Showing papers on "Viscoplasticity published in 2001"

Classical and Computational Solid Mechanics

Abstract: Tensor analysis stress tensor analysis of strain conservation laws elastic and plastic behaviour of materials linearized theory of elasticity solutions of problems in linearized theory of elasticity by potentials two-dimensional problems in linearized theory of elasticity variational calculus, energy theorems, Saint-Venant's principle Hamilton's principle, wave propagation, applications of generalized co-ordinates elasticity and thermodynamics irreversible thermodynamics and viscoelasticity thermoelasticity viscoelasticity large deformation incremental approach to solving some nonlinear problems finite element methods mixed and hybrid formulations finite element methods for plates and shells finite element modelling of nonlinear elasticity, viscoelasticity, plasticity, viscoplasticity and creep.

Intermittent dislocation flow in viscoplastic deformation

Abstract: The viscoplastic deformation (creep) of crystalline materials under constant stress involves the motion of a large number of interacting dislocations. Analytical methods and sophisticated 'dislocation dynamics' simulations have proved very effective in the study of dislocation patterning, and have led to macroscopic constitutive laws of plastic deformation. Yet, a statistical analysis of the dynamics of an assembly of interacting dislocations has not hitherto been performed. Here we report acoustic emission measurements on stressed ice single crystals, the results of which indicate that dislocations move in a scale-free intermittent fashion. This result is confirmed by numerical simulations of a model of interacting dislocations that successfully reproduces the main features of the experiment. We find that dislocations generate a slowly evolving configuration landscape which coexists with rapid collective rearrangements. These rearrangements involve a comparatively small fraction of the dislocations and lead to an intermittent behaviour of the net plastic response. This basic dynamical picture appears to be a generic feature in the deformation of many other materials. Moreover, it should provide a framework for discussing fundamental aspects of plasticity that goes beyond standard mean-field approaches that see plastic deformation as a smooth laminar flow.

A computational model of viscoplasticity and ductile damage for impact and penetration

Abstract: A coupled constitutive model of viscoplasticity and ductile damage for penetration and impact related problems has been formulated and implemented in the explicit finite element code LS-DYNA. The model, which is based on the constitutive model and fracture strain model of Johnson and Cook, and on continuum damage mechanics as proposed by Lemaitre, includes linear thermoelasticity, the von Mises yield criterion, the associated flow rule, non-linear isotropic strain hardening, strain-rate hardening, temperature softening due to adiabatic heating, isotropic ductile damage and failure. For each of the physical phenomena included in the model, one or several material constants are required. However, all material constants can be identified from relatively simple uniaxial tensile tests without the use of numerical simulations. In this paper the constitutive model is described in detail. Then material tests for Weldox 460 E steel and the calibration procedure are presented and discussed. The calibrated model is finally verified and validated through numerical simulations of material and plate perforation tests investigated experimentally.

Applying Anand Model to Represent the Viscoplastic Deformation Behavior of Solder Alloys

Abstract: A unified viscoplastic constitutive law, the Anand model, was applied to represent the inelastic deformation behavior for solders used in electronic packaging. The material parameters of the constitutive relations for 62Sn36Pb2Ag, 60Sn40Pb, 96.5Sn3.5Ag, and 97.5Pb2.5Sn solders were determined from separated constitutive relations and experimental results. The achieved unified Anand model for solders were tested for constant strain rate testing, steady-state plastic flow and stress/strain responses under cyclic loading. It is concluded that the Anand model can be applied for representing the inelastic deformation behavior of solders at high homologous temperature and can be recommended for finite element simulation of the stress/strain responses of solder joints in service. @DOI: 10.1115/1.1371781#

