Showing papers on "Viscoplasticity published in 2004"

A unified treatment of strain gradient plasticity

Abstract: A theoretical framework is presented that has potential to cover a large range of strain gradient plasticity effects in isotropic materials. Both incremental plasticity and viscoplasticity models a ...

A physical model of the twinning-induced plasticity effect in a high manganese austenitic steel

Abstract: The steel Fe–22 wt.% Mn–0.6 wt.% C exhibits a low stacking fault energy (SFE) at room temperature. This rather low value promotes mechanical twinning along with strain which is in competition with dislocation gliding, the so called twinning-induced plasticity effect. The proposed modeling of the mechanical behavior introduces the formation of mechanical microtwins in a viscoplasticity framework based on dislocation glide at the mesoscopic scale in the case of a simple tensile test. The important parameter is the mean free path of the dislocations between twins, whose reduction explains the high hardening rate (by a dynamical Hall–Petch-like effect). It takes into account the typical organization of microtwins observed in electron microscopy (geometrical organization by using a twin-slip intersection matrix). To take into account the polycrystalline disorder, the macroscopic flow stress is calculated by assuming that the deformation work is equal in each grain for each strain step. This model gives an intermediate rule between Taylor and Sachs approximations and is simpler to compute than self-consistent methods. The parameters for gliding are first fitted on results at intermediate temperatures (without twinning), and the whole modeling is then correlated at room temperature. The simulated results (microstructure and mechanical properties) are in good agreement with experience.

Inelastic Analysis of Solids and Structures

Abstract: An Introduction to the Incremental-Iterative Solution of Nonlinear Structural Problems.- Fundamental Notions of Metal Plasticity.- A General Procedure for Stress Integration and Applications in Metal Plasticity.- Creep and Viscoplasticity.- Plasticity of Geological Materials.- Large Strain Elastic-Plastic Analysis.

Elastic consequences of a single plastic event: A step towards the microscopic modeling of the flow of yield stress fluids

Abstract: With the eventual aim of describing flowing elasto-plastic materials, we focus here on the elementary process of such a flow, a plastic event, and compute the long-range perturbation it elastically induces in a medium submitted to a global shear strain. We characterize the effect of a nearby wall on this perturbation, and quantify the importance of finite-size effects. Although most of our explicit formulae refer to 2D situations, our statements hold for 3D situations as well.

Viscoelastic measurement techniques

Abstract: Methods for measuring viscoelastic properties of solids are reviewed The nature of viscoelastic response is first presented This is followed by a survey of time and frequency-domain considerations as they apply to mechanical measurements Subresonant, resonant, and wave methods are discussed, with applications

A study of the static yield stress in a binary Lennard-Jones glass

Abstract: The stress–strain relations and the yield behavior of a model glass (a 80:20 binary Lennard-Jones mixture) [W. Kob and H. C. Andersen, Phys. Rev. E 52, 4134 (1995)] is studied by means of molecular dynamics simulations. In a previous paper [F. Varnik, L. Bocquet, J.-L. Barrat, and L. Berthier, Phys. Rev. Lett. 90, 095702 (2003)] it was shown that, at temperatures below the glass transition temperature, Tg, the model exhibits shear banding under imposed shear. It was also suggested that this behavior is closely related to the existence of a (static) yield stress (under applied stress, the system does not flow until the stress σ exceeds a threshold value σy). A thorough analysis of the static yield stress is presented via simulations under imposed stress. Furthermore, using steady shear simulations, the effect of physical aging, shear rate and temperature on the stress–strain relation is investigated. In particular, we find that the stress at the yield point (the “peak”-value of the stress–strain curve) exh...

