Numerical simulation of thin film failure with MPM

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.