Near-tip mode-I elastic fields in bimaterial layered systems

The micromorphic stress fields in the near-tip region of a Mode-I semi-infinite crack embedded in an infinite elastic bimaterial layered system are investigated. The local and global features of the micromorphic stresses in the heterogeneous near-tip domain are captured through an approximate analytical model uis-his a two-dimensional plane strain finite element model. The studies are carried out within a heterogeneous cut-out region surrounding the physical crack-tip wherein alternating matrix and fiber layers are positioned perpendicular to the crack plane. The approximate analytical model is developed by postulating a general form of displacement field that is obtained by the superposition of the applied homogenized near-tip field and a family of kinematically admissible unit-cell micro-displacements. While preserving the aggregate response of the material, these micro-displacements take into account the effects of material micro-structure. The results indicate that the microstress field in the immediate vicinity of the crack-tip exhibits an r-l’* singularity when the crack-tip is located entirely within the matrix phase and lies sufficiently away from the adjacent interfaces. The structure of the stress field in the matrix region surrounding the crack-tip corresponds to the universal isotropic field dominated by the tip stress intensity factor. In the farfield region (radial distance greater than one unit-cell thickness), the continuous stress components urr and uXYar e found to be dominated by the orthotropic stress intensity factor and found to be in good agreement with their homogeneous orthotropic counterparts. As expected, the discontinuous stress component oYv is found to exhibit strong dependency on the material heterogeneity. While a,,, is dominated by the applied orthotropic stress intensity factor, it is described by a discontinuous spatial eigen-function which has been obtained with the aid of the analytical approximate model. Several parameter studies are presented and implications on the mode-1 brittle fracture in layered systems are discussed. 8 1997 Elsevier Science Ltd.