Stress and displacement fields at the tip of a craze containing a crack

Abstract

AbstractPlane elasticity theory is utilized to obtain expressions for the stress and displacement fields at the tip of a craze containing a crack. The craze is modeled as a very thin elliptical inclusion with different elastic properties from hat of the surrounding bulk polymer. Problem is solved by superimposing the solution of a crack problem onto the solution for a uniformly loaded homogeneous craze. Invoking stress free boundary conditions on the crack surface provides a singular integral equation of Hilbert type with a unique solution. Contour lines of constant hydrostatic stress and constant maximum shear stress around the craze tip are shown graphically. These two stress combinations have played prominent roles in a number of proposed craze growth criteria. Results show that even for relatively long cracks within the craze, very little stress enhancement at the craze tip occurs. Only as the crack tip approaches the craze tip does the enhancement become significant, tending to drive the craze region ahead of the crack.