhee L. Mater Sci Eng A 2008;487:552. Soer WA, De Hosson JTM. Mater Lett 2005;59:3192. Wang MG, Ngan AHW. J Mater Res 2004;19:2478. Oliver WC, Pharr GM. J Mater Res 1992;7:1564. Nishiyama Z. Sci Rep Inst Tohoku Univ 1934;23:637. Wasserman G. Arch Eisenhuttenwes 1933;6:347. Johnson KL. Contact mechanics. Cambridge, UK: Cambridge University Press; 1985. Gerberich WW, Nelson JC, Lilleodden ET, Anderson P, Wyrobek JT. Acta Mater 1996;44:3585. Chiu YL, Ngan AHW. Acta Mater 2002;50:1599. Bahr DF, Kramer DE, Gerberich WW. Acta Mater 1998;46:3605. Cordill MJ, Moody NR, Gerberich WW. Int J Plast 2009;25:281.
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
The blocking effects of interphase precipitation on dislocations’ movement in Ti-bearing micro-alloyed steels Yang Xu, Weina Zhang, Mingxue Sun, Hailong Yi, Zhenyu Liu n State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110819, China
art ic l e i nf o
a b s t r a c t
Article history: Received 25 May 2014 Accepted 19 July 2014 Available online 30 July 2014
The effects of interphase precipitation and random dispersive precipitation on dislocations’ movement in ferrite grains and nano-mechanical properties have been investigated by using an in-situ nanomechanical tester. Through the analyses of load–depth curves, nano-hardness was measured to be 4.19 GPa for interphase precipitation and 3.90 GPa for random dispersive precipitation, respectively. Plateaus are formed in the early stages of load–depth curves for specimens with interphase precipitates, while no plateaus can be observed for specimens with random dispersive precipitates. Mechanism for the interaction between dislocations and precipitates has been established by using Ashby–Orowan theory, which is believed to have been caused by the blockage of parallel precipitates on dislocations, resulting in the drop of applied stress to generate plateaus in load–depth curves. & 2014 Elsevier B.V. All rights reserved.
Keywords: Metals and alloys Interphase precipitation Indentation and hardness Load–depth curve Plateaus
1. Introduction Interphase precipitation can be formed during the advance of austenite/ferrite interface by the ledge, quasi-ledge or bowing mechanisms [1], and is recognized as an effective way to strengthening micro-alloyed steels with Ti, Nb, V, and Mo because these nano-sized precipitates in ferrite grains can provide sufficient precipitation strengthening effects [1–4]. Titanium is a strong carbide forming element from supersaturated austenite and ferrite solid solutions to form random precipitation or during austenite to ferrite transformation to form interphase precipitation. These carbides, which exhibit the NaCl type crystal structure, have the Baker–Nutting (B–N) or Nishiyama–Wassermann (NW) orientation relationship with the ferrite [5]. Most of previous studies have estimated the precipitation strengthening effects by micro hardness testing [4,6], in which the strengthening effects by grain boundaries had inevitably been included. Nano-indentation has been proved an effective method to precisely assessing mechanical behavior such as the hardening effects by grain boundaries and precipitates for metals, and new mechanical phenomenon can usually be discovered when it gets down to micro or nano-scales [7–11]. In order to further clarify the strengthening effects by interphase precipitation and understand the influence of precipitate's spatial arrangement on dislocations’ nucleation and movement, nano-indentations on ferrite grains with
n
Corresponding author. E-mail address: [email protected] (Z. Liu).
http://dx.doi.org/10.1016/j.matlet.2014.07.135 0167-577X/& 2014 Elsevier B.V. All rights reserved.
interphase precipitates and random dispersive precipitates were performed, and their nano-scale mechanical behaviors were investigated.
2. Experimental procedures In present work, composition of the experimental steel has been chosen to be C-0.08, Mn-1.76, Si-0.21, Ti-0.11, Nb-0.058 and Fe-balance (wt%). Cylindrical specimens were prepared from hot rolled plates for thermo-mechanical simulation tests, during which the specimens were reheated to 1523 K with a heating rate of 10 K/s, held for 5 min in order to dissolve niobium and titanium carbonitrides, and cooled at 5 K/s to 1323 K and 1113 K to be hot deformed by the reduction of 30% at the strain rate of 5/s, respectively. After deformation, specimens were cooled to 873 K and 913 K at the rate of 10 K/s, respectively, and then cooled to room temperature at the rate of 0.1 K/s. The samples for OM (optical metallography), EBSD (electron backscattered diffraction) and TEM (transmission electron microscopy) observations were prepared in standard ways. Specimens for nanoindentation were mechanically ground and polished by using SiC papers, followed by electrolytic polishing with the reagent of 12.5% perchloric acid, 81.25% ethanol and 6.25% water under the potential of 45 V for 45 s. For each specimen, 25 indentations with the load of 2000 μN were performed by using triboindenter in-situ nanomechanical testing system with a three-sided pyramidal Berkovich tip.
