Engineering Transactions, 59, 4, pp. 299–348, 2011


Institute of Fundamental Technological Research Polish Academy of Sciences

The main objective of the present paper is to discuss very efficient procedure of the numer-
ical 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 con-
stitutive 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 vol-
ume 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.
Keywords: localized fracture, finite difference method, thermo-elasto-viscoplasticity, micro- damage
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