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Freescale Semiconductor, Inc., MD TX30/ OE21 6501 William Cannon Drive West, Austin, TX 78735, United States Received 29 December 2003, Revised, Accepted, Available online 18 December 2004 The virtual crack closure integral ( VCCI) method is used to evaluate the stress intensity factor ( SIF) and energy release rate ( ERR) of an interface crack under thermal load. The VCCIs used in this work include the traditionally known “ Mode I” and “ Mode II” VCCIs and an additional coupling VCCI. The singularity element is used in the finite element method ( FEM) implementation. The SIF and ERR calculated by the FEM are compared to the exact solution in the case of a joint dissimilar semi-infinite plates with double edge crack under thermal loading. The FEM result agrees well with the exact solution for relatively coarse meshes. The contribution of the mesh density and material mismatch to the FEM error is also explored. The VCCI method is used with the multi-scale FEM in a delamination risk assessment of a low-k integrated circuits device in flip-chip plastic ball grid array packages. The ERR is calculated for different package configurations and the prediction of the delamination risk is confirmed by reliability tests. Keywords Interfacial fracture; Thermal crack; Virtual crack closure integral; Energy release rate; Mode mixity; Stress intensity factor; Finite element method; Sub-modeling Copyright © 2004 Elsevier Ltd. All rights reserved.
a Department of Nano-structure and Advanced Materials, Kagoshima University, Korimoto, Kagoshima 890-0065, Japanb Department of System Design Engineering, Keio University, Hiyoshi, Kohokuku, Yokohama 233-0051, Japan Received 26 September 2007, Revised 11 February 2008, Accepted, Available online This paper proposes a new virtual crack closure-integral method ( VCCM) for quadratic tetrahedral finite element to compute the energy release rates/stress intensity factors. The formulations, numerical implementations and some numerical results of proposed VCCM are presented in this paper. Proposed VCCM enables us to adopt the tetrahedral finite element in 3 D crack problems and us to use automatic mesh generation programs. Therefore process time to perform 3 D crack analysis drastically reduces compared with the case of hexahedral elements. Keywords Metals; Finite element analysis; Fracture mechanics; Stress intensity factors; Surface flaw; Aerospace vehicles; Marine structures; Power plants; Energy release rates; Crack; Tetrahedral finite element; Virtual crack closure-integral method ( VCCM) Copyright © 2008 Elsevier Ltd. All rights reserved.
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