Showing papers on "Viscoplasticity published in 1990"
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28 Sep 1990TL;DR: In this article, the physical mechanisms of deformation and fracture are discussed, including linear elasticity, thermo-elasticity, and viscoelastic properties of real solids.
Abstract: 1. Elements of the physical mechanisms of deformation and fracture 2. Elements of continuum mechanics and thermodynamics 3. Identification and theological classification of real solids 4. Linear elasticity, thermoelasticity and viscoelasticity 5. Plasticity 6. Viscoplasticity 7. Damage mechanics 8. Crack mechanics.
3,644 citations
TL;DR: In this paper, a COHESIVE zone type interface model is used to study the decohesion of a viscoplastic block from a rigid substrate, taking full account of finite geometry changes, and the specific boundary value problem analysed is one of plane strain tension with a superposed hydrostatic stress.
Abstract: A COHESIVE zone type interface model, taking full account of finite geometry changes, is used to study the decohesion of a viscoplastic block from a rigid substrate. Dimensional considerations introduce a characteristic length into the formulation. The specific boundary value problem analysed is one of plane strain tension with a superposed hydrostatic stress. For a perfect interface, if the maximum traction that the viscoplastic block can support is greater than the interfacial strength, decohesion takes place in a primarily tensile mode. If this maximum traction is lower than the interfacial strength, a shear dominated decohesion initiates at the block edge. Imperfections in the form of a non-bonded portion of the interface are considered. The effects of imposed stress triaxiality, size scale, loading rate and interfacial properties on the course of defect dominated decohesion are illustrated. The characterization of decohesion initiation and propagation in terms of rice's (J. appl. Mech. 35, 379, 1968) J-integral is investigated for a variety of interface descriptions and values of the superposed hydrostatic stress.
563 citations
TL;DR: In this paper, the constitutive equations for finite deformation, isotropic, elastic-viscoplastic solids are formulated and a new implicit procedure for updating the stress and other relevant variables is presented.
Abstract: Constitute equations for finite deformation, isotropic, elastic-viscoplastic solids are formulated. The concept of a multiplicative decomposition of the deformation gradient into an elastic and a plastic part is used. The constitutive equation for stress is a hyperelastic relation in terms of the logarithmic elastic strain. Since the material is assumed to be isotropic in every local configuration determined by the plastic part of deformation gradient, the internal variables are necessarily scalars. We use a single scalar as an internal variable to represent the isotropic resistance to plastic flow offered by the internal state of the material. The constitutive equation for stress is often expressed in a rate form, and for metals it is common to approximate this rate equation, under the assumption of infinitesimal elastic strains, to arrive at a hypoelastic equation for the stress. Here, we do not express the stress constitutive equation in a rate form, nor do we make this approximative assumption. For the total form of the stress equation we present a new implicit procedure for updating the stress and other relevant variables. Also, the principle of virtual work is linearized to obtain a consistent, closed-from elasto-viscoplastic tangent operator (the ‘Jacobian’) for use in solving for global balance of linear momentum in implicit, two-point, deformation driven finite element algorithms. The time integration algorithm is implemented in the finite element program ABAQUS. To check the accuracy and stability of the algorithm, some representative problems involving large, pure elastic and combined elastic-plastic deformations are solved.
494 citations
TL;DR: Viscosity can be viewed either as a regularization parameter (computational point of view), or as a substructural/micromechanical parameter to be determined from observed shear-band widths.
Abstract: Viscoplasticity is introduced as a procedure to regularize the elasto-plastic solid, especially for those situations in which the underlying inviscid material exhibits instabilities which preclude further analysis of initial-value problems. The procedure is general, and therefore has the advantage of allowing the regularization of any inviscid elastic-plastic material. Rate-dependency is shown to naturally introduce a length-scale into the dynamical initial-value problem. Furthermore, the width of the localized zones in which high strain gradients prevail and strain accumulations take place, is shown to be proportional to the characteristic length c η, which is the distance the elastic wave travels in the characteristic time η. Viscosity can thus be viewed either as a regularization parameter (computational point of view), or as a substructural/micromechanical parameter to be determined from observed shear-band widths (physical point of view). Finally, from a computational point of view, the proposed approach is shown to have striking advantages: (1) the wave speeds always remain real (even in the softening regime) and are set by the elastic moduli; (2) the elasto-(visco-)plastic constitutive equations are amenable to unconditionally stable integration; (3) the resulting well-posedness of the dynamical initial-value problem guarantees stable and convergent solutions with mesh refinements. The initial-value problems reported in this first part are essentially one-dimensional. They are used because they offer the simplest possible context to illustrate both the physical and computational significance of the proposed viscoplastic regularization procedure. The methods used in multi-dimensional analysis and examples will be reported in Part 2.
