Showing papers on "Viscoplasticity published in 2000"

Continuum Mechanics and Theory of Materials

Abstract: 1 Kinematics.- 2 Balance Relations of Mechanics.- 3 Balance Relations of Thermodynamics.- 4 Objectivity.- 5 Classical Theories of Continuum Mechanics.- 6 Experimental Observation and Mathematical Modelling.- 7 General Theory of Mechanical Material Behaviour.- 8 Dual Variables.- 9 Elasticity.- 10 Viscoelasticity.- 11 Plasticity.- 12 Viscoplasticity.- 13 Constitutive Models in Thermomechanics.- References.

On the plasticity of single crystals: free energy, microforces, plastic-strain gradients

Abstract: This study develops a general theory of crystalline plasticity based on classical crystalline kinematics; classical macroforces; microforces for each slip system consistent with a microforce balance; a mechanical version of the second law that includes, via the microforces, work performed during slip; a rate-independent constitutive theory that includes dependences on plastic strain-gradients. The microforce balances are shown to be equivalent to yield conditions for the individual slip systems, conditions that account for variations in free energy due to slip. When this energy is the sum of an elastic strain energy and a defect energy quadratic in the plastic-strain gradients, the resulting theory has a form identical to classical crystalline plasticity except that the yield conditions contain an additional term involving the Laplacian of the plastic strain. The field equations consist of a system of PDEs that represent the nonlocal yield conditions coupled to the classical PDE that represents the standard force balance. These are supplemented by classical macroscopic boundary conditions in conjunction with nonstandard boundary conditions associated with slip. A viscoplastic regularization of the basic equations that obviates the need to determine the active slip systems is developed. As a second aid to solution, a weak (virtual power) formulation of the nonlocal yield conditions is derived. As an application of the theory, the special case of single slip is discussed. Specific solutions are presented: one a single shear band connecting constant slip-states; one a periodic array of shear bands.

Grain-size effect in viscoplastic polycrystals at moderate strains

Abstract: This work deals with the prediction of grain-size dependent hardening in FCC and BCC polycrystalline metals at moderately high strains (2–30%). The model considers 3–D, polycrystalline aggregates of purely viscoplastic crystals, and simulates quasi-static deformation histories with a hybrid finite element method implemented for parallel computation. The hardening response of the individual crystals is considered to be isotropic, but modified to include a physically motivated measure of lattice incompatibility which is supposed to model, in the continuum setting, the resistance to plastic flow provided by lattice defects. The length-scale in constitutive response that is required on dimensional grounds appears naturally from physical considerations. The grain-size effect in FCC polycrystals and development of Stage IV hardening in a BCC material are examined. Though the grain-size does not enter explicitly into the constitutive model, an inverse relationship between the macroscopic flow stress and grain-size is predicted, in agreement with experimental results for deformation of FCC polycrystals having grain-sizes below 100 microns and at strains beyond the initial yield (>2%). The development of lattice incompatibility is further shown to predict a transition to Stage IV (linear) hardening upon saturation of Stage III (parabolic) hardening.

A study of through-thickness texture gradients in rolled sheets

Abstract: A method to simulate shear effects and through-thickness texture gradients in rolled sheet materials is introduced. The strain history during a rolling pass is idealized by superimposing a sine-shaped evolution of the \(\dot \varepsilon \)13 shear component to a plane-strain state. These generic strain histories are enforced in a visco-plastic self-consistent (VPSC) polycrystal deformation model to simulate texture evolution as a function of through-thickness position. The VPSC scheme is deemed superior to a full constraints (FC) or relaxed constraints (RC) approach, because it allows one to fully prescribe diagonal and shear-strain-rate components while still accounting for grain-shape effects. The idealized strain states are validated by comparison with deformation histories obtained through finite-element method (FEM) calculations. The through-thickness texture gradients are accounted for by introducing a relative variation of the sine-shaped \(\dot \varepsilon \)13 shear with respect to the plane-strain component. The simulation results are validated, in turn, by comparison with typical examples of through-thickness texture gradients observed experimentally in rolled plates and in sheets of fcc and bcc materials.

