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Showing papers on "Viscoplasticity published in 2006"


Journal ArticleDOI
TL;DR: In this article, the results of laboratory tests on the time-dependent behaviour of three argillaceous rocks characterized by a high proportion of clay particles were presented, and the authors highlighted the significant viscoplasticity of these sedimentary rocks.

239 citations


Journal ArticleDOI
TL;DR: In this article, a 3D model of viscoplastic flow and temperature field during friction stir welding (FSW) of 304 austenitic stainless steel were mathematically modelled using spatially variable thermophysical properties using a methodology adapted from well established previous work in fusion welding.
Abstract: Three-dimensional (3D) viscoplastic flow and temperature field during friction stir welding (FSW) of 304 austenitic stainless steel were mathematically modelled. The equations of conservation of mass, momentum and energy were solved in three dimensions using spatially variable thermophysical properties using a methodology adapted from well established previous work in fusion welding. Non-Newtonian viscosity for the metal flow was calculated considering strain rate and temperature dependent flow stress. The computed profiles of strain rate and viscosity were examined in light of the existing literature on thermomechanical processing of alloys. The computed results showed significant viscoplastic flow near the tool surface, and convective transport of heat was found to be an important mechanism of heat transfer. The computed temperature and velocity fields demonstrated strongly 3D nature of the transport of heat and mass indicating the need for 3D calculations. The computed temperature profiles agreed well with the corresponding experimentally measured values. The non-Newtonian viscosity for FSW of stainless steel was found to be of the same order of magnitude as that for the FSW of aluminium. Like FSW of aluminium, the viscosity was found to be a strong function of both strain rate and temperature, while strain rate was found to be the most dominant factor. A small region of recirculating plasticised material was found to be present near the tool pin. The size of this region was larger near the shoulder and smaller further away from it. Streamlines around the pin were influenced by the presence of the rotating shoulder, especially at higher elevations. Stream lines indicated that material was transported mainly around the pin in the retreating side.

225 citations


Journal ArticleDOI
TL;DR: A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented in this paper, where a joint potential function exists such that both the conservation of energy and the balance of linear momentum equations follow as Euler-Lagrange equations.
Abstract: A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented. The coupled thermo-mechanical boundary-value problem under consideration consists of the equilibrium problem for a deformable, inelastic and dissipative solid with the heat conduction problem appended in addition. The variational formulation allows for general dissipative solids, including finite elastic and plastic deformations, non-Newtonian viscosity, rate sensitivity, arbitrary flow and hardening rules, as well as heat conduction. We show that a joint potential function exists such that both the conservation of energy and the balance of linear momentum equations follow as Euler–Lagrange equations. The identification of the joint potential requires a careful distinction between equilibrium and external temperatures, which are equal at equilibrium. The variational framework predicts the fraction of dissipated energy that is converted to heat. A comparison of this prediction and experimental data suggests that α-titanium and Al2024-T conform to the variational framework.

194 citations


Journal ArticleDOI
TL;DR: A model of plant cell morphogenesis that is a first attempt at integrating these two processes based on the theories of thin shells and anisotropic viscoplasticity is developed and it is shown that the mechanical anisotropy built into the model is required to account for observed patterns of wall expansion in plant cells.
Abstract: Plant cell morphogenesis depends critically on two processes: the deposition of new wall material at the cell surface and the mechanical deformation of this material by the stresses resulting from the cell's turgor pressure We developed a model of plant cell morphogenesis that is a first attempt at integrating these two processes The model is based on the theories of thin shells and anisotropic viscoplasticity It includes three sets of equations that give the connection between wall stresses, wall strains and cell geometry We present an algorithm to solve these equations numerically Application of this simulation approach to the morphogenesis of tip-growing cells illustrates how the viscoplastic properties of the cell wall affect the shape of the cell at steady state The same simulation approach was also used to reproduce morphogenetic transients such as the initiation of tip growth and other non-steady changes in cell shape Finally, we show that the mechanical anisotropy built into the model is required to account for observed patterns of wall expansion in plant cells

190 citations


Journal ArticleDOI
TL;DR: In this paper, a rate-dependent neural network (NN) constitutive model is proposed for finite element analysis. But the model is not suitable for analysis of time-dependent behavior of concrete.

