The effect of crack-depth to specimen-width ratio on crack tip opening displacement (CTOD) fracture toughness is an important consideration in relating the results of laboratory tests to the behavior of actual structures. Deeply cracked three-point bend specimens with crack-depth to specimen-width ratios (a/W) of 0.50 are most often used in laboratory tests. However, to evaluate specific weld microstructures or the behavior of structures with shallow surface cracks, specimens with a/W ratios much less than 0.50 often are required. Laboratory tests reveal that three-point bend specimens with short cracks (a/W = 0.15) exhibit significantly larger critical CTOD values than specimens with deep cracks (a/W = 0.5) up to the point of ductile initiation.
In this study, finite element analyses are employed to compare the elastic-plastic behavior of square (cross-section) three-point bend specimens with crack-depth to specimen-width ratios (a/W) ranging between 0.50 and 0.05. The two-dimensional analysis of the specimen with an a/W ratio of 0.15 reveals a fundamental change in the deformation pattern from the deep crack deformation pattern. The plastic zone extends to the free surface behind the crack concurrent with the development of a plastic hinge. For shorter cracks (a/W= 0.10 and 0.05), the plastic zone extends to the free surface behind the crack prior to the development of a plastic hinge. For longer cracks (a/W > 0.20), a plastic hinge develops before the plastic zone extends to the free surface behind the crack.
These results prompted further study of specimens with an a/Wratio of 0.15 using three-dimensional, elastic-plastic finite element analyses. Results of the short crack (a/W = 0.15) analysis are compared to the results of the deep crack (a/W = 0.50) analysis reported previously by the authors. In the linear-elastic regime (characterized by small-scale plastic deformation) the relationship of stress ahead of the crack tip to CTOD is identical for the short crack and the deep crack specimens. At identical CTOD levels in the elastic-plastic regime (large-scale plasticity, hinge formation), the crack tip stress is significantly lower for specimens with a/W = 0.15 than for specimens with a/W = 0.50. Correspondingly, at equivalent stress levels, the CTOD for the short crack is approximately 2.5 times the CTOD for the deep crack. This observation has considerable significance in the application of CTOD results to failure analysis or specification development where the fracture mechanism is cleavage preceded by significant crack tip plasticity.