212 citations
TL;DR: A review of the literature on constitutive modeling of cyclic plasticity and viscoplasticity of metallic materials is presented in this article, where the authors dealt with multiaxial behavior such as hardening and flow of materials under nonproportional loading, inelastic behavior at elevated temperature especially under plasticity-creep interaction conditions, hardening behavior under thermomechanical loading, ratcheting behavior under uniaxially and multiaxonial cyclic loads, and similarities between models.
Abstract: This article is concerned with a review of the literature on recent topics in constitutive modeling of cyclic plasticity and viscoplasticity of metallic materials. The subjects dealt with are: (1) multiaxial behavior such as hardening and flow of materials under nonproportional loading, (2) inelastic behavior at elevated temperature especially under plasticity-creep interaction conditions, (3) hardening behavior under thermomechanical loading, (4) ratcheting behavior under uniaxial and multiaxial cyclic loads, and (5) similarities between models. The literature published in the last five years is mainly reviewed.
165 citations
TL;DR: In this article, a generalized three-dimensional constitutive model for isotropic cohesive soils, based on the concept of the bounding surface in stress space, is developed within the framework of coupled elastoplasticity-viscasticity and critical state soil mechanics.
108 citations
TL;DR: In this article, a discrete variational formulation of plasticity and viscoplasticity is developed based on the principle of maximum plastic dissipation and a discrete inhomogeneous form of Eshelby's conservation law is derived.
Abstract: A discrete variational formulation of plasticity and viscoplasticity is developed based on the principle of maximum plastic dissipation. Lack of invariance of the discrete Lagrangian relative to the group of material translations precludes the classical Eshelby law from being a conservation law. However, a discrete inhomogeneous form of Eshelby's conservation law is derived which leads to a path-domain independent integral
83 citations
TL;DR: In this article, the effect of modeling the viscoplastic response of the material by a-power law was investigated, and it was found that the Bodner-Partom law and the dipolar theory predicted reasonably well the main features of the shear band formation in a HY-100 steel.
Abstract: MARCHAND and Duffy have reported detailed measurements of the temperature and strain as a shear band develops in a HY-100 steel. Assuming their torsional tests in thin-wall tubes can be adequately modeled by a viscoplastic block undergoing overall adiabatic simple shearing deformations. we investigate the effect of modeling the viscoplastic response of the material by a-power law. and flow rules proposed by Litonski, Bodner and Partom, and Johnson and Cook. Each of these flow rules is first calibrated by using the test data at a nominal strain-rate of 3300 s-‘. Then predictions from the use of these flow rules at nominal strain-rates of 1400 s-’ and 1600 s-’ are compared with the experimental findings. It is found that the Bodner-Partom law and the dipolar theory proposed by Wright and Batra predict reasonably well the main features of the shear band formation in a HY-100 steel.
76 citations
TL;DR: In this paper, the authors introduced viscoplasticity as a procedure to regularize the elastic-plastic solid, especially for those situations in which the underlying inviscid material exhibits instabilities which preclude meaningful analysis of the initial value problem.
Abstract: Viscoplasticity is introduced as a procedure to regularize the elastic-plastic solid, especially for those situations in which the underlying inviscid material exhibits instabilities which preclude meaningful analysis of the initial-value problem. The procedure is general and therefore has the advantage of allowing the regularization of any inviscid elastic-plastic material. Rate dependence is shown to naturally introduce a length-scale that sets the width of the shear bands in which the deformations localize and high strain gradients prevail. Then, provided that the element size is appropriate for an adequate description of the shear band geometry, the numerical solutions are shown to be pertinent. Stable and convergent solutions with mesh refinements are obtained which are shown to be devoid of spurious mesh length-scale effects. The numerical framework adopted for this study is realistic and relevant to the solution of large scale nonlinear problems. An efficient explicit time stepping algorithm is used to advance the solution in time, and low-order finite elements with only one stress-point are used. An unconditionally stable stress-point algorithm is used to integrate the nonlinear elasto-(visco-) plastic constitutive equations. Therefore, the only numerical restriction of the proposed computational procedure stems from a time step size restriction which emanates from the explicit time integration of the equations of motion. However, since the wave speeds remain elastic, this restriction is trivially dealt with, resulting in a most efficient computational procedure.
