Integral Representation of Energy Release Rate in Graded Materials

[+] Author and Article Information
Z.-H. Jin1

School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907

C. T. Sun

School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907sun@purdue.edu


Currently at Department of Mechanical Engineering, University of Maine, Orono, ME 04469.

J. Appl. Mech 74(5), 1046-1048 (Nov 21, 2006) (3 pages) doi:10.1115/1.2712236 History: Received November 07, 2006; Revised November 21, 2006

It is well known that, for homogeneous materials, the path-independent J contour integral is the (potential) energy release rate. For general nonhomogeneous, or graded materials, such a contour integral as the energy release rate does not exist. This work presents a rigorous derivation of the extended J integral for general graded materials from the potential energy variation with crack extension. Effects of crack shielding and amplification due to a graded interlayer in an elastic-plastic material system are discussed in terms of this integral.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 3

Contours around the crack tip

Grahic Jump Location
Figure 2

A graded layer between two dissimilar homogeneous substrates

Grahic Jump Location
Figure 1

The cracked body and coordinate systems



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