144 citations


Journal ArticleDOI
TL;DR: In this paper, a geometrically exact generalized continua of Cosserat micropolar type was investigated and a variational form of these models was recalled and extended to finite-strain elasto-plasticity based on the multiplicative decomposition of the deformation gradient.

139 citations


Journal ArticleDOI
TL;DR: The focus of the book on computational plasticity embodies techniques of relevance not only to academic researchers, but also of interest to industrialists engaged in the production of components using bulk or sheet forming processes.
Abstract: The use of computational modelling in all areas of science and engineering has in recent years escalated to the point where it underpins much of current research. However, the distinction must be made between computer systems in which no knowledge of the underlying computer technology or computational theory is required and those areas of research where the mastery of computational techniques is of great value, almost essential, for final year undergraduates or masters students planning to pursue a career in research. Such a field of research in the latter category is continuum mechanics, and in particular non-linear material behaviour, which is the core topic of this book. The focus of the book on computational plasticity embodies techniques of relevance not only to academic researchers, but also of interest to industrialists engaged in the production of components using bulk or sheet forming processes. Of particular interest is the guidance on how to create modules for use with the commercial system Abaqus for specific types of material behaviour. The book is in two parts, the first of which contains six chapters, starting with microplasticity, but predominantly on continuum plasticity. The first chapter on microplasticty gives a brief description of the grain structure of metals and the existence of slip systems within the grains. This provides an introduction to the concept of incompressibility during plastic deformation, the nature of plastic yield and the importance of the critically resolved shear stress on the slip planes (Schmid's law). Some knowledge of the notation commonly used to describe slip systems is assumed, which will be familiar to students of metallurgy, but anyone with a more general engineering background may need to undertake additional reading to understand the various descriptions. Any lack of knowledge in this area however, is of no disadvantage as it serves only as an introduction and the book moves on quickly to continuum plasticity. Chapter two introduces one of several yield criteria, that normally attributed to von Mises (though historians of mechanics might argue over who was first to develop the theory of yielding associated with strain energy density), and its two or three-dimensional representation as a yield surface. The expansion of the yield surface during plastic deformation, its translation due to kinematic hardening and the Bauschinger effect in reversed loading are described with a direct link to the material stress-strain curve. The assumption, that the increment of strain is normal to the yield surface, the normality principle, is introduced. Uniaxial loading of an elastic-plastic material is used as an example in which to develop expressions to describe increments in stress and strain. The full presentation of numerous expressions, tensors and matrices with a clear explanation of their development, is a recurring, and commendable, feature of the book, which provides an invaluable introduction for those new to the subject. The chapter moves on from time-independent behaviour to introduce viscoplasticity and creep. Chapter three takes the theories of deformation another stage further to consider the problems associated with large deformation in which an important concept is the separation of the phenomenon into material stretch and rotation. The latter is crucial to allow correct measures of strain and stress to be developed in which the effects of rigid body rotation do not contribute to these variables. Hence, the introduction of 'objective' measures for stress and strain. These are described with reference to deformation gradients, which are clearly explained; however, the introduction of displacement gradients passes with little comment, although velocity gradients appear later in the chapter. The interpretation of different strain measures, e.g. Green--Lagrange and Almansi, is covered briefly, followed by a description of the spin tensor and its use in developing the objective Jaumann rate of stress. It is tempting here to suggest that a more complete description should be given together with other measures of strain and stress, of which there are several, but there would be a danger of changing the book from an `introduction' to a more comprehensive text, and examples of such exist already. Chapter four begins the process of developing the plasticity theories into a form suitable for inclusion in the finite-element method. The starting point is Hamilton's principle for equilibrium of a dynamic system. A very brief introduction to the finite-element method is then given, followed by the finite-element equilibrium equations and a description of how they are incorporated into Hamilton's principle. A useful clarification is provided by comparing tensor notation and the form normally used in finite-element expressions, i.e. Voigt notation. The chapter concludes with a brief overview of implicit integration methods, i.e. tangent stiffness, initial tangent stiffness and Newton–Raphson. Chapter five deals with the more specialized topic of implicit and explicit integration of von Mises plasticity. One of the techniques described is the radial-return method which ensures that the stresses at the end of an increment of deformation always lie on the expanded yield surface. Although this method guarantees a solution it may not always be the most accurate for large deformation, this is one area where reference to alternative methods would have been a helpful addition. Chapter six continues with further detail of how the plasticity models may be incorporated into finite-element codes, with particular reference to the Abaqus package and the use of user-defined subroutines, introduced via a `UMAT' subroutine. This completes part I of the book. Part II focuses on plasticity models, each chapter dealing with a particular process or material model. For example, chapter seven deals with superplasticity, chapter eight with porous plasticity, chapter nine with creep and chapter ten with cyclic plasticity, creep and TMF. Examples of deep drawing, forming of titanium metal-matrix composites and creep damage are provided, together with further guidelines on the use of Abaqus to model these processes. Overall, the book is organised in a very logical and readable form. The use of simple one-dimensional examples, with full descriptions of tensors and vectors throughout the book, is particularly useful. It provides a good introduction to the topic, covering much of the theory and with applications to give a good grounding that can be taken further with more comprehensive advanced texts. An excellent starting point for anyone involved in research in computational plasticity.