Coupling of a crystal plasticity finite-element model with a probabilistic cellular automaton for simulating primary static recrystallization in aluminium

Abstract: The paper presents a two-dimensional approach for simulating primary static recrystallization, which is based on coupling a viscoplastic crystal plasticity finite-element model with a probabilistic kinetic cellular automaton. The crystal plasticity finite-element model accounts for crystallographic slip and for the rotation of the crystal lattice during plastic deformation. The model uses space and time as independent variables and the crystal orientation and the accumulated slip as dependent variables. The ambiguity in the selection of the active slip systems is avoided by using a viscoplastic formulation that assumes that the slip rate on a slip system is related to the resolved shear stress through a power-law relation. The equations are cast in an updated Lagrangian framework. The model has been implemented as a user subroutine in the commercial finite-element code Abaqus. The cellular automaton uses a switching rule that is formulated as a probabilistic analogue of the linearized symmetric Turnbull kinetic equation for the motion of sharp grain boundaries. The actual decision about a switching event is made using a simple sampling nonMetropolis Monte Carlo step. The automaton uses space and time as independent variables and the crystal orientation and a stored energy measure as dependent variables. The kinetics produced by the switching algorithm are scaled through the mesh size, the grain boundary mobility, and the driving force data. The coupling of the two models is realized by: translating the state variables used in the finite-element plasticity model into state variables used in the cellular automaton; mapping the finite-element integration point locations on the quadratic cellular automaton mesh; using the resulting cell size, maximum driving force, and maximum grain boundary mobility occurring in the region for determining the length scale, time step, and local switching probabilities in the automaton; and identifying an appropriate nucleation criterion. The coupling method is applied to the two-dimensional simulation of texture and microstructure evolution in a heterogeneously deformed, high-purity aluminium polycrystal during static primary recrystallization, considering local grain boundary mobilities and driving forces.

Time and temperature dependence of the scratch properties of poly(methylmethacrylate) surfaces

Abstract: Most existing models describing the scratch properties of materials take into account forces acting at the interface between the material and a grooving tip, but do not consider the stress and strain properties of the material far beneath or ahead of the tip. In the case of polymer scratches, there are no models at all which take into account the viscoelastic viscoplastic behaviour of the material. In standard indentation tests with a non moving tip, the elastic plastic boundary and the limits of the region subjected to hydrostatic pressure beneath the tip are known. These models were used to analyse the geometry of the grooves left on the surface of a viscoelastic viscoplastic body by a moving cone-shaped diamond tip having a radius of about 40 μm. A new apparatus was built to control the velocity of the tip over the range 1 to 104 μm/s, at several different temperatures from −10°C to 100°C. The material was a commercial grade of cast poly(methylmethacrylate) (PMMA). The normal and tangential loads and groove size were used to evaluate the dynamic hardness, which behaved like a stress and temperature activated process. Values of the activation energy and volume of the dynamic hardness and of the interfacial shear stress were in good agreement with those usually attributed to the mechanical properties of PMMA.

Rate dependent constitutive relations based on Anand model for 92.5Pb5Sn2.5Ag solder

Abstract: A rate dependent constitutive model, the Anand model, was applied to represent the inelastic deformation behavior for a Pb-rich solder 92.5Pb5Sn2.5Ag used in electronic packaging and surface mount technology. This rate dependent model is a unified viscoplastic constitutive model using an internal state variable, the deformation resistance, to describe the averaged isotropic resistance to macroscopic plastic flow. In order to obtain the acquired data for the fitting of the material parameters of this unified model for 92.5Pb5Sn2.5Ag solder, a series of experiments of constant strain rate test and constant load creep test were conducted under isothermal conditions at different temperatures ranged from -65/spl deg/C to 250/spl deg/C. A procedure for the determination of material parameters was proposed in this paper. Model simulations and verifications revealed that there are good agreements between model predictions and experimental data. Moreover, some discussions on using this rate dependent model in the finite element simulation of stress/strain responses of solder joints under thermal fatigue loading were presented.

Uniaxial Ratchetting of 316FR Steel at Room Temperature— Part II: Constitutive Modeling and Simulation

Abstract: Uniaxial ratchetting experiments of 316FR steel at room temperature reported in Part 1 are simulated using a new kinematic hardening model which has two kinds of dynamic recovery terms. The model, which features the capability of simulating slight opening of stress-strain hysteresis loops robustly, is formulated by furnishing the Armstrong and Frederick model with the critical state of dynamic recovery introduced by Ohno and Wang (1993). The model is then combined with a viscoplastic equation, and the resulting constitutive model is applied successfully to simulating the experiments. It is shown that for ratchetting under stress cycling with negative stress ratio, viscoplasticity and slight opening of hysteresis loops are effective mainly in early and subsequent cycles, respectively, whereas for ratchetting under zero-to-tension only viscoplasticity is effective.

