Showing papers on "Viscoplasticity published in 1998"

Dynamics of viscoplastic deformation in amorphous solids

Abstract: We propose a dynamical theory of low-temperature shear deformation in amorphous solids. Our analysis is based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. These numerical simulations reveal behavior typical of metallic glasses and other viscoplastic materials, specifically, reversible elastic deformation at small applied stresses, irreversible plastic deformation at larger stresses, a stress threshold above which unbounded plastic flow occurs, and a strong dependence of the state of the system on the history of past deformations. Microscopic observations suggest that a dynamically complete description of the macroscopic state of this deforming body requires specifying, in addition to stress and strain, certain average features of a population of two-state shear transformation zones. Our introduction of these state variables into the constitutive equations for this system is an extension of earlier models of creep in metallic glasses. In the treatment presented here, we specialize to temperatures far below the glass transition and postulate that irreversible motions are governed by local entropic fluctuations in the volumes of the transformation zones. In most respects, our theory is in good quantitative agreement with the rich variety of phenomena seen in the simulations. {copyright} {ital 1998} {ital The American Physical Society}

A plastic-damage concrete model for earthquake analysis of dams

Abstract: A new plastic-damage constitutive model for cyclic loading of concrete has been developed for the earthquake analysis of concrete dams. The rate-independent model consistently includes the effects of strain softening, represented by separate damage variables for tension and compression. A simple scalar degradation model simulates the effects of damage on the elastic stiffness and the recovery of stiffness after cracks close. To simulate large crack opening displacements, the evolution of inelastic strain is stopped beyond a critical value for the tensile damage variable. Subsequent deformation can be recovered upon crack closing. The rate-independent plastic-damage model forms the backbone model for a rate-dependent viscoplastic extension. The rate-dependent regularization is necessary to obtain a unique and mesh objective numerical solution. Damping is represented as a linear viscoelastic behaviour proportional to the elastic stiffness including the degradation damage. The plastic-damage constitutive model is used to evaluate the response of Koyna dam in the 1967 Koyna earthquake. The analysis shows two localized cracks forming and then joining at the change in geometry of the upper part of the dam. The upper portion of the dam vibrates essentially as rigid-body rocking motion after the upper cracks form, but the dam remains stable. The vertical component of ground motion influences the post-cracking response. © 1998 John Wiley & Sons, Ltd.

Elasto-viscoplastic constitutive equations for polycrystalline metals: Application to tantalum

Abstract: Strain-rate and temperature-dependent constitutive equations for polycrystalline metals which are capable of modeling the initial and evolving anisotropy in ductile metallic materials owing to the evolution of crystallographic texture are reviewed and then specialized to reproduce the recently published stress-strain response of commercially pure b.c.c. tantalum for strains up to 60%, at strain rates from quasi-static to 30,000 s −1 , and temperatures from −200 to 525 °C (Hoge and Mukherjee, 1977; Vecchio, 1994; Nemat-Nasser and Isaacs, 1996). The constitutive equations have been implemented in a finite element program, and the computational capability is used to simulate the evolution of crystallographic texture in simple compression, plane-strain compression, and torsion under quasi-static conditions. A comparison of the predictions against corresponding experiments shows that the crystal plasticity-based model predicts the texture evolution and the macroscopic stress-strain curves satisfactorily. The computational capability is also used to simulate the dynamic Taylor rod-impact tests performed by Ting (1992) on pre-textured tantalum cylinders. The numerical simulations reasonably reproduce the final length and the ovalized macroscopic shape of the impact end of the cylinders observed in the experiments.

A constitutive equation for the elasto-viscoplastic deformation of glassy polymers

Abstract: Constitutive equations for finite elastic-plastic deformation of polymers and metals are usually formulated by assuming an isotropic relation between the Jaumann rate of the Cauchy-stress tensor and the strain-rate tensor. However, the Jaumann-stress rate is known to display spurious non- physical behaviour in the elastic region. Replacing the Jaumann-stress rate by a Truesdell-stress rate results in an adequate description in the elastic region, but gives rise to a volume decrease during plastic flow in tensile deformation. In this paper a "compressible-Leonov model" is introduced, in which the elastic volume response is rigorously separated from the elasto-viscoplastic isochoric de- formation. This has the advantage that the model can be extended in a straightforward way to include a spectrum of relaxation times. It is shown that in the limit of small elastic strains, the compressible Leonov model reduces to the Jaumann-stress rate model, but diverges from the Truesdell-stress rate model. Finally, a comparison is made of the above mentioned models in a homogeneous uniaxial ten- sile test and a homogeneous plane-stress shear test, using polycarbonate (PC) as a model system. All models considered in this paper are "single mode" models (i.e. one relaxation time), and, therefore, cannot describe the full (non)linear viscoelastic region, nor the strain-hardening or strain-softening response.