114 citations


Journal ArticleDOI
TL;DR: In this paper, a nonlocal gradient-enhanced theory coupled to visco-coasticity is presented to solve the problem of deformation and failure in ductile metal deformation.
Abstract: During dynamic loading processes, large inelastic deformation associated with high strain rates leads, for a broad class of ductile metals, to degradation and failure by strain localization. However, as soon as material failure dominates a deformation process, the material increasingly displays strain softening and the finite element computations are considerably affected by the mesh size and alignment. This gives rise to a non-physical description of the localized regions. This article presents a theoretical framework to solve this problem with the aid of nonlocal gradient-enhanced theory coupled to viscoinelasticity. Constitutive equations for anisotropic thermoviscodamage (rate-dependent damage) mechanism coupled with thermo-hypoelasto-viscoplastic deformation are developed in this work within the framework of thermodynamic laws, nonlinear continuum mechanics, and nonlocal continua. Explicit and implicit microstructural length-scale measures, which preserve the well-posedness of the differential equations, are introduced through the use of the viscosity and gradient localization limiters. The gradient- enhanced theory that incorporates macroscale interstate variables and their high- order gradients is developed here to describe the change in the internal structure and to investigate the size effect of statistical inhomogeneity of the evolution related plasticity and damage. The gradients are introduced in the hardening internal state variables and are considered dependent on their local counterparts. The derived microdamage constitutive model is destined to be applied in the context of high velocity impact and penetration damage mechanics. The theoretical framework presented in this article can be considered as a feasible thermodynamic approach that enables to derive various gradient (visco) plasticity/(visco) damage theories

108 citations


Journal ArticleDOI
07 Apr 2006-Wear
TL;DR: In this paper, the authors used a microscratch tester to compare the scratch resistance of a thermoplastic polymer (PMMA) and a thermosetting resin (CR39).

98 citations


Journal ArticleDOI
TL;DR: In this article, a scale dependent crystal viscoplasticity model with a second strain gradient effect is introduced, as a simple extension of the conventional crystal plasticity theory, which confine attention to a single crystal undergoing slip on a single slip system under small strain conditions.
Abstract: A scale dependent crystal viscoplasticity model with a second strain gradient effect is introduced, as a simple extension of the conventional crystal plasticity theory. We confine attention to a single crystal undergoing slip on a single slip system under small strain conditions. Connections between this model and other existing theories are investigated in some detail. Furthermore, some basic predictions of the model, due to the second gradients and the material viscosity, are illustrated, using a constrained simple shear problem for a thin strip bounded by two rigid walls. The effect of viscosity on evolution of the boundary layer is examined, as well as the behavior of the thin strip undergoing reverse/cyclic shear loading, and the ability to predict plastic flow localization.

