金属材料在冲击荷载下局部变形的数值模拟及分析

Numerical simulation and analysis for local deformation of metallic materials under impact loads

高应变率载荷作用下金属材料的变形集中于很窄的区域内,即剪切变形局部化。局部化变形带内产生严重的塑性变形,削弱材料的承载能力,甚至导致材料断裂破坏。基于有限元分析软件FEAP(Finite Element Analysis Program),采用混合有限元方法,用Fortran语言编译适用于金属材料在高应变率下的剪切局部化问题的新单元;计算过程中采用与应变、应变率及温度相关的塑性本构关系来描述剪切带现象,同时在能量平衡方程中考虑剪切带形成过程中的热传导作用;同时考虑显式算法与隐式算法的时间离散方法,并将两种算法的结果进行对比。结果表明,虽然剪切带形成过程很短,一般为微秒量级,但剪切带形成过程中的热扩散项与塑性变形产生的热能量级相同,有效地缓解剪切带模拟的网格敏感性;对于金属材料热塑性剪切带问题,为了满足计算精度要求,显式算法需要的时间步太小,计算成本比隐式迭代高很多;而基于该单元采用隐式算法模拟热塑性剪切带问题迭代收敛稳定,计算精度高,且因为考虑了热传导作用,网格敏感性小。

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.