Multi-axial electrical switching of a ferroelectric: theory versus experiment

Abstract: Samples of the polycrystalline ferroelectric ceramic PZT-5H were poled by applying an electric field at room temperature. Subsequently, an electric field was applied to the samples at a range of angles to the poling direction. The measured non-linear responses in electric displacement are used to construct “yield surfaces” in electric field space corresponding to the onset of ferroelectric switching. The results are compared with predictions from three models: (i) a previous self-consistent polycrystal calculation with rate-independent, non-hardening crystal plasticity; (ii) a simplified crystal plasticity model with viscoplastic (rate-dependent) behaviour and a sufficient number of transformation systems to reproduce the polycrystalline behaviour; (iii) a phenomenological model based on rate-independent flow theory, using kinematic hardening and a quadratic yield surface in electric field and stress space. The experiments suggest that the self-consistent crystal plasticity formulation is most able to reproduce the multi-axial electrical response and yield surface of the polycrystal. The phenomenological model is able to reproduce the uniaxial response accurately, but gives relatively poor performance for multi-axial loading paths, in its present form. A tolerable compromise in multi-axial modelling is the simplified crystal plasticity approach. This is able to reproduce multi-axial constitutive behaviour with reasonable accuracy, whilst offering computational simplicity and speed similar to that of the phenomenological model.

Thermal cycling analysis of flip-chip solder joint reliability

Abstract: The reliability concern in flip-chip-on-board (FCOB) technology is the high thermal mismatch deformation between the silicon die and the printed circuit board that results in large solder joint stresses and strains causing fatigue failure. Accelerated thermal cycling (ATC) test is one of the reliability tests performed to evaluate the fatigue strength of the solder interconnects. Finite element analysis (FEA) was employed to simulate thermal cycling loading for solder joint reliability in electronic assemblies. This study investigates different methods of implementing thermal cycling analysis, namely using the "dwell creep" and "full creep" methods based on a phenomenological approach to modeling time independent plastic and time dependent creep deformations. There are significant differences between the "dwell creep" and "full creep" analysis results for the flip chip solder joint strain responses and the predicted fatigue life. Comparison was made with a rate dependent viscoplastic analysis approach. Investigations on thermal cycling analysis of the temperature range, (/spl Delta/T) effects on the predicted fatigue lives of solder joints are reported.

Yield conditions for deformation of amorphous polymer glasses.

Abstract: Shear yielding of glassy polymers is usually described in terms of the pressure-dependent Tresca or von Mises yield criteria. We test these criteria against molecular dynamics simulations of deformation in amorphous polymer glasses under triaxial loading conditions that are difficult to realize in experiments. Difficulties and ambiguities in extending several standard definitions of the yield point to triaxial loads are described. Two definitions, the maximum and offset octahedral stresses, are then used to evaluate the yield stress for a wide range of model parameters. In all cases, the onset of shear is consistent with the pressure-modified von Mises criterion, and the pressure coefficient is nearly independent of many parameters. Under triaxial tensile loading, the mode of failure changes to cavitation, and the von Mises criterion no longer applies.

Rheological properties of wet soils and clays under steady and oscillatory stresses

Abstract: Tilled agricultural soils are in a constant state of change induced by variations in soil strength due to wetting and drying and compaction by farm implements. Changes in soil structure affect many hydraulic and transport properties; hence their quantification is critical for accurate hydrological and environmental modeling. This study highlights the role of soil rheology in determining time-dependent stress-strain relationships that are essential for prediction and analysis of structural changes in soils. The primary objectives of this study were (i) to extend a previously proposed aggregate-pair model to prediction of compaction under external steady or transient stresses and (ii) to provide experimentally determined rheological information for the above models. Rheological properties of soils and clay minerals were measured with a rotational rheometer with parallel-plate sensors. These measurements, under controlled steady shear stress application, have shown that wet soils have viscoplastic behavior with well-defined yield stress and nearly constant plastic viscosity. In contrast, rapid transient loading (e.g., passage of a tractor) is often too short for complete viscous dissipation of applied stress, resulting in an elastic (recoverable) component of deformation (viscoelastic behavior). Measured viscoelastic properties were expressed by complex viscosity and shear modulus whose components denote viscous energy dissipation, and energy storage (elastic). Results show that for low water contents and fast loading (tractor speed), the elastic component of deformation increases, whereas with higher water contents, viscosity and shear modulus decrease. Steady and oscillatory stress application to an aggregate pair model illustrates potential use of rheological properties towards obtaining predictions of strains in soils.

