Thermomechanical State Research Articles

Flow of ultra-hot orogens: A view from the Precambrian, clues for the Phanerozoic

This contribution emphasizes first-order structural and metamorphic characters of Precambrian accretionary orogens to understand the kinematics and thermomechanical state of the continental lithosphere in convergent settings involving massive juvenile magmatism. We define a new class of orogens, called ultra-hot orogens (UHO), in which the weakest type of lithosphere on Earth is deformed. UHO are characterized by (1) distributed shortening and orogen-scale flow combining vertical and horizontal longitudinal advection, under long-lasting convergence, (2) homogeneous thickening by combined downward movements of supracrustal units and three-dimensional mass redistribution in the viscous lower crust, and (3) steady-state, negligible topography and relief leveled by syn-shortening erosion and near-field sedimentation. The flow analysis of UHO provides clues to understanding crustal kinematics beneath high plateaus and suggests that the seismic reflectivity pattern of hot orogens is an image of the layering produced by lateral flow of the lower crust and associated syn-kinematic plutonism. In between the UHO and the modern cold orogens (CO), developed by shortening of lithosphere bearing a stiff upper mantle, two classes of orogens are defined. Hot orogens (HO, representative of Cordilleran and wide mature collisional belts) share flow pattern characteristics with UHO, but involve a less intense magmatic activity and develop high topographies driving their collapse. Mixed-hot orogens (MHO, representative of magmatic arcs and Proterozoic collisional belts) are orogens made of UHO-type juvenile crust and display CO-like structure and kinematics. This classification points to the fundamental link between the presence of a stiff lithospheric mantle and strain localization along major thrusts in convergent settings. A high Moho temperature (> 900 °C), implying thinning of the lithospheric mantle, enhances three-dimensional flow of the lithosphere in response to convergence. Overall, this classification of orogens emphasizes the space and time variability of uppermost mantle temperature in controlling plate interactions and continental growth.

Numerical simulation of thermal stress in cast billets made of AZ31 magnesium alloy during direct-chill casting

A comprehensive two-dimensional (2D) mathematical model based on the ANSYS software has been developed for the computation of the thermomechanical state of the solidifying strand during direct-chill (DC) casting of abnormity ingots and during subsequent cooling. Stress and the strain formation mechanism had been studied. The boundary and initial conditions used for primary and secondary cooling were based on the heat transfer during the solidification of the billet. The effects of casting parameters on the distribution of temperature and stress were researched, which helped to optimize the casting parameters (casting speed, pouring temperature, length of crystallizer, and so on). The simulation results of thermal stress and strain field gave a better understanding of the formation mechanism of some casting defects, which was very useful for optimizing casting parameters and obtaining high-quality billets.

Examination of the thermomechanical state of cylindrical components deposited with layers of austenitic and martensitic steels

Examination of the thermomechanical state of cylindrical components deposited with layers of austenitic and martensitic steels

A thermomechanical model of the formation of a rift valley

A numerical model describing the thermomechanical state of the “cold” upper mantle near a mid-oceanic ridge (MOR) spreading at a moderate rate is constructed in the approximation of the boundary layer theory. The condition of rift valley formation leads to a constraint on the temperature and shows what temperature distribution corresponds to the “cold” upper mantle. Taking into account the dependence of mantle rheology on the pressure, temperature, and viscous stresses, the model distributions of the pressure and normal viscous stresses at the base of the lithosphere result in a bend of the heterogeneous lithosphere near the MOR, producing a seafloor topography typical of a rift valley with a depth of a few hundred meters and a spreading rate of ∼2.5 cm/yr, characteristic of the Atlantic Ocean. The model width of the rift valley (∼10–15 km) agrees with observations fairly well. The model is consistent with the typical heat-flow values observed in the spreading zone.