92 citations


Journal ArticleDOI
TL;DR: Habbitt et al. as discussed by the authors proposed a coupled temperature and strain rate microstructure physically based yield function with Clausius-Duhem inequality and an appropriate free energy definition in a general thermodynamic framework for deriving a three-dimensional kinematical model for thermo-viscoplastic deformations of body centered cubic (bcc) metals.

Journal ArticleDOI
Neil S. Mancktelow1
01 May 2006-Geology
TL;DR: In this paper, it was shown that the mean stress or pressure within a weak, elongate viscous band being stretched is higher than the surrounding matrix, and this is difficult to reconcile with premise (3).
Abstract: Three premises of ductile deformation in the middle and lower crust are widely accepted: (1) rocks flow with power-law viscous rheology, (2) localization in ductile shear zones involves strain softening, and (3) fluid flows into and is channelized within ductile shear zones. Ductile (viscous) shear zones should therefore initially develop along planes of maximum shear stress, strain soften, and rotate as material planes into the field of progressive extension. However, the mean stress or pressure within a weak, elongate viscous band being stretched is higher than the surrounding matrix, and this is difficult to reconcile with premise (3). In contrast, Mohr-Coulomb brittle faults always have lower pressure within the fault zone. Flow of fluid and melt into high-temperature shear zones therefore implies that “ductile” shear zones are not perfectly viscous but have a pressure-dependent viscoplastic rheology. The continued pressure dependence may reflect significant microcracking on the grain scale even when localized deformation does not produce larger-scale discrete fractures.

Journal ArticleDOI
TL;DR: In this paper, a two-phase mathematical model for the study of hot tearing formation is presented, which accounts for the main phenomena associated with the formation of hot tears, i.e., the lack of feeding at the late stages of solidification and the localization of viscoplastic deformation.
Abstract: A two-phase mathematical model for the study of hot tearing formation is presented. The model accounts for the main phenomena associated with the formation of hot tears, i.e., the lack of feeding at the late stages of solidification and the localization of viscoplastic deformation. The model incorporates an advanced viscoplastic constitutive model for the coherent part of the mushy zone, allowing for the possibility of dilatation/densification of the semisolid skeleton under applied deformation. Based on quantities computed by the model, a hot tearing criterion is proposed where liquid feeding difficulties and viscoplastic deformation at the late stages of solidification are taken into account. The model is applied to study hot tearing formation during the start-up phase for direct-chill (DC) casting of extrusion ingots, and to discuss the effect of different phenomena and process parameters. The modeling results are also compared to experimentally measured hot tearing susceptibilities, and the model is able to reproduce known experimental trends such as the effect of the casting speed and the importance of the design of the starting block.


Journal ArticleDOI
TL;DR: Based on the deformation mechanism of closed-packed hexagonal (CPH) structure material, an analytical method, which reflects temperature, strain and strain rate effect by introducing temperature-compensated strain rate (Zener-Hollomon parameter), is proposed in this article.
Abstract: Accurate flow stress model is crucial for investigating magnesium alloys deformation behavior at the elevated temperatures. Based on the deformation mechanism of closed-packed hexagonal (CPH) structure material, an analytical method, which reflects temperature, strain and strain rate effect by introducing temperature-compensated strain rate (Zener–Hollomon parameter), is proposed in this study. The model has been applied on three published experimental data and predicted flow stress curves match well with those measurements.

Journal ArticleDOI
TL;DR: In this paper, the viscoelastic and viscoplastic properties of high density polyethylene (HDPE) under uniaxial monotonic and cyclic loading are modeled using the modified viscasticity theory based on overstress (VBO).
Abstract: The viscoelastic and viscoplastic behaviors of high density polyethylene (HDPE) under uniaxial monotonic and cyclic loading are modeled using the modified viscoplasticity theory based on overstress (VBO). The viscoelastic modeling capabilities of the modified VBO are investigated by simulating the behavior of semicrystalline HDPE under uniaxial compression tests at different strain rates. In addition, the effects of the modification (introducing the variable "C" into an elastic strain rate equation) on VBO that has been made to construct the change in the elastic stiffness while loading and unloading are investigated. During first loading and unloading, the modification in the elastic strain rate equation improves the unloading behavior. To investigate how the variable "C" that is introduced in the elastic strain rate equation evolves during reloading, the cyclic behavior of HDPE is modeled. For a complete viscoelastic and viscoplastic behavior, the relaxation and creep behaviors of HDPE are simulated as well in addition to stress and strain rate dependency. The influences of the strain (stress) levels where the relaxation (creep) experiments are performed are investigated. The simulation results are compared with the experimental data obtained by Zhang and Moore (1997, Polym. Eng. Sci., 37, pp. 404-413). A good match between experimental and simulation results are observed.

