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

A novel split beam model is introduced to account for the local effects at the crack tip of bi-material interface by modeling a bi-layer composite beam as two separate shear deformable beams bonded perfectly along their interface. In comparisons with analytical two-dimensional continuum solutions and finite element analysis, better agreements are achieved for the present model, which is capable of capturing the local deformation at the crack tip in contrast to the conventional composite beam theory. New solutions of two important issues of cracked beams, i.e., local buckling and interface fracture, are then presented based on the proposed split bi-layer shear deformable beam model. Local buckling load of a delaminated beam considering the root rotation at the delamination tip is first obtained. By considering the root rotation at the crack tip, the buckling load is lower than the existing solution neglecting the local deformation at the delamination tip. New expressions of energy release rate and stress intensity factor considering the transverse shear effect are obtained by the solution of local deformation based on the novel split beam model, of which several new terms associated with the transverse shear force are present, and they represent an improved solution compared to the one from the classical beam model. Two specimens are analyzed with the present model, and the corresponding refined fracture parameters are provided, which are in better agreement with finite element analysis compared to the available classical solutions.