Showing papers on "Viscoplasticity published in 1999"

The Thermomechanics of Nonlinear Irreversible Behaviours

Abstract: Introduction - a post-Duhemian thermodynamics thermostatics and thermodynamics various thermodynamics thermodynamics with internal variables applications - general framework viscosity in complex fluids viscoplasticity and plasticity thermodynamics of fracture non-equilibrium thermodynamics of electromagnetic materials waves and reaction-diffusion systems (RDS).

Magnetorheology in viscoplastic media

Abstract: Suspensions of iron particles in media with yield stresses were investigated to determine the effect of the continuous phase yield stress on the magnetorheological (MR) response. The steady-shear MR response was independent of the continuous phase yield stress for yield stresses in the range 0.9–37 Pa. The field-induced suspension yield stress increased sub-quadratically with the flux density. The small amplitude oscillatory shear response exhibited history dependence. The storage modulus depended not only on the magnitude of the applied magnetic field, but also on its history. This history dependence can be explained in terms of the field-dependent evolution of the suspension microstructure.

Nonlinear viscoelastic and viscoplastic constitutive equations with growing damage

Abstract: Nonequilibrium thermodynamics, rate-process theory, viscoelastic fracture mechanics and various experimentally-motivated simplifications are used to develop constitutive equations that account for effects of viscoelasticity, viscoplasticity, growing damage and aging Their form is more general than previously developed by the author, and allows for relatively general tensorial effects of damage Some important special cases are then covered, with emphasis on viscoelasticity Evolution equations for the damage expressed in terms of internal state variables (ISVs) are discussed, comparing formulations using scalar ISVs and tensor ISVs Finally, some experimental support for the theory is described An Appendix illustrates the theory for an aging, linear viscoelastic material with growing cracks

Molecular-dynamics study of ductile and brittle fracture in model noncrystalline solids

Abstract: Molecular-dynamics simulations of fracture in systems akin to metallic glasses are observed to undergo embrittlement due to a small change in interatomic potential. This change in fracture toughness, however, is not accompanied by a corresponding change in flow stress. Theories of brittle fracture proposed by Freund and Hutchinson indicate that strain rate sensitivity is the controlling physical parameter in these cases. A recent theory of viscoplasticity in this class of solids by Falk and Langer further suggests that the change in strain rate sensitivity corresponds to a change in the susceptibility of local shear transformation zones to applied shear stresses. A simple model of these zones is developed in order to quantify the dependence of this sensitivity on the interparticle potential.

The viscoplastic compaction of composite powders

Abstract: A model for the densification of spherical powders is developed for the early stages of cold and hot compaction under general loading. General viscoplastic properties are adopted which reduce to strain hardening plasticity at ambient temperature and to power law creep at elevated temperature. A large strain analysis is carried out to determine the macroscopic compaction behaviour, based on the affine motion of particles with viscoplastic dissipation occurring at the contacts between particles. Random packing is assumed and the model includes the increase in the number of contacts per particle with densification. A general prescription is given for computing the macroscopic stress as a function of strain rate and accumulated strain. Detailed results are presented for yield surfaces and creep dissipation surfaces after isostatic and closed die compaction. A scalar constraint factor is derived for a random mixture of two populations of particles with different sizes and strengths. The predictions include the limiting case of deformable spheres reinforced with rigid spheres of different size.

Elastic viscoplastic modelling of the time- dependent stress-strain behaviour of soils

Abstract: This paper presents a new framework for elastic viscoplastic (EVP) constitutive modelling. In developing the model, a general one-dimensional elastic viscoplastic (1D EVP) relationship is first der...

