Here, the following topics are discussed: (i) a new integral (ΔT1) of relevance in the presence of cracks in an elastic-plastic material characterized by a rate-independent incremental constitutive law under the assumption of infinitesimal deformations, (ii) the conditions for path-independency of this integral, (iii) the physical meaning of (ΔT1) whether or not it is path-independent, (iv) its relation to J under conditions of radial loading when deformation theory of plasticity may be valid. The features of this new parameter (ΔT1) are brought out in a numerical solution of a compact tension specimen which is subject to a history of (displacement-controlled) loading/unloading/reloading. The implications of the present results in the context of more rational elastic-plastic fracture criteria are briefly discussed.

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