Crack Tip Radius Effect on Fatigue Crack Growth and Near Tip Fields in Plastically Compressible Materials

Abstract

Motivated by the prospective uses of plastically compressible materials such as, metallic and polymeric foams, transformation toughened ceramics, toughened structural polymers etc., the present authors investigate the crack-tip radius effect on fatigue crack growth (FCG) of a mode I crack and near-tip stress-strain fields in such plastically compressible solids. These plastically compressible materials have been characterised by elastic-viscoplastic constitutive equations. Simulations are conducted for plane strain geometry with two different hardness functions: one is bilinear hardening and the other one is hardening-softening-hardening. It has been observed that plastic compressibility as well as strain softening lead to significant deviation in the amount of crack growth. It has further been revealed that the nature of FCG is appreciably affected by initial crack-tip radius. Even though it may look from outside that the increase in tip radius will lead to decrease in FCG, but the nature of FCG variation with respect to tip radius is found to be a combined effect of tip radius, plastic compressibility and work or strain softening etc. As to be expected when the crack-tip radius is low (smallest of the expounded variation of the present study), the rate of FCG is found to be maximum for the bilinear hardening material though the nature of FCG variation is different in plastically incompressible and compressible solids. In sharp contrast, when the material exhibits work or strain softening, the FCG rate is found to be dependent on the instantaneous crack-tip radius. For instance, as a quantitative comparison in the present study, after the end of 5th cycle, the normalised crack-tip extension for the bilinear material (plastically compressible) corresponding to the smallest tip radius is 2.9 whereas the same for the largest tip radius is 1.9. Conversely, for the material (plastically compressible) that exhibits strain softening, the corresponding tip extension values are 1.0 and 2.7 for the same smallest and largest radii, respectively.