Surface Instability of Microscale Multilayer Thin Film System
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Surface Instability of Microscale Multilayer Thin Film System Yueguang Wei, Di Jiang, Ajing Cao, Haifeng Zhao LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, P.R. China ABSTRACT Fundamental relations of surface instability for micro-scale multilayer thin film systems are derived based on the Hill and Hutchinson bifurcation theory and the volume average integral. In the present relations, a size effect is considered through generalizing the plastic hardening modulus to include the strain gradient hardening effects. By using the model, firstly, the parameter-controlled instability region is divided and analyzed, secondly, the surface instability of the multilayer thin films are analyzed. In the surface instability analysis, several kinds of failure band formations are obtained, such as the kink bands and the compressive buckling bands in vertical direction and in inclined direction. Moreover, the failure mechanism of the multilayer thin film system due to surface instability is used to interpret the microstructure features of the surface-nanocrystallization materials. INTRODUCTION The micro-scale multilayer thin film system (MMTFS), with its special characteristics, is relevant to many advanced materials applications and widely used in the MEMS- as well as surface- and interfacial-engineering areas. Fundamental roles in the MEMS and in the advanced materials played by the MMTFS can be described as: protecting, connecting, strengthening, toughening, as well as some function devices, etc. [1,2]. Typical failure modes of MMTFS include interfacial cracking, thin film cracking perpendicular to the interface, and failure initiating at the surface, etc. The last failure formation is caused by material surface instability. It is well known that due to the residual compressive stress related to film deposition, or direct external compression, surface instability occurs as the main failure mode. In this case, the surface kink bands and damage bands are formed near the material surface. Additionally, the surface instability is accompanied by some kinds of failure patterns appearing on the material surface, such as surface layer thin film delamination, buckling, damaging, etc. The surface instability is as a major failure formation not only for a multilayer thin film material, but also for a uniform or a single crystal material, such as the damage bands within the surface layer of nanocrystalline Al [3], as shown in Figures 1(a) and (b). In order to investigate the failure mechanism related to surface instability, in the present research, a theoretical model considering strain gradient effect is presented and developed based on the Hill and Hill-Hutchinson’s bifurcation theory [4-6]. The surface instability description for the MMTFS is formulated through homogenizing a set of field equations of multilayer uniform thin film materials. Motivated by the development of strain gradient hardening theory, the surface instability analysis is extended to the micro-scale case through generalizing the plast
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