Conditions for the localisation of plastic deformation in temperature sensitive viscoplastic materials (original) (raw)
Related papers
Localization of Adiabatic Deformations in Thermoviscoplastic Materials
Theory, Numerics and Applications of Hyperbolic Problems II, 2018
We study an instability occurring at high strain-rate deformations, induced by thermal softening properties of metals, and leading to the formation of shear bands. We consider adiabatic shear deformations of thermoviscoplastic materials and establish the existence of a family of focusing self-similar solutions that capture this instability. The self-similar solutions emerge as the net response resulting from the competition between Hadamard instability and viscosity. Their existence is turned into a problem of constructing a heteroclinic orbit for an associated dynamical system, which is achieved with the help of geometric singular perturbation theory.
The catastrophic development of shear localization in thermoviscoplastic materials
Le Journal de Physique IV, 1994
rQumC : Le couplage thermo-mkanique et l'adoucissement therrnique sont les propriCt6s du mat6riau qui sont B l'origine du dkveloppement des bandes de cisaillement adiabatique. Cependant les d6fauts g6om6triques ou mktallurgiques fournissent les sites oh le processus de localisation de la dkformation plastique est initi6. Dans cet article, les effets de la forrne et de l'amplitude des d6fauts sur la localisation de la deformation de cisaillement simple sont analyses B l'aide d'un modhle non lin6aire : on formule des critkres smcturels de localisation asymptotique dans lesquels l'acuit6 des defauts module l'influence des facteurs rh6ologiques, et l'on montre que, plus que leur amplitude, la forme des d6fauts permet dinterpreter la dispersion observ6e des d6fomations nominales B la rupture. abstract: Thermomechanical coupling and thermal softening are the critical material properties in the development of adiabatic shear bands. Besides the material effects, the sample geometrical imperfections and the material structural defects are regarded as providing the sites for the onset of the localization process. In this paper, the influence of the shape and size of the imperfections on the localization of the plastic flow in simple shear are analyzed within the framework of a nonlinear model: localization criteria are given in which the sharpness of the defects modulates the rheological effects. It is shown that, more than their size, the sharpness of the local imperfections may help to explain the observed scatter in the nominal failure deformation.
Acta Mechanica, 1991
We suggest here a generalization of the conventional constitutive models of viscoplasticity. This is accomplished by the inclusion of spatial gradients of the equivalent stress and strain in the evolution equation for the equivalent plastic strain rate. We restrict attention to plane deformation and elastic effects are neglected for simplicity. The implications of the new terms in the constitutive model are discussed for the case of a general eigenvalue problem of an initially homogeneous and stationary viscous flow. It turns out that the nonclassical material parameters can be chosen in such a way that the governing differential equations are always strongly elliptic irrespective of whether the material is strain softening. As it is well known, the latter typically leads to loss of ellipticity in the conventional theories. Explicit results are presented for the case of a shear band instability. Within the framework of the present theory, and in contrast to conventional models, the shear band kinematics have a well defined geometrical structure.
On the thermal elastoplastic transition in viscoplasticity of metals
The objective of this paper is to describe viscoplastic behaviour of a metal body in the vicinity of yield limit in the initial as well as subsequent elastic ranges with special account to the transition from elastic into viscoplastic behaviour. Mechanical as well as thermal isotropy in the initial elastic range is assumed.
Acta Mechanica, 1994
Summary We study dynamic thermomechanical deformations of an elasto-viscoplastic body deformed in plane strain compression at a nominal strain-rate of 5 000 sec− 1. The boundaries of the block are assumed to be perfectly insulated. We model the thermoviscoplastic response of the material by the Brown-Kim-Anand constitutive relation in which the evolution of the microstructural changes is accounted for by two internal variables, viz. a scalar and a traceless symmetric second order tensor. The former accounts for the ...
