Numerical and analytical modeling of crack path for three-dimensional mixed mode crack problem using global approach

Abstract

Civil engineering and mechanical structures are usually submitted to mixed mode loading. Consequently, a mixed mode crack path process occurs. In three-dimensional crack problem, the study of this problem is very important due to multiple problems that require more understanding of the corner point effect and the local effect due to the torsion mode (mode III) and also due to the necessity to take into account thickness effect. In order to study the mixed mode loading for three-dimensional crack problem, a new three-dimensional contour integral entitled M3D integral is modeled using global approach. Combining real and virtual mechanical displacement fields, this new integral is used to separate numerically mode I, mode II and mode III in the mixed mode ratio. In earlier research works, Moutou Pitti et al [1] have proposed a new specimen called Mixed Mode Crack Growth (MMCG), and El kabir et al [2] have studied numerically the stability of this specimen for various geometries in two-dimensional case. This work deals with numerical and analytical modeling to study the crack path stability in real three-dimensional case for mixed mode crack problem. Using MMCG specimen, the non-dependence of integration domain is presented, and the stability of the calculation of M3D Integral with respect to various geometries and thicknesses is shown for the opening mode (Mode I), the shear mode (Mode II), the out-of-plan shear mode (Mode III) and also for the mixed mode ratio by computing the energy release rate versus the crack length. Finally, the analytical generalization of the M3D-integral is done. That will allow to take into account the mixed-mode crack growth analysis coupling mechanical and thermal loads.