76 citations
75 citations
TL;DR: In this paper, simple shearing deformations of a block made of an elastic-viscoplastic material are studied and the effect of modeling the material of the block as a dipolar material in which the strain gradient is also taken as an independent variable has been investigated.
01 Dec 1990-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this paper, the authors present the mathematical model ALSPEN, in which the thermally induced strains and stresses which develop during direct chill (DC) semicontinuous casting of aluminum billets are calculated by a finite-element method.
Abstract: This paper presents the mathematical model ALSPEN, in which the thermally induced strains and stresses which develop during direct chill (DC) semicontinuous casting of aluminum billets are calculated by a finite-element method. The metal is assumed to be an isotropic elasticviscoplastic material with strongly temperature-dependent properties. In the material description, the viscoplastic strain is treated in a “unified” manner, in which low-temperature (approximately) time-independent plasticity and creep at high temperatures occur as special cases. Furthermore, in the numerical time stepping procedure, all of these plastic material properties, which are present simultaneously in the solution domain as a result of the large temperature differences, are treated in a similar way. To demonstrate some of the capabilities of ALSPEN, we have modeled the casting of an AlMgSi alloy, AA6063. The material properties of this alloy have been studied in parallel with the development of the mathematical model.
TL;DR: In this paper, a phenomenologically based time and rate-dependent bounding surface model is introduced which can be classified among the unified creep-plasticity theories, motivated mainly by experimental behaviors over a wide range of strain rates with particular emphasis on the behavior of metals under nonproportional loading.
Abstract: A phenomenologically based time- and rate-dependent bounding surface model is introduced which can be classified among the unified creep-plasticity theories. The model is motivated chiefly by experimental behaviors over a wide range of strain rates with particular emphasis on the behavior of metals under nonproportional loading where bounding surface theories have found success in modeling rate-independent behavior. In addition, a micromechanical interpretation is given for two kinematic hardening variables which lead to the rate-dependent bounding surface interpretation. The definition of the image point for the directional indices of kinematic hardening is left unspecified to maintain generality. The distinction between instantaneous rate sensitivity and rate sensitivity of material hardening is discussed and a framework for partitioning material rate sensitivity is presented. The relationship of the model to previously proposed formulations is discussed. Asymptotic and parametric behaviors of the model are examined with reference to experimentally observed behavior. A rate-independent idealization of the theory is obtained as a limiting, special case of the more general rate-dependent bounding surface framework.
TL;DR: In this paper, consistent tangent moduli for the generalized Duvaut-Lions viscoplasticity model are derived based on consistent linearization of the residual functions associated with two alternative unconditionally stable constitutive integration algorithms; namely, the implicit backward Euler and the full integration.
Abstract: Consistent (algorithmic) tangent moduli for the generalized Duvaut-Lions viscoplasticity model are derived in this work. The derivations are based on consistent linearization of the residual functions associated with two alternative unconditionally stable constitutive integration algorithms; namely, the implicit backward Euler and the “full integration” algorithms. This “consistent linearization” procedure is equally applicable to the Perzyna-type viscoplasticity formulations. In particular, the von Mises isotropic/kinematic hardening viscoplasticity model is chosen as a model problem for demonstration. Consistent viscoplastic tangent moduli for other choices of (single or multiple) loading surfaces can be derived in a similar fashion provided that consistent elastoplastic (inviscid) tangent moduli are available. It is noted that since continuum tangent moduli do not exist at all for viscoplasticity, use of the proposed consistent tangent modul is not only desirable but necessary in the Newton-type finite-element computations. In addition, due to the difference in the two constitutive integration algorithms used, the corresponding consistent tangent moduli are not the same even when time steps are small. Numerical examples are also presented to illustrate the remarkable quadratic performance of the proposed consistent tangent moduli for the generalized Duvaut-Lions viscoplasticity model.
TL;DR: In this article, a continuum theory is presented for representing the high-temperature deformation behavior of metallic composite materials, where the composite is considered pseudohomogeneous with its own properties that can be measured for the composite as a whole.
Abstract: A continuum theory is presented for representing the high‐temperature deformation behavior of metallic composite materials. The composite is considered pseudohomogeneous with its own properties that can be measured for the composite as a whole. A class of constitutive equations in which the inelastic strain rate and internal state are expressible as gradients of a dissipation potential function is extended for a composite. The potential is taken to depend on invariants that reflect local transverse isotropy. Applications illustrate the capability of the theory of representing the time‐dependent, hereditary, anisotropic behavior typical of these materials at elevated temperature.