Inelastic deformation of polycrystalline face centered cubic materials by slip and twinning

Abstract: There have been considerable recent advances in the understanding of anisotropy due to crystallographic texturing, and a reasonably successful elasto-viscoplasticity theory for the deformation of face-centeredcubic (f.c.c.) single crystals and polycrystals with high stacking fault energies is now at hand. The high stacking fault energy f.c.c. materials (e.g. Cu, Al) deform predominantly by crystallographic slip. In contrast, for materials with low stacking energies, e.g. α-brass, in addition to crystallographic slip, deformation twinning plays an important role in maintaining generalized plastic flow. A direct manifestation of twinning is the different crystallographic texture that is observed in 70−30 brass as compared to pure copper. In this paper we formulate a rate-independent constitutive model which accounts for both slip and twinning. We have also developed a new scheme to determine the active systems and the shear increments on the active slip and twin systems. We have implemented our constitutive equations and computational procedures in the finite-element program ABAQUS/Explicit (1995). By using comparisons between model predictions and macroscopically-measured stress-strain curves and texture evolution we have deduced information about the values of the single-crystal parameters associated with slip and twin system deformation resistances and hardening due to slip and twinning. We show that our model is able to reproduce both the experimentally measured pole figures and the stress strain curves in plane strain compression for α-brass. With the model so calibrated, we show that the predictions for the texture and stress-strain curves from the model are also in reasonably good agreement with experiments in simple compression. We have also evaluated the applicability of a Taylor-type model for combined slip and twinning. Our calculations show that for the high-symmetry f.c.c. brass, a Taylor-type model for crystals deforming by combined slip and twinning is able to reasonably well predict the macroscopic stress-strain curves and crystallographic texture evolution. Our calculations show that in plane strain as well as simple compression, the crystallographic texture that develops is a result of lattice rotation due to both slip and twinning, and that as suggested by Wassermann (1963), in contrast to copper which does not twin under normal circumstances, it is twinning which is responsible for the brass-type texture that is observed in f.c.c. metals with low stacking fault energies.

