Abstract
The bi-material interface arc crack has been the focus of interest in the composite community, where it is usually referred to as the fiber-matrix interface crack. In this work, we investigate the convergence properties of the Virtual Crack Closure Technique (VCCT) when applied to the evaluation of the Mode I, Mode II and total Energy Release Rate of the fiber-matrix interface crack in the context of the Finite Element Method (FEM). We first propose a synthetic vectorial formulation of the VCCT. Thanks to this formulation, we study the convergence properties of the method, both analytically and numerically. It is found that Mode I and Mode II Energy Release Rate (ERR) possess a logarithmic dependency with respect to the size of the elements in the crack tip neighborhood, while the total ERR is independent of element size.
•The Virtual Crack Closure Technique is analyzed in its Finite Element-discretized form.•A new vectorial formulation of the VCCT is proposed, considering crack propagation direction and mesh discretization.•The convergence of the VCCT in the solution of the circular bi-material arc-crack is studied.•The total Energy Release Rate is shown to be, both analytically and numerically, invariant to linear transformations.•Mode I and Mode II ERR are shown, both analytically and numerically, to depend on the logarithm of crack tip element size.