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.

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