Procedure for testing VVÉR-1000 fuel in the MIR reactor under the conditions of an accident with ejection of a control rod

A procedure for performing dynamical experiments to study the behavior of VVER fuel under the conditions of an anticipated accident with the introduction of positive reactivity has been developed and adopted on the MIR reactor. A power pulse is produced by removing the screen from the absorber in the initial state of the surrounding fuel element. A reactivity compensator, which is moved synchronously with the screen, is provided to decrease the effect on the core. A three-element fragment of a VVER-1000 fuel assembly is used as an experimental fuel assembly. The volume of the installed measuring sensors and the rate at which the parameters are recorded are adequate for calculating the thermomechanical state of a fuel element. The precedure developed makes it possible to obtain in an experiment the lineal power density of fuel elements and the pulse parameters that correspond to the computed values for an anticipated accident.

Magnetic resonance imaging of phase transitions in nitinol

Magnetic resonance images are prone to artifacts caused by metallic objects. Apart from being a source of image degradation, such artifacts can also provide information about the magnetic properties of the foreign object. In this work, we aim to explore the potential of magnetic resonance imaging to detect and characterize changes in magnetic properties of nitinol undergoing temperature- or strain-induced phase changes. A spin echo and a gradient echo method were used to measure the magnetization changes related to the phase transformations. Results of both methods were in agreement and in accordance with the independent measurements using a vibrating sample magnetometer. Magnetic resonance imaging turned out to be a suitable method to visualize and quantify magnetization and phase changes in situ. It is not restricted to a single imaging strategy and does not require any modification of the test object. The results indicate the potential of magnetic resonance imaging to provide direct feedback of the thermomechanical state of the alloy.

Shock waves and the heterogeneity of materials

In a shock front, the evolution of thermomechanical state variables, although being continuous, occurs with a characteristic length smaller than the size of an elementary relevant volume (E.R.V.) of the material. So, the problem should be solved at this mesoscopic scale; nonetheless, we show that it is possible to derive jump relations on mean values at the macroscopic scale so long as the local problem satisfies some properties of homogeneisability.

A thermodynamic finite-strain model for pseudoelastic shape memory alloys

A thermodynamic finite-strain model describing the pseudoelastic response of shape memory alloys is proposed. The model is based on a self-consistent Eulerian theory of finite deformations using the logarithmic rate. Purely elastic material response is derived from a hyperelastic potential. The mass fraction of martensite is introduced as internal state variable to indicate the thermomechanical state of the phase transforming material. The evolution of martensite is governed by a kinetic law which is derived from the Helmholtz free energy of the two-phase solid and takes the heat generated during phase transition into account. The material model is implemented into a finite element code in an updated Lagrangian scheme and calibrated to experimental data. Simulations under different loading conditions illustrate the characteristics of the model.

3D Stress Model with Friction in and of Mould for Round Billet Continuous Casting

A three-dimensional, thermo-elasto-plastic finite element stress model with temperature-dependent thermal-physical mechanical properties, to compute the thermo-mechanical state of the solidifying shell and the distortion of mould during continuous casting of steel for a round billet has been developed to investigate the influence of mould friction on the strand stress. A method is applied to prevent penetration of the shell into the mold wall due to the ferrostatic pressure and excessive mould taper. Slag film thickness, air gap size and the contact state between the shell and mould have been predicted based on shell shrinkage and mould distortion including the mould taper, associated with their temperature fields. Ultimately, the influence of mould friction on the strand stress was also investigated. And the calculation results show that the magnitudes of the influence of mould friction on strand stress vary with various contact states, such as liquid slag film, direct contact, and air gap, between the shell and mould from one location to another.