Experimental investigations of material models for Ti-6A1-4V and 2024-T3

Abstract: This report describes studies of the deformation and failure behavior of Ti-6Al-4V and 2024-T3 aluminum. Data was obtained at high strain rates and large strains using the split Hopkinson pressure bar technique. This information, plus additional data from the literature, was used to critically evaluate the ability of the Johnson Cook material model to represent the deformation and failure response of Ti-6AMV and 2024-T3 under conditions relevant to simulations of engine containment and the influence of uncontained engine debris on aircraft structures. This model is being used in the DYNA3D finite element code, which is being developed/validated for evaluating aircraft/engine designs relative to the federal airworthiness standards and for improving mitigation/containment technology. The results of the experimental work reported here were used to define a new set of material constants for the strength component of the Johnson Cook model for Ti-6Al-4V and 2024-T3. The capabilities and limitations of the model are reviewed. The model can accurately represent the stress-strain response of the materials. The major concern with the Johnson Cook material model is its ability to accurately represent the stress - strain rate response at strain rates greater than 10{sup 3}-10{sup 4} s{sup {minus}1}. Additional work is also needed to adequately account for failure via shear localization, which was the dominant failure mode at high strain rates in both materials. Failure modeling in both Ti-6Al-N and 2024-T3 will be considered further in future reports.

Self-consistent polycrystal models: a directional compliance criterion to describe grain interactions

Abstract: Viscoplastic self-consistent polycrystal models have been successful in addressing and explaining features of plastic deformation which cannot be treated with the Taylor condition of isostrain. In particular, these models have been applied to the simulation of plastic deformation and texture development in materials with hexagonal, trigonal, orthorhombic and triclinic symmetry. An important assumption required to solve the equilibrium equation within self-consistent formulations is that the strain-rate varies linearly with the stress in the homogeneous effective medium surrounding the inclusion. The characteristic of such a linear relation has been a matter of debate and two extreme cases can be identified: the tangent and the secant approaches. The secant approach has associated with it a stiffer inclusion-matrix interaction than the tangent approach and is closer to the Taylor approach. In this work we perform a systematic study of the implications of both assumptions on the response of cubic and hexagonal materials (texture development, system activity, stress and strain-rate deviations). In addition, we argue that the strength of the matrix-inclusion interaction should not be constant but should depend on the capability of each orientation to accommodate the particular deformation mode imposed externally. As a consequence, we propose a relative directional compliance (RDC) criterion for defining a variable interaction between grain and matrix depending on their relative compliances and compare the predictions of the RDC approach with the predictions of the secant and the tangent schemes.

Modeling dynamic recrystallization of olivine aggregates deformed in simple shear

Abstract: Experiments by Zhang and Karato [1995] have shown that in simple shear dislocation creep of olivine at low strains, an asymmetric texture develops with a [100] maximum rotated away from the shear direction against the sense of shear. At large strain where recrystallization is pervasive, the texture pattern is symmetrical, and [100] is parallel to the shear direction. The deformation texture can be adequately modeled with a viscoplastic self-consistent polycrystal plasticity theory. This model can be expanded to include recrystallization, treating the process as a balance of boundary migration (growth of relatively underformed grains at the expense of highly deformed grains) and nucleation (strain-free nuclei replacing highly deformed grains). If nucleation dominates over growth, the model predicts a change from the asymmetric to the symmetric texture as recrystallization proceeds and stabilization in the “easy slip” orientation for the dominant (010)[100] slip system. This result is in accordance with the experiments and suggests that the most highly deformed orientation components dominate the recrystallization texture. The empirical model will be useful to simulate more adequately the development of anisotropy in the mantle where olivine is largely recrystallized.

Large amplitude oscillatory shear of ER suspensions

Abstract: Electrorheological (ER) fluids are fascinating materials that undergo dramatic reversible changes in their rheological properties upon the application of electric fields. In many proposed applications, the fluids will be subjected to a dynamic stimulus with finite deformation. We use a particle-level simulation method to investigate the dynamic behavior of monolayer ER fluids. ER fluids are linear viscoelastic for only very small strain amplitudes. The transition to nonlinear deformation arises from very slight rearrangements of unstable structures. At large strain amplitudes, the behavior is viscoplastic, while at large dimensionless frequencies (∝ ω/E02, where ω is the oscillation frequency and E0 is the electric field strength), the response is Newtonian for all strain amplitudes. Simulation results agree qualitatively with experiments. The dependence of the flow behavior on the strain amplitude and dimensionless frequency is summarized in the form of a Pipkin diagram.

