Fracture initiation under gross yielding: Strain energy density criterion

The damage of metal alloys at the continuum level can be described by a combined process of yielding and fracture. Yielding is generally associated with excessive distortion and fracture with excessive dilatation. With the increased use of low strength alloys, gross yielding can often precede the initiation of macrocracking. This paper applies the strain energy density concept for examining failure by crack growth in a fully plastic material in order to show that the criterion applies to linear elastic as well as nonlinear plastic materials. The incremental theory of plasticity is employed in conjunction with the finite element method for determining the stresses in a tensile specimen containing a center crack. Net section yield is developed. Calculated are the different levels of intensity of yielding around the crack. As in the elastic case, crack growth in a fully plastic material also tends to coincide with the direction along which the strain energy density function d W/d V attains a relative minimum. The onset of crack growth is assumed to occur when (d W/d V)_min reaches some critical value (d W/d V)_c^* which must now be obtained from the true stress and strain curve of the material undergoing gross yielding.