Instytut Podstawowych Problemów Techniki

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The main objective of the present paper is to discuss very efficient procedure of the numerical investigation of the propagation of shear band in inelastic solids generated by impact-loaded adiabatic processes. This procedure of investigation is based on utilization the finite element method and ABAQUS system for regularized thermo-elasto-viscoplastic constitutive model of damaged material. A general constitutive model of thermo-elasto-viscoplastic polycrystalline solids with a finite set of internal state variables is used. The set of internal state variables is restricted to only one scalar, namely equivalent inelastic deformation. The equivalent inelastic deformation can describe the dissipation effects generated by viscoplastic flow phenomena.

As a numerical example we consider dynamic shear band propagation 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. Shear band advance, shear band velocity 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.

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The objective of the present article is to show the formulation for elastic-viscoplastic material model accounting for intrinsic anisotropic microdamage. The strain-induced anisotropy is described by the evolution of the intrinsic microdamage process — defined by the second-order microdamage tensor. The first step of the possibility of identification procedure (calibration of parameters) are also accounted and illustrated by numerical examples.

Słowa kluczowe:

microdamage, anisotropy

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The main objective of the paper is the investigation of the interaction and reflection of elastic-viscoplastic waves which can lead to localization phenomena in solids. The rate type constitutive structure for an elastic-viscoplastic material with thermomechanical coupling is used. An adiabatic inelastic flow process is considered. Discussion of some features of rate dependent plastic medium is presented. This medium has dissipative and dispersive properties. In the evolution problem considered in such dissipative and dispersive medium the stress and deformation due to wave reflections and interactions are not uniformly distributed, and this kind of heterogeneity can lead to strain localization in the absence of geometrical or material imperfections. Numerical examples are presented for a 2D specimens subjected to tension, with the controlled displacements imposed at one side with different velocities. The initial-boundary conditions which are considered reflect the asymmetric (single side) tension of the specimen with the opposite side fixed, which leads to non-symmetric deformation. The influence of the constitutive parameter (relaxation time of mechanical perturbances) is also studied in the examples. The attention is focused on the investigation of the interactions and reflections of waves and on the location of localization of plastic deformations.

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The main objective of this paper is the investigation of the interaction and reflection of elastic–viscoplastic waves which can lead to localization phenomena in solids. The rate type constitutive structure for an elastic–viscoplastic material with thermomechanical coupling is developed. An adiabatic inelastic flow process is considered. The Cauchy problem is investigated and the conditions for well-posedness are examined. Discussion of fundamental features of rate-dependent plastic medium is presented. This medium has dissipative and dispersive properties. Mathematical analysis of the evolution problem (the dynamical initial-boundary value problem) is presented. The dispersion property implies that in the viscoplastic medium any initial disturbance can break up into a system of group of oscillations or wavelets. On the other hand, the dissipation property causes the amplitude of a harmonic wavetrain to decay with time. In the evolution problem considered in such dissipative and dispersive medium, the stress and deformation due to wave reflections and interactions are not uniformly distributed, and this kind of heterogeneity can lead to strain localization in the absence of geometrical or material imperfections.

Since the rate-independent plastic response is obtained as the limit case, when the relaxation time Tm tends to zero, the theory of viscoplasticity offers the regularization procedure for the numerical solution of the dynamical initial-boundary value problems with localization of plastic deformation.

Numerical examples are presented for a steel bar axisymmetric specimen subjected to tension, with the controlled displacements imposed at one or two opposite sides with different velocities. Two cases of the initial-boundary conditions are considered; (A) symmetric (double side) tension of the specimen which results in symmetric pattern of deformations; (B) asymmetric (single side) tension of the specimen with the opposite side fixed, which leads to non-symmetric deformation.

For both cases of boundary conditions a set of examples is computed with different initial velocities changing between 0.5 and 20 m/s. The final states are defined by prescribed value of the total elongation of a specimen. In the numerical examples the attention is focused on the investigation of the interactions and reflections of waves and on the location of localization of plastic deformation. The distribution of plastic equivalent strain, temperature and vector plots of velocities represents the results. The computations are performed using the industrial finite element program ABAQUS (explicit method).

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The aim of the presentation is focused on two aspects which are the influance of the waves propagation in specimens on the choise of places of strain localization and the discussion of numerical models that serve the recognition of this phenomenon. There are some experimental tests which are under consideration (thin plate, axisymmetric bar, 3-D specimen) which are numericaly studied. The experiments are made in the Hopkinson tube with the typical velocity of deformations of order 104 s-1 so the processes could be treated as adiabatic. For ductile materials under such conditions to avoid the mathematical consequences due to thermal softening (ill-posedness) the viscoplastic constitutive description is used. In numerical simulations we have shown the well-posedness of the solution of governing equations by showing the insensitivity of the results to spatial discretization. The set of numerical examples proofs that it is possible to estimate the places of strain localization by observing the velocities of particles. Intensive plastic zones appear in the places where the local velocities are close to zero. In the formulation we have accepted the constitutive viscoplastic model, finite deformations and the evolution of porosity. The computations were performed in the environment of ABAQUS finite element program.

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