Journal ArticleDOI
TL;DR: In this article, a general framework for constitutive viscoelastic models in finite strain regime is presented, which is qualified as variational since the constitutive updates obey a minimum principle within each load increment.
Abstract: The purpose of this article is to present a general framework for constitutive viscoelastic models in finite strain regime. The approach is qualified as variational since the constitutive updates obey a minimum principle within each load increment. The set of internal variables is strain-based and employs, according to the specific model chosen, a multiplicative decomposition of strain into elastic and viscous components. The present approach shares the same technical procedures used for analogous models of plasticity or viscoplasticity, such as the solution of a minimization problem to identify inelastic updates and the use of exponential mapping for time integration. However, instead of using the classical decomposition of inelastic strains into amplitude and direction, we take advantage of a spectral decomposition that provides additional facilities to accommodate, into simple analytical expressions, a wide set of specific models. Moreover, appropriate choices of the constitutive potentials allow the reproduction of other formulations in the literature. The final part of the paper presents a set of numerical examples in order to explore the characteristics of the formulation as well as its applicability to usual large-scale FEM analyses. Copyright © 2005 John Wiley & Sons, Ltd.

01 Feb 2006
TL;DR: In this article, a rigid closed-cell polyurethane foam PMDI with a nominal density of 20 pcf (320 kg/m{sup 3}) was used for three separate types of compression experiments on foam specimens.
Abstract: The foam material of interest in this investigation is a rigid closed-cell polyurethane foam PMDI with a nominal density of 20 pcf (320 kg/m{sup 3}). Three separate types of compression experiments were conducted on foam specimens. The heterogeneous deformation of foam specimens and strain concentration at the foam-steel interface were obtained using the 3-dimensional digital image correlation (3D-DIC) technique. These experiments demonstrated that the 3D-DIC technique is able to obtain accurate and full-field large deformation of foam specimens, including strain concentrations. The experiments also showed the effects of loading configurations on deformation and strain concentration in foam specimens. These DIC results provided experimental data to validate the previously developed viscoplastic foam model (VFM). In the first experiment, cubic foam specimens were compressed uniaxially up to 60%. The full-field surface displacement and strain distributions obtained using the 3D-DIC technique provided detailed information about the inhomogeneous deformation over the area of interest during compression. In the second experiment, compression tests were conducted for cubic foam specimens with a steel cylinder inclusion, which imitate the deformation of foam components in a package under crush conditions. The strain concentration at the interface between the steel cylinder and the foam specimen was studied in detail.more » In the third experiment, the foam specimens were loaded by a steel cylinder passing through the center of the specimens rather than from its end surface, which created a loading condition of the foam components similar to a package that has been dropped. To study the effects of confinement, the strain concentration and displacement distribution over the defined sections were compared for cases with and without a confinement fixture.« less

Journal ArticleDOI
TL;DR: In this paper, a variational formulation of viscoplastic constitutive updates for porous elastoplastic materials is presented, which combines von Mises plasticity with volumetric plastic expansion as induced by the growth of voids and defects in metals.
Abstract: This paper presents a variational formulation of viscoplastic constitutive updates for porous elastoplastic materials. The material model combines von Mises plasticity with volumetric plastic expansion as induced, e.g., by the growth of voids and defects in metals. The finite deformation theory is based on the multiplicative decomposition of the deformation gradient and an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small strains to finite deformations. Thus the time-discretized version of the porous-viscoplastic constitutive updates is described in a fully variational manner. The range of behavior predicted by the model and the performance of the variational update are demonstrated by its application to the forced expansion and fragmentation of U-6%Nb rings.