Material Instabilities in Solids

Abstract: Introduction to Material Instabilities in Solids (E. van der Giessen & R. de Borst). Stability of Layered Geological Structures: An Asymptotic Solution (Y. Leroy & N. Triantafyllidis). Analysis of Shear Failure in Concrete Materials (K. William, et al.). On the Effects of Inertial Coupling on the Wave-Speeds of Elastic-Plastic Fluid-Saturated Porous Media (B. Loret & E. Rizzi). Microstructured Solids: Non-Linear Model and Analysis of Magneto-Elastic Wave Processes (V. Erofeyev & S. Kovalev). Thermodynamics of Crystal Viscoplasticity and Instability Phenomena (P. Perzyna). Instability Issues in Single Crystal Plasticity (P. Steinmann). On the Use of Strain-Softening Models for the Simulation of Strong Discontinuities in Solids (J. Oliver, et al.). Thermomechanics Based Theory and Analysis of Cracking Localization in Concrete Dam under Earthquake Excitation (H. Horii, et al.). Localisation Patterns in Ductile and Brittle Geomaterials (J. Desrues).In-Plane Crushing of a Polymeric Honeycomb (S. Papka & S. Kyriakides). Experimental and Numerical Investigation of Size Scale Effects in Concrete Fracture (M. van Vliet & J. van Mier). Post-Peak Behaviour of Rocks and Natural Building Stones in Uniaxial Compression (I. Vardoulakis, et al.). Inelastic Deformation of F.C.C. Single Crystals by Slip and Twinning (A. Staroselsky & L. Anand). Effects of Strain Paths on Sheet Metal Limit Strains (P. Wu, et al.). Three-Dimensional Analysis of Localized Necking (A. Benallal). Effects of Heterogeneities and Localization on Polymer Deformation and Recovery (M. Boyce & C. Chui). Strain Localization and Void Growth in Polymers (A. Steenbrink & E. van der Giessen). Nonaffine Network Model for Glassy Polymer and Prediction of Instability Propagation (Y. Tomita & T. Adachi). Damage Localisation in Short Fibre Cementitious Composites (B. Karihaloo & J. Wang). Fracture Instabilities in Heterogeneous Materials: Brittleness, Size Effects and Fractality (A. Carpinteri). Compression Fracture-Mechanics of Damage Localization and Size Effect (Z. Bazant). Nonlinear Modelling of Geomaterials and Self-Organization Phenomena (V. Nikolaevskiy). Quasi-Static and Dynamic Characteristics of Strain Gradient Dependent Non-Local Constitutive Models (F. Oka, et al.). Higher-Order Damage Models for the Analysis of Fracture in Quasi-Brittle Materials (M. Geers, et al.). On Gradient Regularization for Numerical Analyses in the Presence of Damage (C. Comi & L. Driemeier). Localisation of Damage in Quasi-Brittle Materials and Influence of Chemically Activated Damage (G. Pijaudier-Cabot, et al.). Nonlocal Damage Effects on Plastic Flow Localization under Dynamic Loading (V. Tvergaard & A. Needleman). Instabilities and Size Effects in Plasticity: Continuum and Dislocation Approaches (H. Zbib). Macroscopic Modelling of Stationary and Propagative Instabilities (L. Sluys & W. Wang). A Discussion of Strain Gradient Plasticity Theories and Application to Shear Bands (N. Fleck & J. Hutchinson). A Beam Theory for Gradient Continua (H.-B. Muhlhaus & P. Hornby). Recent Progress on Gradient Theory and Applications (E. Aifantis). Index.

Testing and modeling high strain rate behavior of polymeric composites

Abstract: The present study was aimed at modeling the high strain rate response of the unidirectional S2Glass/8553-40 polymeric composite material system. High strain rate experiments were conducted on a split Hopkinson pressure bar (SHPB), on balanced symmetric laminates from which the stress, strain and strain rate histories within the laminates were recovered. Strain rates of the order of 1000/s were achieved in the specimen. A 3-D viscoplasticity model was used to describe the high strain rate response of the composite. A computer code was written to incorporate the constitutive equations into the finite element code ABAQUS, which was subsequently used to analyze the dynamic response of the composite specimen in the high strain rate SHPB experiment. Comparison of the analysis result with experimental data indicates that the viscoplasticity model determined using low strain rate testing can still be valid for modeling the high strain rate responses.

Squeeze-flow of a Herschel–Bulkley fluid

Abstract: Squeeze-flow experiments of a Herschel–Bulkley material between two rigid plates, investigated both experimentally and computationally by Adams et al. (J. Non-Newtonian Fluid Mech. 71 (1997) 41) are compared against an approximate analysis for generalised Newtonian fluids presented by Sherwood and Durban (J. Non-Newtonian Fluid Mech. 62 (1996) 35), for the case in which the interface between the material and the plates is lubricated. The analysis presented here assumes a rigid-viscoplastic material, rather than the elastic-viscoplastic material of Adams et al., but the viscoplastic model for flow is identical. However, the shear stress boundary condition at the plates differs from the Coulomb friction law of Adams et al.: the shear stress is here assumed to be a constant fraction of the effective stress (and consequently turns out to be independent of position). A simple expression for the total force required to push the plates together is obtained for the case when friction at the plates is small. Agreement between this expression and the experimentally-measured force is good at high strain, though the elastic deformation observed prior to yield is not captured by the rigid-viscoplastic analysis.

Analytical and Experimental Evaluation of Nonlinear Viscoelastic-Viscoplastic Composite Laminates under Creep, Creep-Recovery, Relaxation and Ramp Loading

Abstract: A numerical procedure to predict long-term laminate properties of fibre reinforced composite materials was developed. In the procedure, we extended the classical laminate theory to include time related response of composite materials for membrane and flexural loading. The material response, dependent on the stress history, was modelled using the Schapery single integral equation. The integrals were handled by an approximate method that uses the Prony's series and only requires the storing of the current stress and some internal strain components. An efficient semi-direct time-integration scheme, providing a stable integration process, was derived to be included in the numerical procedure. Comparisons of theoretical results were made with experiments conducted on composite materials under creep-creep recovery, relaxation and ramp loading.

