Modeling core-spreading of interface dislocation and its elastic response in anisotropic bimaterial

doi:10.1007/s10483-017-2163-9

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (2): 231-242.doi: https://doi.org/10.1007/s10483-017-2163-9

Modeling core-spreading of interface dislocation and its elastic response in anisotropic bimaterial

Jie LIU¹, Yuheng ZHANG¹, Haijian CHU^1,2

1. Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
2. Department of Mechanics, College of Sciences, Shanghai University, Shanghai 200444, China

收稿日期:2016-04-06 修回日期:2016-08-05 出版日期:2017-02-01 发布日期:2017-02-01
通讯作者: Haijian CHU,E-mail:hjchu@shu.edu.cn E-mail:hjchu@shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No.11672173),the Shanghai Eastern-Scholar Plan,and the Innovation Program of Shanghai Municipal Education Commission

Modeling core-spreading of interface dislocation and its elastic response in anisotropic bimaterial

Jie LIU¹, Yuheng ZHANG¹, Haijian CHU^1,2

1. Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
2. Department of Mechanics, College of Sciences, Shanghai University, Shanghai 200444, China

Received:2016-04-06 Revised:2016-08-05 Online:2017-02-01 Published:2017-02-01
Contact: Haijian CHU E-mail:hjchu@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No.11672173),the Shanghai Eastern-Scholar Plan,and the Innovation Program of Shanghai Municipal Education Commission

摘要/Abstract

摘要：

Interfacial dislocation may have a spreading core corresponding to a weak shear resistance of interfaces. In this paper, a conic model is proposed to mimic the spreading core of interfacial dislocation in anisotropic bimaterials. By the Stroh formalism and Green's function, the analytical expressions of the elastic fields are deduced for such a dislocation. Taking Cu/Nb bimaterial as an example, it is demonstrated that the accuracy and efficiency of the method are well validated by the interface conditions, a spreading core can greatly reduce the stress intensity near the interfacial dislocation compared with the compact core, and the elastic fields near the spreading core region are significantly different from the condensed core, while they are less sensitive to a field point that is 1.5 times the core width away from the center of the spreading core.

关键词: elastic field, interface dislocation, anisotropic bimaterial, core spreading

Abstract:

Key words: core spreading, elastic field, anisotropic bimaterial, interface dislocation

中图分类号:

O77⁺2

Jie LIU, Yuheng ZHANG, Haijian CHU. Modeling core-spreading of interface dislocation and its elastic response in anisotropic bimaterial[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(2): 231-242.

