Singular stress fields at V-notch tips in elastoplastic pressure-sensitive materials

Abstract

Elastoplastic solutions with the higher-order terms for V-notches in materials exhibiting pressure-sensitive yielding and plastic volumetric deformations are presented. It is shown that under plane strain conditions the variable-separable solution exists within some limited pressure-sensitivities. The limit values grow significantly with increasing notch angle. The leading singularity is a decreasing function of notch angle. The small notch angle can hardly affect the singularity. The plane stress fields are generally more singular than the plane strain ones under the same conditions. The pressure-sensitivity does not affect the plane strain field singularity, but the angular stress distributions. The plane stress singularity is slightly increased by the high pressure-sensitivities at the large notch angles. The second-order exponent grows significantly with increasing notch angle. At a notch angle greater than 60°, the elasticity enters the second-order terms in all materials under plane strain conditions, while the plane stress second-order solutions contain the elasticity effects for all notches. It implies that the second-order terms in the notch analysis may not give a significant improvement in characterising the full stress fields. For an apex notch bounded to a rigid substrate, the leading-order singularity falls with increasing notch angle more slowly than that in the homogeneous pressure-sensitive materials. It vanishes at a notch angle of about 125° for all strain-hardening exponents. The elasticity affects the second-order solutions when notch angle becomes large. Whereas the stress fields are dominated by the hoop stress under assumptions of the traction-free crack surfaces, the shear stress is significant for large angle notches.