The Strain Energy Release Rate of a Bi-Material Beam with Interfacial Crack

Abstract

Multi-layer structures are common in electronic package especially for the micro devices manufactured via the semi-conductor processes or MEMS processes. Interfacial crack due to the delamination significantly weakens the multi-layer structure. It is desired to understand the interfacial fracture properties of the electronic packaging materials. In this research, three specimens named Doubled Cantilever Beam (DCB), End-Notched Flexure (ENF), and Four-Point-Bending are proposed to investigate the fracture toughness associated with mode I, mode II and mixed mode. Basing on the Euler-Bernoulli beam theory, the strain energy in a bi-layer beam is derived. The strain energy before and after the propagation of the interfacial crack are calculated, lead to the determination of the strain energy release rate. The analytical results of strain energy release rate derived in this investigation are compared with the numerical results obtained from finite element method. The effects of material properties and thickness between the adjacent layers of interfacial crack are examined through the parametric study.