Journal ArticleDOI
TL;DR: In this paper, the viscoplastic consistency model is extended to the integration of a thermoviscoplastic constitutive equation for J2 plasticity and adiabatic conditions.

Journal ArticleDOI
TL;DR: In this article, a finite element homogenization approach is presented for calculating the evolution of macro-scale properties during processing of microstructures, and a mathematically rigorous sensitivity analysis is presented that is used to identify optimal forging rates in processes that would lead to a desired microstructure response.

Journal ArticleDOI
TL;DR: In this paper, a new method for the identification of material parameters is presented, which uses neural networks, which are trained on the basis of finite element simulations, to solve the inverse problem.
Abstract: In this paper, a new method for the identification of material parameters is presented. Neural networks, which are trained on the basis of finite element simulations, are used to solve the inverse problem. The material parameters to be identified are part of a viscoplasticity model that has been formulated for finite deformations and implemented in the finite element code ABAQUS. A proper multi-creep loading history was developed in a previous paper using a phenomenological model for viscoplastic spherical indentation. Now, this phenomenological model is replaced by a more realistic finite element model, which provides fast computation and numerical solutions of high accuracy at the same time. As a consequence, existing neural networks developed for the phenomenological model have been extended from a power law hardening with two material parameters to an Armstrong-Frederick hardening rule with three parameters. These are the yield stress, the initial slope of work hardening, and maximum hardening stress of the equilibrium response. In addition, elastic deformation is taken into account. The viscous part is based on a Chaboche-like overstress model, consisting of two material parameters determining velocity dependence and overstress as a function of the strain rate. The method has been verified by additional finite element simulations. Its application for various metals will be presented in Part II, [J. Mater. Res. 21, 677 (2006)].

Journal ArticleDOI
TL;DR: In this paper, the authors analyzed plane strain deformations of a representative volume element (RVE) to evaluate effective thermophysical parameters of a particulate composite comprised of two perfectly bonded heat conducting elasto-thermo-visco-plastic constituents.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the fragmentation of an elastic visco-plastic ring in the one-dimensional framework and showed that the fragment size is controlled by the unloading wave propagations in the ultimate fragmentation stage.

Journal ArticleDOI
TL;DR: In this paper, the drag force on two spheres moving at very low controlled velocity in a viscoplastic fluid was studied as a function of the distance separating them and the influence of the surface roughness of the spheres governing fluid adherence and slip at the wall was quantified.
Abstract: The drag force on two spheres moving at very low controlled velocity in a viscoplastic fluid was studied as a function of the distance separating them. Two configurations were studied, namely two spheres with their centre lines along or perpendicular to the flow. The influence of the surface roughness of the spheres governing fluid adherence and slip at the wall was quantified. The drag force on an isolated sphere was also measured and used as a reference. Correlations for predicting the drag coefficient and stability criterion, with respect to sedimentation, are proposed. These results show that viscoplasticity reduces the extent of the interactions in comparison with the case of a Newtonian fluid.

Journal ArticleDOI
TL;DR: In this article, an Eulerian, sharp interface, fixed Cartesian grid method is applied to study hot-spot formation in an energetic material (HMX) subject to shock loading.
Abstract: An Eulerian, sharp-interface, fixed Cartesian grid method is applied to study hot-spot formation in an energetic material (HMX) subject to shock loading. The mass, momentum, and energy equations are solved along with evolution equations for deviatoric stresses and equivalent plastic strain. Pressure is obtained from the Mie-Griineisen equation of state. The material is modeled as a viscoplastic solid. High-order accurate essentially-nonoscillatory (ENO) shock-capturing schemes along with a particle-level set technique are used to evolve sharp immersed boundaries. The details of void collapse under shock loading and the resulting conversion of mechanical energy into localized regions of high thermal energy (hot spots) in the solid material are analyzed. Insights into the precise mechanisms of initiation sensitivity as a result of hot-spot formation in porous energetic materials are obtained.

