Showing papers on "Viscoplasticity published in 1994"

A self-consistent viscoplastic model: prediction of rolling textures of anisotropic polycrystals

Abstract: The plastic properties of anisotropic polycrystalline aggregates and polyphase materials are in general non-homogeneous and, as a consequence, so is the local plastic deformation. We present in this work a model that describes the plastic behaviour of non-homogeneous materials composed of anisotropic regions (grains or phases). Our model is based on describing each region as a viscoplastic inclusion embedded in the effective medium represented by the other grains, and incorporates explicitly the grain interaction with its surroundings and the plastic anisotropy of grain and matrix. Within the model the grain response is coupled to the overall response of the polycrystal and the grain deformation may differ from the polycrystal's. A characteristic of our approach is that those deformation systems with lower critical resolved shear stress tend to be more active, and less than five systems per grain are sufficient to accomodate the imposed overall deformation. In this work we explore the consequences and the limits of the model, and its dependence on the assumed rate sensitivity as well. We combine the self-consistent formulation with a volume fraction transfer scheme for treating the reorientation due to twinning, and simulate rolling textures of brass (f.c.c.), Zircaloy (h.c.p.), calcite (trigonal) and uranium (orthorhombic). We compare the results with experimental measurements and Taylor-type predictions, infer information concerning the microscopic deformation mechanisms and discuss the limits of applicability of the approach.

Equivalent times and one-dimensional elastic viscoplastic modelling of time-dependent stress-strain behaviour of clays

Abstract: This paper describes the recent concept of equivalent time and how it can be used in a revised version of an earlier elastic viscoplastic model for one-dimensional straining of clays. It clarifies ...

A Proposed Three-Dimensional Constitutive Model for Shape Memory Alloys

Abstract: The shape memory alloy (SMA) stress-strain response associated with martensitic twinning hysteresis and austenite-martensite/martensite-austenite superelasticity is modeled using constitutive equations. Compared to the modeling work done on viscoelastic and viscoplastic be havior, this has been an area of limited study. The equations which are presented here express the growth of inelastic strain in a rate-type formulation similar to viscoplastic laws. This constitutive model is obtained by extending a one-dimensional evolutionary model of SMA behavior to three dimensions. The resulting model is then reduced to meet the loading conditions of three special cases: uniaxial loading, shear loading, and non-proportional biaxial loading (combined axial- torsional loading). The model which is being considered, although nonlinear, is relatively simple in that only two evolutionary equations are required to model inelastic strain and a generalized back stress at a material point. Thus the model being presented use...

A nonproportionality parameter and a cyclic viscoplastic constitutive model taking into account amplitude dependences and memory effects of isotropic hardening.

Abstract: The present paper is concerned with the formultion of a viscoplastic constitutive model describing both cyclic hardening and cyclic softening under proportional and nonproportional loading conditions. First a nonproportionality parameter and the relevant internal structural tensor to describe the nonproportional hardening is discussed in detail. Internal variables and the related evolution equations to describe the amplitude dependence of cyclic hardening/softening are also examined. Then the history effects of cyclic hardening and softening are considered in the evolution equations of isotropic hardening variable. The proposed model is established by incorporating these equations into Chaboche model

Modeling of ratchetting: evaluation of various approaches

Abstract: In the first part, some classical experimental results are briefly recalled. The second part reviews various ways of improving the constitutive models for the description of both monotonic and cyclic rate-independent plasticity and the correct modeling of ratchetting effets. In particular, it is shown that simple modifications of the dynamic recovery terms in the kinematic hardening rules offer the possibility of large improvements. Two specific models are then considered in detail, showing the great similarities in their mathematical structure and their numerical responses for uniaxial and multiaxial ratcheting conditions

Micromechanical modeling of reinforcement fracture in particle-reinforced metal-matrix composites

Abstract: Finite element analyses of the effect of particle fracture on the tensile response of particle-reinforced metal-matrix composites are carried out. The analyses are based on two-dimensional plane strain and axisymmetric unit cell models. The reinforcement is characterized as an isotropic elastic solid and the ductile matrix as an isotropically hardening viscoplastic solid. The reinforcement and matrix properties are taken to be those of an Al-3.5 wt pct Cu alloy reinforced with SiC particles. An initial crack, perpendicular to the tensile axis, is assumed to be present in the particles. Both stationary and quasi-statically growing cracks are analyzed. Resistance to crack growth in its initial plane and along the particle-matrix interface is modeled using a cohesive surface constitutive relation that allows for decohesion. Variations of crack size, shape, spatial distribution, and volume fraction of the particles and of the material and cohesive properties are explored. Conditions governing the onset of cracking within the particle, the evolution of field quantities as the crack advances within the particle to the particle-matrix interface, and the dependence of overall tensile stress-strain response during continued crack advance are analyzed.