A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin

Abstract: This study develops a gradient theory of small-deformation viscoplasticity based on: a system of microforces consistent with its peculiar balance; a mechanical version of the second law that includes, via the microforces, work performed during viscoplastic flow; a constitutive theory that accounts for the Burgers vector through a free energy dependent on curl H p , with Hp the plastic part of the elastic–plastic decomposition of the displacement gradient. The microforce balance and the constitutive equations, restricted by the second law, are shown to be together equivalent to a nonlocal flow rule in the form of a coupled pair of second-order partial differential equations. The first of these is an equation for the plastic strain-rate E p in which the stress T plays a basic role; the second, which is independent of T, is an equation for the plastic spin W p . A consequence of this second equation is that the plastic spin vanishes identically when the free energy is independent of curl H p , but not generally otherwise. A formal discussion based on experience with other gradient theories suggests that sufficiently far from boundaries solutions should not differ appreciably from classical solutions, but close to microscopically hard boundaries, boundary layers characterized by a large Burgers vector and large plastic spin should form. Because of the nonlocal nature of the flow rule, the classical macroscopic boundary conditions need be supplemented by nonstandard boundary conditions associated with viscoplastic flow. As an aid to solution, a variational formulation of the flow rule is derived. Finally, we sketch a generalization of the theory that allows for isotropic hardening resulting from dissipative constitutive dependences on ∇ E p .

Characterization of Models for Time-Dependent Behavior of Soils

Abstract: Different classes of constitutive models have been developed to capture the time-dependent viscous phenomena (creep, stress relaxation, and rate effects) observed in soils. Models based on empirica...

