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A nanometer scale mechanism for micro crack propagation under uniaxial tension in single crystals is investigated using phase field crystal (PFC) simulation. The uniaxial tensile loading is strain controlled. And three initial typical stresses of pre-existing center crack in (111) crystal plane of face centered cubic structure are chosen to study the effects of initial stress state on micro-crack propagation. Moreover, the influences of different crystal orientations, when the crystal suffers from uniaxial tension, are also investigated. Due to the influence of time scale and length scale in the PFC method, the motion of dislocations, vacancies, shear band and twinning structure should be observed and described during the propagation process of micro cracks. In addition, the free energy curves of different processes are drawn and discussed in order to explain the different behaviors of the crystal in the propagation of cracks. Simulation results show that the propagation behavior of micro cracks can be closely associated with the initial stress state. It is found that the propagation behavior mainly occurs in the 11>(111) slip system. Besides, the crystal orientation has a significant effect on the mechanism of activation and evolution. In the pre-stretching system, slip dislocation is induced near the micro-crack tip, and then its slide in [011] direction will cause the cleavage of a certain crystal plane, and promote the micro cracks to extend. However, to a certain level, the propagating direction of the micro-crack tip will turn to another slip direction [101]. As a result, zigzag edge appears. By contrast, in the pre-shear system, the tip of the micro crack propagates in a cleavage mode, and results in the appearance of slip dislocation [101] near the micro-crack tip. Afterwards, the motion of slip dislocation promotes the production of vacancies. And owing to the aggregation and combination of vacancies, secondary cracks form and propagate in the process that follows. At the same time, in a pre-deviatoric system, the micro crack propagates forward with direct cleavage of [101] slip direction near the micro-crack tip until the single crystal sample fractures. Furthermore, no slip dislocation appears during the whole process. The mechanism of micro-crack tip propagating behavior varies with crystal orientation. When the crystal orientation angle is lower, the micro-crack tip prefers to produce slip dislocation around it, and the following dislocation slide will induce vacancies, then a secondary crack also forms because of the aggregation and combination of vacancies. On the other hand, when the aggregation degree is higher, the micro-crack tip is inclined to directly propagate in a cleavage mode, and its propagating direction is nearly perpendicular to the stretching direction.
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Keywords:
- phase field crystal /
- micro-crack propagation /
- stress state /
- orientation angle
[1] Zhang J X, Ghosh S 2013 J Mech. Phys. Solids. 61 1670
[2] Cao L X, Wang C Y 2006 Chin. Phys. 15 2092
[3] Ma L, Xiao S, Deng H, Hu W 2014 Int. J. Fatigue. 68 253
[4] Li D, Meng F Y, Ma X Q, Qiao L J, Chu W Y 2011 J. Mater. Sci. Technol. 27 1025
[5] Guo Wu R, Tie G T 2014 Chin. Phys. B 23 118704
[6] Cadini F, Zio E, Avram D 2009 Probabilist. Eng. Mech. 24 367
[7] Ganchenkova M G, Borodin V A 2004 Mater. Sci. Eng. A-struct. 387 372
[8] Arafin M A, Szpunar J A 2009 Corros. Sci. 51 119
[9] Mergheim J 2009 Int. J. Numer. Meth. Eng. 80 269
[10] Loehnert S, Prange C, Wriggers P 2012 Int. J. Fracture. 178 147
