Showing papers on "Viscoplasticity published in 2012"

Investigation of deformation and failure features in hot stamping of AA6082: Experimentation and modelling

Abstract: This paper introduces a set of coupled viscoplastic constitutive equations for deformation and damage in hot stamping and cold die quenching of AA6082 panel parts The equation set can be used to predict viscoplastic flow and plasticity-induced damage of AA6082 under hot forming conditions Deformation and damage depend upon a coupled set of evolving internal state variables, eg dislocation density, which in turn is affected by thermally activated and deformation-dependent recrystallisation and recovery A phenomenological description of damage is derived based on the expected physical scaling with temperature, strain and strain rate The resulting equations were implemented in the commercial software ABAQUS via the user-defined subroutine VUMAT for carrying out forming process simulations An experimental programme was designed, and specialised testing facilities developed for calibrating and validating the FE process modelling results A good agreement between the process simulation and the experimental results has been achieved This confirms that the physical dependencies in the constitutive equations are correctly formed, and that the equations and FE model can be calibrated and used for hot stamping of AA6082 panel parts Further, forming process optimisation was carried out using the model to identify the optimal forming parameters for a basic panel part with a circular hole in the middle The study concludes with a discussion of the potential impact of the constitutive model, experimental characterisation and modelling results on AA6082 panel parts manufacture

Determination of Anand constants for SAC solders using stress-strain or creep data

Abstract: The Anand viscoplastic constitutive model is often used to represent the deformation behavior of solders in electronic assemblies. In the Anand model, plasticity and creep are unified and described by the same set of flow and evolution relations. The nine parameters of the Anand constitutive model are typically determined from uniaxial stress-strain tests at several strain rates and temperatures using a standard multistep model parameter determination procedure. Conversely, creep data are often measured for solders, but typically are not used to determine Anand model constants.

Continuum damage mechanics : a continuum mechanics approach to the analysis of damage and fracture

Abstract: Preface.- List of Symbols.- PART I Foundations of Continuum Damage Mechanics.- 1. Material Damage and Continuum Damage Mechanics.- 1.1 Damage and its Microscopic Mechanisms.- 1.2 Representative Volume Element and Continuum Damage Mechanics.- 2. Mechanical Representation of Damage and Damage Variables.- 2.1 Mechanical Modeling of Damage.- 2.2 Mechanical Representation of Three-Dimensional Damage State.- 2.3 Effective Stress and Hypothesis of Mechanical Equivalence.- 2.4 Elastic Constitutive Equation and Elastic Modulus Tensor of Damaged Material.- 2.5 Procedure of Continuum Damage Mechanics and its Refinement.- 3. Thermodynamics of Damaged Material.- 3.1 Thermodynamics of Continuum.- 3.2 Thermodynamic Constitutive Theory of Inelasticity with Internal Variables.- 3.3 Extension of Thermodynamic Constitutive Theory of Inelasticity.- 4. Inelastic Constitutive Equations and Evolution Equations of Material with Isotropic Damage.- 4.1 One-Dimensional Inelastic Constitutive Equation of Material with Isotropic Damage.- 4.2 Three-Dimensional Inelastic Constitutive Equations of Material with Isotropic Damage.- 4.3 Strain Energy Release Rate and Stress Criterion for Damage Development in Elastic-Plastic Damage.- 4.4 Inelastic Damage Theory based on Hypothesis of Total Energy Equivalence.- 5. Inelastic Constitutive Equation and Damage Evolution Equation of Material with Anisotropic Damage.- 5.1 Elastic-Plastic Anisotropic Damage Theory based on Second-Order Symmetric Damage Tensor.- 5.2 Elastic-Plastic Anisotropic Damage Theory in Stress Space.- 5.3 Fourth-Order Symmetric Damage Tensor and its Application to Elastic-Plastic-Brittle Damage.- PART II Application of Continuum Damage Mechanics.- 6. Elastic-Plastic Damage.- 6.1 Constitutive and Evolution Equations of Elastic-Plastic Damage - Ductile Damage, Brittle Damage and Quasi-Brittle Damage.- 6.2 Ductile Damage and Ductile Fracture.- 6.3 Application to Metal Forming Process.- 6.4 Analysis of Sheet Forming Limit by Anisotropic Damage Theory.- 6.5 Constitutive Equations of Void-Containing Ductile Material.- 6.6 Continuum Damage Mechanics Theory with Plastic Compressibility.- 7. Fatigue Damage.- 7.1 High Cycle Fatigue .- 7.2 Low Cycle Fatigue.- 7.3 Uncoupled Numerical Analysis of Very Low Cycle Fatigue.- 8. Creep Damage and Creep-Fatigue Damage.- 8.1 Creep Damage and Phenomenological Theory of Creep Damage.- 8.2 Viscoplastic Damage Theory of Creep Damage.- 8.3 Creep-Fatigue Damage.- 8.4 Effect of Damage Field on Stress Field at a Creep Crack Tip.- 9. Elastic-Brittle Damage.- 9.1 Damage of Elastic-Brittle Material.- 9.2 Isotropic Damage Theory of Concrete.- 9.3 Anisotropic Brittle Damage Theory by Second-Order Damage Tensor.- 9.4 Anisotropic Brittle Damage Theory with Elastic Modulus Tensor as Damage Variable.- 9.5 Anisotropic Brittle Damage Theory with Compliance Tensor as Damage Variable.- 10. Continuum Damage Mechanics of Composite Material.- 10.1 Damage of Laminate Composites.- 10.2 Elastic-Brittle Damage of Ceramic Matrix Composites.- 10.3 Local Theory of Metal Matrix Composites.- 11. Local Approach to Damage and Fracture Analysis.- 11.1 Local Approach to Fracture Based on Continuum Damage Mechanics and Finite Element Method.- 11.2 Mesh-Sensitivity in Time-Independent Deformation.- 11.3 Regularization of Strain and Damage Localization in Time-Independent Materials.- 11.4 Mesh-Sensitivity in Time-Dependent Deformation.- 11.5 Causes of Mesh-Sensitivity in Time-Dependent Deformation.- APPENDIX Foundations of Tensor Analysis.- A.1 Vectors and Tensors.- A.2 Vector Product, Tensor Product and the Components of Tensors.- A.3 Orthogonal Transformation, Invariants and Eigenvalues of Tensors.- A.4 Differentiation and Integral of Tensor Fields.- A.5 Differential Calculus of Tensor Functions.- A.6 Representation Theorem for Tensor Functions.- A.7 Matrix Representation of Tensors and Tensor Relations.- Reference Books and Bibliography.- Subject Index.

