Showing papers on "Viscoplasticity published in 1988"

Non‐smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms

Abstract: Rate-independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non-smooth fashion are considered in detail. It is shown that the standard Kuhn-Tucker optimality conditions lead to the only computationally useful characterization of plastic loading. On the computational side, an unconditionally convergent return mapping algorithm is developed which places no restrictions (aside from convexity) on the functional forms of the yield condition, flow rule and hardening law. The proposed general purpose procedure is amenable to exact linearization leading to a closed-form expression of the so-called consistent (algorithmic) tangent moduli. For viscoplasticity, a closed-form algorithm is developed based on the rate-independent solution. The methodology is applied to structural elements in which the elastic domain possesses a non-smooth boundary. Numerical simulations are presented that illustrate the excellent performance of the algorithm.

Phenomenological Modeling of Hardening and Thermal Recovery in Metals

Abstract: Modeling of hardening and thermal recovery in metals is considered within the context of unified elastic-viscoplastic theories. Specifically, the choices of internal variables and hardening measures, and the resulting hardening response obtained by incorporating saturation-type evolution equations into two general forms of the flow law are examined. Based on the analytical considerations, a procedure for delineating directional and isotropic hardening from uniaxial hardening data has been developed for the Bodner-Partom model and applied to a nickel-base superalloy, B1900 + Hf. Predictions based on the directional hardening properties deduced from the monotonic loading data are shown to be in good agreement with results of cyclic tests.

Plastic and viscoplastic flow of void‐containing metals. Applications to axisymmetric sheet forming problems

Abstract: A formal analogy between the equations of pure plastic and viscoplastic flow theory for void-containing metals and those of standard non-linear elasticity is presented. The formulation is particularized for the analysis of axisymmetric sheet metal forming problems using simple two node linear finite elements. Details of the treatment of friction and strain hardening phenomena, time increment computation and elastic effects are also given. Examples of the effect of void porosity on the hemispherical stretching of a circular sheet are presented.

Optimal Structural Design Under Creep Conditions

Abstract: Optimal design of structures, or rather just of simple structural elements working under creep conditions, belongs to the most recent branches of structural optimization. It was initiated by four papers published in the years 1967-1968 (Reitman, Prager, Nemirovsky, and Zyczkowski). The most important differences with respect to elastic design are as follows: factor of time appearing in the constraints, a great variety of constitutive equations of creep or viscoplasticity, creep rupture hypotheses, creep buckling theories, various definitions of creep stiffness, etc. Moreover, the constraints related to stress-relaxation are quite new. So, it is almost impossible to establish a sufficiently general theory, and various types of problems must be treated separately by appropriate methods. On the other hand, the problems of optimization under creep conditions are important in view of metal structures working at elevated temperatures, structures made of plastics, concrete, etc. This review article gives a classification of problems and then a review of results obtained for bars, columns, arches, trusses, frames, plates, and shells. Over thirty percent of these results were obtained at the Cracow University of Technology. This is an extended and updated version of an earlier review article published in AMR41 (12), December, 1988, discusses specific features of the branch of optimal structural design under consideration, as well as perspectives for future research. This review article contains 187 references.

The Mechanical Behaviour of Cemented Carbides at High Temperatures

Abstract: Specimens of WC-11.wt%Co were tested under three-point bending conditions at temperatures ranging between 20 and 1000°C to investigate the effect of chromium and ruthenium additions on the mechanical behaviour of cemented carbides. Below 800 °C, a linear elastic brittle behaviour is observed. Above 800 °C, creep exponents of about n = 2 and activation energies between 3 and 5 eV were measured. Pore formation and growth were observed during creep. These results agree well with models based on creep by grain boundary sliding and pore formation. Displacement-controlled bend tests of chevron-notched specimens were performed to introduce stable crack growth. Above 800 °C, creep crack growth occurs owing to pore formation and growth. The pore distribution around the crack tip has been observed using a scanning acoustic microscope. It is shown that the equivalent strain distribution around a creep crack according to the models of Riedel agrees well qualitatively with the experimentally determined pore density. The transition between the linear elastic and viscoplastic behaviour (i.e. creep) is accompanied by a Portevin-Le Chatelier type of effect. If creep occurs in a tool made from this material, the edge blunts and is no longer useful for cutting. A characteristic time t ft is introduced describing the transition between the brittle and creep behaviour. It is shown that cemented carbides with a ruthenium addition have longer transition times than those without. Therefore, cemented carbides with ruthenium are advantageous as cutting tool materials since they can be used for longer times at a high temperature.

