Under high strain rates, metallic materials’ deformations are concentrated in a very narrow zone, this phenomenon is called shear deformation localization. In a localized deformation band, there are serious plastic deformations to weaken materials’ load-bearing capacity and even lead to materials’ fracture and damage. Based on the finite element software FEAP (finite element analysis program), a new element was adopted in the code using Fortran language for the simulation of shear localization problems of metallic materials under high strain rates with the mixed finite element method. A plastic constitution relation correlated to strain, strain rate and temperature was employed to describe shear deformation band phenomena in computation process. The heat conduction in forming process of shear bands was considered in the energy balance equation. For time integration, both the implicit method and the explicit method were considered, the results obtained using the implicit time integration algorithm were compared with those using the explicit one. It was shown that the shear band forming process is extremely fast within some micro-seconds, but the energy level of thermal diffusion term in forming process of shear bands is the same as that of heat caused by plastic deformation, so the grid sensitivity of shear bands simulation was effectively relieved; for thermal plastic shear band problems of metallic materials, the explicit algorithm needs much small time step to meet the requirements of calculation accuracy, its computation cost is much higher than that of the implicit one; the simulation of thermal plastic shear band problems using the implicit algorithm and the new element has stable iteration and convergence, the grid sensitivity is small due to considering heat conduction.
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
References
[1] 徐永波，白以龙.动态载荷下剪切变形局部化、微结构演化与剪切断裂研究进展.力学进展，2007，37 (4)：496-516.
XU Yongbo, Bai Yilong. Shear localization, microstructure evolution and fracture under high-strain rate [J]. Advances in Mechanics,2007,37(4): 496-516
[2] Wright T W and Batra.R C. The initiation and growth of adiabatic shear bands [J]. International Journal of Plasticity, 1985,1(3): 205-212.
[3] Dodd B and Bai Y. Adiabatic Shear Localization (Second Edition) [M]. Elsevier, Oxford, second edition, 2012.
[4] Osovski S, Rittel D, Landau P, and Venkert A. Microstructural effects on adiabatic shear band formation. Scripta Materialia, 2012, 66(1): 9-12.
[5] Osovski S, Rittel D, and Venkert A. The respective influence of microstructural and thermal softening on adiabatic shear localization [J]. Mechanics of Materials, 2013, 56:11- 22.
[6] Wright T W. The physics and mathematics of adiabatic shear bands [M]. Cambridge University Press, 2002.
[7] Marchandand A and Duffy J. An experimental study of the formation process of adiabatic shear bands in a structural steel [J]. Journal of the Mechanics and Physics of Solids,1988, 36(3): 251-283.
[8] Johnson G R and Cook W H. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures [J]. In Proceedings of the 7th International Symposium on Ballistics, The Hague, The Netherlands,1983, 21: 541-547.
[9] Li S, Liu W K, Rosakis A J, Belytschko T, and Hao W. Mesh free galerkin simulations of dynamic shear band propagation and failure mode transition [J]. International Journal of Solids and Structures, 2002, 39(5): 1213-1240.
[10] Belytschko T, Chiang H Y and Plaskacz E. High resolution two dimensional shear band computations: imperfections and mesh dependence [J]. Computer Methods in Applied Mechanics and Engineering, 1994, 119(1): 1-15.
[11] 王猛,杨明川,罗荣梅等. 钨合金杆式弹穿甲侵彻开坑阶段绝热剪切失效的数值模拟.振动与冲击, 2016, 35(18): 111-116.
WANG Meng, YANG Ming-chuan, LUO Rong-mei et. al. Numerical simulation on the adiabatic shear failure at cratering stage for tungsten alloy long rod penetrator piercing into armor [J]. Journal of Vibration and Shock. 2016, 35(18): 111-116.
[12] Needleman A. Material rate dependence and mesh sensitivity in localization problems [J]. Computer Methods in Applied Mechanics and Engineering, 1988, 67(1): 69-85.
[13] 白以龙，郑哲敏和俞善炳. 关于热塑剪切带的演变.力学学报,1986, 18(S2): 377-383.
BAI Yi-long, CHENG Zhe-ming and YU Shan-bing. On evolution of thermo-plastic shear band [J]. Chinese Journal of Theoretical and Applied Mechani, 1986, 18(s2): 377-383.
[14]白以龙，郑哲敏和俞善炳. 热塑剪切带后期演变的准定常近似.固体力学学报, 1987, 2:153-158.
BAI Yi-long, CHENG Zhe-ming and YU Shan-bing. Quasi steady approximation to the late stage evolution of thermo-plastic shear band [J]. Chinese Journal of Solid Mechanics, 1987, 2: 153-158.
[15] Taylor R L. FEAP-A Finite Element Analysis Program, April 2011.
[16] Zhou M, Ravichandran G, and Rosakis A J. Dynamically propagating shear bands in impact-loaded pre-notched plates-II. numerical simulations [J]. Journal of the Mechanics and Physics of Solids, 1996, 44(6): 1007- 1032.
[17] McAuliffe C and Waisman H. A pian-sumihara type element for modeling shear bands at finite deformation. Computational Mechanics, 2013, 53(5): 925-940.
[18] Schur J. Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind [J]. Journal für die reine und angewandte Mathematik, 1917, 147:205-232.
[19] Berger-Vergiat L, McAuliffe C, and Waisman L. Isogeometric analysis of shear bands [J]. Computational Mechanics, 2014, 54(2): 503-521.
[20] Hughes T J R. The finite element method: linear static and dynamic finite element analysis [M]. Dover, 2nd edition, 2000.
{{custom_fnGroup.title_en}}
Footnotes
{{custom_fn.content}}
PDF(1430 KB)
