Experimental evaluation of the J or C^* parameter for a range of cracked geometries

In the current ASTM Standard Test Method for Measurement of Creep Crack Growth Rates in Metals (E 1457) the experimental C^* parameter is related to the load and creep load line displacement rate through the geometry related η factor. In this work η factors for a range of geometries are presented. The geometries examined are the compact tension specimen, C(T), single edge notch specimen in tension, SEN(T), and bending, SEN(B), double edge notch specimen in tension, DEN(T), middle crack specimen in tension, M(T) and the C-shaped specimen in tension CS(T). Calculations have been performed for a linear elastic-power law hardening material but the resulting η factors are applicable to either power law plastic or power law creeping materials. Values for η^LLD and η^CMOD, based on the load line displacement and crack mouth opening displacement, respectively, have been determined. A wide range of crack depths, 0.1≤a/W≤0.7, where a is crack length and W is specimen width, and hardening exponents, 3 ≤W ≤10, under plane stress and plane strain conditions have been examined using the finite element method. The influence of specimen length, crack length, material properties and out of plane stress state on the η factor has also been considered. It has been found that for shallow cracks the value of η depends quite strongly on the exponent, N in the material power law, regardless of whether η is defined based on the load line displacement or crack mouth opening displacement. The η^LLD factor has also been found to be strongly sensitive to plane stress/strain conditions imposed, a/W and specimen length, whereas η^CMOD depends more weakly on a/W and is almost independent of specimen length for the cases examined. There is, however, no clear trend in these variations over the range of specimen geometries and a/W examined. These results are found to be consistent with those in the literature. Recommendations are made regarding the most appropriate values for η, depending on the specimen type and geometry while taking into account the variability due to the material properties, out of plane stress state and variations between the numerical analyses.