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

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.

Some examples involving uniform, compressible isotropic materials

This chapter details analytical solutions for unconstrained materials using tractable strain–energy functions. Three-dimensional and plane–strain deformations are illustrated. These include a formulation of the cavtitation problem in compressible materials and a discussion of so-called Harmonic materials.