Multi-Scale Modeling of Free-Edge Micro-Cracks with XFEM

A multi-scale analysis of free-edge micro-cracks using traditional displacement based finite element submodeling and XFEM was used to explain the experimental observation that micro-cracks did not grow unless they were of sufficient length. Analysis of the stressintensity factors along the micro-crack front revealed that penny shaped micro-cracks in the 90° plies of the [±25°/90°]s family of laminates of length two fiber diameters or longer are under mode I dominated loading conditions when oriented parallel or perpendicular to the laminate loading direction. The maximum observed KI along the crack-front of these modeled micro-cracks was no larger than 26% of the ultimate KIC of the matrix material, under the application of a uniform temperature change (ΔT=-150°C) and uniform extension equal to the experimentally measured ultimate failure strain of the laminate. This indicates that insufficient energy is supplied to these small micro-cracks to facilitate crack growth, confirming what was experimentally observed. A method for estimating a critical microcrack length based upon the results of the fracture mechanics analysis was developed, and predictions for this critical crack length were between 26 and 255 fiber diameters with a nominal prediction of approximately 73 fiber diameters, which agreed quite well with the experimentally observed critical micro-crack length of approximately 50 fiber diameters.