Rice contour integral

Energy required to create unit area of crack surface for adhesive failure Rice contour integral Inverse spring constant Sgdv... 

This is the contour integral described by Rice wiuch is usually denoted by J for non-linear elastic materials and becomes G for the linear case given here. The result is important since, if a stress analysis for a cracked body is performed in which the stress and displacement fields are found, then G may be determined. 

The contour integral [17] was applied to fracture analysis in 1968 by Rice [18] to characterize elastic-plastic material behavior ahead of a crack. This nonlinear energy release rate was expressed in the form of a line integral, which was described as the J-integral. evaluated along an arbitrary contour around the crack. The analyses [ 19.20] showed that J can yield a nonlinear stress intensity parameter as well as energy release rate. 

Rice defined a quantity termed the 7-integral, which describes the flow of energy into the crack tip region. It is defined for the two-dimensional problem of a straight crack in the x direction (Figure 12.18), and F is any contour surrounding the crack tip. Formally... 

The J-integral has been defined by Rice (1968) initially for non-linear elastic materials as a linear integral on a closed contour T,- ... 

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