TL;DR: In this article, the elastoplastic-viscoplastic bounding surface model for isotropic cohesive soils is presented, and a brief overview of its theoretical aspects and numerical implementation is described.
TL;DR: The importance of the role of plastic spin in the rate-dependent response of materials at large deformations is discussed in this paper, where an isotropic/kinematic hardening and an orthotropic viscoplastic model are used to analyze the stress-strain response under simple shear and biaxial loading at different rates.
TL;DR: In this paper, a set of microscopic flow relations having a direct counterpart in the macroscopic formulation of plasticity and viscoplasticity is deduced for the simple shear problem, especially in evaluating the development of the axial stress normal to the shear plane.
Abstract: Considering the configuration of a single slip and employing a scale invariance argument, it is possible to deduce a set of “microscopic” plastic flow relations having a direct counterpart in the “macroscopic” formulation of plasticity and viscoplasticity. In particular, a microscopic form of the plastic spin and its macroscopic counterpart for the case of anisotropy induced by kinematic hardening are obtained in terms of elementary physical arguments. Moreover the evolution equation for the back-stress is rigorously derived. Parameters which were assumed to be constant and/or independent from each other in a macroscopic development, are now found to be interrelated and dependent on the accumulated plastic strain. These findings are used for the analysis of the simple shear problem, especially in evaluating the development of the axial stress normal to the shear plane. A preliminary qualitative comparison with available data from fixed-end torsion experiments is discussed.
TL;DR: In this paper, the effects of thermal history on constitutive behavior were evaluated for a cast nickel-base superalloy by using variable temperature tensile, creep, and cyclic tests in the 538-982 C temperature range.
Abstract: The objective of this paper is to evaluate, both experimentally and analytically, the appropriate forms of the hardening evolution equations in unified constitutive models for conditions involving nonisothermal loading. Critical experiments were performed for a cast nickel-base superalloy by using variable temperature tensile, creep, and cyclic tests in the 538-982 C temperature range. These experimental results were compared with both isothermal data and predictions of the Bodner-Partom-Bodner, 1987 elastic-viscoplastic theory to assess the effects of thermal history on constitutive behavior. The results indicate that the hardening evolution equations based on isothermal data are applicable for nonisothermal loading of these precipitation strengthened alloys. Additional thermal history effect terms in the hardening evolution equations were not required beyond those accounting for the variation of material constants with temperature. Using material constants determined solely from isothermal data, the inelastic deformation behavior of B1900 + Hf subject to thermomechanical loading were adequately predicted by the Bodner-Partom model.
TL;DR: In this paper, a new constitutive equation has been developed that, when incorporated into the kinematic and dynamic equations that describe the blown film process, for the first time yields qualitatively correct predictions of all process variables.
Abstract: The blown film process has been modeled through the transition from liquidlike to solidlike behavior at the freeze line. A new constitutive equation has been developed that, when incorporated into the the kinematic and dynamic equations that describe the process, for the first time yields qualitatively correct predictions of all process variables. It is suggested that the demarcation between liquidlike behavior and solidlike behavior be altered from the conventional, kinematically based constraint, dr/dz = O, to a rheologically based constraint, the plastic-elastic transition (PET). The results are qualitive in nature since the material is modeled as an elastic solid above the PET instead of as a viscoelastic material. The model is tested using the polystyrene data of Gupta (1981).
TL;DR: In this article, the authors present results from the stress analysis of single lap joints, both with and without a crack, and with viscoelastic and viscoplastic adhesives.
TL;DR: In this paper, the Perzyna viscoplastic constitutive theory is used for uniaxial deformation with multiaxially stress, which is typical of that occurring in flyer plate impact experiments.
Abstract: The Perzyna viscoplastic constitutive theory, is used. The damage parameter for materials, is taken to be the void volume fraction. The hardening law is a nonlinear law that allows for the saturation of the hardening with increase of strain. The modified constitutive equations are then specialized to uniaxial deformation with multiaxial stress, which is typical of that occurring in flyer plate impact experiments
TL;DR: In this paper, an additive decomposition of the rate of deformation into the elastic and the inelastic parts is assumed, where the hypoelastic relation is used.
