The effect of the mixed mode ratio on the plastic zone size and shape and the J-integral

The purpose of this thesis is to examine from a general perspective the mixed mode loading of a semi-infinite plate with an edge crack in order to assess the resulting plastic zone size and shape, and to evaluate the J-integral. The theoretical approach allows the determination of the displacement, strain and stress field at every point around the crack tip for any mixed-mode loading condition. This permits, by using a numerical parametric normalization scheme. the generalization of the obtained results. The plastic zone size and shape, around the crack tip, for a specific mixed mode ratio and increasing loading is estimated using the 'Von Mises yield criterion." To generalize the size and shape of the plastic zone results, for a given mixed-mode ratio and Yarying loading, it is made dimensionless by normalizing each point on and inside the plastic zone boundary with respect torY, the distance from the crack tip to the plastic zone boundary ahead of the crack tip and parallel to the crack length. Also, the J -integral is numerically evaluated along many different contours, close and far from the crack tip and plastic zone, to assess its behavior as the mixed-mode and loading change. Generalized J-integral results are obtained by normalizing the obtained mixed-mode J-integral values with respect to the J-integral value for opening mode, at the loading being considered. This approach leads to a single curve for the J -integral under mixed-mode loading conditions.