A new theory for free-surface formation in solid continua

Abstract

In essence, fracture mechanics consist of the conventional boundary-value problem formulation of continuum mechanics, along with a variety of fracture criteria that govern the advance of crack fronts. The assumption that the material response is governed by a local constitutive model everywhere in the body, even at points that are arbitrarily close to the crack front, generally leads to an unbounded stress field as the crack front is approached. Also, processes such as metal-cutting and penetration share with fracture the essential feature of new-free-surface formation, but do not fit easily within the conventional fracture theory. For these and other reasons, it seems worthwhile to seek a broader theoretical construct which encompasses surface separation in a more general setting. With this motivation, a new theory is proposed which applies generally to surface separation in solid continua, but which nonetheless yields fracture-mechanics-type predictions in appropriate special cases. The proposed exclusion region theory involves identification of a small material neighborhood that contains the separation front. A generalized constitutive description that derives directly from the local constitutive model is constructed for the exclusion region. A separation criterion is formulated with reference to tractions on, and/or distortion of, the exclusion region. The direction-of-advance of the separation front is determined as a natural consequence of the separation criterion. The material parameters appearing in the separation criterion can generally be determined from conventional fracture tests. The theory has been implemented in a finite element code. Two example problems illustrating certain important aspects of the theory are presented.