THE VARIATION OF THE DYNAMIC ELASTIC-MODULUS BY A PROPAGATING EDGE CRACK

The rapidly propagating crack tip in a plane-stress specimen causes a drastic change in the mechanical properties of the material around it. The static values of the elastic moduli and Poisson's ratios become variable quantities during the passage of the crack, sometimes taking very different values. The dynamic elastic modulus, E(d), becomes a transient quantity which influences considerably the distribution of stresses and strains in the elastic field. A method is presented in this paper for the evaluation of the local transitory values of E(d) at the vicinity of a propagating crack. The dynamic expressions of the Cartesian stress- and strain-rate components were used as initial values together with the known static value for the elastic modulus E. A relationship was also established experimentally for the particular material studied, connecting the strain rate epsilon and the dynamic elastic modulus E(d) by performing a simple dynamic tension test. In the first step of an iterative process, using these initial data, new values for the strain rates epsilon(t) were established, which were subsequently used as initial values for subsequent iterative cycles, which yielded new local values for E(d) and epsilon(t) at different points of the stress field. This iterative process was continued until the maximum differences in subsequent cycles were kept smaller than a predetermined infinitesimal value for the strain rate. It was shown that a rapid convergence was achieved in this iteration process, necessitating only a few iteration cycles. It was found that positions of extreme values for E(d) exist at orientations different from the mean direction of propagation of the crack, whose polar angles are very close to the respective branching angles for dynamically propagating cracks.