The Finite Element Method for Three-Dimensional Thermomechanical Applications

Abstract: Preface.Nomenclature.1 Displacements, Strain, Stress and Energy.1.1 The Reference State.1.2 The Spatial State.1.3 Strain Measures.1.4 Principal Strains.1.5 Velocity.1.6 Objective Tensors.1.7 Balance Laws.1.7.1 Conservation of mass.1.7.2 Conservation of momentum.1.7.3 Conservation of angular momentum.1.7.4 Conservation of energy.1.7.5 Entropy inequality.1.7.6 Closure.1.8 Localization of the Balance Laws.1.8.1 Conservation of mass.1.8.2 Conservation of momentum.1.8.3 Conservation of angular momentum.1.8.4 Conservation of energy.1.8.5 Entropy inequality.1.9 The Stress Tensor.1.10 The Balance Laws in Material Coordinates.1.10.1 Conservation of mass.1.10.2 Conservation of momentum.1.10.3 Conservation of angular momentum.1.10.4 Conservation of energy.1.10.5 Entropy inequality.1.11 The Weak Form of the Balance of Momentum.1.11.1 Formulation of the boundary conditions (material coordinates).1.11.2 Deriving the weak form from the strong form (material coordinates).1.11.3 Deriving the strong form from the weak form (material coordinates).1.11.4 The weak form in spatial coordinates.1.12 The Weak Form of the Energy Balance.1.13 Constitutive Equations.1.13.1 Summary of the balance equations.1.13.2 Development of the constitutive theory.1.14 Elastic Materials.1.14.1 General form.1.14.2 Linear elastic materials.1.14.3 Isotropic linear elastic materials.1.14.4 Linearizing the strains.1.14.5 Isotropic elastic materials.1.15 Fluids.2 Linear Mechanical Applications.2.1 General Equations.2.2 The Shape Functions.2.2.1 The 8-node brick element.2.2.2 The 20-node brick element.2.2.3 The 4-node tetrahedral element.2.2.4 The 10-node tetrahedral element.2.2.5 The 6-node wedge element.2.2.6 The 15-node wedge element.2.3 Numerical Integration.2.3.1 Hexahedral elements.2.3.2 Tetrahedral elements.2.3.3 Wedge elements.2.3.4 Integration over a surface in three-dimensional space.2.4 Extrapolation of Integration Point Values to the Nodes.2.4.1 The 8-node hexahedral element.2.4.2 The 20-node hexahedral element.2.4.3 The tetrahedral elements.2.4.4 The wedge elements.2.5 Problematic Element Behavior.2.5.1 Shear locking.2.5.2 Volumetric locking.2.5.3 Hourglassing.2.6 Linear Constraints.2.6.1 Inclusion in the global system of equations.2.6.2 Forces induced by linear constraints.2.7 Transformations.2.8 Loading.2.8.1 Centrifugal loading.2.8.2 Temperature loading.2.9 Modal Analysis.2.9.1 Frequency calculation.2.9.2 Linear dynamic analysis.2.9.3 Buckling.2.10 Cyclic Symmetry.2.11 Dynamics: The alpha-Method.2.11.1 Implicit formulation.2.11.2 Extension to nonlinear applications.2.11.3 Consistency and accuracy of the implicit formulation.2.11.4 Stability of the implicit scheme.2.11.5 Explicit formulation.2.11.6 The consistent mass matrix.2.11.7 Lumped mass matrix.2.11.8 Spherical shell subject to a suddenly applied uniform pressure.3 Geometric Nonlinear Effects.3.1 General Equations.3.2 Application to a Snapping-through Plate.3.3 Solution-dependent Loading.3.3.1 Centrifugal forces.3.3.2 Traction forces.3.3.3 Example: a beam subject to hydrostatic pressure.3.4 Nonlinear Multiple Point Constraints.3.5 Rigid Body Motion.3.5.1 Large rotations.3.5.2 Rigid body formulation.3.5.3 Beam and shell elements.3.6 Mean Rotation.3.7 Kinematic Constraints.3.7.1 Points on a straight line.3.7.2 Points in a plane.3.8 Incompressibility Constraint.4 Hyperelastic Materials.4.1 Polyconvexity of the Stored-energy Function.4.1.1 Physical requirements.4.1.2 Convexity.4.1.3 Polyconvexity.4.1.4 Suitable stored-energy functions.4.2 Isotropic Hyperelastic Materials.4.2.1 Polynomial form.4.2.2 Arruda-Boyce form.4.2.3 The Ogden form.4.2.4 Elastomeric foam behavior.4.3 Nonhomogeneous Shear Experiment.4.4 Derivatives of Invariants and Principal Stretches.4.4.1 Derivatives of the invariants.4.4.2 Derivatives of the principal stretches.4.4.3 Expressions for the stress and stiffness for three equal eigenvalues.4.5 Tangent Stiffness Matrix at Zero Deformation.4.5.1 Polynomial form.4.5.2 Arruda-Boyce form.4.5.3 Ogden form.4.5.4 Elastomeric foam behavior.4.5.5 Closure.4.6 Inflation of a Balloon.4.7 Anisotropic Hyperelasticity.4.7.1 Transversely isotropic materials.4.7.2 Fiber-reinforced material.5 Infinitesimal Strain Plasticity.5.1 Introduction.5.2 The General Framework of Plasticity.5.2.1 Theoretical derivation.5.2.2 Numerical implementation.5.3 Three-dimensional Single Surface Viscoplasticity.5.3.1 Theoretical derivation.5.3.2 Numerical procedure.5.3.3 Determination of the consistent elastoplastic tangent matrix.5.4 Three-dimensional Multisurface Viscoplasticity: the Cailletaud Single Crystal Model.5.4.1 Theoretical considerations.5.4.2 Numerical aspects.5.4.3 Stress update algorithm.5.4.4 Determination of the consistent elastoplastic tangent matrix.5.4.5 Tensile test on an anisotropic material.5.5 Anisotropic Elasticity with a von Mises-type Yield Surface.5.5.1 Basic equations.5.5.2 Numerical procedure.5.5.3 Special case: isotropic elasticity.6 Finite Strain Elastoplasticity.6.1 Multiplicative Decomposition of the Deformation Gradient.6.2 Deriving the Flow Rule.6.2.1 Arguments of the free-energy function and yield condition.6.2.2 Principle of maximum plastic dissipation.6.2.3 Uncoupled volumetric/deviatoric response.6.3 Isotropic Hyperelasticity with a von Mises-type Yield Surface.6.3.1 Uncoupled isotropic hyperelastic model.6.3.2 Yield surface and derivation of the flow rule.6.4 Extensions.6.4.1 Kinematic hardening.6.4.2 Viscoplastic behavior.6.5 Summary of the Equations.6.6 Stress Update Algorithm.6.6.1 Derivation.6.6.2 Summary.6.6.3 Expansion of a thick-walled cylinder.6.7 Derivation of Consistent Elastoplastic Moduli.6.7.1 The volumetric stress.6.7.2 Trial stress.6.7.3 Plastic correction.6.8 Isochoric Plastic Deformation.6.9 Burst Calculation of a Compressor.7 Heat Transfer.7.1 Introduction.7.2 The Governing Equations.7.3 Weak Form of the Energy Equation.7.4 Finite Element Procedure.7.5 Time Discretization and Linearization of the Governing Equation.7.6 Forced Fluid Convection.7.7 Cavity Radiation.7.7.1 Governing equations.7.7.2 Numerical aspects.References.Index.

