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1991
Conference Paper
Titel
On integral criteria of fracture mechanics and local parameters based on the energy-momentum tensor
Abstract
The application of integral criteria to assess flaws in structural components is of common use in fracture mechanics. Crack initiation and crack growth are described by Rice's J integral in elastic-plastic materials, whereas crack growth under steady-state creep conditions is correlated with the so-called C * integral. In the paper it will be shown that these integral parameters (and modifications to them) are derived from the translational invariance of the energy balance equation of general continuum mechanics. The J integral evaluated along a path surrounding a crack tip may be interpreted as a point force (or material point force) acting on the crack tip, in analogy to the classical physical force. The integranl of the J integral, i.e. the energy-momentum tensor is the dual quantity to the stress tensor, i.e., the integral of the line (or surface) integral to calculate the resultant (physical) force on the enclosed part of the body. The strength of homogeneous materials is assessed by local concepts based on the components of the stress tensor. The question, therefore, arises, whether the energy-momentum tensor, or, equivalent quantities constructed from its components, may serve as a local parameter to assess damage processes in a material containing defects. For that reason, special features of the energy-momentum tensor are presented and a modification of bij is discussed.