Large‐scale modeling of localized dissipative mechanisms in a local continuum: applications to the numerical simulation of strain localization in rate‐dependent inelastic solids

Abstract: This paper presents a general framework for the formulation of constitutive models that incorporate a localized dissipative mechanism. The formalism of strong discontinuities is employed, allowing for the decoupling of the constitutive characterization of the continuum and localized responses of the material. A procedure for incorporating the localized small-scale effects of the material response in the large-scale problem characterized by the standard local continuum is described in detail. The resulting large-scale model is able to capture objectively the localized dissipation observed in localized failures of solids and structures. A localized viscous slip model is presented as a model example. The finite element implementation of the proposed formulation arises naturally as a local element enhancement of the finite element interpolations, with no regularization of the discontinuities. The above considerations are formulated first in the infinitesimal range, and then extended to the finite strain regime. Furthermore, it is shown that the proposed framework allows for the development of effective finite element methods capturing in the large scale the localized dissipation observed in the failure of rate-dependent materials, avoiding the resolution of small length scales associated to the localization bands in these regularized models. Several representative numerical simulations are presented to illustrate these ideas. Copyright © 1999 John Wiley & Sons, Ltd.

Modified Johnson-Cook model for vehicle body crashworthiness simulation

Abstract: Dynamic response prediction of vehicle bodies is important for vehicle crashworthiness evaluation. The dynamic behaviour of vehicle body materials is dependent on material strain rates. One of the typical high strain rate tensile tests is the split Hopkinson bar test. In this paper, experiments have been conducted based on a new split Hopkinson bar apparatus specially designed,for the dynamic tensile test of sheet metals. Results from both quasistatic and dynamic tests show that the strain rate hardening effect for sheet metals cannot be described by the original Johnson-Cook constitutive relation. This relation has been modified to include a higher-order term for the hardening effect. The modified constitutive relation represents a more accurate simulation than the original model for the dynamic behaviour of vehicle body structures.

A finite element analysis for the characteristics of temperature and stress in micro-machining considering the size effect

Abstract: In this paper, a finite element method for predicting the temperature and the stress distributions in micro-machining is presented. The work material is oxygen-free-high-conductivity copper (OFHC copper) and its flow stress is taken as a function of strain, strain rate and temperature in order to reflect realistic behavior in machining process. From the simulation, a lot of information on the micro-machining process can be obtained; cutting force, cutting temperature, chip shape, distributions of temperature and stress, etc. The calculated cutting force is found to agree with the experiment result with the consideration of friction characteristics on the chip–tool contact surface. Because of considering the tool edge radius, this cutting model using the finite element method can analyze micro-machining with a very small depth of cut, almost the same size of tool edge radius, and can observe the `size effect' characteristic. Also, the effects of temperature and friction on micro-machining are investigated.

Thermo-mechanical modeling of orthogonal machining process by finite element analysis

Abstract: A plane strain finite element method is used with a new material constitutive equation for 1020 steel to simulate orthogonal machining with continuous chip formation. Deformation of the workpiece material is treated as elastic–viscoplastic with isotropic strain hardening, and the numerical solution accounts for coupling between plastic deformation and the temperature field, including treatment of temperature-dependent material properties. To avoid numerical errors associated with large deformation of elements, automatic remeshing is used, with at least 15 rezonings required to achieve a satisfactory solution. Effects of the uncertainty in the constitutive model on the distributions of strain, stress and temperature around the shear zone are presented, and the model is validated by comparing average values of the predicted stress, strain, strain rate and temperature at the shear zone with experimental results. Parametric effects associated with cutting speed and initial work temperature are considered in the simulations.

On cavitation, post-cavitation and yield in amorphous polymer-rubber blends

Abstract: The deformation behaviour of amorphous polymer–rubber blends is investigated in terms of an axisymmetric unit cell model containing an initially spherical rubber particle. The behaviour of the rubber is described by an incompressible non-Gaussian network theory, while for the matrix we adopt a recent large strain elastic–viscoplasticity model that incorporates the intrinsic softening upon yield and the subsequent progressive orientation hardening typical for amorphous glassy polymers. Guided by simple analytical estimates, cavitation of the rubber particle is interpreted in terms of the unstable growth of a pre-existing small void. It is shown that cavitation and yield are essentially coupled processes. On the macroscopic scale, both are softening mechanisms : If macroscopic yield takes place before the limit stress for cavitation is reached, cavitation is prohibited. Furthermore, and contrary to common belief, it is found from the interfacial stress history that, using realistic material parameters, the rubber particle continues to significantly affect plasticity in the matrix in the post-cavitation regime, i.e. after it has cavitated, so that cavitated particles cannot always be considered to be equivalent to particle-sized voids.