Micromechanical modeling of the elastic-viscoplastic behavior of polycrystalline steels having different microstructures

Abstract: A micromechanical model based on a new and non-conventional self-consistent formulation has been applied to describe the elastic-viscoplastic behavior of steels with different microstructures in a wide range of strain rates. Good agreement between experimental and model predictions is found concerning the behavior of a ferritic single-phase interstitial free steel (IF) during quasi-static and dynamic tensile loadings. Due to the introduction of key physical parameters in the mathematical model, a good description is obtained of the differences observed between the constitutive behaviors of IF, high-strength low alloy (HSLA) and dual-phase (DP450, DP500 and DP600) steels. These differences concern strength, strain hardening as well as strain rate sensitivity.

Use of the Distinct Element Method to Model the Deformation Behavior of an Idealized Asphalt Mixture

Abstract: This paper investigates the use of distinct element modelling to simulate the behavior of a highly idealized bituminous mixture in an uniaxial compressive creep test. The effect of bitumen is represented as shear and normal contact stiffnesses. Elastic contact properties have been used to investigate the effect of sample size and the effect of the values of the shear and normal contact stiffnesses on bulk material properties. It was found that a sample containing at least 4,500 particles is required for Young's modulus and Poisson's ratio to be within 2% of the values calculated using a much larger number of particles. The bulk modulus was found to be linearly dependent on the normal contact stiffness and independent of the shear contact stiffness. Poisson's ratio was found to be dependent on only the ratio of the shear contact stiffness to the normal contact stiffness. A simple elasto-visco-plastic Burger's model was introduced to give time dependent shear and normal contact stiffnesses.

Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals

Abstract: A recently developed “second-order” homogenization procedure (Ponte Castaneda (J. Mech. Phys. Solids 50 (2002a, b) 737, 759)) is extended to viscoplastic polycrystals and applied to compute the effective response of a certain special class of isotropic polycrystals. The method itself reduces to a simple expression requiring the computation of the averages of the stress field and the covariances of its fluctuations over the various grain orientations in an optimally selected “linear comparison polycrystal”. Therefore, the method not only allows the determination of the effective behavior of the polycrystal, but as a byproduct also yields information on the heterogeneity of the stress and strain-rate fields within the polycrystal. An application is given for a model 2-dimensional, isotropic polycrystal with power-law behavior for the constituent grains. The resulting predictions for the effective behavior are found to satisfy sharp bounds available from the literature and to be consistent with the results of recent numerical simulations. The associated averages and fluctuations of the stresses and strain rates are found to depend strongly on the strain-rate sensitivity (i.e., nonlinearity) and grain anisotropy. In particular, the stress and strain-rate fluctuations were found to grow and become strongly anisotropic with increasing values of the nonlinearity and grain anisotropy parameters.

Linear and nonlinear viscoelastic analysis of the microstructure of asphalt concretes

Abstract: The paper at hand presents a methodology for analyzing the viscoelastic behavior of asphalt concretes, whose microstructure is captured through two-dimensional imaging techniques. The paper describes the viscoelastic behavior of the binder through mechanistic models fitted to rheological data obtained at different strain levels. The resulting binder stress-strain behavior is computed through a convolution integral approach and implemented into a subroutine defining material behavior in a commercially available finite element program. The use of a convolution integral approach is shown to facilitate incorporating the binder nonlinear viscoelatic behavior in the analysis of the asphalt concrete microstructure response. This is conducted by assigning the binder model constants as a function of strain level. The model is tested by comparing asphalt concrete shear modulus G* predictions to earlier predictions obtained with a generalized piecewise linear viscoelastic model, as well as measurements obtained with a simple shear tester. The model is used to explain some of the discrepancies observed between experimentally obtained axial and shear dynamic moduli.

Experimental and Three-Dimensional Finite Element Study of Scratch Test of Polymers at Large Deformations