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Y. Xu et al. / Materials Letters 139 (2015) 177–181
Fig. 1. Optical metallographs, EBSD orientation imaging maps, TEM and selection area diffraction pattern in ferrite for the experimental steel, (a), (c) and (e) 873 K, (b), (d) and (f) 913 K.
Y. Xu et al. / Materials Letters 139 (2015) 177–181
3. Results and discussion Fig. 1(a) and (b) show the typical metallographs under the coiling temperatures of 873 K and 913 K, which clearly indicate that the microstructure in the specimen coiled at 873 K is comprised of ferrite, bainite and small amount of pearlite, while the microstructure in the specimen coiled at 913 K is comprised of only ferrite and pearlite. High resolution EBSD scans of the microstructure at 873 K and 913 K where nano-indentation was performed are shown in Fig. 1(c) and (d). There are several preferred orientations for ferrite around {1 1 1} and {1 0 1} at 913 K while the orientation of ferrite is random at 873 K. Fig. 1(e) and (f) show the TEM micrographs and the corresponding selected area diffraction patterns (SADP) for the specimens coiled at 873 K and 913 K, which clearly show that random precipitates have been formed in ferrite grains at the coiling temperature of 873 K, while precipitates regularly arranged in parallel rows have been formed in ferrite grains at the coiling temperature of 913 K. The SADP along the zone axis ½0 1 1ferrite ==½1 1 1carbide for interphase precipitation, Fig. 1 (f) shows that the precipitates obey the N–W orientation relationship of ð0 1 1Þferrite ==ð1 1 1Þcarbide , ½1 0 0ferrite ==½1 1 0carbide with respect to the ferrite matrix [12,13]. Fig. 2(a) shows the typical indentation morphologies by nanoindenter and the elastic load–depth curve calculated by Hertzian elastic contact solution [14], where the radius of curvature for the Berkovich indenter is approximately 150 nm and the reduced modulus is 215 GPa. Fig. 2(b) and (c) show the typical load–depth curves for specimens coiled at 913 K and 873 K, from which the
179
average nano-hardness values were measured to be 4.19 GPa and 3.90 GPa by using the Oliver–Pharr method [11]. It is well known that the hardness of ferrite grains depends upon the carbon content, density of dislocations and precipitation. In present work, the specimens were slowly cooled at 0.1 K/s during the coiling processes, so that carbon content should be close to the equilibrium concentration with low dislocation density. Therefore, the most possible strengthening effect is believed to have been resulted from the precipitates in ferrite grains. It has been consistently noted that plateaus occurred in the early stages of the load–depth curves for the specimen coiled at 913 K, while no plateaus can be observed at all for the specimens coiled at 873 K. Fig. 2(d) shows the converted nanohardness-depth curves, which clearly indicates that the nanohardness for the specimen coiled at 913 K drastically decreased after the peak. For the indentations at 913 K, the average depth for the onset of plateaus has been measured to be about 7 nm with the load of about 90 μN, and the plateaus may last for about 9 nm. Previous studies concluded that the plateaus in load–depth curves had been caused by the blocking effects by oxide layers, grain boundaries on dislocations’ movements, dislocation nucleation and dislocation source activation [10,15–18]. In present work, since all of the specimens had undergone the same electrolytic polishing process and the indentations were kept away from ferrite grain boundaries, the influences of oxide layers and grain boundaries, therefore, could be excluded. The effect of interphase precipitation on plateau phenomenon may like grain boundary studied in Soer's research [9], and implying that the interaction between dislocations and precipitates may also lead to the plateau
Fig. 2. Indentation response of ferrite grain: (a) indents in the microstructure, (b) representative load–depth curves, (c) image of the plateau area, (d) nanohardness-depth curves.
