Showing papers on "Viscoplasticity published in 1987"
Book•
01 Jan 1987
TL;DR: In this article, an augmented Lagrangian method for the solution of variational problems is proposed. But this method is not suitable for continuous media and their mathematical modeling, such as viscoplasticity and elastoviscasticity.
Abstract: 1. Some continuous media and their mathematical modeling 2. Variational formulations of the mechanical problems 3. Augmented Lagrangian methods for the solution of variational problems 4. Viscoplasticity and elastoviscoplasticity in small strains 5. Limit load analysis 6. Two-dimensional flow of incompressible viscoplastic fluids 7. Finite elasticity 8. Large displacement calculations of flexible rods References Index.
1,329 citations
TL;DR: In this article, a dual framework for elastic cap damage was proposed, where a strain-and a stress-based approach was employed, and a viscous regularization of strain-based, rate-independent damage models was also developed.
1,158 citations
TL;DR: In this paper, a large deformation viscoplastic polycrystal theory is formulated and a self-consistent approach is developed, where each grain is assumed to be a single ellipsoidal inclusion in a homogeneous equivalent medium.
968 citations
TL;DR: In this article, critical conditions for shear localization in thermoviscoplastic materials are obtained in closed form for idealized models of simple shearing deformations, which are viewed as quite acceptable for many applications in which shear bands occur.
Abstract: : Critical conditions for shear localization in thermoviscoplastic materials are obtained in closed form for idealized models of simple shearing deformations. The idealizations, which include the neglect of heat conduction, inertia, and elasticity, are viewed as quite acceptable for many applications in which shear bands occur. Explicit results obtained for the idealized, but fully nonlinear problem show the roles of strain rate sensitivity, strain hardening, and initial imperfection on the localization behavior. Numerical solutions for two steels are shown to exhibit the principal features reported for torsional Kolsky bar experiments on these steels. Mathematically exact critical conditions obtained for the fully nonlinear problem are compared with critical conditions obtained by means of linear perturbation analysis gives better agreement with the predictions fo the fully nonlinear analysis.
238 citations
TL;DR: In this article, the authors examined the derivation of constitutive relations from the free energy and the dissipation function of an elastic body and found that if the deformation of a body is neither isothermal nor adiabatic, the strain tensor has to be supplemented by the additional independent state variable.
Abstract: Publisher Summary This chapter examines the derivation of constitutive relations from the free energy and the dissipation function. Continuum mechanics allows one to establish constitutive relations, deducing them from a single pair of scalar functions characterizing the material. The simplest materials dealt with in continuum mechanics are elastic. More general processes and those taking place in more general materials are irreversible and require more constitutive relations, connecting the dissipative forces with the velocities. The orthogonality condition and the equivalent extremum principles have been established for velocities in the form of vectors or symmetric tensors. It is found that if the deformation of an elastic body is neither isothermal nor adiabatic, the strain tensor has to be supplemented by the additional independent state variable. The connection between stress and elastic strain is given by the generalized Hooke's law and connects the stress with the plastic strain and its time rate. It is found that orthogonality in velocity space, which is essentially responsible for the results, does not necessarily imply orthogonality in force space.
226 citations
216 citations
TL;DR: In this article, the authors used a simplified thermo/visco/plastic flow law to study the dynamics of adiabatic shear band formation and found that temperature and plastic strain rate begin to localize immediately but only slowly, whereas the stress first evolves almost as if there were no perturbation, but then collapses rapidly when severe localization occurs.
Abstract: T he dynamics of adiabatic shear band formation is considered making use of a simplified thermo/visco/plastic flow law. A new numerical solution is used to follow the growth of a perturbation from initiation, through early growth and severe localization, to a slowly varying terminal configuration. Asymptotic analyses predict the early and late stage patterns, but the timing and structure of the abrupt transition to severe localization can only be studied numerically, to date. A characteristic feature of the process is that temperature and plastic strain rate begin to localize immediately, but only slowly, whereas the stress first evolves almost as if there were no perturbation, but then collapses rapidly when severe localization occurs.
199 citations
Metz1
TL;DR: In this article, a simple shear test at high strain rate with inertia effects is described, and a new relative perturbation method accounting for non-steadiness of plastic flow is presented.