Abstract: Additive decomposition of the rate of deformation into the elastic and the inelastic parts is assumed. For the elastic part, the hypoelastic relation is used. For the inelastic part, the flow law of VBO is augmented by a term quadratic in the overstress together with a modified Jaumann stress rate which jointly or separately allow the modeling of second-order effects
TL;DR: In this paper, the effect of modeling the material inhomogeneity by introducing a temperature perturbation or assuming the existence of a weak material within the block, and introducing two defects symmetrically placed on the vertical axis of the block was explored.
TL;DR: In this article, the authors investigated the thermocoupled flow localization of plane strain tension blocks with a relatively low strain rate sensitivity and comply with an elasto-viscoplastic constitutive equation which has a viscoplastic strain rate noncoaxial with the stress tensor.
TL;DR: In this article, a methodology is developed for solving problems involving the interaction between micro-scale phenomena, such as localization, and the overall macroscopic behavior of a structure, which is accomplished by enriching the strain field in a single direction within the framework of a Hu-Washizu variational principle.
Abstract: A methodology is developed for solving problems involving the interaction between micro-scale phenomena, such as localization, and the overall macroscopic behavior of a structure. This is accomplished by enriching the strain field in a single direction within the framework of a Hu-Washizu variational principle. Results are obtained for a viscoplastic bar which is stretched beyond its bifurcation point. The results show that the shear bands in viscplastic solids have a cusped structure, which is accurately resolved by enriching this method.
TL;DR: In this paper, a three-dimensional viscoelastic-plastic model for flow of particle filled polymer melts has been formulated based upon a modification of the Leonov model by introducing a structure function describing stress generated by the presence of the dispersed phase under the assumption that the material obeys the von Mises yielding criterion before flow takes place.
Abstract: A three‐dimensional viscoelastic‐plastic model for flow of particle filled polymer melts has been formulated. The approach is based upon a modification of the Leonov model by introducing a structure function describing stress generated by the presence of the dispersed phase under the assumption that the material obeys the von Mises yielding criterion before flow takes place. The model has been applied to steady simple shear and to transient shear flows, and equations have been derived for the components of stress tensor for each flow situation. A verification of the model has been made against limited experimental data available in the literature, indicating that the model is in fair agreement with experiments.
TL;DR: In this article, the authors examined the theoretical generality of constitutive models for the transient creep of polycrystalline ice and the ability of such models to represent knowledge derived from experimentation in a physically consistent manner.
TL;DR: In this paper, a front tracking finite element method is used for the calculation of temperature and stress field development in a solidifying pure metal, where the solid/liquid interface position and its velocity are considered as primary variables of the heat transfer analysis.
Abstract: In assessing the quality of castings, a major consideration is the formation of cracks due to the induced thermal stress field. A means for understanding the casting process is the development and numerical implementation of mathematical models which account for all the heat transfer and deformation phenomena occurring in a solidifying body. In this paper a front tracking finite element method is used for the calculation of temperature and stress field development in a solidifying pure metal. The solid/liquid interface position and its velocity are considered as primary variables of the heat transfer analysis. A rate form of the virtual work principle and a rate dependent viscoplastic-hypoelastic constitutive model are employed to solve the equilibrium equations and to account for the hydrostatic stress state on the freezing interface and the fact that the material is in a state of residual stress immediately after solidification. Examples of the applicability of the technique are given with the analysis of the solidification of pure aluminium under realistic cooling rates and material representation. The effects of melt pressure, cooling conditions and geometry of a continuously cast metal strand on the residual stress pattern are examined and reported.
TL;DR: In this paper, the multiaxial deformation behavior of Ni-based alloy B1900 + Hf has been studied at elevated temperatures in the range of 649-982 C Combined tension/torsion cyclic tests were performed on thin-wall tubular specimens under both in-phase and out-of-phase strain-controlled loading cycles.
Abstract: The multiaxial deformation behavior of the Ni-based alloy B1900 + Hf has been studied at elevated temperatures in the range of 649-982 C Combined tension/torsion cyclic tests were performed on thin-wall tubular specimens under both in-phase and out-of-phase strain-controlled loading cycles Both straining conditions resulted in stress loci of comparable magnitude, exhibiting no difference in cyclic hardening response A phase angle was observed between the deviatoric stress and the incremental plastic strain vectors during 90-deg out-of-phase strain cycling, and nonproportional stress relaxation occurred under biaxial strain hold The overall results have been used to assess the flow law, the hardening equations, and the applicability of the J2-based, elastic-viscoplastic model of Bodner-Partom (1979) for multiaxial loading conditions The overall agreement between theory and experiment is good Discrepancies are discussed in relation to micromechanical considerations