Viscoplastic Anand model for solder alloys and its application

Abstract: A viscoplastic constitutive model, the Anand model, in which plasticity and creep are unified and described by the same set of flow and evolutionary relations, was applied to represent the inelastic deformation behavior for solder alloys. After conducting creep tests and constant strain rate tests, the material parameters for the Anand model of the Pb‐rich content solder 92.5Pb5Sn2.5Ag were determined from the experimental data using a nonlinear fitting method. The material parameters for 60Sn40Pb, 62Sn36Pb2Ag and 96.5Sn3.5Ag solders were fitted from the conventional model in the literature where plasticity and creep are artificially separated. Model simulations and verifications reveal that there is good agreement between the model predictions and experimental data. Some discussion on this unified model is also presented. This viscoplastic constitutive model for solder alloys possesses some advantages over the separated model. The achieved Anand model has been applied in finite element simulation of stress/strain responses in solder joints for chip component, thin quad flat pack and flip‐chip assembly. The simulation results are in good agreement with the results in the literature. It is concluded that the Anand model could be recommended as a useful material model for solder alloys and can be used in the finite element simulation of solder joint reliability in electronic packaging and surface mount technology.

Uniaxial Ratchetting of 316FR Steel at Room Temperature— Part I: Experiments

Abstract: Uniaxial ratchetting characteristics of 316FR steel at room temperature are studied experimentally. Cyclic tension tests, in which maximum strain increases every cycle by prescribed amounts, are conducted systematically in addition to conventional monotonic, cyclic, and ratchetting tests. Thus hysteresis loop closure, cyclic hardening and viscoplasticity are discussed in the context of constitutive modeling for ratchetting. The cyclic tension tests reveal that very slight opening of hysteresis loops occurs, and that neither accumulated plastic strain nor maximum plastic strain induces significant isotropic hardening if strain range is relatively small. These findings are used to discuss the ratchetting tests. It is thus shown that uniaxial ratchetting of the material at room temperature is brought about by slight opening of hysteresis loops as well as by viscoplasticity, and that kinematic hardening governs almost all strain hardening in uniaxial ratchetting if stress range is not large.

Mechanics of Materials and Interfaces: The Disturbed State Concept

Abstract: INTRODUCTION Prelude Philosophical Motivation Reference States Engineering Materials and Matter Continuous , Discontinuous or Mixture Transformation and Self Adjustment Disturbed Sate Concept Disturbance and Damage Models DSC and Other Models Scope THE DISTURBED STATE CONCEPT: Preliminaries Introduction Engineering Behavior Mechanism Fully Adjusted State Characteristic Dimension Observed Behavior Formulation of DSC Alternative Formulations of DSC Material Element Composed of Two Materials DSC-Multi -Component System DSC For Porous Media Composite Materials Bonded Materials Self Organized Criticality RELATIVE INTACT AND FULLY ADJUSTED STATES AND DISTURBANCE Specializations Disturbance and Function Laboratory Tests Stiffening or Healing Representations of Disturbance Creep Behavior Rate Dependence Disturbance Based on Disorder (Entropy) and Free Energy Material Parameters DSC EQUATIONS AND SPECIALIZATIONS Relative Intact Response Fully Adjusted Response Specializations Thermal Effects Disturbance Models DSC With and Without Relative Motions Critical State for FA Response DSC Euqations with Critical State Strain Equations General Formulation Examples 1 to 4 THEORY OF ELASTICITY IN DSC Linear Elasticity Nonlinear Elasticity Relative Intact Behavior Fully Adjusted Behavior Disturbance Function Material Parameters Thermal Effects Examples 1 to 8 THEORY OF PLASTICITY IN DSC Mechanisms Theoretical Development Continuous Yielding or Hardening To Hierarchical Single Surface Models Incremental Equations Parameters and Determination from Laboratory Tests Thermoplasticity Examples 1 to 7 HIERARCHICAL SINGLE SURFACE PLASTICITY MODELS IN DSC Basic HISS Model Specializations of HISS Model Material Parameters Thermal Effects Rate Effects Repetitive Loading Derivation of Elastoplastic Equations Incremental Iterative Analysis Correction Procedures Thermoplasticity Examples including Validations 1 to 16 Sensitivity Analysis CREEP BEHAVIOR: VISCOELASTIC AND VISCOPLASTIC MODELS Elastoviscoplastic Model (Perzyna) Mechanism of Viscoplastic Solution Elastoviscoplastic Equations One-Dimensional Formulation of Perzyna's Model Disturbance Function Finite Element Equations Rate Dependent Behavior Parameters for Viscoplastic Model Temperature Dependence Multi-component DSC and Overlay Models Specializations: Elastic(e), Viscoelastic(ve), Elastoviscoplastic(evp), Material Parameters in Overlay Models Examples 1 to 9 DSC FOR SATURATED AND UNSATURATED MATERIALS Brief Review Fully Saturated Materials Equations Terzaghi's Equation Incremental DSC Equations Disturbance Effective Stress Parameter Residual Flow Concept HISS and DSC Models Softening, Degradation and Collapse Material Parameters Examples 1 to 3 DSC FOR STRUCTURED AND STIFFENED MATERIALS Definition of Disturbance Structured Soils Dislocation, Softening and Stiffening Reinforced and Jointed Systems Equivalent Composite Individual Solid and Joint Elements Rest Periods: Unloading Examples 1 to 3 DSC FOR INTERFACES AND JOINTS General Problem Review Thin Layer Interface Model Disturbed State Concept Disturbance Function Incremental Equations Determination of Parameters Mathematical and Physical Characteristics of DSC Testing Examples 1 to 11 Computer Implementation MICROSTRUCTURE, LOCALIZATION AND INSTABILITY Microstructure Wellposedness Localization Nonlocality and Characteristic Dimension Regularization and Nonlocal Models Rate Dependent Models Continuum Damage Model Nonlocal Continuum Strain and Energy Based Models Gradient Enrichment of Continuum Models Cosserat Continuum Stability Disturbed State Concept: Nonlocality, Micro-crack Interaction, Characteristic Mesh Dependence Instability Approximate Decoupled DSC Stability Analysis of DSC Examples 1 to 4 Appndix 12-1: Thermodynamical Analysis of DSC IMPLEMENTATION OF DSC IN COMPUTER PROCEDURES Finite Element Formulation Solution Schemes Algorithms for Creep Behavior Algorithms for Coupled Dynamic Behavior Partially Saturated Systems Cyclic and Repetitive Loading Initial Conditions Hierarchical Capabilities and Options Mesh Adaption Using DSC Examples of Applications: Field and Laboratory Simulated Tests 1 to 12 CONCLUSIONS AND FUTURE TRENDS APPENDIX I : DISTURBED STATE, CRITICAL STATE AND SELF ORGANIZED CRITICALITY CONCEPTS APPENDIX II : DSC PARAMETERS, OPTIMIZATION AND SENSITIVITY