Thermoviscoplastic model with application to copper

Abstract: A viscoplastic model is developed which is applicable to anisothermal, cyclic, and multiaxial loading conditions. Three internal state variables are used in the model; one to account for kinematic effects, and the other two to account for isotropic effects. One of the isotropic variables is a measure of yield strength, while the other is a measure of limit strength. Each internal state variable evolves through a process of competition between strain hardening and recovery. There is no explicit coupling between dynamic and thermal recovery in any evolutionary equation, which is a useful simplification in the development of the model. The thermodynamic condition of intrinsic dissipation constrains the thermal recovery function of the model. Application of the model is made to copper, and cyclic experiments under isothermal, thermomechanical, and nonproportional loading conditions are considered. Correlations and predictions of the model are representative of observed material behavior.

Thermal fatigue of mar-m509 superalloy—ii. evaluation of life prediction models

Abstract: — Thermal fatigue data on MAR-M509 reported in a companion paper were used to evaluate four life prediction models The temperature-stress-strain history of the critical element at the thin edge of wedge specimens was computed for this purpose The analysis method uses a finite element computation of the temperature field and a uniaxial calculation of the stress-strain cycle using a cyclic viscoplastic constitutive equation The influence of specimen geometry and of maximum temperature on the thermal fatigue life to initiate a macroscopic crack was accounted for by variations in stress and mechanical strain ranges at the thin edge The accumulated and cyclic creep damage models were found to overestimate thermal fatigue life in all the cases Models which describe oxidation fatigue crack growth interactions, and which are borne out by metallographic observations on wedge specimens, were found to give reliable predictions of thermal fatigue life

Exact closed‐form solution of the return mapping algorithm in plane stress elasto‐viscoplasticity

Abstract: In Simo and Taylor, the classical radial return algorithm of Wilkins and Krieg and Key for plane strain and three‐dimensional J2‐flow theory, is extended to the case of plane stress. In three dimensions (or plane strain), enforcement of the discrete consistency condition reduces to a simple radial scaling of the trial stress onto the yield surface; i.e., the return map is radial. In plane stress, on the other hand, the return map, that restores the trial stress back to the yield surface, is constrained to remain in the plane stress subspace, and thus no longer reduces to a simple radial scaling. The determination of the final stress point from the trial stress now involves the solution by Newton's method of a non‐linear scalar equation, referred to as the discrete consistency equation in what follows, that yields the discrete consistency parameter λn+>0. The requirement that λn+>1 be positive is a direct consequence of the discrete Kuhn‐Tucker optimality conditions.

A viscoplastic constitutive theory for metal matrix composites at high temperature

Abstract: A viscoplastic constitutive theory is presented for representing the high temperature deformation behavior of metal matrix composites. The point of view taken is a continuum one where the composite is considered a material in its own right, with its own properties that can be determined for the composite as a whole. It is assumed that a single preferential (fiber) direction is identifiable at each material point (continuum element) admitting the idealization of local transverse isotropy. A key ingredient is the specification of an experimental program for the complete determination of the material functions and parameters for characterizing a particular metal matrix composite. The parameters relating to the strength of anisotropy can be determined through tension/torsion tests on longitudinally and circumferentially reinforced thin walled tubes. Fundamental aspects of the theory are explored through a geometric interpretation of some basic features analogous to those of the classical theory of plasticity.

A viscoplastic theory applied to copper

Abstract: A phenomenologically based viscoplastic model is derived for copper. The model is thermodynamically constrained by the condition of material dissipativity. Two internal state variables are considered. The back stress accounts for strain-induced anisotropy, or kinematic hardening. The drag stress accounts for isotropic hardening. Static and dynamic recovery terms are not coupled in either evolutionary equation. The evolution of drag stress depends on static recovery, while the evolution of back stress depends on dynamic recovery. The material constants are determined from isothermal data. Model predictions are compared with experimental data for thermomechanical test conditions. They are in good agreement at the hot end of the loading cycle, but the model overpredicts the stress response at the cold end of the cycle.

Constitutive equations for the coupling between elasto-plasticity damage and aging

Abstract: Coupled constitutive equations for metallic materials behavior are developed and used in structural analyses. Different mechanisms which can occur during deformation processes are associated with internal variables. The different kinds of couplings between the mechanisms are classified. From this classification, the formulation of the thermodynamical potential is determined, giving the associated variables. The potential of dissipation gives the evolution laws of the internal variables. Constitutive equations are written in the case of elasto-plasticity coupled with damage and aging. A first application is concerned with an analysis of a structure with an indented notch.The initial fields of plastic strain and damage are introduced from microhardness measurements. The calculation is performed with the Abaqus code in which coupled constitutive laws have been implemented. The second application is concerned with the coupling between aging and plastic deformation. The measurement of aging for different types of prior strainings has permitted the determination of a coupled constitutive law. A structural analysis with this law gives the aging field in a notched component.