参考文献

[1] Bai, G. F., Petrenko, V. F., and Baker, I. On the electrical properties of dislocations in ZnS using electric force microscopy. Scanning, 23, 160-164(2001)
[2] Chen, K. X., Dai, Q., Lee, W., Kim, J. K., Schubert, E. F., Grandusky, J., Mendrick, M., Li, X., and Smart, J. A. Effect of dislocations on electrical and optical properties of n-type Al_0.34Ga_0.66N. Applied Physics Letters, 93, 192108(2008)
[3] Gromov, V. E., Ivanov, Y. F., Stolboushkina, O. A., and Konovalov, S. V. Dislocation substructure evolution on Al creep under the action of the weak electric potential. Materials Science and Engineering A, 527, 858-861(2010)
[4] Ghoniem, N. M., Chen, Z. Z., and Kioussis, N. Influence of nanoscale Cu precipitates in α-Fe on dislocation core structure and strengthening. Physical Review B, 80, 184104(2009)
[5] Pennycook, S. J. Investigating the optical properties of dislocations by scanning transmission electron microscopy. Scanning, 30, 287-298(2008)
[6] Anderson, P. M. and Li, Z. A Peierls analysis of the critical stress for transmission of a screw dislocation across a coherent, sliding interface. Materials Science and Engineering A, 319-321, 182-187(2001)
[7] Püschl, W. Models for dislocation cross-slip in close-packed crystal structures:a critical review. Progress in Materials Science, 47, 415-461(2002)
[8] Otsuka, K., Kuwabara, A., Nakamura, A., Yamamoto, T., Matsunaga, K., and Ikuhara, Y. Dislocation-enhanced ionic conductivity of yttria-stabilized zirconia. Applied Physics Letters, 82, 877-879(2003)
[9] Zheng, S. L., Ni, Y., and He, L. H. Phase field modeling of a glide dislocation transmission across a coherent sliding interface. Modelling and Simulation in Materials Science and Engineering, 23, 035002(2015)
[10] Akasheh, F., Zbib, H. M., Hirth, J. P., Hoagland, R. G., and Misra, A. Dislocation dynamics analysis of dislocation intersections in nanoscale metallic multilayered composites. Journal of Applied Physics, 101, 084314(2007)
[11] Akasheh, F., Zbib, H. M., Hirth, J. P., Hoagland, R. G., and Misra, A. Interactions between glide dislocations and parallel interfacial dislocations in nanoscale strained layers. Journal of Applied Physics, 102, 034314(2007)
[12] Hirth, J. P. and Lothe, J. Theory of Dislocations, Krieger Publishing, Florida (1982)
[13] Li, L. and Ghoniem, N. M. Twin-size effects on the deformation of nanotwinned copper. Physical Review B, 79, 075444(2009)
[14] Mara, N. A., Bhattacharyya, D., Dickerson, P., Hoagland, R. G., and Misra, A. Deformability of ultrahigh strength 5 nm Cu/Nb nanolayered composites. Applied Physics Letters, 92, 231901(2008)
[15] Mara, N. A., Bhattacharyya, D., Hirth, J. P., Dickerson, P., and Misra, A. Mechanism for shear banding in nanolayered composites. Applied Physics Letters, 97, 021909(2010)
[16] Misra, A. Twinning in nanocrystalline metals. Journal of the Minerals Metals and Materials Society, 60, 59-59(2008)
[17] Wang, J., Hoagland, R. G., Hirth, J. P., and Misra, A. Room-temperature dislocation climb in metallic interfaces. Applied Physics Letters, 94, 131910(2009)
[18] Wang, J., Hoagland, R. G., and Misra, A. Mechanics of nanoscale metallic multilayers:from atomic-scale to micro-scale. Scripta Materialia, 60, 1067-1072(2009)
[19] Wang, J. and Misra, A. An overview of interface-dominated deformation mechanisms in metallic multilayers. Current Opinion in Solid State and Materials Science, 15, 20-28(2011)
[20] Shen, Y. and Anderson, P. M. Transmission of a screw dislocation across a coherent, slipping interface. Acta Materialia, 54, 3941-3951(2006)
[21] Shen, Y. and Anderson, P. M. Transmission of a screw dislocation across a coherent, non-slipping interface. Journal of the Mechanics and Physics of Solids, 55, 956-979(2007)
[22] Hoagland, R. G., Hirth, J. P., and Misra, A. On the role of weak interfaces in blocking slip in nanoscale layered composites. Philosophical Magazine, 86, 3537-3558(2006)
[23] Wang, J., Misra, A., Hoagland, R. G., and Hirth, J. P. Slip transmission across fcc/bcc interfaces with varying interfaceshear strengths. Acta Materialia, 60, 1503-1513(2012)
[24] Chu, H. J., Wang, J., Beyerlein, I. J., and Pan, E. Dislocation models of interfical shearing induced by an approaching lattice glide dislocation. International Journal of Plasticity, 41, 1-13(2013)
[25] Wang, J., Hoagland, R. G., Hirth, J. P., and Misra, A. Atomistic simulations of the shear strength and sliding mechanisms of copper-niobium interfaces. Acta Materialia, 56, 3109-3119(2008)
[26] Gao, H., Zhang, L., and Baker, S. P. Dislocation core spreading at interfaces between metal films and amorphous substrates. Journal of the Mechanics and Physics of Solids, 50(10), 2169-2202(2002)
