Thermo-viscoplastic Model Research Articles

Modeling and Simulation of the Aging Behavior of a Zinc Die Casting Alloy

While zinc die-casting alloy Zamak is widely used in vehicles and machines, its solidified state has yet to be thoroughly investigated experimentally or mathematically modeled. The material behavior is characterized by temperature and rate sensitivity, aging, and long-term influences under external loads. Thus, we model the thermo-mechanical behavior of Zamak in the solid state for a temperature range from −40 °C to 85 °C, and the aging state up to one year. The finite strain thermo-viscoplasticity model is derived from an extensive experimental campaign. This campaign involved tension, compression, and torsion tests at various temperatures and aging states. Furthermore, the thermo-physical properties of temperature- and aging-dependent heat capacity and heat conductivity are considered. One significant challenge is related to the multiplicative decompositions of the deformation gradient, which affects strain and stress measures relative to different intermediate configurations. The entire model is implemented into an implicit finite element program and validation examples at more complex parts are provided so that the predicability for complex parts is available, which has not been possible so far. Validation experiments using digital image correlation confirm the accuracy of the thermo-mechanically consistent constitutive equations for complex geometrical shapes. Moroever, validation measures are introduced and applied for a complex geometrical shape of a zinc die casting specimen. This provides a measure of the deformation state for complex components under real operating conditions.

Numerical Investigation of the Damage Effect on the Evolution of Adiabatic Shear Banding and Its Transition to Fracture during High-Speed Blanking of 304 Stainless Steel Sheets.

This paper investigates numerically the effect of damage evolution on adiabatic shear banding (ASB) formation and its transition to fracture during high-speed blanking of 304 stainless steel sheets. A structural-thermal-damage-coupled finite element (FE) analysis is developed in LS-DYNA considering the modified Johnson-Cook thermo-viscoplastic model for both plasticity flow rule and damage law, while further, a temperature-dependent fracture criterion is implemented by introducing a critical temperature. The modeling approach is initially validated against experimental data regarding the fracture profile and ASB width. Next, FE simulations are conducted to examine the effect of strain rate and temperature dependence on damage law, while the effect of damage coupling is also evaluated, aiming to highlight the connection between thermal and damage softening and attribute them a specific role regarding ASB formation and transition to fracture. Also, the influence of dynamic recrystallization (DRX) softening is studied macroscopically, while further, a parametric analysis of the Taylor-Quinney coefficient is conducted to highlight the effect of plastic work-to-internal heat conversion efficiency on ASB formation. The results revealed that the implementation of damage coupling reacts to reduced ASB width and provides an S-shaped fracture profile, while it also decreases the peak force and results in an earlier fracture. Both findings are enhanced when accounting further for DRX softening and a higher value of the Taylor-Quinney coefficient. Finally, the simulations indicated that thermal softening precedes damage softening, showing that the temperature rise is responsible for ASB initiation, while instead, damage evolution drives ASB propagation and fracture.

Two-temperature thermodynamics and a viscoplasticity model for FCC metals with grain boundary effect

A non-equilibrium thermodynamic route is pursued to model viscoplasticity, including the evolving grain boundary, in face-centered cubic (FCC) metals. The thermodynamic description includes two subsystems: the configurational subsystem describing the relatively slower motion of dislocations and grain boundaries, and a fast-evolving kinetic-vibrational (K-V) subsystem depicting atomic vibrations about equilibrium positions in the lattice. Grain boundary and dislocation densities as well as their interactions are incorporated within the model. The model is initially developed for homogeneous plastic deformation, which is then generalized to the inhomogeneous case via spatial variations in the thermodynamic states over a wide range of strain rate and temperature. The model is implemented as a user material subroutine (VUMAT) in ABAQUS to simulate a problem of industrial interest, viz. deep drawing on an AA 7075 aluminum alloy. Finally, the thermo-viscoplasticity model is used to predict negative strain rate sensitivity in the AA 2219 aluminum alloy at room temperature, for which an experiment is performed at a facility of the VSSC. The predictive quality of the model is demonstrated by a comparison of numerical simulations with the experimental evidence.