Abstract: S hear band formation in a thermal viscoplastic heat conducting material is described in a simple shear test at high strain rate with inertia effects. The classical perturbation method is discussed, and a new relative perturbation method accounting for non-steadiness of plastic flow is presented. They respectively provide instability and localization criteria which are compared. Furthermore both are compared to available nonlinear exact results and to experimental data. The influence of material parameters, initial imperfections, and boundary conditions is described.
157 citations
TL;DR: In this paper, a three-dimensional generalization of the linear perturbation stability analysis for the onset of shear localization is presented, which considers isotropic, incompressible, viscoplastic materials which exhibit strain hardening (or softening), strain-rate hardening, thermal softening and pressure hardening.
Abstract: An outstanding problem in mechanics is the modeling of the phenomenon of initiation and development of localized shear bands, in materials whose inelastic deformation behavior is inherently rate-dependent. C lifton (1980) and B ai (1981, 1982) have presented a linear perturbation stability analysis for the initiation of shear bands in viscoplastic solids deforming in simple shear. This localization analysis is essentially one-dimensional in nature. In this paper, we present a three-dimensional generalization of this linear perturbation stability analysis for the onset of shear localization. We neglect elastic effects and consider isotropic, incompressible, viscoplastic materials which exhibit strain hardening (or softening), strain-rate hardening, thermal softening and pressure hardening. For this class of materials, we derive the general characteristic stability equation. Next, we focus our attention on the special version of this equation for plane motions and consider the two physically important limiting cases of (1) quasi-static, isothermal deformations, and (2) dynamic, adiabatic deformations. For these cases, we derive (a) the critical conditions for the formation of shear bands, (b) the most probable directions along which the bands can form, and (c) information regarding the incipient rate of growth of the emergent shear bands. The results, which are presented in detail in the body of the paper, provide new insight into the important phenomenon of shear localization under both quasi-static and rapid deformation of many materials including both metals and polymers.
145 citations
TL;DR: In this article, the general yield function in the hierarchical approach for constitutive modelling of materials is used with Perzyna's theory to characterize viscoplastic behaviour of geologic materials: a sand and rock salt.
Abstract: The general yield function in the hierarchical approach for constitutive modelling of materials is used with Perzyna's theory to characterize viscoplastic behaviour of geologic materials: a sand and rock salt. Particular attention is given to determination of the constants from laboratory quasistatic or short term, and creep tests. The proposed model is verified with respect to observed laboratory response of the sand and salt. It is implemented in a non-linear finite element procedure and applied to analyse time-dependent behaviour of a cavity in the rock salt.
137 citations
TL;DR: In this paper, the effect of porosity on flow localization and failure in a porous material is analyzed numerically using an elastic viscoplastic constitutive relation for porous plastic solids.
Abstract: T he effect of a nonuniform distribution of porosity on flow localization and failure in a porous material is analyzed numerically. The void density distribution and properties used to characterize the material behavior were obtained from measurements on partially consolidated and sintered iron powder. The calculations were carried out using an elastic viscoplastic constitutive relation for porous plastic solids. Local material failure is incorporated into the model through the dependence of the flow potential on void volume fraction. The region modelled is a small portion of a larger body, subject to various triaxial stress conditions. Both plane strain and axisymmetric deformations are considered with imposed periodic boundary conditions. Interactions between regions with higher void fractions promote plastic flow localization into a band. Local failure occurs by void growth and coalescence within the band. The results suggest a failure criterion based on a critical void volume fraction that is only weakly dependent on stress history. The critical void fraction does. however, depend on the initial void distribution and material hardening characteristics.
01 Jan 1987
TL;DR: In this article, the authors considered both elastic and plastic deformations to be generally non-zero at all stages of loading and derived the form of the equations and the material constants from measurements of microstructural quantities.
Abstract: Although inelastic response of solid materials at low stress levels has been observed and measured for over a century and a half (an account of the early work is given by Bell1), engineering thinking on material behavior has been dominated by the considerable success of the classical elastic and plastic theories. In contrast, the work on ‘dislocation dynamics’ in the 1950s and early 1960s by Johnston and Gilman2,3 and by Hahn4 and others was based on the concept of considering both elastic and plastic deformations to be generally non-zero at all stages of loading. Those formulations were one-dimensional and restricted to simple loading histories such as uniaxial extension and creep. One of the main interests in those studies was to obtain the form of the equations and the material constants from measurements of microstructural quantities.
