Finite element analysis of interfacial crack propagation based on local shear, part I—Near tip deformation

Abstract

Full-field, plane-strain elastoplastic solutions for an interface crack in adhesive bonds deforming in shear are obtained from a finite element analysis. The analysis, which considers very large strains and includes the effect of contact and friction between the debonded interfaces, is particularized to a nearly elastic ideally-plastic interlayer obeying J2 flow, which is sandwiched between either rigid or compliant substrates. Guided by experimental evidence, the analysis focuses on the interface ahead of the crack tip, where crack propagation occurs. The engineering shear strain at the crack tip along the interface, γ, is characterized by a power-law singularity of the form γ = K (x/h)−δ, where h is the bond thickness, x is the horizontal axis originating from the crack tip and K and δ are the numerically obtained functions of bond-average shear strain, γ¯. The singular field under small-scale yielding (δ = 1) is maintained up to γ¯ = 0.03 ∼ 0.05, which is close to the yield strain in shear of the adhesive (0.06). For larger remote shear strains, the strength of the singularity monotonically decreases with γ¯. This apparently new characteristic results from the interaction of the deformation field at the crack tip with the opposing interface of the bond. The distribution of shear strain ahead of the crack tip compares well with experimental results. The effect of interfacial friction appears to be significant only for relatively large loading (γ¯ > 0.2).