Investigation and Modification of a CSSM-Based Elastic–Thermoviscoplastic Model for Clay

Investigation and Modification of a CSSM-Based Elastic–Thermoviscoplastic Model for Clay

Study of the Thermal History upon Residual Stresses during the Dry Drilling of Inconel 718

The main objective of this article was to show for the first time that heat transfer plays a major role in residual stress generation during the dry drilling of Inconel 718, and to propose a numerical strategy capable of simulating such thermo-mechanical phenomena. An X-ray diffraction (XRD) analysis shows that without lubrication, high tensile residual stresses can be observed on the surface of a deep through drilled hole. Such a situation can be highly detrimental for the fatigue lifetime of a mechanical component. A thermal history in five phases is first identified by means of temperature measurements exhibiting an overheating of approximately 500 ∘C on the created hole surface just before the end of the drilling operation. A 3D thermo-viscoplastic model is herein improved in terms of boundary conditions to show that this phenomenon is triggered by the progressive decrease in the Inconel 718 volume under the cutting zone. To the authors’ knowledge, such a phenomenon has never been reported and simulated before in the literature. Then, a 3D thermo-elasto-plastic simulation including elasticity is proposed to compute residual stresses from the thermal results of the previous model. It shows for the first time that the overheating stage induces sufficiently intense plasticity to produce high tensile residual stresses of approximately 900 MPa as we experimentally observed.

A thermo-viscoplasticity model for metals over wide temperature ranges- application to case hardening steel

In this contribution, a model for the thermomechanically coupled behaviour of case hardening steel is introduced with application to 16MnCr5 (1.7131). The model is based on a decomposition of the free energy into a thermo-elastic and a plastic part. Associated viscoplasticity, in terms of a temperature-depenent Perzyna-type power law, in combination with an isotropic von Mises yield function takes respect for strain-rate dependency of the yield stress. The model covers additional temperature-related effects, like temperature-dependent elastic moduli, coefficient of thermal expansion, heat capacity, heat conductivity, yield stress and cold work hardening. The formulation fulfils the second law of thermodynamics in the form of the Clausius–Duhem inequality by exploiting the Coleman–Noll procedure. The introduced model parameters are fitted against experimental data. An implementation into a fully coupled finite element model is provided and representative numerical examples are presented showing aspects of the localisation and regularisation behaviour of the proposed model.

Thermoviscoplasticity in Body-Centered Cubic Metals: A Two-Temperature Model With Grain Boundary Evolution

Abstract In this work, we develop a thermo-viscoplasticity model for body-centered cubic (BCC) metals based on a two-temperature theory of nonequilibrium thermodynamics. Modeling the plastic deformation here involves two subsystems, viz., a configurational subsystem related to grain growth, dislocation motion, and a kinetic vibrational subsystem describing the vibration of atoms. Due to a separation of the time scales, the two subsystems are described by two different temperatures. In this study, we introduce a grain boundary density, in addition to the mobile and forest dislocation densities, as an internal variable. The focus in this paper is on how large plastic deformation is affected by the evolving grain boundaries. In order to check the predictive quality of the model, numerical simulations are conducted and validated against available experimental evidence wherever possible.

A Critical Review and Assessment of Different Thermoviscoplastic Material Models for Simultaneous Hot/Cold Forging Analysis