TL;DR: In this paper, it is stated that plastic strain takes time to develop and the existnce of an equilibrium stress is postulated at which plastic strain is fully developed, similar to the back stress used in materials science.
Abstract: Phenomenological and microstructural motivations for the terms appearing in the title are found in a literature survey. Although the interpretations differ with various investigators a strong tendency is observed to consider plastic flow as rate dependent. It is stated that plastic strain takes time to develop and the existnce of an equilibrium stress is postulated at which plastic strain is fully developed. It is similar to the back stress used in materials science. The drag stress introduced from microdynamical studies performs the same function as the isotropic variable in plasticity. Most of the theories that describe the transient and steady-state behavior of metallic alloys make the inelastic strain rate a function of the over (effective) stress. It is shown that this concept has considerable advantages in the modeling of changes of viscous (time- or rate-dependent) and plastic (time- or rate-independent) contributions to hardening that are observed in cyclic loading and dynamic plasticity.
TL;DR: In this article, a large deformation viscoplastic model is proposed, which includes the effects of static and dynamic recovery in its strain rate response as well as the plastic spin in its rotational response.
Abstract: We propose a new large deformation viscoplastic model which includes the effects of static and dynamic recovery in its strain rate response as well as the plastic spin in its rotational response. The model is directly obtained from single slip dislocation considerations with the aid of a maximization procedure and a scale invariance argument. It turns out that the evolution of the back stress and the expression for the plastic spin are coupled within the structure of the theory. The model is used for the prediction of nonstandard effects in torsion, namely the development of axial stress and strain as well as the directional softening of the shear stress. The comparisons between the present continuum model and both experiments and self-consistent polycrystalline calculations are very encouraging.
Book•
31 Jul 1987
TL;DR: In this paper, the authors proposed a model for dynamic elastic loading of a simply supported bar and showed that it is possible to detect the presence of elastic loading on the bar by measuring the initial velocity of the bar.
Abstract: 1. Introduction.- 1.1 Forms of Dynamic Buckling.- 1.2 Examples of Dynamic Pulse Buckling.- 2. Impact Buckling of Bars.- 2.1 Introduction.- 2.2 Elastic Buckling of Long Bars.- 2.2.1 Equations of Motion.- 2.2.2 Static Elastic Buckling of a Simply Supported Bar.- 2.2.3 Theory of Dynamic Elastic Buckling of a Simply Supported Bar.- 2.2.4 Amplification Functions.- 2.2.5 Dynamic Elastic Buckling under Eccentric Load.- 2.2.6 Dynamic Elastic Buckling with Random Imperfections.- 2.2.7 Framing Camera Observations of Dynamic Elastic Buckling.- 2.2.8 Streak Camera Observations--Effects of the Moving Stress Wave.- 2.2.9 Experiments on Rubber Strips--Statistical Observations.- 2.2.10 Buckling Thresholds in Aluminum Strips.- 2.3 Dynamic Plastic Flow Buckling of Bars.- 2.3.1 Introduction.- 2.3.2 Differential Equation of Motion.- 2.3.3 The Initially Straight Bar.- 2.3.4 The Nearly Straight Bar.- 2.3.5 Comparisons of Theoretical Model and Experimental Results.- 3. Dynamic Pulse Buckling of Rings and Cylindrical Shells From Radial Loads.- 3.1 Introduction.- 3.2 Dynamic Plastic Flow Buckling of Rings and Long Cylindrical Shells From Uniform Radial Impulse.- 3.2.1 Introduction.- 3.2.2 Postulated Character of the Motion-Dynamic Flow Buckling.- 3.2.3 Equation of Motion.- 3.2.4 Perfectly Circular Ring, Almost Uniform Initial Radial Velocity.- 3.2.5 Strain Rate Reversal.- 3.2.6 The Buckling Terms-Representative Numerical Cases.