Stability analysis of thermo-visco-plastic materials undergoing high-rate shear deformations
Quarterly of Applied Mathematics, 1999
In this paper we present an energy estimate for two systems of partial differential equations that govern thermo-mechanical behavior of materials undergoing simple and anti-plane shear deformations. A linearized stability analysis is then carried out for the case of simple shear deformation with an exponentially softening stress-strain law. A series of numerical experiments on the fully nonlinear one-dimensional system of partial differential equations constitutes the final section of the paper.
International Journal of Impact Engineering, 2007
We analyze the stability of homogeneous simple tensile/compressive deformations of an isotropic heat-conducting thermoviscoplastic bar by studying the growth of infinitesimal perturbations superimposed upon a homogeneous deformation. The smallest axial strain at which the superimposed perturbation has a positive initial growth rate is called the instability strain. Two criteria are used to determine the shear band spacing; (i) the wave number, x m , of the perturbation that has the maximum initial growth rate gives the spacing, L s ¼ 2p=x m , between adjacent shear bands, and (ii) L s ¼ inf t0X0 2p=x m ðt 0 Þ where t 0 is the time when the homogeneous solution is perturbed. It is found that the geometric softening/hardening significantly affects the instability strain and the value of L s . The effect of varying the thermal conductivity, the strain-rate hardening exponent and the average axial strain rate on L s has been delineated. It is found that L s / ðnominal axial strain rateÞ À0:757 . However, for L s / ðthermal conductivityÞ¯w, the value ofw strongly depends upon the strain rate hardening exponent m. No scaling law is found between L s and the Taylor-Quinney parameter. For L s / ðspecific heatÞ w , the value of w depends upon the strain-rate hardening exponent m and increases monotonically with an increase in the value of m. r
2004
This study develops a general consistent and systematic framework for the analysis of heterogeneous media that assesses a strong coupling between rate-dependent plasticity and anisotropic rate-dependent damage for dynamic problems within the framework of thermodynamic laws and gradient theories. The proposed formulation includes thermo-elasto-viscoplasticity (rate-dependent plasticity) with anisotropic thermo-viscodamage (rate-dependent damage); a dynamic yield criterion of a von Mises type and a dynamic damage growth criterion; the associated flow rules; thermal softening; non-linear strain hardening; strain-rate hardening; strain hardening gradients; and strain-rate hardening gradients. Since the material macroscopic thermomechanical response under dynamic loading is governed by different physical mechanisms on the meso-and macroscale levels, the proposed three-dimensional kinematical model is introduced with manifold structure accounting for discontinuous fields of dislocation interactions (plastic flow) and crack and void interactions (damage growth). The gradient theory of rate-independent plasticity and rate-independent damage that incorporates macroscale interstate variables and their higher-order gradients is generalized here for rate-dependent plasticity and rate-dependent damage to properly describe the change in the internal structure and in order to investigate the size effect of statistical inhomogeneity of (G.Z. Voyiadjis). the evolution-related rate-and temperature dependent materials. The idea of bridging length-scales is made more general and complete by introducing spatial higher-order gradients in the temporal evolution equations of the internal state variables that describe hardening in coupled viscoplasticity and viscodamage models, which are considered here physically and mathematically related to their local counterparts. Furthermore, the constitutive equations for the damaged material are written according to the principle of strain energy equivalence between the virgin material and the damaged material; that is, the damaged material is modeled using the constitutive laws of the effective undamaged material in which the nominal stresses and strains are replaced by their effective ones. In addition, computational issues concerned with the current gradient-dependent formulation of initial-boundary value problems are introduced in a finite element context. A weak (virtual work) formulation of the non-local dynamic viscoplastic and viscodamage conditions is derived, which can serve as a basis for the numerical solution of initial boundary value problems in the sense of the finite element method. Explicit expressions for the generalized tangent stiffness matrix and the generalized nodal forces are given. The model presented in this paper can be considered as a feasible thermodynamic approach that enables one to derive various coupled gradient viscoplasticity and viscodamage theories by introducing simplifying assumptions. #