Journal ArticleDOI
TL;DR: In this paper, a reduced form of the "purely dissipative" model was proposed as a general continuum model for the rheology of noncolloidal particle dispersions, ranging from Stokesian suspensions to non-cohesive granular media.
Abstract: This article examines a reduced form of the 'purely dissipative' model proposed several years ago as a general continuum model for the rheology of non-colloidal particle dispersions, ranging from Stokesian suspensions to non-cohesive granular media. Essential to the model is a positive-definite viscosity tensor η, depending on the history of deformation and providing a crucial restriction on related models for anisotropic fluids and suspensions. In the present treatment, η is assumed to be as an isotropic function of a history-dependent second-rank 'texture' or 'fabric' tensor A. A formula for η (A) borrowed from the analogous theory of linear elasticity, and its subsequent expansion for weak anisotropy provides an explicit expression for the stress tensor in terms of fabric, strain-rate and eight material constants. Detailed consideration is given to the special case of Stokesian suspensions, which represent an intriguing subset of memory materials without characteristic time. For this idealized fluid one finds linear dependence of all stresses, including viscometric normal stress, on present deformation rate, with the provision for an arbitrary fabric evolution ('thixotropy') in unsteady deformations. As a concrete example, a co-rotational memory integral is adopted for A in terms of strain-rate history, and a memory kernel with two-mode exponential relaxation gives close agreement with the rather sparse experimental data on transient shear experiments. In the proposed model, an extremely rapid mode of relaxation is required to mimic the incomplete reversal of stress observed in experiments involving abrupt reversal of steady shearing, supporting the conclusion of others that non-hydrodynamic effects, with breaking of Stokesian symmetry, may be implicated in such experiments. Qualitative comparisons are made to a closely related model, derived from a micro-mechanical analysis of Stokesian suspensions, but also involving non-Stokesian effects. The present analysis may point the way to improved micro-mechanical analysis and to further experiments. Possible extensions of the model to the viscoplasticity of dry and liquid-saturated granular media also are discussed briefly.

Journal ArticleDOI
Dirk Helm1
TL;DR: In this paper, a constitutive theory in the framework of continuum thermomechanics is introduced to represent the viscoplastic behavior of metals at finite deformations, and an improved numerical integrator is developed on the basis of the original backward Euler method.

ReportDOI
01 Aug 2006
TL;DR: In this article, the authors present the formulation of a crystal elasto-viscoplastic model and the corresponding integration scheme, which is suitable to represent the isothermal, anisotropic large deformation of polycrystalline metals.
Abstract: This report presents the formulation of a crystal elasto-viscoplastic model and the corresponding integration scheme. The model is suitable to represent the isothermal, anisotropic, large deformation of polycrystalline metals. The formulation is an extension of a rigid viscoplastic model to account for elasticity effects, and incorporates a number of changes with respect to a previous formulation [Marin & Dawson, 1998]. This extension is formally derived using the well-known multiplicative decomposition of the deformation gradient into an elastic and plastic components, where the elastic part is additionally decomposed into the elastic stretch V{sup e} and the proper orthogonal R{sup e} tensors. The constitutive equations are written in the intermediate, stress-free configuration obtained by unloading the deformed crystal through the elastic stretch V{sup e-}. The model is framed in a thermodynamic setting, and developed initially for large elastic strains. The crystal equations are then specialized to the case of small elastic strains, an assumption typically valid for metals. The developed integration scheme is implicit and proceeds by separating the spherical and deviatoric crystal responses. An ''approximate'' algorithmic material moduli is also derived for applications in implicit numerical codes. The model equations and their integration procedure have been implemented in both a materialmore » point simulator and a commercial finite element code. Both implementations are validated by solving a number of examples involving aggregates of either face centered cubic (FCC) or hexagonal close-packed (HCP) crystals subjected to different loading paths.« less

Journal ArticleDOI
TL;DR: In this article, a fitting procedure has been developed for the parameters identification on the base of deformation and lifetime data from strain-controlled low cycle fatigue (LCF) tests without and with hold time as well as creep tests.