Viscoplasticity of elastomeric materials: experimental facts and constitutive modelling

Abstract: A characteristic of filled elastomers is their ability to undergo very large deformations without damaging their internal structure. The material behaviour is mainly elastic, however, elastomers show hysteresis effects leading to damping properties, which are quite important as regards their applications in various fields of mechanical engineering. A series of experiments (tension, torsion and combinations of both) was carried out on cylindrical bars made of a carbon-black filled rubber mixture. In addition to a pronounced nonlinear rate-dependence, relaxation and viscosity properties are observed as being influenced by the process histories. The behaviour of elastomeric materials is modelled on the basis of a free energy function and evolution equations for additional internal variables. Incorporating or disregarding the very small rate-independent hysteresis, the constitutive modelling may be classified under viscoplasticity or viscoelasticity. The constitutive equations are formulated for isothermal processes in a thermodynamically consistent manner. Particular attention is focused on nonlinear rate-dependence as well as on process-dependent relaxation properties. Numerical simulations on the basis of identified material parameters show that the proposed constitutive model is able to represent the main elastic and inelastic phenomena.

Unified Plasticity for Engineering Applications

Abstract: 1. Formulation of a Unified Constitutive Theory of Elastic-Viscoplastic Behavior.- 1.1. Introduction.- 1.2. Concepts and Basic Equations.- 1.3. Extensions and General Applications of the Basic Equations.- 1.3.1. Variable Rate of Hardening/Cyclic Loading.- 1.3.2. Thermodynamic Considerations Stored Energy of Cold Work.- 1.3.3. Strain Rate Dependence of Hardening Rate.- 1.3.4. Creep of Metals.- 1.3.5. Continuum Damage as a State Variable.- 1.3.6. Non-Proportional Loadings.- 1.3.7. Viscoplastic Buckling.- 1.3.8. Rate Sensitivity in Dynamic Plasticity Problems.- 1.4. Integration of Constitutive Equations.- 2. Specific Applications.- 2.1. Material Constants and Applications.- 2.1.1. Background.- 2.1.2. Methods for Determination of Material Constants.- 2.1.3. Examples.- 3. Commentaries.- 3.1. Status of the B-P Constitutive Theory.- 3.2. Further Developments.- 3.2.1 Large Deformations.- 3.2.2 Anisotropic Materials.- Appendix - Computer Program.- References.

Squeeze flow of Bingham plastics

Abstract: The axisymmetric squeeze flow of a viscoplastic material is examined. The deformation and flow of such materials is important, since many multicomponent fluids encountered in industrial processes, are viscoplastic. The Bingham plastic constitutive equation is used and the transition from the solid state to the fluid one takes place at the “yield surface”. The aspect ratio of the geometry e (half the distance between the disks to their radius) is taken to be the small parameter of the analysis and a non-standard luorication approximation is employed.

SECTION 4.6 – Kinematic Hardening Rule with Critical State of Dynamic Recovery

Abstract: This chapter deals with the explanation of kinematic hardening rule and with critical state of dynamic recovery. It is a kinematic hardening rule that enables to represent multilinear, as well as nonlinear, stress-strain relations under cyclic loading. This rule, which is formulated by introducing a critical state in dynamic recovery, is capable of simulating well ratcheting and cyclic stress relaxation. Moreover, the rule has the advantage of allowing to determine the material parameters. A rate-independent constitutive model of plasticity based on this kinematic hardening rule is implemented in commercially available FEM software by utilizing the implicit integration equation and consistent tangent modulus derived for the model, though the rule itself is valid for both rate-independent and rate-dependent materials. The kinematic hardening model presented in the chapter can be used as a translation rule of yield surfaces and viscoplastic potentials. For the rate-independent constitutive model an implicit integration equation and a consistent tangent modulus are available, so that the constitutive model is implemented using a user subroutine UMAT in ABAQUS. The integration equation, which is based on return mapping, allows taking large strain increments without sacrificing accuracy.

Modeling the viscoplastic behaviour of clays during consolidation: application to Berthierville clay in both laboratory and field conditions

Abstract: To analyze the effects of strain rate and viscoplastic strain on consolidation of natural clay, this paper presents a nonlinear viscoplastic model in which viscoplastic behaviour is modeled by a un...

