Mechanics of Bimaterial Interface: Shear Deformable Split Bilayer Beam Theory and Fracture

Abstract

A bi-material or bi-layer system is a common configuration in structural applications, and it is usually manufactured by monolithically forming the two parts together. Interlaminar delamination is one of the most popular failure modes in this type of layered structures. A split bi-material beam is resulted from the delamination of a bi-layer structure. Requirement of effective analysis of the split beam is encountered frequently, such as the delamination buckling of laminated composites (1), data reduction technique of fracture tests (2), crack identification (3), and vibration analysis of delaminated structures (4). Conventional analysis of split beam in the literature simulates the cracked segment of the beam as two separate beams and the uncracked segment as one composite beam. At the connection of the cracked and uncracked segments where a joint is formed to connect three beams, the cross sections of the three beams are assumed to remain in one plane and perpendicular to the mid-plane of the virgin beam. This conventional model neglects the elastic deformation of the joint, such as the root rotation at the crack tip (5) and thus forms a rigid connector. Extra errors are introduced, and unfavorable results are obtained by this conventional split beam model, such as the unconservative loading of delamination buckling of composites (6), under-evaluated energy release rate of fracture (5), and rough dynamic analysis at the crack tip (3). The reason for this unfavorable feature of the available split beam model is explained by the nature of the assumptions used in the beam model, which are unable to describe the severe local deformation at the crack tip of the split beam. In the cases where the local deformation is of no interest or of little importance, the conventional split beam model is applicable; however, in the cases where the local deformation is significant, a new and improved model is required to account for the deformation at the crack tip.