A plastic damage model for finite element analysis of cracking of silicon under indentation
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A modified plastic damage model that accounts for tensile damage and compressive plasticity as well as interactions among them is adopted to simulate the indentationinduced cracking of silicon under Berkovich, cube corner, and Vickers indenters. Simulations with this model capture not only the well-known cracking geometries in indented ceramics, such as radial, median, lateral, and half penny (Vickers indenter) cracks, but also the recent experimentally discovered quarter penny cracks under Berkovich and cube corner pyramidal indenters. The quarter penny cracks are found to be formed by the coalescence of radial and median cracks for the first time in the simulation. Loads at which radial and half penny cracks are initiated in silicon are generally close to the experimental values reported in the literature, and the crack lengths on the sample surface agree well with both the current experimental measurements and analytical results by fracture mechanics.
I. INTRODUCTION
Silicon, a key material for the integrated circuit (IC) industry, is easily damaged on the surface or even entirely fractured during manufacturing processes.1–2 A kind of failure often seen in the IC industry is the cracking of a die or chip indented by hard foreign particles on the surface of a pressing pedestal or a holder.1–3 Indentation-induced cracking morphologies in singlecrystal silicon have been identified in cross-sectional views using optical microscope, scanning electron microscope (SEM), or transmission electron microscope (TEM),3–8 and it has been found that there are five major cracks types, cone, radial, median, half penny, and lateral cracks, as shown in Fig. 1. Even though silicon is famous for its brittleness, plastic flow is observed to develop to a certain extent in the indentation.6–7,9–11 In order to account for the plastic flow’s influence on the cracking initiation and propagation, a usual simplified analytical treatment is to calculate the stress intensify factor (K) from the cracking geometry and the elastoplastic stress field that is calculated assuming no cracking, and then judge the development of the cracking based on the comparison between the calculated K and the fracture toughness of silicon (KC).12–16 However, the analytical solutions are limited by the simplifications such as the perfect elastoplastic a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2010.0270
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http://journals.cambridge.org
J. Mater. Res., Vol. 25, No. 11, Nov 2010 Downloaded: 02 Apr 2015
material model12–16 and stress field solutions from the cavity model.12,14,16 The finite element method (FEM) has been widely adopted to simulate indentation-induced cracking in brittle materials.17–21 One merit of FEM is that the stress and strain fields can be precisely obtained for the real geometry of the specimen based on complex constitutive models (e.g., strain hardening).22–23 A simple Rankine criterion is usually used to detect cracking initiation; that is, a crack is initiated where the local maximum pri
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