Calculation of intergranular stresses based on a large-strain viscoplastic self-consistent polycrystal model

Abstract: We present here an extension of the viscoplastic self-consistent (VPSC) polycrystal model for the calculation of the intergranular Cauchy stresses in an aggregate. This method, which is based on the self-consistent treatment of incompressible aggregates proposed in 1987 by Molinari et al, is formulated using the inclusion formalism and full anisotropy is incorporated into it. The complete stress state in the grains is obtained by computing the deviatoric and the hydrostatic local deviations with respect to the overall corresponding magnitudes applied to the polycrystal. The extended VPSC model, followed by an elastic self-consistent unloading, is used to obtain the intergranular residual strains in the aggregate after large plastic deformation. The texture evolution and the hardening of the material are explicitly taken into account in the model. As an application, the model is used to predict intergranular residual states in Incoloy-800 plate after uniaxial deformation.

Behaviour of granular materials

Abstract: P-Y. Hicher: Experimental Behaviour of Granular Materials.- J.P. Bardet: Introduction to Computational Granular Mechanics.- B. Cambou: Micromechanical Approach in Granular Materials.- D. Kolymbas: Coupling: Pore Fluid-Grains Interaction.- D. Kolymbas, I. Herle: Hypoplasticity: a Framework to Model Granular Materials.- Z. Mroz: Elastoplastic and Viscoplastic Constitutive Models for Granular Materials.- I. Vardoulakis: Strain Localization in Granular Materials.

Large deformation rheological behaviour of a model particle gel

Abstract: We report on some aspects of the large deformation rheology of model three-dimensional networked particle gels. Model gels with a particle volume fraction of 5% are formed by aggregation in a Brownian dynamics simulation from soft spherical particles incorporating flexible surface-to-surface bonds that restrict the subsequent angular reorganization and infer structural stability on the resulting percolating, fractal structure. The interaction potential allows some control over the final fractal dimension of the gel and bonds may be either breakable or essentially permanent depending on the choice of parameters. The use of continuous potentials allows the rheology to be studied at constant strain-rate and at constant stress by the incorporation of a homogeneous strain algorithm. For systems with ‘permanent’ bonds, strain hardening is observed when the strain-rate is very low compared with the structural relaxation time. At relatively high strain-rates the stress response is more nearly proportional to the strain. These systems also show strain recovery when the stress is removed. For systems with short breakable bonds, a yield stress is observed at slow constant strain. Here, we have studied the yielding behaviour of these systems by applying a steadily increasing stress and we find that, under these conditions, the structure degrades in three distinct stages. The initial breakage of bonds does not immediately disrupt the gel but allows some viscoelastic flow. This is followed by breakdown into a small number of relatively large aggregates. The ensuing viscoplastic flow causes the further rupture of aggregates that culminates in a catastrophic break-up to smaller entities at a critical point that presages true viscous flow. These transitions between viscoelastic and viscoplastic flow and between viscoplastic and viscous flow correspond to the static and dynamic yield stresses that have been observed experimentally in colloidal systems at high volume fraction. The oscillatory response for systems with permanent bonds shows non-linear behaviour expressed as overtone modes for strain amplitudes in excess of 0.05. The effective modulus for these systems also increases with strain amplitude while for systems with breakable bonds the modulus decreases or passes through a maximum as a consequence of structural decay. This behaviour compares favourably with experimental studies on chemical and physical gels.

Squeezing Flow of Viscoplastic Fluids Subject to Wall Slip

Abstract: Polymer processing operations such as compression molding, sheet forming and injection molding can be modeled by squeezing flows between two approaching parallel surfaces in relative motion. Squeezing flows also find applications in the modeling of lubrication systems, and in the determination of rheological properties. Here, analytical solutions are developed for the constant-speed squeezing flow of viscoplastic fluids. It is assumed that the fluid is purely viscous, and hence viscoelastic effects unimportant. The rheological behavior of the viscoplastic fluids is represented by the Herschel-Bulkley viscosity function. The deformation behavior of commonly encountered viscoplastic fluids is generally complicated by the presence of wall slip at solid walls, which is a function of the wall shear stress. The slip coefficient that relates the slip velocity to the shear stress is affected by the material of construction and also the roughness of the solid surfaces, leading to the possibility of different slip coefficients at various solid surfaces. The model developed in this study accommodates the use of different slip coefficients at different solid surfaces. The accuracy of the solutions is established, and the effects of various parameters such as slip coefficient and apparent yield stress are examined. The solutions provide useful design expressions that can be utilized for squeezing flows of viscoplastic fluids, with or without wall slip at the solid boundaries.

