On Criteria for J-Dominance of Crack-Tip Fields In Large-Scale Yielding

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Abstract
Very detailed finite-strain/finite-element analyses of deeply cracked plane-strain center-notch panel and single-edge crack bend specimens were generated using nonhardening and power-law-hardening constitutive laws. The deformation was followed from small-scale yielding into the fully plastic range. The objective was to provide insight as to the minimum specimen size limitations, relative to the characteristic crack-tip opening dimension J/σo, necessary to assure a J-based dominance of the crack-tip region. The criterion used to judge the degree of dominance was the extent of agreement of the present stress and deformation fields at the blunted crack tips with those calculated by McMeeking for small-scale yielding. For deeply cracked bend specimens, we find very close agreement of the near-tip fields with those of small-scale yielding up to J values of σoL/25, where L represents the remaining uncracked ligament (and in the deeply cracked case, the only pertinent specimen dimension). This value is consistent with previously proposed J testing size limitations. However, we find that quite detectable deviation from the small-scale yielding fields occurs in both hardening and nonhardening center-crack specimens at considerably smaller J values relative to ligament dimension. This suggests that minimum specimen size requirements necessary to ensure a J-based characterization of the crack tip region may well be more stringent for center-crack or other low plastic constraint configurations than in bend-type specimens. A perhaps overly conservative value of 200 is proposed as the minimum ligament-to-J/σo ratio which ensures a sensible J-based characterization of the crack-tip region in center-crack specimens of materials exhibiting moderate to low strain hardening.

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