Effects of yield surface shape and round-off vertex on crack-tip fields for pressure-sensitive materials

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Asymptotic crack-tip fields for both power-law hardening and perfectly-plastic pressuresensitive materials based on a modified Drucker-Prager yield criterion are obtained under plane strain conditions. The Drucker-Prager yield criterion is expressed as a linear combination of the effective stress and the mean stress. Because of the mathematically in difficulty in developing the HRRtype asymptotic crack-tip fields due to the vertex of the yield surface based on the Drucker-Prager yield criterion, the vertex is rounded off and replaced by a curved yield surface which is based on a quadratic function of the effective stress and the mean stress. The HRR-type asymptotic solutions become available after rounding-off the vertex under the conditions where the asymptotic solution procedure breaks down based on the original Drucker-Prager yield criterion. The crack-tip fields for materials with large pressure sensitivity are sensitive to the ratio of the mean stress to the effective stress where the yield surface becomes quadratic. Specifically, as the stress ratio decreases, ahead of the tip the opening stress. becomes larger than the radial stress, and the plastic deformation becomes concentrated to the front of the crack tip. As the stress ratio increases, the stress state ahead of the tip is shown to approach to purely hydrostatic tension, and the plastic deformation shifts backward to concentrate below and above the tip. As pressure sensitivity increases and the stress ratio decreases, the generalized effective stress contour, which can be regarded as an approximate plastic zone contour, shifts to the front of the tip. The elongated shape of approximate plastic zones for materials with large pressure sensitivity agrees with the experimental observations of the shear yielding zones near cracks in rubber-modified plastics and with the computational results for materials based on the Drucker-Prager yield criterion with large pressure sensitivity.