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 sys tem are investigated. The local and global features of the micromorphi c stresses in the heterogeneous near-tip domain are captured through a n approximate analytical model vis-lr-ais a two-dimensional plane stra in finite element model. The studies are carried out within a heteroge neous cut-out region surrounding the physical crack-tip wherein altern ating matrix and fiber layers are positioned perpendicular to the crac k plane. The approximate analytical model is developed by postulating a general form of displacement field that is obtained by the superposi tion of the applied homogenized near-tip field and a family of kinemat ically admissible unit-cell micro-displacements. While preserving the aggregate response of the material, these micro-displacements take int o account the effects of material micro-structure. The results indicat e that the microstress field in the immediate vicinity of the crack-ti p exhibits an r(-1/2) singularity when the crack-tip is located entire ly within the matrix phase and lies sufficiently away from the adjacen t interfaces. The structure of the stress field in the matrix region s urrounding 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 sigma(xx) and sigma(xy) are found to be dominated by the orthotropic stress intensity factor and found to be in good agree ment with their homogeneous orthotropic counterparts. As expected, the discontinuous stress component sigma(yy) is found to exhibit strong d ependency on the material heterogeneity. While sigma(yy) is dominated by the applied orthotropic stress intensity factor, it is described by a discontinuous spatial eigen-function which has been obtained with t he aid of the analytical approximate model. Several parameter studies are presented and implications on the mode-I brittle fracture in layer ed systems are discussed. (C) 1997 Elsevier Science Ltd.