The Ubiquitous η Factor

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Abstract
The η factor relates G or J to elastic or plastic work per unit ligament area rather than to the differential of work per unit crack advance. In principle this adds nothing to the understanding of fracture, but in practice it provides convenient relationships for the analysis of several fracture problems. The η factor can be expressed in terms of compliance, load or displacement, instead of work, and can be determined experimentally or analytically. Expressions are given for a selection of elastic, nonlinear, and plastic cases in some of which deep and shallow notch behavior differs markedly. Application to elastic and plastic test analyses, a J based design curve including an approximate treatment of residual stresses, and both elastic and plastic instability problems are outlined.