Jestimation for shallow notch SE(B) specimens: 3 and 4 point bending vs. ?pure? bending

Abstract

Conventional fracture mechanics tests to measure the initiation toughness of a material under elastic-plastic conditions in terns of J (or equivalently CTOD, 5) commonly utilize deep-notch bend specimens, SE(B)s, subjected to three-point loading (see for example ASTM E-813 and E-1290 [1,2]). Sumpter [9] and Wu et al. [10] developed early J estimation schemes for shallow notch SE(B)s using limit load and slip-line solutions. The extensive plane-strain, finite element analyses recently described by Kirk and Dodds [5], Kirk and Wang [6] provide simple formulae to estimate applied J-values for a wide range of crack depth to specimen width ratios, a/W, and material strain hardening properties. These studies focused on small a/W ratios routinely employed in weldment testing. The estimation scheme divides J into elastic and plastic components, with a plastic "eta" factor to relate the measured plastic work done on the remaining ligament to Jp. For shallow crack specimens, use of the plastic component of the crack mouth opening displacment (CMOD), rather than load-line displacement, provides eta factors strongly insensitive to strain hardening properties of the material.Occasionally, testing procedures employ four-point loading which places the crack plane within a constant moment region and allows unobstructed access to both the tension and compression faces of the specimen, for example, to permit additional instrumentation. However, as of this writing no standard test methods for elastic-plastic fracture permit the use of four-point bending. Test procedures use similar geometric proportions for three and four-point loading of SE(B)s, with differences only in the loading arrangement; the region over which pure bending exists typically ranges from 2-3 x W. A longer span (S) may also be used to accommodate the four-point loading while maintaining conventional B x B or B x 2B cross-sections. Finite element analyses of these configurations reveal only minor differences with three-point loading in the J-CMOD relationship, and thus very similar plastic eta factors (for use with measured CMOD values).Int ~ourn of Fracture 77 (1996) RI2Recent studies by Luxmoore and co-workers [3,7] have demonstrated a marked effect of material strain hardening features, specifically the presence of L~ider's strain (see Fig. 1), on the increase of J with remote strain in shallow notch SE(B) specimens loaded in "pure" bending, i.e., a linearly varying displacement field imposed over the remote end of the specimen. The motivation to examine this configuration derives from the need to approximate conditions of global bending in a large structural component containing a small crack. The striking differences in the evolution of J for this configuration compared to those for three and four-point bending prompted this discussion.The "pure" bending configuration used by Luxmoore et al. [3.4] allows unconstrained plastic flow to develop over the full length of the specimen in much the same manner as occurs for a small crack in a large, tension ...