Dynamic localized fracture in inelastic solids

Abstract

The paper aims at the investigation of ductile localized fracture phenomena in dynamic adiabatic processes in inelastic solids. Particular attention is focused on the dependence of fracture phenomenon upon the evolution of constitutive properties of the material. The micro-damage mechanism is treated as a sequence of nucleation, growth and coalescence of microcracks. To accomplish in one model the description of the rate sensitivity of the material and rate dependent micro-damage mechanism the theory of thermoviscoplasticity is developed within a framework of the rate type covariance material structure with finite set of internal state variables. This theory takes into consideration the effects of micro-damage mechanism and thermomechanical coupling. The rate dependent, internal state variables approach has the exciting feature of being directly connected to the evolution of microstructural properties of the material. The relaxation time is used as characteristic time which can thus be viewed as a regularization parameter, or as a micromechanical parameter to be determined from physical experimental observations. By assuming that the relaxation time tends to zero the rate independent thermoplastic response of the material with rate independent micro-damage mechanism is considered. The dynamic fracture criterion within localized shear band region is proposed. This criterion implies that the fracture is the time dependent process, i.e. it depends strongly on time duration of the stress impulse. Rate dependency (viscosity) allows the spatial differential operator in the governing equations to retain its ellipticity, and the initial-value problem is well-posed. The viscoplastic regularization procedure assures the stable integration algorithm by using the finite element method. Particular attention is focused on the well-posedness of the evolution problem (the initial-boundary value problem) as well as on its numerical solutions. Convergence, consistency and stability of the discretised problem are discussed. The validity of the Lax equivalence theorem is examined. Utilizing the finite element method and ABAQUS system for regularized elasto-viscoplastic model the numerical investigation of the three dimensional dynamic adiabatic deformation in particular body is presented. Two particular examples have been considered, namely dynamic adiabatic processes for a thin-walled steel tube and for a thin steel plate. In each case a thin shear band region of finite width which undergoes significant deformations and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. It has been investigated how the localized fracture mode depends on various constitutive parameters (namely the relaxation time and the irreversibility coefficient).