Abstract

A new, macroscopic theory of fracture has been developed as an extension of the “Poynting effect” of finite elasticity. Poynting (1909) noted that some materials expand slightly as they are subjected to finite shear strains. It is well known in experimental rock mechanics that many rocks exhibit dilatancy prior to fracture. These observations form the basis for a new theory of fracture: Fracture occurs when the elastic strain energy exceeds the work of dilatation, which is in turn equal to the critical volume expansion times the confining pressure plus an “internal pressure” equal to the tensile strength. This new theory has several advantages over the classic “Mohr-Coulomb” theory of fracture: 1) it is able to inter-relate shear and tensile fracturing; 2) it can explain the parabolic shape of the “fracture envelope” on a Mohr diagram; 3) it can provide a physical explanation for pre-fracture shear dilatancy; and finally, 4) the new theory does away with the troublesome concept of “internal friction” which involves friction on a surface that does not yet exist. Further, since it deals with fracture on the macroscopic scale, the new theory eliminates most of the complexity and arbitrary assumptions of the various microscopic theories based on the “Griffith crack” concept. This new theory of fracture has obvious applications to many fields of geology, geophysics, and rock mechanics.