Micromechanical analysis of a continuous fiber metal matrix composite including the effects of matrix viscoplasticity and evolving damage

Abstract: A thermomechanical analysis of a metal matrix continuous fiber composite is performed herein. The analysis includes the effects of matrix inelasticity and interface cracking. Due to these nonlinearities, the analysis is performed computationally using the finite element method. Matrix inelasticity is modeled with a rate dependent viscoplasticity model. Interface fracture is modeled by the use of a nonlinear interface constitutive model. The problem formulation is summarized, and results are given for a typical SiC-Ti composite at elevated temperature. Preliminary results indicate that rate dependent viscoplasticity can be a significant mechanism for dissipating the energy available for interface fracture, thus contributing to improved macroscopic ductility of the composite.

A fourth-order plastic potential for anisotropic metals and its analytical calculation from the texture function

Abstract: A fourth-order potential is proposed for anisotropic metals, assuming orthotropic symmetry. It may be used as a yield criterion, but here it is used as a dual potential depending on the strain-rate. The concept of dual potential is recalled and the implementation in simulation codes is discussed, along with the extension to viscoplasticity. The coefficients depend linearly on the texture coefficients, up to a scale factor determinable by one mechanical test. The adjustment of the dual potential from texture data is numerically tested for steels, and compared with mechanical tests. A significant improvement of the flow rule (strain ratio R) is obtained as compared with both the Taylor model and the texture-adjusted Hill criterion. The predicted stress ratios are close to those predicted with the latter criterion, which were previously found to be in a good experimental agreement.

Nonlinear finite element simulation of thermoviscoplastic deformation of C4 solder joints in high density packaging under thermal cycling

Abstract: A nonlinear finite element model has been used to simulate the thermally induced viscoplastic deformation of the controlled collapse chip connection (C4) solder joints in a high density single chip module (SCM). The dependence of solder joint deformation on the tin content was demonstrated for various lead-rich Pb-Sn alloys with the tin content varying from 2 wt% to 10 wt%. A thermoviscoplasticity theory was introduced for modeling inelastic stress-strain response of the Pb-Sn alloys. In the theory, the creep and plasticity were separately considered and formulated. The Garafalo hyperbolic sine law was used to model the creep behavior, while the Prandtl-Reuss equation was used for the rate independent plastic deformation. The modeled SCM consists of a 5 mm silicon chip attached to 50 mm alumina substrate by an array of C4 with diameter of O.1 mm on a 0.2 mm I/O pitch. A cyclic temperature load of 0 to 100/spl deg/C at frequency of 3 cycles per hour was applied to the SCM, and a nonlinear finite element program ABAQUS was used to numerically study the effect of the tin content on the stress-strain response of the C4. It is concluded that the decrease of the tin content induces a decrease of the equivalent creep strain and Mises stress, but an increase of the equivalent plastic strain for the edge C4 in the SCM. >

Instability phenomena and adiabatic shear band localization in thermoplastic flow processes

Abstract: The main objective of the paper is the development of the viscoplastic regularization procedure valid for a broad class of thermodynamic plastic flow processes in damaged solids. The additional aim is to investigate instability phenomena and adiabatic shear band localization criteria when spatial covariance, thermomechanical coupling, strain induced anisostropy and micro-damage softening effects are taken into consideration. This investigation is based on an analysis of acceleration waves and takes advantage of a notion of the instantaneous adiabatic acoustic tensor. In the first part of the paper the formulation of an inelastic flow process is given and particular attention is focussed on the thermomechanical coupling effects. The thermodynamic theory of elastic-viscoplastic damaged solids is presented within a framework of the rate type covariance material structure with a finite set of the internal state variables. A notion of covariance is understood in the sense of invariance under an arbitrary spatial diffeomorphism. Rate sensitivity effect is introduced by the assumption of the viscoplastic overstress conception. A notion of a relaxation time has been used to control the description of mechanical as well as thermal disturbances. By the assumption that the mechanical relaxation time is equal to zero the thermo-elastic-plastic (rate independent) response of the damaged material is accomplished. In the second part of the paper the existence of a solution to the initial-boundary value problem is examined and its stability property is investigated based on the application of nonlinear semi-group methods and an analysis of continuity of evolution operators. For an adiabatic process the investigation of acceleration waves is given. The determination of eigenvalues of the appropriate acoustic tensor is presented. This helps to assess the well-posedness of the initial-value problems which describe the thermodynamic plastic flow processes. Differences for two constitutive assumptions, namely for rate dependent and rate independent responses, are examined. In the case of an adiabatic process and elastic-viscoplastic response of a material the conditions for the existence, uniqueness and well-posedness of the initial value problem have been investigated. Criteria for adiabatic shear band localization of plastic deformation are obtained by assuming that some eigenvalue of the instantaneous adiabatic acoustic tensor for rate independent response is equal to zero. Several particular cases of the constitutive model have been considered.