Integral formulation and self-consistent modelling of elastoviscoplastic behavior of heterogeneous materials

Abstract: Based on projection operators, an integral formulation is proposed for elastoviscoplastic heterogeneous materials. The problem requires a complete mechanical formulation, including the static equilibrium property concerning the known field σ, in addition to the classical field equations concerning the unknown fields ɛ˙ and σ˙. The formulation leads to an integral equation, in which elasticity and viscoplasticity effects interact through an homogeneous elastoviscoplastic medium with elastic moduli C and viscoplastic moduli B. To approximate the integral equation, the self-consistent scheme is followed. In order to obtain consistent approximation conditions, we introduce fluctuations of elastic and viscoplastic strain rate fields with respect to known kinematically compatible fields. It results in a strain rate concentration relation connecting the strain rate at each point to the macroscopic loading conditions and the local stress field. The results are presented and compared with other models and with experimental data in the case of a two-phase material.

Limiting conditions for compression testing of flat specimens in the split hopkinson pressure bar

Abstract: The split Hopkinson pressure bar (SHPB) technique is analyzed during the initial stages of loading by means of axisymmetric finite element simulations of dynamic compression tests. Limiting strains as functions of the test parameters such as the specimen diameterd and heighth were found to ensure a one-dimensional stress state and axial stress homogeneity in specimens of elastic-perfectly plastic material. The one-dimensional stress state is necessary and sufficient for accurate test results for flat specimens (h/d≤0.5) and nonflat specimens, respectively, with diameters up to half of the bar diameter. Only very small values of the Coulomb friction constraint (μ≈0.01) seem to be acceptable. The significance of the determined limiting conditions to the more practical case of a rate dependent material is investigated using an elastic-viscoplastic material for the specimen. The stress and strain rate reconstructed from the calculated bar signals (according to the SHPB analysis) are compared with stresses and strain rates averaged over the cross section of the specimen. Well-known inertia corrections improve the results of the SHPB procedure, but errors remain for small strains and highly time dependent strain rates.

Harper-Dorn Creep — a Myth?

Abstract: Compression creep tests with changes in stress were performed to determine the stress exponent n of the creep rate in the steady state of deformation of pure Al at 923 K, i.e. close to the melting point. The tests confirm that n increases with decreasing σ and e. The decrease in n to 1 reported in the literature and associated with an autonomous dislocation mechanism of viscous deformation called Harper-Dorn creep could not be reproduced.

Thermodynamically Founded CDM Models for Creep and Other Conditions

Abstract: The fundamental concepts of Continuum Damage Mechanics are reviewed, with the objective to conform to a sufficiently general thermodynamic framework. The theories are developed at a macroscopic level, with the capability to describe various types of materials, ductile or brittle, metallic, concrete, composites,… etc., in an unique framework. For that, we consider both elasticity coupled with damage, plasticity and viscoplasticity coupled with damage and the damage growth equations themselves. Moreover, we discuss the important but difficult problems associated with the damage deactivation effects that can take place under compressive loadings.

Integration algorithm for modeling the elasto-viscoplastic response of polycrystalline materials

Abstract: An integration scheme is presented for modeling the texture evolution and stress–strain response of elasto-viscoplastic polycrystalline materials. Single crystal kinematics based on a multiplicative decomposition of the deformation gradient is used to obtain an evolution equation for the crystal elastic deformation gradient. An implicit scheme to integrate this equation is presented which is stable and efficient. The reorientation of the crystal as well as the elastic strain can then be obtained from a polar decomposition of the elastic deformation gradient. Numerical studies are presented using material parameters for aluminum (FCC crystals) and zircaloy (HCP crystals) to demonstrate the general nature of the model. Predictions of the model are also compared with those obtained using a rigid-viscoplastic polycrystal model which neglects the elastic response. Retaining the elastic response makes the model useful for large deformation analyses where both anisotropy due to texture as well as elastic effects such as springback and residual stresses are important.