The simultaneous hot/cold forging is an innovative production process, taking advantage of the high accuracy for cold forming and low forces for hot forming. However, the choice of a suitable material model for such a large temperature range is a difficult issue and insufficiently regarded. Hence, the aim of this contribution is a critical review and assessment of the prediction capability and accuracy of three already existing thermo-viscoplasticity models. Therefore, the simulation results of the Bammann, Chiesa and Johnson (BCJ) model, the Evolving Microstructural M odel of I nelasticity (EMMI) and a recently proposed user defined constitutive model by Bröcker and Matzenmiller, based on an enhanced concept of rheological elements, are compared to test data considering a large range from room temperature up to approximately 1400 K (1127 ∘C). All three material models may represent the thermo-viscoplastic characteristics of metals, whereby each investigated material model comprises different approaches for the temperature dependency of the initial yield stress, nonlinear isotropic hardening, and strain rate sensitivity. All material parameters are identified with the test data of the low alloy steel 50CrV4/51CrV4, the case hardening steel 16MnCr5, the low carbon steel C15 and the aluminium alloy AlMgSi1 by using the commercial optimisation software LS-OPT. The prediction capability and accuracy of each model is evaluated on the basis of the mean squared error by means of a comparsion of real and predicted stress-strain curves for the four different metals. Finally, an industrial oriented hot/cold forging process for the production of a gear shaft made of the low alloy steel 51CrV4 is simulated with LS-DYNA using the three material models and, subsequently, their performance is discussed. As achievement of this model assessment, suitable as well as inappropriate temperature dependent approaches are identified for this large temperature range providing new insights into suitable material models for the analysis of a simultaneous hot/cold forging process.

Thermo-viscoplastic numerical modeling of metal forging process by Pseudo Inverse Approach

Constant demands of light-weighting have forced many industries to resort to manufacturing practices that promise a component with a higher strength-to-weight ratio. Hot forging is one such method used to produce parts using difficult-to-form materials as well as to achieve complex geometries. Although numerical methods provide an efficient means to predict the material yield and the stress/strain states of the product at different stages of forming and classical methods are accurate enough to provide a suitable representation of the process, they tend to be computationally expensive. This limits their use in process optimization studies. The Pseudo Inverse Approach (PIA) developed in the context of 2D axisymmetric cold forming, provides a quick and fairly accurate estimate of the stress and strain fields in the final product for a given initial shape. In this work, the PIA is extended to include the thermal and viscoplastic effects associated with the hot forging process. The results are compared with commercially available software based on the classical approaches to show the efficiency and the limitations of PIA.

Improved subloading thermo-viscoplastic model for soil under strictly isotropic conditions

This paper presents a thermo-viscoplastic subloading soil model with a mobile centre of homothety. The model is formulated to describe the influence of non-isothermal conditions on the stress–strain-time behaviour of soils and is restricted to isotropic stress and strain conditions. Numerical simulations of three isotropic drained heating tests, two of which followed by a cooling stage, at constant isotropic effective stress for different overconsolidation ratios were performed. The model was able to accurately reproduce the experimental results, including the cooling behaviour, mainly due to the introduction of a direct influence of temperature on the mobile centre of homothety hardening law and also rate dependency.

Experimental characterization, material modeling, identification and finite element simulation of the thermo-mechanical behavior of a zinc die-casting alloy

Many industrially manufactured parts consist of a zinc die-cast material. Since classical constitutive models cannot predict the thermo-mechanical structural behavior of such a material – which exhibits highly non-linear rate-dependent effects, distinct aging properties as well a size-dependence of thin-walled parts –, it is necessary to carry out mechanical experiments under varying conditions as a basis for constitutive modeling. In this article, one major goal is the investigation of the rate-dependence at different temperatures of a zinc die-casting alloy. On the basis of several experiments on thin-walled, cylindrical tubes of Zamak 5, a thermo-mechanically consistent thermo-viscoplasticity model without a yield surface is proposed. Moreover, a concept of material parameter identification is provided and the implementation of the model into a finite element program is shown. Finally, the applicability of the model is proven by comparing an experiment of a complex component part with finite element simulations.

Existence of solutions of a thermoviscoplastic model and associated optimal control problems

A quasistatic, thermoviscoplastic model at small strains with linear kinematic hardening, von Mises yield condition and mixed boundary conditions is considered. The existence of a unique weak solution is proved by means of a fixed-point argument, and by employing maximal parabolic regularity theory. The weak continuity of the solution operator is also shown. As an application, the existence of a global minimizer of a class of optimal control problems is proved.