Abstract: An experimental and numerical study of the scratch test on polymers near their surface is presented. The elastoplastic response of three polymers is compared during scratch tests at large deformations: polycarbonate, a thermosetting polymer and a sol-gel hard coating composed of a hybrid matrix (thermosetting polymer-mineral) reinforced with oxide nanoparticles. The experiments were performed using a nanoindenter with a conical diamond tip having an included angle of 30 deg and a spherical radius of 600 nm. The observations obtained revealed that thermosetting polymers have a larger elastic recovery and a higher hardness than polycarbonate. The origin of this difference in scratch resistance was investigated with numerical modelling of the scratch test in three dimensions. Starting from results obtained by Bucaille (J. Mat. Sci., 37, pp. 3999-4011, 2002) using an inverse analysis of the indentation test, the mechanical behavior of polymers is modeled with Young's modulus for the elastic part and with the G'sell-Jonas' law with an exponential strain hardening for the viscoplastic part. The strain hardening coefficient is the main characteristic parameter differentiating the three studied polymers. Its value is equal to 0.5, 4.5, and 35, for polycarbonate, the thermosetting polymer and the reinforced thermosetting polymer, respectively. Firstly, simulations reveals that plastic strains are higher in scratch tests than in indentation tests, and that the magnitude of the plastic strains decreases as the strain hardening increases. For scratching on polycarbonate and for a penetration depth of 0.5 μm of the indenter mentioned above, the representative strain is equal to 124%. Secondly, in agreement with experimental results, numerical modeling shows that an increase in the strain hardening coefficient reduces the penetration depth of the indenter into the material and decreases the depth of the residual groove, which means an improvement in the scratch resistance.

A selfconsistent formulation for the prediction of the anisotropic behavior of viscoplastic polycrystals with voids

Abstract: In this work we consider the presence of ellipsoidal voids inside polycrystals subjected to large strain deformation. For this purpose, the originally incompressible viscoplastic selfconsistent (VPSC) formulation of Lebensohn and Tome (Acta Metall. Mater. 41 (1993) 2611) has been extended to deal with compressible polycrystals. In doing this, both the deviatoric and the spherical components of strain-rate and stress are accounted for. Such an extended model allows us to account for the void and for porosity evolution, while preserving the anisotropy and crystallographic capabilities of the VPSC model. The formulation can be adjusted to match the Gurson model, in the limit of rate-independent isotropic media and spherical voids. We present several applications of this extended VPSC model, which address the coupling between texture, plastic anisotropy, void shape, triaxiality, and porosity evolution.

Velocity Profiles in Slowly Sheared Bubble Rafts

Abstract: Measurements of average velocity profiles in a bubble raft subjected to slow, steady shear demonstrate the coexistence between a flowing state and a jammed state similar to that observed for three-dimensional foams and emulsions [P. Coussot et al., Phys. Rev. Lett. 88, 218301 (2002)]. For sufficiently slow shear, the flow is generated by nonlinear topological rearrangements. We report on the connection between this short-time motion of the bubbles and the long-time averages. We find that velocity profiles for individual rearrangement events fluctuate, but a smooth, average velocity is reached after averaging over only a relatively few events.

Fundamental structure of steady plastic shock waves in metals

Abstract: The propagation of steady plane shock waves in metallic materials is considered. Following the constitutive framework adopted by R. J. Clifton [Shock Waves and the Mechanical Properties of Solids, edited by J. J. Burke and V. Weiss (Syracuse University Press, Syracuse, N.Y., 1971), p. 73] for analyzing elastic–plastic transient waves, an analytical solution of the steady state propagation of plastic shocks is proposed. The problem is formulated in a Lagrangian setting appropriate for large deformations. The material response is characterized by a quasistatic tensile (compression) test (providing the isothermal strain hardening law). In addition the elastic response is determined up to second order elastic constants by ultrasonic measurements. Based on this simple information, it is shown that the shock kinetics can be quite well described for moderate shocks in aluminum with stress amplitude up to 10 GPa. Under the later assumption, the elastic response is assumed to be isentropic, and thermomechanical coupling is neglected. The model material considered here is aluminum, but the analysis is general and can be applied to any viscoplastic material subjected to moderate amplitude shocks. Comparisons with experimental data are made for the shock velocity, the particle velocity and the shock structure. The shock structure is obtained by quadrature of a first order differential equation, which provides analytical results under certain simplifying assumptions. The effects of material parameters and loading conditions on the shock kinetics and shock structure are discussed. The shock width is characterized by assuming an overstress formulation for the viscoplastic response. The effects on the shock structure of strain rate sensitivity are analyzed and the rationale for the J. W. Swegle and D. E. Grady [J. Appl. Phys. 58, 692 (1985)] universal scaling law for homogeneous materials is explored. Finally, the ability to deduce information on the viscoplastic response of materials subjected to very high strain rates from shock wave experiments is discussed.