Regularization of the damage mechanics for predicting crack initiation

Abstract

Several damage models/theories were postulated in the past decades to overcome the actual deficiencies of the traditional fracture theory in predicting crack initiation. Recent reserarch indicates the reasonability of damage theories in predicting crack initiation as well as the degradation of material properties in varying degrees. However, in spite of the achievement of the novel developed damage theory on its way to predict crack initiation, there remains the intrinsic drawback of the response dependence of material point on its infinitesimal neighborhood invoked in classic continuum mechanics. In the present paper, the origin of the intrinsic drawback of the specialized ductility dissipation based damage theory in predicting crack initiation of pre-cracked specimens is outlined first; then, two regularizations, i.e., intrinsic mesh size and post non-localization methodologies, are employed to eliminate the drawback of the damage theory within the framework of classic continuum mechanics. The essence of the damage theory is that unrecoverable deformation inevitably results in the degradation of the deformation-carrying capacity. In turn this irreversible dissipation can be reasonably taken as the damage variable to characterize the deterioration of the deformation-carrying capacity of material. Surely, the bases of both regularizations are that the movements of material elements and the evolutions of microstructures are highly correlated and synergetic; they lead to the formation of slip-bands and stretched zones. Furthermore, pre-cracked specimens are taken as examples to show the rationality of the improvements.