Improved predictions of lead free solder joint reliability that include aging effects

Abstract: It has been demonstrated that isothermal aging leads to large reductions (up to 50%) in several key material properties for lead free solders including stiffness (modulus), yield stress, ultimate strength, and strain to failure. In addition, even more dramatic evolution has been observed in the creep response of aged solders, where up to 10,000X increases have been observed in the steady state (secondary) creep strain rate (creep compliance). Such degradations in the stiffness, strength, and creep compliance of the solder material are expected to be universally detrimental to reliability of solder joints in electronic assemblies. Traditional finite element based predictions for solder joint reliability during thermal cycling accelerated life testing are based on solder constitutive equations (e.g. Anand viscoplastic model) and failure models (e.g. energy dissipation per cycle models) that do not evolve with material aging. Thus, there will be significant errors in the calculations with lead free SAC alloys that illustrate dramatic aging phenomena. In our current research, we are developing new reliability prediction procedures that utilize constitutive relations and failure criteria that incorporate aging effects, and then validating the new approaches through correlation with thermal cycling accelerated life testing experimental data. In this paper, we report on the first step of that development, namely the establishment of a revised set of Anand viscoplastic stress-strain relations for solder that include material parameters that evolve with the thermal history of the solder material. The effects of aging on the nine Anand model parameters have been examined by performing stressstrain tests on SAC305 samples that were aged for various durations (0–6 months) at a temperature of 100 C. For each aging time, stress-strain data were measured at three strain rates (0.001, 0.0001, and 0.00001 1/sec) and five temperatures (25, 50, 75, 100, and 125 C). Using the measured stress-strain data, the Anand model material parameters have been determined for various aging conditions. Mathematical expressions were then developed to model the evolution of the Anand model parameter with aging time. Our results show that 2 of the 9 constants remain essentially constant during aging, while the other 6 show large changes (30–70%) with up to 6 months of aging at 100 C. Preliminary finite element simulations have also shown that the use of the modified Anand model leads to a strong dependence of the calculated plastic work dissipated per cycle on the aging conditions prior to thermal cycling.