Thermal Effects in a Physically Nonlinear Cylinder under Impulsive Loading

A coupled dynamic problem of thermomechanics is formulated based on a thermodynamically consistent modification of the Bodner-Partom model. This formulation is used to analyze the thermomechanical state of an aluminum cylinder under axial impulsive loading. The problem is solved by the finite-element method. Time integration is performed by the Crank-Nicholson scheme. Reversible and irreversible thermal changes are studied

Dissipative Heating of a Viscoelastic Cylinder under a Load Steadily Moving over Its Surface

The Fourier method is used to find the analytical solutions to two-dimensional quasistatic problems of stationary polyharmonic vibrations and dissipative heating of a linearly viscoelastic cylinder. The influence of the cylinder thickness and the width of the loading area on the thermomechanical state of the cylinder is studied based on numerical data

A local model for the thermomechanical conditions in friction stir welding

The conditions under which the deposition process in friction stir welding is successful are not fully understood. However, it is known that only under specific thermomechanical conditions does a weld formation occur. If these conditions are not present, void formation will occur leading to a faulty weld. The objective of the present work is to analyse the primary conditions under which the cavity behind the tool is filled. For this, a fully coupled thermomechanical three-dimensional FE model has been developed in ABAQUS/Explicit using the arbitrary Lagrangian–Eulerian formulation and the Johnson–Cook material law. The model accounts for the compressibility by including the elastic response of the aluminium matrix. The contact forces are modelled by Coulomb's Law of friction, making the contact condition highly solution dependent. Furthermore, separation between the workpiece and the tool is allowed. This is often neglected in other models. Once non-recoverable separation is estimated by the model, a void develops. This is suggested as a preliminary criterion for evaluating the success of the deposition process. Of special interest is the contact condition along the tool/matrix interface, which controls the efficiency of the deposition process. In most models presented previously in the literature, the material flow at the tool interface is prescribed as boundary conditions. In all other contact models, the material is forced to keep contact with the tool. Therefore, the models are unable to predict when the suitable thermomechanical conditions and welding parameters are present. In the present work, the quasi-stationary thermomechanical state in the workpiece is established by modelling the dwell and weld periods. The different thermomechanical states in the colder, stiffer far-field matrix and the hotter, softer near-field matrix (under the tool) result in contact at the tool/matrix interface, thus, no void formation is observed. The steady-state model results are compared to the plunge force and heat generation observed in experimental welds in AA2024-T3.

Influence of the thermo-mechanical residual state on the power assembly modellization

During the assembly process of a power chip on its thermal dissipator, it appears a residual stress store, due to the difference between the thermal expansion coefficients of the assembly components: silicon, solder alloy, copper. The goal of this study is to show the influence of the residual stresses and strains on the solder joint thermal fatigue. Three numerical simulations of thermal cycles have been carried out by taking into account the residual stresses or not. A simple assembly model is used to reduce the simulation run time. For each case, the strain energy density accumulated in the solder joint is computed during each thermal cycle. The comparison of these values for each case shows that the residual stresses must be taken into account in the assembly lifetime study.

An Eulerian Model for Pseudoelastic Shape Memory Alloys

AbstractA thermodynamic model describing pseudoelasticity is proposed. The kinematics are based on a self‐consistent Eulerian theory of finite deformations using the logarithmic rate. The thermomechanical state of the material is described by means of the mass fraction of martensite as internal state variable. From the Helmholtz free energy of the two‐phase solid, a kinetic law for the evolution of martensite is derived, taking into account the heat generated during phase transition. The material model is implemented into a finite element code in an updated Lagrangian scheme. Its parameters are calibrated to experimental data. The characteristics of the model are illustrated by simulations under different loading conditions.

A Two-dimensional Finite Element Thermomechanical Approach to a Global Stress-Strain Analysis of Steel Continuous Casting

This paper addresses the two-dimensional finite element simulation of steel continuous casting using a global non steady-state approach. The method aims at the calculation of the thermomechanical state (temperature, deformation, stresses) of steel all along the continuous casting machine. Both plane deformation and axisymmetric versions have been developed. The first one addresses the simulation of continuous casting of slabs, taking into account the possible curvature of the machine, whereas the second one applies to cylindrical billets. The implementation of the method is validated by comparison with results from the literature. It is applied to the study of a slab continuous caster for which successive depressive and compressive stress states are revealed in the secondary cooling region.

