A simplified stress-based engineering method of calculating fracture mechanics parameters for prediction of crack initiation from an interface corner of bi-material structures

Abstract

It is highly demanded to predict accurately crack initiation and growth from interface corners or edges of bi-material structures such as those commonly existed in advanced integrated circuit packaging structures, yet the issue has not been well addressed. This paper proposes a novel engineering method for assessing the risk of interfacial fracture at interface corners, which is based on the small-scale cracking solutions and allows direct calculation of fracture mechanics parameters of short interfacial cracks originating from the interface corners using stress data obtained from finite element analyses. We first analyze the generalized stress intensity factor H and its corresponding dimensionless coefficient a at the interface corner of a non-cracked bi-material wedge structure. Subsequently, the stress intensity factor K and its corresponding dimensionless coefficient b at the tip of the interfacial crack located at the interface corner is analyzed. By establishing a relationship between the above two dimensionless coefficients a and b, the dimensionless coefficient c depending on the elastic mismatch at the interface and the interface corner angle can be determined. A correlation is then established between the stress intensity factor at the tip of the interfacial crack and the tangential and shear stresses, which is expressed by the coefficient d and can be deduced from the coefficient c. This relationship enables the straightforward determination of the stress intensity factor, strain energy release rate and phase angle of the interfacial cracks at singularities under different external boundaries using stresses at finite element nodes. It is found that the present method needs to satisfy the condition that the cracks are confined within the H-field of the stress singularity. An example is presented to demonstrate the practical applicability of the present method for analysis of interfacial cracks originating from interfacial corners of underfill/die and underfill/substrate interfaces in flip-chip package structures typically used in integrated circuits. The results exhibit a significant level of agreement between the fracture mechanics parameters calculated by the present method and those obtained from the finite element analysis.