[11] Colombo D, Massin P 2011 Comput. Method. Appl. M. 200 2160
[12] Elder K R, Grant M 2004 Phys. Rev. E. 70 51605
[13] Spatschek R, Brener E, Karma A 2011 Philos. Mag. 91 75
[14] Song Y C, Soh A K, Ni Y 2007 J. Phys. D: Appl. Phys. 40 1175
[15] Abdollahi A, Arias I 2015 Arch. Comput. Method. E. 22 153
[16] Humadi H, Ofori-Opoku N, Provatas N, JHoyt J 2013 JOM. 65 1103
[17] Berry J, Grant M, Elder K R 2006 Phys. Rev. E. 73 31609
[18] Haataja M, Provatas N, Stefanovic P 2009 Phys. Rev. E. 80 46107
[19] Zhao Y L, Chen Z, Long J, Yang T 2013 Acta Phys. Sin. 62 118102 (in Chinese) [赵宇龙, 陈铮, 龙建, 杨涛 2013 物理学报 62 118102]
[20] Ren X, Wang J C, Yang Y J, Yang G C 2010 Acta Phys. Sin. 59 3595 (in Chinese) [任秀, 王锦程, 杨玉娟, 杨根仓 2010 物理学报 59 3595]
[21] Tian S G, Xue Y C, Zeng Z, Shu D L, Xie J 2014 Rare. Metal. Mat. Eng. 43 1092 (in Chinese) [田素贵, 薛永超, 曾征, 舒德龙, 谢君 2014 稀有金属材料与工程 43 1092]
[22] Shao Y F, Wang S Q 2010 Acta Phys. Sin. 10 7258 (in Chinese) [邵宇飞, 王绍青 2010 物理学报 10 7258]
[23] Xiao J M, Gu B, Zhang J W, Qiao L J, Chen Q Z 1994 Acta Metall. Sin. 30 362 (in Chinese) [肖纪美,谷飙,张静武,乔利杰,陈奇志 1994 金属学报 30 362]
[24] Li J X, Chu W Y, Gao K W, Qiao L J 2003 Acta Metall. Sin. 39 359 (in Chinese) [李金许, 褚武扬, 高克玮, 乔利杰 2003 金属学报 39 359]
[25] Gao K W, Chen Q Z, Chu W Y, Xiao J M 1994 Sci. China. Ser. A 24 993 (in Chinese) [高克玮, 陈奇志, 褚武扬, 肖纪美 1994 中国科学(A辑) 24 993]
[26] Tan Q 1991 Acta Metall. Sin. 27 21 (in Chinese) [谭启 1991 金属学报 27 21]
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[1] Zhang J X, Ghosh S 2013 J Mech. Phys. Solids. 61 1670
[2] Cao L X, Wang C Y 2006 Chin. Phys. 15 2092
[3] Ma L, Xiao S, Deng H, Hu W 2014 Int. J. Fatigue. 68 253
[4] Li D, Meng F Y, Ma X Q, Qiao L J, Chu W Y 2011 J. Mater. Sci. Technol. 27 1025
[5] Guo Wu R, Tie G T 2014 Chin. Phys. B 23 118704
[6] Cadini F, Zio E, Avram D 2009 Probabilist. Eng. Mech. 24 367
[7] Ganchenkova M G, Borodin V A 2004 Mater. Sci. Eng. A-struct. 387 372
[8] Arafin M A, Szpunar J A 2009 Corros. Sci. 51 119
[9] Mergheim J 2009 Int. J. Numer. Meth. Eng. 80 269
[10] Loehnert S, Prange C, Wriggers P 2012 Int. J. Fracture. 178 147
[11] Colombo D, Massin P 2011 Comput. Method. Appl. M. 200 2160
[12] Elder K R, Grant M 2004 Phys. Rev. E. 70 51605
[13] Spatschek R, Brener E, Karma A 2011 Philos. Mag. 91 75
[14] Song Y C, Soh A K, Ni Y 2007 J. Phys. D: Appl. Phys. 40 1175
[15] Abdollahi A, Arias I 2015 Arch. Comput. Method. E. 22 153
[16] Humadi H, Ofori-Opoku N, Provatas N, JHoyt J 2013 JOM. 65 1103
[17] Berry J, Grant M, Elder K R 2006 Phys. Rev. E. 73 31609
[18] Haataja M, Provatas N, Stefanovic P 2009 Phys. Rev. E. 80 46107
[19] Zhao Y L, Chen Z, Long J, Yang T 2013 Acta Phys. Sin. 62 118102 (in Chinese) [赵宇龙, 陈铮, 龙建, 杨涛 2013 物理学报 62 118102]
[20] Ren X, Wang J C, Yang Y J, Yang G C 2010 Acta Phys. Sin. 59 3595 (in Chinese) [任秀, 王锦程, 杨玉娟, 杨根仓 2010 物理学报 59 3595]
[21] Tian S G, Xue Y C, Zeng Z, Shu D L, Xie J 2014 Rare. Metal. Mat. Eng. 43 1092 (in Chinese) [田素贵, 薛永超, 曾征, 舒德龙, 谢君 2014 稀有金属材料与工程 43 1092]
[22] Shao Y F, Wang S Q 2010 Acta Phys. Sin. 10 7258 (in Chinese) [邵宇飞, 王绍青 2010 物理学报 10 7258]
[23] Xiao J M, Gu B, Zhang J W, Qiao L J, Chen Q Z 1994 Acta Metall. Sin. 30 362 (in Chinese) [肖纪美,谷飙,张静武,乔利杰,陈奇志 1994 金属学报 30 362]
[24] Li J X, Chu W Y, Gao K W, Qiao L J 2003 Acta Metall. Sin. 39 359 (in Chinese) [李金许, 褚武扬, 高克玮, 乔利杰 2003 金属学报 39 359]
[25] Gao K W, Chen Q Z, Chu W Y, Xiao J M 1994 Sci. China. Ser. A 24 993 (in Chinese) [高克玮, 陈奇志, 褚武扬, 肖纪美 1994 中国科学(A辑) 24 993]
[26] Tan Q 1991 Acta Metall. Sin. 27 21 (in Chinese) [谭启 1991 金属学报 27 21]
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