A consistency check for strongly interacting multiple crack problems in isotropic, bimaterial and orthotropic bodies

Abstract

A consistency check is proposed to examine numerical results, from the physical point of view, for strongly interacting multiple crack problems in isotropic elastic materials, in bimaterials, and in orthotropic materials, respectively. The basic idea starts from the projected conservation relations of the well-known J _k -integral vector. The path chosen to evaluate the J _k -vector is one surrounding each of the multiple cracks completely in a local coordinate system such that the total contributions of the multiple cracks to the J-integral in a global coordinate system could be formulated by a summation of the projected values of the J _k -vector. The summation should be zero, due to the remote stress conditions. The consistency check is then introduced which is concerned only with the stress intensity factors at all crack tips, the stress parallel to the faces of every crack, and the oriented angle of every crack. Thus, no matter how the numerical results for the interacting crack problems are derived by whatever kind of technique, any mistakes occurring in manipulations which may escape the traditional comparisons with previously known results in some special cases can then be recognized and avoided, since they will certainly lead to unsatisfactory conclusions contrary to the consistency check in relatively general cases. The consistency check is performed for two interacting cracks in the three kinds of materials mentioned above. It is concluded that the check really provides a powerful tool for examining the numerical results for the multiple crack problems.