Statistical continuum theory for large plastic deformation of polycrystalline materials

Abstract: This paper focuses on the application of statistical continuum mechanics to the prediction of mechanical response of polycrystalline materials and microstructure evolution under large plastic deformations. A statistical continuum mechanics formulation is developed by applying a Green's function solution to the equations of stress equilibrium in an infinite domain. The distribution and morphology of grains (crystals) in polycrystalline materials is represented by a set of correlation functions that are described by the corresponding probability functions. The elastic deformation is neglected and a viscoplastic power law is employed for crystallographic slip in single crystals. In this formulation, two- and three-point probability functions are used. A secant modulus-based formulation is used. The statistical analysis is applied to simulate homogeneous deformation processes under uniaxial tension, uniaxial compression and plane strain compression of an FCC polycrystal. The results are compared to the well-known Taylor upper bound model and discussed in comparison to experimental observations.

Constitutive Relations for Asphalt Concrete Under High Rates of Loading

Abstract: A main characteristic of asphalt concrete (AC) is its tendency to behave elastically and viscoplastically during cold and hot seasons, respectively. An understanding of the mechanical behavior of AC under various loading conditions is crucial to a more rational design of flexible pavements and requires more elaborate and comprehensive constitutive relations for AC. AC behavior under high rates of loading was experimentally studied using uniaxial, triaxial compression, and pavement simulation tests. The loading matrix followed in the testing program consisted of 0.05-, 0.1-, and 0.2-s loading durations; three stress levels of 207, 414, and 827 kPa; and three temperatures of 24°C, 35°C, and 41°C. The experimental results indicated that AC materials display an elastic-viscoplastic response under uniaxial stress pulses. The viscoplastic response was characterized by the rate dependency of the plastic response and was found to be linearly strain hardening. The results revealed that the yielding point is depend...

Dissipation in porous metal plasticity and ductile fracture

Abstract: The framework of thermodynamics of irreversible processes (TIP) enables the coherent formulation of constitutive equations for porous metal plasticity and viscoplasticity, expressions for the dissipated and stored energies, and a new form of the heat balance equation including void growth damage. These expressions are in good agreement with existing thermographic measurements, which provides additional confidence in the model. The linear stability analysis of a perturbation is applied to the whole set of equations. It gives some features of ductile fracture. Depending on the material parameters and on strain rate, shear localisation is induced by thermal softening, void growth damage, or a combination of both. Localisation is classically inhibited by inertia terms at very high strain rates, and postponed by viscosity. The combination of these phenomena creates an “adiabatic nose” in a strain–strain rate diagram. In the case of an axisymmetric stress tensor, that prevails for example in the centre of the necking zone of a round tensile specimen, a pure opening localisation can be obtained. The limitations of the analyses are mentioned.

The effects of underfill and its material models on thermomechanical behaviors of a flip chip package

Abstract: In this paper, the effects of underfill on thermomechanical behavior of two types of flip chip packages with different bumping size and stand-off height were investigated under thermal cycling both experimentally and two-dimensional (2-D) finite element simulation. The materials inelasticity, i.e., viscoelasticity of underfill U8437-3 and viscoplasticity of 60 Sn40 Pb solder, were considered in the simulations. The results show that the use of underfill encapsulant increases tremendously (/spl sim/20 times) the thermal fatigue lifetime of SnPb solder joint, weakens the effects of stand-off height on the reliability, and changes the deformation mode of the package. It was found that the thermal fatigue crack occurs in the region with maximum plastic strain range, and the Coffin-Manson type equation could then be used for both packages with and without underfill. Solder joint crack initiation occurred before delamination when using underfill with good adhesion (75 MPa) and the underfill delamination may not be a dominant failure mode in the present study. The interfacial stresses at the underfill/chip interface were calculated to analyze delamination sites, which agree with the results from acoustic image. Moreover, the effects of material models of underfill, i.e., constant elasticity (EC) and temperature dependent elasticity (ET) as well as the viscoelasticity (VE), on the thermomechanical behaviors of flip chip package were also studied in the simulation. The VE model gives comparatively large plastic strain range and large displacements in the shear direction, as well as decreased solders joint lifetime. The ET model gives similar results as the VE model and could be used instead of VE in simulations for the purpose of simplicity.