Ductile fracture due to plastic flow, void growth and localization for 3D randomly voided materials

Safety and dependability are always the main concerns in material and structural design. In engineering applications, ductile materials, that experience large plastic deformation, strain hardening and tremendous energy absorbance before failure, are obviously a good choice in view of their 'forgiving' characteristics. In this investigation, deformation due to uniaxial tension of isotropic incompressible power law plastic material is studied from a new point of view. Solutions of strain bifurcation equation are identified as the first application of Lambert W function to material localization. This strain localization is also proved to be a supercritical pitchfork bifurcation and thus various imperfections can be interpreted as universal unfoldings of the bifurcation.; Far more general than the uniaxial case, the fracture mechanisms of ductile materials are investigated by modeling the materials as three dimensional randomly voided rate independent continuous media. A theoretical framework is developed to judge plastic localization based on bifurcation theory and stability analysis. The dynamic method of Lyapunov's theory for stability analysis is introduced and extended to judge three dimensional material instability with large deformations. Three dimensional constitutive bifurcation criteria for both necking and shear band modes of ductile fracture are proposed, verified and applied. Methodologies to include microvoid effects in the regime of continuum mechanics for predicting ductile fracture in the macroscale are developed based on constitutive bifurcation induced plastic localization and void evolution during post bifurcation.; Additional factors that influence ductile fracture prediction including the form and size of initial imperfections, mesh size effects, triaxiality effects and effects of shape evolution are studied both qualitatively and quantitatively.