Semi-empirical elastic–thermoviscoplastic model for clay

Clays exhibit creep in compression and shear. In one-dimensional compression, creep is commonly known as “secondary compression” even though it is also a significant component of deformations resulting from shear straining. It reflects viscous behaviour in clays and therefore depends on load duration, stress level, the ratio of shear stress to compression stress, strain rate, and temperature. Research described in the paper partitions strains into elastic (recoverable) and plastic (nonrecoverable) components. The plastic component includes viscous strains defined by a creep rate coefficient ψ that varies with plasticity index and temperature (T), but not with stress level or overconsolidation ratio (OCR). Earlier elastic–viscoplastic (EVP) models have been modified so that ψ = ψ(T) in a new elastic–thermoviscoplastic (ETVP) model. The paper provides a sensitivity analysis of simulated results from undrained (CIŪ) triaxial compression tests for normally consolidated and lightly overconsolidated clays. Axial strain rates range from 0.15%/day to 15%/day, and temperatures from 28 to 100 °C.

Numerical investigations of optimum turning parameters—AA2024-T351 aluminum alloy

ABSTRACTAerospace aluminum alloys have gained the prime significance due to their excellent machining characteristics. Numerous experimental and numerical studies have been conducted to establish the optimum cutting parameters of these alloys. In the numerical cutting models, the authenticity of computational results is suspected particularly because of the complex interaction at tool–chip interface, which involves a high material strain rate and thermal processes. The fidelity of cutting simulation results is appraised by a parametric sensitivity analysis and actual experimentation. In this research, the orthogonal turning of AA2024-T351 aluminum is simulated in Abaqus/Explicit by using a thermoviscoplastic damage model and Coulomb friction model for the contact interfaces. A parametric sensitivity analysis is performed to comprehend the chip morphology, tool–chip interface temperature, reaction force, and strain. Different simulations are performed with varied cutting speeds (200, 400, 600, and 800 m/min), rake angles (5°, 10°, 14.8°, 17.5°), feeds (0.3, 0.4 mm), and friction coefficients (0.1, 0.15). It is observed that an increased rake angle decreases the cutting force and increases tool–chip interface temperature. Similarly, the cutting depth has prominent effect on chip–tool interface temperature as compared to the friction. The computational results are found in close approximation with the published experimental data of AA2024-T351.

A comparative study of refined and simplified thermo-viscoplastic modeling of a thrust chamber with regenerative cooling

The thermostructural response of the cooling channel of a regeneratively cooled thrust chamber employed for rocket applications can be evaluated by means of analytical and numerical methods. The heat fluxes produced by the combustion inside the thrust chamber cause elevated temperatures in the copper structure composed of ligaments separating the coolant flow from the combustion gases. Those thermal loads together with the mechanical loads due to the flowing coolant and hot gases, lead to a non linear structural response. In the present work a comprehensive study of the viscoplastic phenomena is carried out and a simplified finite element model, which does not take into account strain rate-dependent effects, is adopted.The aim of the work is twofold: understanding and detail modeling of the thermo-viscoplastic phenomena occurring in the copper inner liner of a rocket thrust chamber and evaluating the degree of importance of strain-hardening rate-dependent phenomena. The present paper demonstrates that the simplified viscoplastic model adopted in this work is suitable in the preliminary design phase since the percentage difference detected with respect to rate dependent models, such as Perzyna's and Robinson's ones, is slightly larger than 10%. Furthermore, this model is particularly useful when the results of strain hardening tests, aimed at evaluating strain rate dependent properties, are not available for the chosen material.