Adaptive Finite Element Methods for Problems in Solid and Fluid Mechanics

Abstract: In this paper, a general class of h methods for adaptive finite element approximations is described that has been applied successfully to three classes of problems in solid and fluid mechanics: (1) supersonic flow of compressible gases in two-dimensional domains; (2) flow interaction in supersonic rotor-stator simulations; (3) quasi-static problems in viscoplasticity of metals under elevated temperatures.

A viscoplastic formulation with elasticity for transient metal forming

Abstract: A formulation for elastic-viscoplastic flow is presented which retains the basic structure of viscoplastic formulations. The constitutive theory is based on a multiplicative decomposition of the deformation gradient into elastic parts. The decomposition is cast in a rate form and the reference configuration for the decomposition is updated at each solution time to coincide with the intermediate configuration. Small elastic strains due to applied stresses are assumed. Volumetric strains due to thermal expansion are allowed to be finite. The inelastic behavior is described by a rate-dependent internal variable constitutive model. In the finite element formulation the elasticity is included in an integral sense over a time step by modifying the flow properties of the material to account for the change in the elastic strain over the step. The geometric update is made by a semi-implicit Euler integration of the velocity field so that the current geometry and state depend on the current solution for the velocity. Application to analytical and experimental benchmarks in metal forming indicate the accuracy and stability of the method.

Thermal and mechanical fields in continuous casting slab — A steady state analysis incorporating solidification

Abstract: A finite element scheme is presented in this paper to simulate fields of temperature and deformation as well as stress in the steady continuous casting process. A steady heat conduction equation incorporating heat generation due to solidification is formulated when considering the effect of flow rate. A viscoplastic constitutive model capable to describing elastic-viscoplastic solids as well as a viscous fluid is developed for the stress analysis. As an illustrative example a vertical continuous casting process is simulated by use of the finite element method, and the calculated results of temperature, deformation and stress in a slab are discussed.

Borehole Closure In Salt

Abstract: Constitutive law parameters are determined from salt behavior characterization experiments. The results are applied to predict creep (time-dependent) closure of boreholes in salt specimens subjected to various loading configurations. Rheological models (linear and nonlinear viscoelastic and viscoplastic models), empirical models, and physical theory models have been formulated from the results of uniaxial creep tests, strain and stress rate controlled uniaxial tests, constant strain rate triaxial tests, cyclic loading tests, and seismic velocity measurements. Analytical solutions for a thick-walled cylinder subjected to internal and external pressures and for a circular hole in an infinite plate subjected to a biaxial or uniaxial stressfield have been derived from each of the linear viscoelastic models and from one of the empirical laws. The experimental results indicate that the salt samples behave as an elastic-viscoplastic material. The elastic behavior tends to be linear and time-independent. The plastic deformation is time-dependent. The stress increment to strain rate increment ratio gradually decreases as the stress level increases. The transient potential creep law seems to give the simplest satisfactory governing equation describing the viscoplastic behavior of salt during the transient phase. 204 refs., 27 figs., 29 tabs.

A velocity approach to finite element calculation of elastoplastic and viscoplastic deformation processes

Abstract: The constitutive equations for the deformation of elastoplastic, viscoplastic or compressible materials are presented for the small strain approximation and for the large strain theory of Hill. A velocity approach is proposed for time discretization, which leads to a second order approximation for small strain, and an incrementally objective second order approximation for large deformation processes. Two other quasi second order formulations are discussed. The finite element space discretization is outlined and the solution procedure is described.

Structure of a viscoplastic theory

Abstract: The general structure of a viscoplastic theory is developed from physical and thermodynamical considerations. The flow equation is of classical form. The dynamic recovery approach is shown to be superior to the hardening function approach for incorporating nonlinear strain hardening into the material response through the evolutionary equation for back stress. A novel approach for introducing isotropic strain hardening into the theory is presented, which results in a useful simplification. In particular, the limiting stress for the kinematic saturation of state (not the drag stress) is the chosen scalar-valued state variable. The resulting simplification is that there is no coupling between dynamic and thermal recovery terms in each evolutionary equation. The derived theory of viscoplasticity has the structure of a two-surface plasticity theory when the response is plasticlike, and the structure of a Bailey-Orowan creep theory when the response is creeplike.

Effects of non‐proportional loadings in cyclic elasto‐viscoplasticity: experimental, theoretical and numerical aspects

Abstract: An elasto‐viscoplastic constitutive model valid under general complex cyclic loadings is proposed to describe the multiaxial behaviour of engineering metallic materials. Its numerical implementation in the framework of the finite element method is underlined. Its application to the prediction of some various tests is compared to the experimental responses.

Analysis of Viscoplastic Sandwich Beams Using Influence Functions

Abstract: A method of analyzing inelastic structures is presented, in which inelastic strains are interpreted as sources of eigenstresses in the linear elastic structure. Stresses due to inelastic strains are calculated by means of influence functions. The method is applied to viscoplastic sandwich beams.