Creep and recovery of epoxy/MWCNT nanocomposites

Abstract: Creep and creep–recovery of epoxy/multi-wall carbon nanotube (MWCNT) composites was studied in a wide range of applied loads in order to evaluate the contribution of nanotubes on the time-dependent behaviour of the epoxy matrix. Incorporation of up to 1 wt.% of C150P MWCNTs has negligible influence on the elastic, viscoelastic and viscoplastic response of the epoxy system. No systematic changes of the creep characteristics depending on the content of nanotubes are noticed in the range of stresses from 0.3 up to 0.75 from the ultimate strength. Creep resistance and recovery performance of the epoxy matrix is not negatively affected by the addition of MWCNTs and the same analytical model – Schapery’s nonlinear model – is applicable for the creep description of the nanocomposites. Addition of significant amounts of nanotubes allows using the conventional epoxy system as a material with multifunctional properties without sacrificing their long-term mechanical performance.

A phase field model incorporating strain gradient viscoplasticity: Application to rafting in Ni-base superalloys

Abstract: The first formulation of a phase field model accounting for size-dependent viscoplasticity is developed to study materials in which microstructure evolution and viscoplastic behavior are strongly coupled. Plasticity is introduced using a continuum strain gradient formalism which captures the size effect of the viscoplastic behavior. First, the influence of this size effect on the mechanical behavior of the material is discussed in static microstructures. Then, the dynamic coupling between microstructure evolution and viscoplastic activity is addressed and illustrated by the rafting of the microstructure observed in Ni-base superalloys under creep conditions. It is found that the plastic size effect has only a moderate impact on the shape of the rafts but is crucial to reproduce the macroscopic mechanical behavior of that particular material.

Characterizing Permanent Deformation and Fracture of Asphalt Mixtures by Using Compressive Dynamic Modulus Tests

Abstract: Permanent deformation and fracture may develop simultaneously when an asphalt mixture is subjected to a compressive load. The objective of this research is to separate viscoplasticity and viscofracture from viscoelasticity so that the permanent deformation and fracture of the asphalt mixtures can be individually and accurately characterized without the influence of viscoelasticity. The undamaged properties of 16 asphalt mixtures that have two binder types, two air void contents, and two aging conditions are first obtained by conducting nondestructive creep tests and nondestructive dynamic modulus tests. Testing results are analyzed by using the linear viscoelastic theory in which the creep compliance and the relaxation modulus are modeled by the Prony model. The dynamic modulus and phase angle of the undamaged asphalt mixtures remained constant with the load cycles. The undamaged asphalt mixtures are then used to perform the destructive dynamic modulus tests in which the dynamic modulus and phase angle of the damaged asphalt mixtures vary with load cycles. This indicates plastic evolution and crack propagation. The growth of cracks is signaled principally by the increase of the phase angle, which occurs only in the tertiary stage. The measured total strain is successfully decomposed into elastic strain, viscoelastic strain, plastic strain, viscoplastic strain, and viscofracture strain by employing the pseudostrain concept and the extended elastic-viscoelastic correspondence principle. The separated viscoplastic strain uses a predictive model to characterize the permanent deformation. The separated viscofracture strain uses a fracture strain model to characterize the fracture of the asphalt mixtures in which the flow number is determined and a crack speed index is proposed. Comparisons of the 16 samples show that aged asphalt mixtures with a low air void content have a better performance, resisting permanent deformation and fracture.

Thermodynamic-based model for coupling temperature-dependent viscoelastic, viscoplastic, and viscodamage constitutive behavior of asphalt mixtures

Abstract: SUMMARY Based on the continuum damage mechanics, a general and comprehensive thermodynamic-based framework for coupling the temperature-dependent viscoelastic, viscoplastic, and viscodamage behaviors of bituminous materials is presented. This general framework derives systematically Schapery-type nonlinear viscoelasticity, Perzyna-type viscoplasticity, and a viscodamage model analogous to the Perzyna-type viscoplasticity. The resulting constitutive equations are implemented in the well-known finite element code Abaqus via the user material subroutine UMAT. A systematic procedure for identifying the model parameters is discussed. Finally, the model is validated by comparing the model predictions with a comprehensive set of experimental data on hot mix asphalt that include creep-recovery, creep, uniaxial constant strain rate, and repeated creep-recovery tests in both tension and compression over a range of temperatures, stress levels, and strain rates. Comparisons between model predictions and experimental measurements show that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions. Copyright © 2011 John Wiley & Sons, Ltd.

