基于Voronoi图理论的微体积成形数值建模及验证

Modeling and numerical simulation of micro-plastic forming based on Voronoi diagram

数值模拟作为微塑性成形技术的核心方法之一,与实验相结合,能够减少工艺开发的时间和成本,具有经济和学术价值。文章基于Voronoi图理论,利用MATLAB和Python汇编语言建立了一种在ABAQUS软件中运行的多晶几何模型,对微塑性成形进行有限元建模和数值模拟,根据晶粒分布和取向特点以及表面层模型理论,修正宏观的Hall-Petch公式,建立了一种区域化本构模型,再利用所建立的几何模型和本构模型,通过有限元软件ABAQUS实现了微塑性成形的数值模拟。结果表明:三维多晶几何模型的数值模拟可以更真实地表现试样的晶粒形状,有限元多晶模型证实了尺度效应现象及晶粒分布的不均匀性;所建立的材料多晶几何模型和区域化本构模型具有一定的可靠性,提出的建模方法可用于分析微塑性成形过程的尺寸效应现象。

Numerical simulation is one of the core methods of micro-plastic forming technology.The numerical simulation method is used to analyze,adjust and optimize the process plan and combine it with the experiment,which can reduce the process development time and cost.In this paper,based on Voronoi diagram theory,the finite element modeling and numerical simulation of micro-plastic forming are studied.By means of MATLAB and Python assembly language,a method of establishing polycrystalline geometric model in ABAQUS software is proposed,which can be applied to the finite element modeling of micro-plastic forming.According to the characteristics of grain distribution and orientation as well as the surface layer model theory,the macroscopic Hall-Petch formula was revised to establish a regional constitutive model.Then,the geometric model and constitutive model were used to realize the numerical simulation of micro-plastic forming by the finite element software ABAQUS.The results show that the numerical simulation of three-dimensional polycrystalline geometry model can show the grain shape of the sample more realistically.The finite element polycrystalline model confirms the phenomenon of scale effect and the inhomogeneity of grain distribution.The model of polycrystalline geometry and the regional constitutive model are reliable.The modeling method can be used to analyze the size effect of micro-plastic forming process.