- 3.2.7 Experimental Technique and Characteristic Results.- 3.2.8 Comparison of Experiment with Theory.- 3.2.9 Buckling Threshold.- 3.3 Dynamic Elastic Buckling of Rings and Cylindrical Shells From Uniform Radial Impulse.- 3.3.1 Introduction.- 3.3.2 Theory of Elastic Shell Motion.- 3.3.3 Initial Growth of the Flexural Modes--The Stability Parameter.- 3.3.4 Small Initial Velocity--Autoparametric Vibrations.- 3.3.5 Intermediate Initial Velocity--Onset of Pulse Buckling.- 3.3.6 High Initial Velocity--Pulse Buckling.- 3.4 Critical Radial Impulses for Elastic and Plastic Flow Buckling of Rings and Long Cylindrical Shells.- 3.4.1 Approach.- 3.4.2 Strain Hardening in Engineering Metals.- 3.4.3 Equations of Motion.- 3.4.4 Plastic Flow Buckling.- 3.4.5 Summary of Formulas for Critical Impulse.- 3.4.6 Buckling with a Cosine Impulse Distribution.- 3.4.7 Effects of Strain Rate Reversal.- 3.5 Dynamic Pulse Buckling of Cylindrical Shells From Transient Radial Pressure.- 3.5.1 Approach and Equations of Motion.- 3.5.2 Donnell Equations for Elastic Buckling.- 3.5.3 Fourier Series Solution--Static Buckling.- 3.5.4 Critical Pressure-Impulse Curves for Dynamic Buckling.- 3.5.5 Simple Formulas for Critical Curves.- 3.5.6 Experimental Results and Comparison with Theory.- 4. Flow Buckling Of Cylindrical Shells From Uniform Radial Impulse.- 4.1 Plastic Flow Buckling With Hardening and Directional Moments.- 4.1.1 Theory of Plastic Cylindrical Shells.- 4.1.2 Effect of Shell Length on Strain Rates.- 4.1.3 The Unperturbed Motion.- 4.1.4 Axial Strain Distribution.- 4.1.5 Perturbed Motion.- 4.1.6 Directional Moments.- 4.1.7 Governing Equation.- 4.1.8 Modal Solution.- 4.1.9 Amplification Functions.- 4.1.10 Asymptotic Solutions for Terminal Motion.- 4.1.11 Strain Hardening Moments Only.- 4.1.12 Directional Moments Only.- 4.1.13 Directional and Hardening Moments.- 4.1.14 Displacement and Velocity Imperfections.- 4.1.15 Threshold Impulse.- 4.1.16 Comparison of Theory and Experiment.- 4.2 Viscoplastic Flow Buckling with Directional Moments.- 4.2.1 Viscoplastic Moments.- 4.2.2 Theory of Viscoplastic Cylindrical Shells.- 4.2.3 The Unperturbed Motion.- 4.2.4 Perturbed Motion.- 4.2.5 Governing Equation.- 4.2.6 Modal Solution.- 4.2.7 Amplification Functions.- 4.2.8 Approximate Solutions for Terminal Motion.- 4.2.9 Preferred Modes and Threshold Impulses.- 4.2.10 Displacement and Velocity Imperfections.- 4.2.11 Viscoplastic and Directional Moments.- 4.2.12 Comparison of Theory and Experiment.- 4.3 Critical Velocity for Collapse of Cylindrical Shells Without Buckling.- 4.3.1 Strain-Hardening Moments Only.- 4.3.2 Strain Rate Moments Only.- 5. Dynamic Buckling of Cylindrical Shells Under Axial Impact.- 5.1 Dynamic Buckling of Cylindrical Shells Under Elastic Axial Impact.- 5.1.1 Analytical Formulation.- 5.1.2 Static Buckling.- 5.1.3 Amplification Functions for Dynamic Buckling.- 5.1.4 Buckling From Random Imperfections.- 5.1.5 Impact Experiments.- 5.1.6 Formula for Threshold Buckling.- 5.1.7 Dynamic Buckling Under Step Loads.- 5.2 Axial Plastic Flow Buckling of Cylindrical Shells.- 5.2.1 Introduction.- 5.2.2 Unperturbed Motion.- 5.2.3 Perturbed Motion.- 5.2.4 Governing Equations.- 5.2.5 Modal Solutions.- 5.2.6 Amplification Functions.- 5.2.7 Preferred Mode and Critical Velocity Formulas.- 5.2.8 Directional and Hardening Moments.- 5.2.9 Description of Experiments.- 5.2.10 Comparison of Theory and Experiment.- 5.2.11 Slow Buckling.- 5.2.12 Axial Impact of Plates.- 5.3 Forces and Energy Absorption During Axial Plastic Collapse of Tubes.- 5.3.1 Axial Collapse Experiments.- 5.3.2 Theoretical Estimates of Collapse Forces.- 5.3.3 Comparison of Theory and Experiment.- 6. Plastic Flow Buckling of Rectangular Plates.- 6.1 Introduction.- 6.2 Perturbational Flexure.- 6.3 Governing Equation.- 6.3.1 General Loading.- 6.3.2 Uniaxial Compression.- 6.4 Uniaxial Compression of Simply Supported Plates.- 6.4.1 Modal Solution.- 6.4.2 Amplification Functions.- 6.4.3 Preferred Mode and Critical Velocity Formulas.- 6.4.4 Directional and Hardening Moments.- 6.5 Uniaxial Compression of Unsupported Plates.- 6.5.1 Governing Equation, Modal Solution, and Amplification Functions.- 6.5.2 Preferred Mode and Critical Velocity Formulas.- 6.6 Comparison of Theoretical and Experimental Results.- 6.7 Slow Buckling.
