A special finite element method applied to off-axis tunnel cracking in laminates

Off-axis oriented tunnel cracking in a laminated structure is modeled using a special 2D off-axis finite element formulation, thus replacing full 3D finite element simulations with much less demanding 2D simulations. The 2D off-axis element is formulated as a user element in the commercial finite element code ABAQUS, and the user element code is made available for the reader. The finite element formulation is used to predict the steady-state energy release rate and the mode-mixity for either one isolated crack or multiple interacting tunnel cracks in the central ply of a [0/θ/0/−θ]s layup. The laminate is loaded uni-axially or bi-axially, and analyses are presented for glass and carbon fiber composites for arbitrary layup angles θ. The 2D finite element model is found to give precise predictions when comparing the detailed simulations made by a full 3D finite element model. It is demonstrated that despite being a 2D method, the model rigorously provides detailed solutions for the out-of-plane deflection and strain. With a speed-up of more than four orders of magnitudes, it is thus possible to perform new, detailed, and very accurate studies of the dependency of laminate thickness as well as neighboring cracks on off-axis tunnel cracking.