180
Y. Xu et al. / Materials Letters 139 (2015) 177–181
Fig. 3. Schematic drawing for the Ashby–Orowan modeling of the interaction between precipitates and dislocations’ movement; (a) and (g): the slip plane and distribution of particles, (b) and (h): variation of nanohardness-depth curve, (c) and (i), (d) and (j), (e) and (k), (f) and (l): pinning up and bypassing of the dislocations along the slip plane at stage I, II, III and IV shown in (b) and (h).
formation. As shown in Fig. 2(c), sample with random precipitation is easier access into plastic deformation during indention rather than sample with interphase precipitation. It reveals that dislocations, which are considered geometrically necessary dislocation and nucleated around the indenter tip before plateau point, could be hindered effectively by the row of precipitate particles. The blocking effects of precipitates on dislocations’ movements can be explained by the classic Ashby–Orowan theory. Fig. 3 shows the modeling for the influence of random precipitates on dislocations’ movements, with Fig. 3(b) representing different stages in the load–depth curve, and Fig. 3(c)–(f) showing the schematic interactions between dislocations and precipitate particles for random precipitation. In the beginning, Fig. 3(c), the indentation load is monotonously increased with depth when dislocations are generated and approaching the precipitate particles; then, the dislocation is blocked by the particle and started to bend around it, leading the indentation load to reaching the peak; in the later
stage, the dislocation has bypassed the precipitate particle, leaving dislocation loop behind, resulting in decrease of the indentation load; finally, the indentation loading is in a stable process because dislocations are continuously blocked by and have bypassed the random precipitate particles. Fig. 3(g)–(l) shows the Ashby–Orowan model for dislocations moving along the slip plane across interphase precipitate particles, which are aligned in parallel rows, with the sheet plane and slip plane being shown in Fig. 3(g). Fig. 3(h) represents different stages in a typical load–depth curve, and Fig. 3(i)–(l) shows the dislocation's movement along slip plane interacting with interphase precipitates. In the first stage, the load is increased with the indentation depth when dislocations approach a row of precipitate particles; then, dislocations begin to bend around the row of interphase precipitate particles when they are blocked, and the indentation load reaches the peak; after that, the dislocation has to bypass the row of particles simultaneously leaving the dislocation loops behind, resulting in the decrease of indentation load. After
Y. Xu et al. / Materials Letters 139 (2015) 177–181
more and more dislocations have bypassed the rows of precipitate particles, more resistance has to be overcome, leading to the increase of indentation load with depth in the later stages of loading.
181
One of the authors (Yang Xu) thanks the Graduate Research Innovation Program Funded Project (N110607006) for financial supports. The authors would like to thank Ms Wenying Xue and Dr. Yifeng Shen for the analyses of the nano-mechanical tests.
4. Conclusion Interphase precipitation was found in ferrite grains coiled at 913 K while random dispersed precipitates were formed at 873 K. The nano-hardness values for ferrite grains with interphase precipitation and random dispersive precipitation were measured to be 4.19 GPa and 3.90 GPa, respectively. Plateaus can be observed at the initial stage of load–depth curves for the ferrite grains with interphase precipitation. The Ashby–Orowan models for random dispersive precipitates and interphase precipitates have been established to account for the different loading behaviors of ferrite grains with random dispersive and interphase precipitates. It has been worked out that the blocking effect by parallel rows of precipitates can be the reason for the formation of plateaus in the load–depth curves when interphase precipitates are formed in the steel.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
Acknowledgements This work was supported by the Major Innovative Research Project by Education Ministry of China under the contract of N120807001.
[16] [17] [18]
Honeycombe RWK. Metall Trans A 1976;7:915. Brito RM, Kestenbach HJ. J Mater Sci 1981;16:1257. Sakuma T, Honeycombe RWK. Met Sci 1984;18:449. Yen HW, Chen PY, Huang CY, Yang JR. Acta Mater 2011;59:6254. Jang JH, Heo YU, Lee CH, Bhadeshia HDK, Suh. DW. Mater Sci Technol 2013;29:309. Campos SS, Morales EV, Kestenbach HJ. Metall Trans A 2001;32:1245. Arzt E. Acta Mater 1998;46:5611. Joonoh M, Sanghoon K, Jae-il J, Jongbong L, Changhee L. Mater Sci Eng A 2008;487:552. Soer WA, De Hosson JTM. Mater Lett 2005;59:3192. Wang MG, Ngan AHW. J Mater Res 2004;19:2478. Oliver WC, Pharr GM. J Mater Res 1992;7:1564. Nishiyama Z. Sci Rep Inst Tohoku Univ 1934;23:637. Wasserman G. Arch Eisenhuttenwes 1933;6:347. Johnson KL. Contact mechanics. Cambridge, UK: Cambridge University Press; 1985. Gerberich WW, Nelson JC, Lilleodden ET, Anderson P, Wyrobek JT. Acta Mater 1996;44:3585. Chiu YL, Ngan AHW. Acta Mater 2002;50:1599. Bahr DF, Kramer DE, Gerberich WW. Acta Mater 1998;46:3605. Cordill MJ, Moody NR, Gerberich WW. Int J Plast 2009;25:281.