Analysis of thermomechanical behaviour in billet casting with different mould corner radii

A finite element thermal stress model to compute the thermomechanical state of the solidifying shell during continuous casting of steel in a square billet casting mould has been applied to investigate longitudinal cracks. A two-dimensional thermoelastoviscoplastic analysis was carried out within a horizontal slice of the solidifying strand which moves vertically within and just below the mould. The model calculates the temperature distributions, the stresses, the strains in the solidifying shell, and the intermittent air gap between the casting mould and the solidifying strand. Model predictions were verified with both an analytical solution and a plant trial. The model was then applied to study the effect of mould corner radius on longitudinal crack formation for casting in a typical 0·75%/m tapered mould with both oil and mould powder lubrication. With this inadequate linear taper, a gap forms between the shell and the mould in the corner region. As the corner radius of the billet increases from 4 to 15 mm, this gap spreads further around the corner towards the centre of the strand and becomes larger. This leads to more temperature non-uniformity around the billet perimeter as solidification proceeds. Longitudinal corner surface cracks are predicted to form only in the large corner radius billet, owing to tension in the hotter and thinner shell along the corner during solidification in the mould. Off corner internal cracks form more readily in the small corner radius billet. They are caused by bulging below the mould, which bends the thin, weak shell around the corner, creating tensile strain on the solidification front where these longitudinal cracks are ultimately observed.

The Coupled Thermomechanical State of a Notched Viscoelastic Rectangular Plate Under Harmonic Loading

The thermomechanical state of a notched viscoelastic rectangular plate under cyclic planar bending is analyzed within the framework of a coupled thermoviscoelastic problem. It is shown that under sufficiently intensive loading a zone of melted polymer forms near the notch and moves deep into the body, which may cause thermal fatigue failure of the polymer.

Thermo-elastic transformations in nickel-aluminium

Here we introduce a novel thermo-mechanical Solid State Additive Manufacturing (SSAM) process referred to as Additive Friction Stir (AFS) manufacturing that provides a new and alternative path to fusion-based additive manufacturing processes for developing fully-dense, near-net shape components with a refined-equiaxed grain morphology. This study is the first to investigate the beneficial grain refinement and densification produced by AFS in IN625 that results in advantageous mechanical properties (YS, UTS, εf) at both quasi-static and high strain rate. Electron Backscatter Diffraction (EBSD) observed grain refinement during the layer deposition in the AFS specimens, where the results identified fine equiaxed grain structures with even finer grain structures forming at the layer interfaces. The EBSD quantified grains as fine as 0.27 µm in these interface regions while the average grain size was approximately 1 µm. Additionally, this is the first study to report on the strain rate dependence of AFS IN625 through quasi-static (QS) (0.001/s) and high strain rate (HR) (1500/s) tensile experiments using a servo hydraulic frame and a direct tension-Kolsky bar, respectively, which captured both yield and ultimate tensile strengths increasing as strain rate increased. The HS results exhibited an approximately 200 MPa increase in engineering strength over the QS results, with the fracture surfaces at both strain rates aligned with the maximum shear plane and exhibiting localized microvoids.

THERMOMECHANICAL COUPLING EFFECTS NEAR DEFECTS IN INELASTIC BODIES

Models used to study thermal effects in elastoviscoplastic and viscoelastic bodies deformed under monotonic and harmonic loading are considered. They allow us to obtain qualitative and quantitative information on the thermomechanical state of the material. Numerical results can be used in a nondestructive analysis and in predicting thermal fatigue failure of inelastic bodies

Numerical modeling of the thermal-stressed state of cooled pulsed solenoids of electrophysical apparatus

Mathematical models, a finite-element algorithm, and software for computer simulation of coupled electromagentic, thermal, and mechanical processes in water-cooled pulsed solenoids are developed. The thermomechanical state of a high-voltage pulsed solenoid under actual water-cooling conditions is investigated.