Transient Heat and Material Flow Modeling of Friction Stir Processing of Magnesium Alloy using Threaded Tool

Abstract: A three-dimensional transient computational fluid dynamics (CFD) model was developed to investigate the material flow and heat transfer during friction stir processing (FSP) in an AZ31B magnesium alloy. The material was assumed to be a non-Newtonian viscoplastic fluid, and the Zener-Hollomon parameter was used to describe the dependence of material viscosity on temperature and strain rate. The material constants used in the constitutive equation were determined experimentally from compression tests of the AZ31B Mg alloy under a wide range of strain rates and temperatures. A dynamic mesh method, combining both Lagrangian and Eulerian formulations, was used to capture the material flow induced by the movement of the threaded tool pin. Massless inert particles were embedded in the simulation domain to track the detailed history of material flow. The actual FSP was also carried out on a wrought Mg plate where temperature profiles were recorded by embedding thermocouples. The predicted transient temperature history was found to be consistent with that measured during FSP. Finally, the influence of the thread on the simulated results of thermal history and material flow was studied by comparing two models: one with threaded pin and the other with smooth pin surface.

A Phenomenological Constitutive Model for Describing Thermo-Viscoplastic Behavior of Al-Zn-Mg-Cu Alloy Under Hot Working Condition

Abstract: In order to predict the high-temperature deformation behavior of Al-Zn-Mg-Cu alloy, the hot compression tests were conducted in the strain rate range of (0.001–0.1)s−1 and the forming temperature range of (573–723) K. Based on the experimental results, Johnson-Cook model was found inadequate to describe the high-temperature deformation behavior of Al-Zn-Mg-Cu alloy. Therefore, a new phenomenological constitutive model is proposed, considering the coupled effects of strain, strain rate and forming temperature on the material flow behavior of Al-Zn-Mg-Cu alloy. In the proposed model, the material constants are presented as functions of strain rate. The proposed constitutive model correlates well with the experimental results confirming that the proposed model can give an accurate and precise estimate of flow stress for the Al-Zn-Mg-Cu alloy investigated in this study.

Steady Couette flows of elastoviscoplastic fluids are nonunique

Abstract: The Herschel–Bulkley rheological fluid model includes terms representing viscosity and plasticity. In this classical model, below the yield stress the material is strictly rigid. Complementing this model by including elastic behavior below the yield stress leads to a description of an elastoviscoplastic (EVP) material such as an emulsion or a liquid foam. We include this modification in a completely tensorial description of cylindrical Couette shear flows. Both the EVP model parameters, at the scale of a representative volume element, and the predictions (velocity, strain and stress fields) can be readily compared with experiments. We perform a detailed study of the effect of the main parameters, especially the yield strain. We discuss the role of the curvature of the cylindrical Couette geometry in the appearance of localization; we determine the value of the localization length and provide an approximate analytical expression. We then show that, in this tensorial EVP model of cylindrical Couette shear f...

Compressive Viscoplastic Response of 6082‐T6 and 7075‐T6 Aluminium Alloys Under Wide Range of Strain Rate at Room Temperature: Experiments and Modelling

Abstract: In this work, the viscoplastic behaviour of 6082-T6 and 7075-T6 aluminium alloys is examined over a wide range of strain rates. Three different testing techniques were applied to this investigation: low-rate experiments were performed using a regular servo-hydraulic testing machine, high-rate tests were conducted using a split Hopkinson bar apparatus and very-high-rate experiments were carried out using a miniaturised direct impact test arrangement. The latter testing set-up allowed for the characterisation of material flow at strain rates up to . These experimental results showed a sharp increase in the rate sensitivity of the materials once a threshold loading rate of is exceeded. This behaviour may be attributed to the presence of viscous drag on high-velocity dislocation motion. In addition, the thermo-viscoplastic behaviour of the 6082-T6 and 7075-T6 aluminium alloys was analytically described using the extended Rusinek–Klepaczko model of viscous drag effects. Satisfactory correlation was observed between the experiments and the constitutive model results over the entire range of strain rates studied,