[27] Zbib, H. M., Dízde la Rubia, T., Rhee, M., and Hirth, J. P. 3D dislocation dynamics:stress-strain behavior and hardening mechanisms in fcc and bcc metals. Journal of Nuclear Materials, 276, 154-165(2000)
[28] Zbib, H. M., Overman, C. T., Akasheh, F., and Bahr, D. Analysis of plastic deformation in nanoscale metallic multilayers with coherent and incoherent interfaces. International Journal of Plasticity, 27, 1618-1639(2011)
[29] Ghoniem, N. M. and Han, X. Dislocation motion in anisotropic multilayer materials. Philosophical Magazine, 85, 2809-2830(2005)
[30] Wang, Z. Q., Ghoniem, N. M., and LeSar, R. Multipole representation of the elastic field of dislocation ensembles. Physical Review B, 69, 174102(2004)
[31] Wang, Z. Q., Ghoniem, N. M., Swaminarayan, S., and LeSar, R. A parallel algorithm for 3D dislocation dynamics. Journal of Computational Physics, 219, 608-621(2006)
[32] Cai, W., Bulatov, V.V., Pierce, T. G., Hiratani, M., Rhee, M., Bartelt, M., and Tang, M. Massively-parallel dislocation dynamics simulations. Solid Mechanics and its Applications, 115, 1-11(2004)
[33] Bulatov, V. V., Rhee, M., and Cai, W. Periodic boundary conditions for dislocation dynamics simulations in three dimensions. MRS Proceedings, 653, Z1-3(2001)
[34] Vattré, A. J. and Demkowicz, M. J. Effect of interface dislocation Burgers vectors on elastic fields in anisotropic bicrystals. Computational Materials Science, 88, 110-115(2014)
[35] Lubarda, V. A. The effect of couple stresses on dislocation strain energy. International Journal of Solids and Structures, 40(15), 3807-3826(2003)
[36] Chu, H. J. and Pan, E. Elastic fields due to dislocation arrays in anisotropic bimaterials. International Journal of Solids and Structures, 51(10), 1954-1961(2014)
[37] Chu, H. J., Pan, E., Wang, J., and Beyerlein, I. J. Three-dimensional elastic displacements induced by a dislocation of polygonal shape in anisotropic elastic crystals. International Journal of Solids and Structures, 48(7), 1164-1170(2011)
[38] Pan, E. Three-dimensional Green's functions in anisotropic magneto-electro-elastic bimaterials. Journal of Mathematical Physics, 53, 815-838(2003)
[39] Pan, E. Three-dimensional Green's functions in anisotropic elasticbimaterials with imperfect interfaces. Journal of Applied Mechanics, 70, 180-190(2003)
[40] Dholabha, P. P., Pilania, H., Aguiar, J. A., Misra, A., and Uberuaga, B. P. Termination chemistrydriven dislocation structure at SrTiO₃/MgO heterointerfaces. Nature Communications, 5, 5043(2014)
[41] Barnett, D. M. and Lothe, J. An image force theorem for dislocations in anisotropic bicrystals. Journal of Physics F:Metal Physics, 4, 1618-1635(1974)
[42] Dundurs, J. and Mura, T. Interaction between an edge dislocation and a circular inclusion. Journal of the Mechanics and Physics of Solids, 12(3), 177-189(1964)
[43] Ting, T. C. T. Anisotropic Elasticity:Theory and Applications, Oxford University Press, New York (1996)
[44] Stroh, A. N. Dislocations and cracks in anisotropic elasticity. Philosophical Magazine, 3, 625-646(1958)
[45] Stroh, A. N. Steady state problems in anisotropic elasticity. Journal of Mathematical Physics, 41, 77-102(1962)
[46] Misra, A., Demkowicz, M. J., Zhang, X., and Hoagland, R. G. The radiation damage tolerance of ultra-high strength nanolayered composites. The Journal of the Minerals, Metals and Materials Society, 59(9), 62-65(2007)
[47] Li, N., Wang, J., Huang, J. Y., Misra, A., and Zhang, X. In situ TEM observations of room temperature dislocation climb at interfaces in nanolayered Al/Nb composites. Scripta Materialia, 63, 363-366(2010)
[48] Li, L., Anderson, P. M., Lee, M. G., Bitzek, E., Derlet, P., and van Swygenhoven, H. The stressstrain response of nanocrystalline metals:a quantized crystal plasticity approach. Acta Materialia, 57, 812-822(2009)
[49] Li, L., van Petegem, S., van Swygenhoven, H., and Anderson, P. M. Slip-induced intergranular stress redistribution in nanocrystalline Ni. Acta Materialia, 60, 7001-7010(2012)

Modeling core-spreading of interface dislocation and its elastic response in anisotropic bimaterial

Modeling core-spreading of interface dislocation and its elastic response in anisotropic bimaterial

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

编辑推荐

Metrics

本文评价

[1]	Xu WANG, P. SCHIAVONE. Elastic field near the tip of an anticrack in a decagonal quasicrystalline material[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(3): 401-408.
[2]	李显方;范天佑. ELECTROELASTIC FIELD FOR AN IMPERMEABLE ANTI-PLANE SHEAR CRACK IN A PIEZOELECTRIC CERAMICS PLATE[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(2): 194-202.
[3]	刘金喜;王彪;杜善义. TWO-DIMENSIONAL ELECTROELASTIC FUNDAMENTAL SOLUTIONS FOR GENERAL ANISOTROPIC PIEZOELECTRIC MEDIA[J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(10): 949-956.