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

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.

An assessment of various crack tip displacement based elastic-plastic fracture parameters to characterise ductile crack growth resistance

“…Shear lips are regions where the crack tip constraint is low and so this suggests that although the crack tip constraint in the central region of the specimen is the same for different geometries, the average crack tip constraint is lower for geometries with lower plastic constraint factors. The greater difficulty in maintaining high constraint in geometries with low plastic constraint factors is consistent with the results from finite element studies [11].…”

Advances in Physical Metallurgy and Processing of Steels. The Limits of Strength and Toughness in Steel.

“…It is well known from elasticplastic finite-element analyses (FEM) that the normal stress ahead of a sharp crack can, theoretically, reach values that are more than four times the yield strength. 36) It follows that tough steels with yield strength much above 2 GPa are liable to normal stresses of the order of 10 GPa.…”

“…The most thoroughly researched is 5.5Ni steel (typical composition: Fe-5.9Ni-1.2Mn-0.7Cr-0.2Mo-0.06C), which can serve as an example. 36) The intent of the QLT treatment is to achieve a dense distribution of stable austenite precipitates like that in 9Ni steel with lower Ni content. If a 6Ni steel is tempered like 9Ni steel very little austenite is formed, and that which does appear is thermally unstable.…”

Critical assessment of the application of the J-integral and CTOD concepts to circumferentially cracked copper bars

“…Moran et al [21] have demonstrated that as in other geometries [22], the size of the finite strain zone in a circumferentially cracked bar is equal to about two ~CTOD. In the present case, the values of ~c are very large (even though they decrease with decreasing ligament diameters) and the small strain zone does not cover the major part of the ligament area as it usually does.…”