This chapter presents a concise description of nonlinear-elastic fracture mechanics, starting with Hutchinson, Rice, Rosengren (HRR) singularity and the definitions of the J-contour integral in terms of a characterizing parameter of the HRR crack-tip stress and displacement fields, a path-independent integral, and as a rate of change in potential energy per unit increase in crack area for a nonlinear-elastic solid. The use of J as a fracture criterion, together with J-solutions for various cracked geometries, is described as a basis for the measurement of the fracture toughness in the presence of plasticity; we provide further assessment of the crack growth toughness that can be quantified in terms of J-based resistance curves. Finally, we explain how modifications of the crack-tip fields in cracked configurations with lower constraint can be characterized in terms of the T-stress, and use this as a basis for a brief introduction to two-parameter characterizations of fracture.
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