Stress Magnification due to Stretching and Bending of Thin Ligaments between Voids

Stress magnification in thin ligaments between small and large cylindrical voids is obtained by matching the inner field approximation by beam theory to the outer rigid-body field in the bulk of the material. A void between two larger voids is modeled as a large hole within a strip of straight edges (boundaries of the holes with infinite radii of curvature). Both stretching and bending types of loading are applied to the strip. Comparison of different orders of stress magnification for different geometries and loading conditions is made. It is shown that the order of stress magnification in thin ligaments is (R/δ) ⁿ , where n=1/2 in the ligament between one small and one large void, n=1 in the ligament between one small void and two large voids, or between two small and two large voids, and n=2 in the ligament between a large void and a small void coalescing with another large void. The relevance of these results for the study of material failure by void growth and coalescence is discussed.