Modelling unanticipated pore-water pressures in soft clays

Abstract: Field observations in thin soft clay layers may show pore-water pressures that increase for some time after the loading is applied. Reasons for these observations are not well understood. The paper shows how an elastic viscoplastic constitutive model incorporated into the consolidation equation can predict these pore-water pressure increases in soils that exhibit significant creep behaviour (or secondary compression). The phenomenon has been related to relaxation in regions of the profile from which drainage has not yet begun. Key words : clay, consolidation, creep, secondary compression, viscous, relaxation, pore-water pressure, elastic–plastic.

Modeling of hardening at very high strain rates

Abstract: A modification of the Bodner–Partom elastic‐viscoplastic constitutive model is proposed to account for strain rate dependence of the evolution of hardening. The suggested procedure is for the rate of hardening in the hardening evolution equation to be a direct function of total strain rate. Material constants are determined for oxygen‐free‐electronic copper and simulations of response behavior at very high rates of straining appear to be consistent with test observations.

Evolution of crack tip process zones

Abstract: A variety of crack tip profiles can appear under the fracture processes controlled by an anisotropic damage law taking into account the deterioration effects of plastic flow, stress triaxiality and initial draw direction. When combined with a hyperelastic and viscoplastic constitutive framework at finite deformation, the anisotropic damage theory enables us to simulate numerically five typical crack tip profiles: crack tip superblunting, a branching or spearhead profile, trident damage channeling, sharp notch and blunted notch. To obtain a combined micro/macroscopic appreciation on interfacial fracture along a metal/ceramic interface, a triple-layer configuration is proposed which consists of a nanoscopic core disc made by atomistic assembly, an overlapping elastic annulus incorporating discrete plasticity accumulated by dislocation motion, and an enveloping macroscopic layer described by an elastic-viscoplastic continuum. Preliminary computations are conducted to characterize the zigzag formation of a thermally adhered metal/ceramic interface, to delineate the atomistic determination of interfacial fracture patterns, and to simulate the transmission of crack tip dislocations from the atomistic assembly to the overlapping continuum.

The plastic deformation of polycrystalline dolomite: comparison of experimental results with theoretical predictions

Abstract: The trigonal carbonate mineral dolomite is plastically highly anisotropic with some orientations much more favored for slip over others. The plastic behaviour for polycrystalline dolomite in compression is modelled using a model of single slip, the Taylor theory of homogeneous strain and the viscoplastic self-consistent theory of Molinari et al . The theoretical results are compared with the findings of optical and TEM microstructural analyses of 175 individual grains in polycrystals of Crevola dolomite that had been deformed in the temperature range 25–900 °C. There is broad agreement between experiment and theory from some viewpoints ( e.g. the expected mechanisms are operative and the stress axes of grains move in the senses which are predicted), but discrepancies also exist at both the macroscopic and microscopic level. Taking into account all grains that can be analyzed, the number of plastic deformation mechanisms observed averages to 1.9 per grain, which is below the value of 4.9 (for high temperature) and 4.3 (for low temperature) predicted from a viscoplastic Taylor model, counting those systems which contribute at least 10% to the total shear in each grain. It is closer to predictions from a viscoplastic self-consistent model with an average of 1.7 and 3.1 systems respectively. The heterogeneity which is caused by such a small number of slip systems, is partly expressed by brittle and grain boundary effects. In addition it is manifest as a sub-grainscale variability of slip activity and dislocation density that is at least equally important. The deformation mechanisms operative do not always agree with predictions based on Schmid factors which is mainly due to local interaction between grains and their neighbors.

Growth of voids in porous ductile materials at high strain rate

Abstract: A hollow‐sphere model, with temperature‐dependent viscoplastic material response, is developed to investigate the inertial and thermal effects on dynamic growth of voids in ductile materials. Theoretical analysis indicates that the inertial effect (kinetic energy of void growth) mainly dominates the behavior of the void growth in temperature‐dependent and high‐strain‐rate cases. Otherwise, the viscoplastic effect dominates and the inertial effect can be neglected. The rate of the dynamic growth of voids increases when the thermal effect is considered. An expression of the threshold stress for the void growth is obtained, which depends on the initial porosity, the porosity, the yield strength, the density of surface energy of voids, the initial temperature, and the melting temperature.