TL;DR: The coupling between kinematics and kinetics and the invariance requirements under superposed rigid body rotations, determine unambiguously the proper general form of the elastoplastic rate constitutive equations, in terms of the values of the state variables and their rates in reference to the current and any choice of the unstressed configuration.
Abstract: The coupling between kinematics and kinetics and the invariance requirements under superposed rigid body rotations, determine unambiguously the proper general form of the elastoplastic rate constitutive equations, in terms of the values of the state variables and their rates in reference to the current and any choice of the unstressed configuration. Topics such as the effect of changing the stress rate, small elastic deformations with or without large volumetric elastic strains, rate effects and viscoplasticity, an example on single slip, the effect of the plastic spin constitutive relations and the concept of an effectively unstressed configuration, are addressed in detail. Issues and different approaches debated in the past are discussed, compared and clarified.
TL;DR: In this article, four current viscoplastic models are compared experimentally for Inconel 718 at 593 C. This material system responds with apparent negative strain rate sensitivity, undergoes cyclic work softening, and is susceptible to low cycle fatigue.
Abstract: Four current viscoplastic models are compared experimentally for Inconel 718 at 593 C. This material system responds with apparent negative strain rate sensitivity, undergoes cyclic work softening, and is susceptible to low cycle fatigue. A series of tests were performed to create a data base from which to evaluate material constants. A method to evaluate the constants is developed which draws on common assumptions for this type of material, recent advances by other researchers, and iterative techniques. A complex history test, not used in calculating the constants, is then used to compare the predictive capabilities of the models. The combination of exponentially based inelastic strain rate equations and dynamic recovery is shown to model this material system with the greatest success. The method of constant calculation developed was successfully applied to the complex material response encountered. Backstress measuring tests were found to be invaluable and to warrant further development.
TL;DR: In this paper, specific unified constitutive equations for an elastic-viscoplastic material are developed which in the limit of infinite resistance to plastic flow become those of a general hyperelastic isotropic material; and in the case of zero resistance to the plastic flow, the Reiner-Rivlin fluid becomes a general Reiner Rivlin fluid.
TL;DR: In this paper, the mathematical structure of the overstress type elasto-viscoplastic constitutive model is discussed and the analytical solution of undrained strength for Adachi and Oka model is derived.
TL;DR: In this paper, a general constitutive equation for rocks is proposed, which can describe their elastic and viscoplastic properties for any triaxial compressive stress state and the peculiarities of the creep phenomenon as described by the model are discussed.
TL;DR: In this article, the authors studied the thermomechanical problem involving simple shearing of a finite slab made of an isotropic and viscoplastic material with the objective of finding the effect of the strain hardening parameter, strain-rate hardening parameters, thermal softening coefficient and thermal conductivity on the initiation and growth of adiabatic shear bands.
