Asymptotic crack-tip fields for dynamic crack growth in compressive power-law hardening materials

Abstract

The effect of material compressibility on the stress and strain fields for a mode-I crack propagating steadily in a powerlaw hardening material is investigated under plane strain conditions. The plastic deformation of materials is characterized by the J 2 flow theory within the framework of isotropic hardening and infinitesimal displacement gradient. The asymptotic solutions developed by the present authors [Zhu, X.K., Hwang K.C., 2002. Dynamic crack-tip field for tensile cracks propagating in power-law hardening materials. International Journal of Fracture 115, 323-342] for incompressible hardening materials are extended in this work to the compressible hardening materials. The results show that all stresses, strains, and particle velocities in the asymptotic fields are fully continuous and bounded without elastic unloading near the dynamic crack tip. The stress field contains two free parameters r eq0 and s 330 that cannot be determined in the asymptotic analysis, and can be determined from the full-field solutions. For the given values of r eq0 and s 330 , all field quantities around the crack tip are determined through numerical integration, and then the effects of the hardening exponent n, the Poisson ratio m, and the crack growth speed M on the asymptotic fields are studied. The approximate behaviors of the proposed solutions are discussed in the limit of m ! 0.5 or n ! 1.

Dynamic delamination in laminated fiber reinforced composites: A continuum damage mechanics approach

“…Asymptotic crack tip stress-strain fields have been developed by (Zhu and Hwang 2008) for the case of dynamic fractures. Rate-dependent models for damage and plastic deformation of brittle and ductile materials under dynamic loading have also been extensively investigated (Zuo et al 2010.…”