Time and temperature dependence of the scratch properties of poly(methylmethacrylate) surfaces

Abstract: Most existing models describing the scratch properties of materials take into account forces acting at the interface between the material and a grooving tip, but do not consider the stress and strain properties of the material far beneath or ahead of the tip. In the case of polymer scratches, there are no models at all which take into account the viscoelastic viscoplastic behaviour of the material. In standard indentation tests with a non moving tip, the elastic plastic boundary and the limits of the region subjected to hydrostatic pressure beneath the tip are known. These models were used to analyse the geometry of the grooves left on the surface of a viscoelastic viscoplastic body by a moving cone-shaped diamond tip having a radius of about 40„m. A new apparatus was built to control the velocity of the tip over the range 1 to 10 4 „m/s, at several different temperatures from i10 ‐ Ct o 100 ‐ C. The material was a commercial grade of cast poly(methylmethacrylate) (PMMA). The normal and tangential loads and groove size were used to evaluate the dynamic hardness, which behaved like a stress and temperature activated process. Values of the activation energy and volume of the dynamic hardness and of the interfacial shear stress were in good agreement with those usually attributed to the mechanical properties of PMMA. C ∞ 2000 Kluwer Academic Publishers

An anisotropic Gurson type model to represent the ductile rupture of hydrided Zircaloy-4 sheets

Abstract: The aim of this work is to model the ductile fracture of Zircaloy-4 sheets containing various amount of embrittling hydride precipitates. The proposed model is based on the Gurson–Tvergaard–Needleman model which is extended to take into account plastic anisotropy and viscoplasticity. The mechanical behavior is identified by conducting tensile tests and the damage nucleation rate (hydride cracking) is measured using quantitative metallography. The model is then used in a Finite Element software to represent crack propagation in Center Crack Panel specimens. Results are strongly mesh size dependent. The mesh size has to be identified by comparison with experimental results. Finally the model is validated by simulating crack initiation and growth in moderately complex structures (sheets containing holes).

Statistical analysis of dislocation dynamics during viscoplastic deformation from acoustic emission

Abstract: We present experimental data of acoustic emission (AE) induced by dislocation motion during “pure” viscoplastic (ductile) deformation of singlecrystals and polycrystals of ice which provide opportunity to revisit collective dislocation dynamics as a critical phenomenon, as recently proposed for brittle fracturing. The data were recorded during compression and torsion creep experiments. AE statistics of power law type were systematically obtained under different experimental conditions. Among the possible candidates for such a system with threshold dynamics exhibiting power law statistics, critical points, disordered first-order transitions, and self-organized criticality should be considered. The revisitation of dislocation dynamics as a critical phenomenon allows rationalization of collective effects as well as of the heterogeneity and complexity of viscoplastic deformation of crystalline materials. Such critical behavior implies that dislocation avalanches and strain localizations are unpredictible, in a deterministic sense, in space, time, and energy domains and that large plastic instabilities account for most of the viscoplastic deformation.