TL;DR: In this paper, steady shearing solutions are found as quadratures within the context of a simple theory of viscoplasticity, which includes thermal softening and heat conduction.
Abstract: S teady shearing solutions are found as quadratures within the context of a simple theory of viscoplasticity, which includes thermal softening and heat conduction. The solutions are illustrated by numerical examples for four commonly used versions of viscoplasticity, where each version has first been calibrated against the same hypothetical data set. It is found that, although they all predict qualitatively similar morphology, the four flow laws give results that differ in detail and one in particular differs substantially from the other three at the more extreme conditions. Although definitive data do not exist, there appears to be rough agreement with physical measurements of adiabatic shear bands. The conjecture is made that steady solutions correspond to central boundary layers for the full unsteady theory.
01 Mar 1987
TL;DR: In this article, a simple version of thermo/viscoplasticity is used to model the formation of adiabatic shear bands in high rate deformation of solids.
Abstract: A simple version of thermo/viscoplasticity is used to model the formation of adiabatic shear bands in high rate deformation of solids. The one dimensional shearing deformation of a finite slab is considered. Equations are formulated and numerical solutions are found for dipolar plastic materials. These solutions are contrasted and compared with previous solutions for simple materials.
TL;DR: In this paper, a numerical method for analyzing non-isothermal viscoplastic deformation problems has been developed, where a modified Bishop's method is used to solve the thermo-plasticity problem in decoupled form at each time step.
TL;DR: In this paper, a hydro-pneumatic tensile test apparatus was developed which allows dynamic tensile testing at room temperature with and without superimposed ultrasonic oscillations, and the results at low strain rates (10 −3 s −1 ) agree favourably with previous measurements but at high rates (50 s − 1 ) at 20% lower flow stress is observed.
TL;DR: In this article, a viscoplastic constitutive model with an evolving internal state variable, called hardness, has been developed for commercially pure aluminium, where hardness distributions may be predicted throughout the workpiece.
Abstract: A viscoplastic constitutive model with an evolving internal state variable, called hardness, has been developed for commercially pure aluminium. One application of such a constitutive model is in process modelling where hardness distributions may be predicted throughout the workpiece. This paper assesses the accuracy with which microhardness measurements of quenched specimens correlate with the hardness predicted by the constitutive model for various imposed thermomechanical histories. Using axisymmetric compression, different hardness values are achieved by various tests, both underdeveloped (increasing hardness) and overdeveloped (decreasing hardness) structures being produced during deformation. The steady state flow stress and hardness for a particular strain rate and temperature may be achieved with less strain by first deforming at a high strain rate and then decreasing the strain rate. The constitutive model accurately predicts the amount of prestrain required at the higher strain rate. Dif...
TL;DR: In this paper, a method for including a constitutive equation utilizing a single scalar internal variable in a model for transient thermomechanical phenomena is presented for determining material parameters in the context of a particular material (304 Stainless Steel).
TL;DR: In this paper, an incremental approach to the trial solution was devised to improve the convergence of the Newton-Raphson method for non-linear finite-element modeling (FEM) problems.
01 Jan 1987
TL;DR: In this article, the cyclic neutral theory of viscoplasticity based on over-stress was applied to predict the zero-to-tension ratchetting behavior of a Tialloy at room temperature.
Abstract: The cyclic neutral version of the theory of viscoplasticity based on over-stress (VBO) is introduced and applied to predict the zero-to-tension ratchetting behavior of a Tialloy at room temperature. The experiments show ratchetting to depend on stress rate and this fact together with the accumulated ratchet strains is well represented by VBO. A cyclic hardening version of the theory is shown to correlate the out-of-phase hardening of type 304 stainless steel at room temperature. This is accomplished through the use of two new measures for path length one of which accumulates only in nonproportional loading.
TL;DR: In this paper, the influence of material strain-rate sensitivity on neck propagation during the cold drawing of polymeric films is examined and the entire load-deformation behaviour of a rectangular specimen as well as the evolution of the specimen profile and the stress and strain distributions at various stages of the deformation process are computed.