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薄膜破坏过程数值模拟的MPM方法

Numerical simulation of thin film failure with MPM

  • 摘要: 将连续与不连续本构模型相结合用于薄膜破坏过程的模拟计算. 采用vonMises关联塑性本构模型描述材料的弹塑性变形过程,在塑性硬化和软化阶段通过检查分岔是否发生, 从而判断是否有破坏出现,即材料出现应变局部化现象. 一旦出现破坏,则在发生破坏的区域采用位移不连续(decohesion)本构模型进行模拟, 直到破坏面两侧材料完全分离.分离阶段采用相应的分离算法同时运用黏性边界条件以提高计算效率. 结果表明结合连续与不连续本构模型的方法, 能很好地模拟材料从局部化到完全破坏的过程,体现了材料破坏连续建模的思想,可用于预测材料发生破坏的环境和形式, 从而通过改变材料工作环境提高其使用寿命;同时数值算例也显示了物质点法(material-point-method, 简称MPM)的健壮性和有效性.

     

    Abstract: Thin metallic films under compressive loads often fail dueto delaminating away from the substrates, which has been observed in manyexperiments and arouses many researchers' interests. Recently, much researchhas been conduced to model and simulate this physical phenomenon fromtheoretical and computational aspects and most of them are based on theconventional elastic stability theory and interfacial fracture mechanics(Shen 2004). In fact, the thin film failure often involves both localizationand decohesion processes and the evolution of localization in the film isquite possible is the reason of delamination (Chen 2003), which ischaracterized by the interaction between geometrical and materialinstabilities. To simulate such a multi-physical phenomenon, a carefuldesigned model should be constructed. Before localization occurs, thin filmsundergo usually elastoplastic deformations, and after that displacement jumpappears in some local areas, which can be modeled by a decohesion-basedmodel (Schreyer et al. 2002, Chen et al. 2003). It was pointed out that theinitiation of localization could be regarded as the transition fromcontinuous to discontinuous failure modes (Chen 1996), which can bedetermined via a bifurcation analysis of the acoustic tensor.The purpose of this paper is to simulate thin film failure phenomenon withthe combination of continuous and discontinuous constitutive models and theMaterial Point Method (MPM, Sulsky et al. 1994). The MPM is chosen as a basicmethod in this paper because of its simplicity and high performance inmodeling large deformation, impact/contact, blast, penetration and otherchallenging physical processes. At the beginning of the deformations of thesegment, associated von Mises elastoplasticity constitutive model is used.Whether a local failure will appear in the segment can be identified throughthe bifurcation analysis in the plastic deformation stage, namely,localization. If localization occurs, the decohesion-based model will beadopted to describe the motions of the material points in the local regionuntil separation emerges. Under the assumptions of the deformations aresmall in the evolution of material failure and no contact occurs betweenmaterial points in a short period after separation (these assumptions arereasonable because the film failure occurs very quickly and the case afterfailure will not be considered in this paper), a special algorithm will beused to describe the motion post separation. Also we adopt a silent boundarywith viscous damping stresses to improve the computational efficiency.Numerical results show that: (1) Shear band modes are predicted easily withusing the MPM and coupled models; (2) Thin film failure modes vary withdifferent load cases and structural sizes. Failure starts from the topsurface of the film in dynamic case but from the interface of the film andthe substrate in quasi-static one. The period between bifurcation andseparation occur in the former is longer than that in the latter; (3) Themethod coupled continuous and discontinuous models is appropriate for thesimulation of material failure problems; (4) The MPM is a robust andefficient method for material modeling.

     

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