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Micromechanics of localized fracture phenomena in inelastic solids generated by impact-loaded adiabatic processes

Perzyna P.

Engineering Transactions

2011

Vol. 59, iss. 4

299-348

The main objective of the present paper is to discuss very efficient procedure of the numerical investigation of localized fracture in inelastic solids generated by impact-loaded adiabatic processes. Particular attention is focused on the proper description of a ductile mode of fracture propagating along the shear band for high impact velocities. This procedure of investigation is based on utilization the finite difference method for regularized thermo-elasto-viscoplastic constitutive model of damaged material. A general constitutive model of thermo-elasto-viscoplastic damaged polycrystalline solids with a finite set of internal state variables is used. The set of internal state variables consists of two scalars, namely equivalent inelastic deformation and volume fraction porosity. The equivalent inelastic deformation can describe the dissipation effects generated by viscoplastic flow phenomena and the volume fraction porosity takes into account the microdamage evolution effects. The relaxation time is used as a regularization parameter. Fracture criterion based on the evolution of microdamage is assumed. As a numerical example we consider dynamic shear band propagation and localized fracture in an asymmetrically impact-loaded prenotched thin plate. The impact loading is simulated by a velocity boundary condition which are the results of dynamic contact problem. The separation of the projectile from the specimen, resulting from wave reflections within the projectile and the specimen, occurs in the phenomenon. A thin shear band region of finite width which undergoes significant deformation and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. Shear band advance, microdamage and the development of the temperature field as a function of time have been determined. Qualitative comparison of numerical results with experimental observation data has been presented. The numerical results obtained have proven the usefulness of the thermo-elasto-viscoplastic theory in the investigation of dynamic shear band propagations and localized fracture.

A new integration procedure for thermo-elasto-viscoplasticity

Dornowski W.

Archives of Mechanics

2002

Vol. 54, nr 5-6

389-410

A numerical integration algorithm for thermo-elasto-viscoplastic constitutive equations is presented. This algorithm satisfies the principle of material objectivity with respect to the total motion (translation, rotation and strain) of a material element. For this purpose, the properties of convective description are used. The explicit-implicit integration scheme for the plastic flow rule plays the crucial role in the proposed algorithm. The method of determining the stress state for inelastic deformations is based on the iterative solution of the dynamic yield condition with respect to the norm of the viscoplastic deformation rate tensor. The constitutive model being the subject of numerical analyses is described. Results of numerical calculations, which show an excellent performance of the proposed procedure, are presented.