Effect of Material Thermo-viscoplastic Modeling on the Prediction of Forming Limit Curves of Aluminum Alloy 5086

A solution to improve the formability of aluminum alloy sheets can consist in investigating warm forming processes. The optimization of forming process parameters needs a precise evaluation of material properties and sheet metal formability for actual operating environment. Based on the analytical M-K theory, a finite element (FE) M-K model was proposed to predict forming limit curves (FLCs) at different temperatures and strain rates. The influences of initial imperfection value (f 0) and material thermos-viscoplastic model on the FLCs are discussed in this work. The flow stresses of AA5086 were characterized by uniaxial tensile tests at different temperatures (20, 150, and 200 °C) and equivalent strain rates (0.0125, 0.125, and 1.25 s−1). Three types of hardening models (power law model, saturation model, and mixed model) were proposed and adapted to correlate the experimental flow stresses. The three hardening models were implemented into the FE M-K model in order to predict FLCs for different forming conditions. The predicted limit strains are very sensitive to the thermo-viscoplastic modeling of AA5086 and to the calibration of the initial geometrical imperfection which controls the onset of necking.

Automatic differentiation for stress and consistent tangent computation

In the field of nonlinear finite element analysis, the linearization within the Newton–Raphson and the Multilevel-Newton–Raphson algorithm requires the computation of the stresses and the so-called consistent tangent operator. There are several possibilities for coding the derivatives either by deriving analytical expressions, by using numerical differentiation schemes, or by applying the concept of automatic differentiation. In this article, the three possibilities are compared for three different kinds of constitutive models in order to ascertain particular differences. These models are a finite strain hyperelasticity relation, a more sophisticated finite strain viscoplasticity model, and a small strain von Mises-type thermo-viscoplasticity model. Especially for the last example, it is required to provide a number of tangents to be derived within a monolithic, fully coupled finite element computation. Numerical examples investigate the advantages and disadvantages of analytical, numerical, and automatic differentiation. It is shown that the latter one is a very helpful tool in the developing stage of constitutive modeling.

Elevated temperature creep of pearlitic steels: an experimental–numerical approach

Pearlitic steels are well known for their high strength and hardness. This makes them the natural choice for applications in which structural integrity and minimum irreversible deformation over time are required. Although their room-temperature mechanical response has been intensively studied in the past, little information can be found in the literature regarding the effect of temperature on the mechanical response of pearlitic steels. In this paper, an experimental–numerical approach is used to study the mechanical response of pearlitic steels in the temperature range 20–500 °C. A finite-strain thermo-viscoplastic model is presented together with a set of elevated temperature tests (tensile and creep tests). The aim of the tests is twofold: first, to provide insight into the elevated-temperature mechanical response of the material; and second, to provide the data required to identify the corresponding material parameters. Furthermore, the model and the experimental data are instrumental in showing that the influence of temperature on the mechanical behavior of pearlitic steels becomes significant for temperatures above 350–400 °C.

Analysis of the high speed sliding interaction between titanium alloy and tantalum

Dry friction under extreme conditions between tantalum and titanium alloy (Ti–6Al–4V) was analyzed by using a finite element model of asperity interaction. To combine high sliding speed and high normal pressure, an experimental set-up based on a ballistic device with air gun launch, is presented. A single friction pass is realized at 38m/s to understand the initial stage of the friction and wear process. Contribution of the interface mechanical phenomena on the rough surface contact is investigated through a finite element approach considering the contact at the scale of asperities. A thermo-viscoplastic model coupled with damage law is proposed to explore the micro-contact conditions. Experimental observations obtained by light white profilometer are conducted to correlate the modeling.The simulation results show that the shearing of asperities occurs at high strain rate and large deformation. The material transfer mainly occurring from titanium alloy to tantalum, is the result of a competition between thermal softening and plastic hardening. The thermo-mechanical aspect seems to be the primary cause of metal transfer and wear. Shear localization may explain the frictional heating due to high strain rates. It was found that the localized temperatures combined with high normal pressures favor micro-weldings generated at the extremity of asperities.

Accelerating constitutive modeling by automatic tangent generation

AbstractWithin the framework of finite elements the linearization within a Newton‐like method requires the computation of the so‐called consistent tangent operator. There are several possibilities to get these derivatives. Three methods, namely analytical, numerical and automatic differentiation, for tangent generation will be analyzed concerning the simulation time and applicability for three different constitutive models. These models are a finite strain hyperelasticity model, finite strain viscoplasticity model for metal powders and a small strain thermoviscoplasticity model. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)