Chip scale package (CSP) solder joint reliability and modeling

Abstract: A viscoplastic constitutive model was used to analyze the thermally induced plastic and creep deformation and low cycle fatigue behaviour of the solder joints in chip scale packages (CSP) mounted on PCBs. The time-dependent and time-independent viscoplastic strain rate and plastic hardening work factors of solder material were used in 2D plane strain finite element models. The viscoplastic strain rate data was fitted to the viscoplastic flow equation. The plastic hardening factors were considered in the evolution equation. Finite element models, incorporating the viscoplastic flow and evolution equations, were verified by temperature cycling tests on assembled CSPs. The effect of the cyclic frequency, dwell time, and temperature ramp rate on the response of the viscoplastic deformation was studied for a tapeless lead-on-chip (LOC) CSP and a flexible substrate CSP. The ramp rate significantly affects the equivalent stress range in solder joints, while a dwell time in excess of 10 minutes per half cycle does not result in increased strain range. The failure data from the experiments was fitted to the Weibull failure distribution and the Weibull parameters were extracted. After satisfactory correlation between experiment and model was observed, the effect of material properties and package design variables on the fatigue life of solder joints in CSPs was investigated, and the primary factors affecting solder fatigue life were subsequently presented. Furthermore, a simplified model was proposed to predict the solder fatigue life in CSPs.

Large viscoplastic deformations of shells. Theory and finite element formulation

Abstract: The paper is concerned with large viscoplastic deformations of shells when the constitutive model is based on the concept of unified evolution equations. Specifically the model due to Bodner and Partom is modified so as to fit in the frame of multiplicative viscoplasticity. Although the decomposition of the deformation gradient in elastic and inelastic parts is employed, no use is made of the concept of the intermediate configuration. A logarithmic elastic strain measure is used. An algorithm for the evaluation of the exponential map for nonsymmetric arguments as well as a closed form of the tangent operator are given. On the side of the shell theory itself, the shell model is chosen so as to allow for the application of a three-dimensional constitutive law. The shell theory, accordingly, allows for thickness change and is characterized by seven parameters. The constitutive law is evaluated pointwise over the shell thickness to allow for general cyclic loading. An enhanced strain finite element method is given and various examples of large shell deformations including loading-unloading cycles are presented.

Viscous hardening plasticity for concrete in high-rate dynamics

Abstract: This paper presents a constitutive model for concrete in high-rate dynamics. The main feature outlined in this paper concerns the modeling of strength enhancement attributed to rate effects at the macrolevel of material description. It is accounted for in the constitutive modeling of strain and stresses within the theory of elastoplasticity by extending the classical plastic model to viscous hardening plasticity. Rate effects are associated with a viscous phenomenon occurring within the pores of concrete. The model is worked out in a thermodynamic framework that allows one to account for couplings between viscous and plastic evolutions. The determination of the material parameters associated with the viscous phenomenon is achieved by using available data from dynamic direct tensile tests. By way of example, the three-parameter Willam-Warnke plasticity criterion is adapted to account for isotropic viscous hardening. Finally, some applications are shown to illustrate the capabilities of the model to capture the basic features of concrete behavior in high-rate dynamics, with a minimum of material parameters of clear physical significance and accessible by existing material tests.

Determination of the true stress–strain behaviour of polypropylene

Abstract: The true tensile and compressive stress–strain curves for a typical semicrystalline polymer (polypropylene) were constructed with a new experimental technique. This is based on a non-contact method of strain measurement along the specimen gauge length. The viscoplastic behaviour obtained in this manner was then described with a nonlinear viscoelastic constitutive model mentioned analytically elsewhere. This consideration leads to a satisfactory description of yield and post yield behaviour, including strain softening, and strain hardening. The rate effect was also predicted with a high accuracy.