Numerical modelling of elementary failure mechanisms and associated caustics in two-phase composite structures

Abstract

An overview about basic investigations concerning the strength and fracture behaviour of composites is given where the differences of the micro- and macromechanical theories of composite mechanics have been taken into consideration. Further, the numerical modelling of elementary failure mechanisms like matrix and fibre-matrix interface cracks will be demonstrated for two-phase composite structures consisting of brittle fibres and elastic matrices. Fracture mechanical quantities like strain energy release rates, stress intensity factors and crack opening displacements, are thereby determined by means of a finite element calculation. Moreover, the continuum mechanical modelling of branched thermal crack systems arising in disk-like models of two-phase brittle matrix composite structures, due to special thermal loadings, leads to mixed boundary value problems of the thermoelasticity. The corresponding solutions were obtained, not only numerically by the finite element method, but also experimentally by the so-called shear stress difference procedure and the shadow optical method of caustics. A comparison of those experimentally gained fracture mechanical quantities mentioned above with associated finite element calculations performed by using the local as well as the global energy method showed a very good agreement in the region of stable crack propagation. Furthermore, in a second part of the paper a cracked two-phase solid (matrix: Araldite B, fibre: modified epoxy) has been studied containing a matrix crack as well as interface cracks in the material interface between a cylindrical inclusion and the matrix material in a modified compact-tension specimen. By using the displacement vector field around the tips of a straight matrix crack and an interface crack, shadow spots and associated caustics are simulated and corresponding strain energy release rates are determined by means of a finite element calculation.