Thermomechanical Boundary Conditions Research Articles

Finite element analysis of a generalized rotating FGM vessel subjected to thermo-mechanical loadings: Effect of Poisson ratio and inhomogeneity parameters

Cylinders and thick walled cylindrical shells are commonly utilized in several industries to transport and store fluids under certain pressure and temperature conditions. In the present paper, a numerical solution is developed in order to investigate displacement, temperature and stress fields in a rotating pressure vessel made of generalized functionally graded material (FGM) subjected to different thermo-mechanical boundary conditions. The aim is to investigate the effect of Poisson ratio, internal pressure and temperature and inhomogeneity parameters on the stress and deformation distributions of the rotating pressure vessel. The material is considered isotropic nonhomogeneous and linearly elastic with its properties varying along the radial direction. Additionally, certain conditions, such as exterior or interior problems where r → ∞ or r → 0, respectively, are impossible to resolve using the variation of attributes as a power-law distribution. An approach to the spatial Young modulus distribution that is more broad has been suggested in the literature which can be applied to such physical challenges. The rotation of the pressure vessel is considered in the analysis, and the temperature distribution is assumed to be non-uniform. Since an analytical solution to the differential equation is not accessible, the conventional Galerkin discretization approach of the Finite Element Method (FEM) is applied, nowadays is considered one of the main numerical tools for solving Boundary Value Problems (BVP). It is addressed how stress, strain, and displacement are affected by the inhomogeneity parameter, rotation speed, pressure, temperature, and Poisson ratio. The examination of the various findings indicates that changes in the temperature profile, rotation, and inhomogeneity parameter on the thermoelastic field have a substantial impact on the stress and strain in the FGM cylinder. The findings indicate that the Poisson ratio and inhomogeneity parameters have a significant impact on the stress and deformation distributions. According to the results, the above-mentioned parameters can be adapted to control the thermoelastic filed in a FGM cylinder. The present research offers significant perspectives on the development and enhancement of rotating FGM pressure vessels intended for high-temperature applications.

Thermoelastic analysis of variable thickness truncated conical shell subjected to thermomechanical load with internal heat generation using perturbation technique

In this article, the behavior of the truncated conical shell subjected to thermomechanical loading in their inner and outer layers with internal heat generation source is investigated. The displacement field obeys kinematic of the first order shear deformation theory and the first-order temperature theory is used. Two-dimensional temperature analysis has been performed along the thickness and axis of the shell, which can be defined under various loading and thermomechanical boundary conditions. The set of governing equations is a system of differential equations with variable coefficients which are solved by using the analytical matched asymptotic expansion of the perturbations technique. The mentioned solution has little computational cost, therefore can be used well in parametric studies for optimization. It was shown, axial displacement is somehow independent of the radial axis and its maximum value occurs near the upper boundary. The conical shell has expanded in the radial direction. Also the maximum temperature happens approximately in the middle of the length of the conical shell. The parametric study showed, with the increase heat flux in the outer layer thereby expanding the area of heat application which would let more heat in than out. Also it was found, controlling the lifetime of the structure is the result of directing the cone angle. The results obtained from the analytical solution were compared with the Finite Element Method (FEM) analysis and the results of similar related articles, only to show a good agreement.

Phenomenon-Based Model for Virtual Hot Strip Rolling

Every year digitalization is taking a bigger role in the steel industry. Models for predicting metallurgical phenomena, roll forces and microstructure have been commonly used in development of novel steel grades. These individual models may predict certain phenomena thoroughly, but input values are usually based on an assumption or on a “good guess”. To produce reliable boundary conditions for these models of individual phenomena, a virtual rolling model is developed. This model computes the whole process of the hot strip mill from roughing to accelerated water cooling on a run-out table. Strip location and temperature evolution is calculated continuously. Thermal and thermo-mechanical (rolling stands) boundary conditions are according to process layout. Input data for the model is automatically read from raw process data. Rolling parameters are calculated using a coupled ARCPRESS model, which is developed by authors, and calculates normal and frictional shear stress distributions in the roll gap to predict roll forces and displacements of the work roll surface. Recrystallization is considered when calculating the flow stress of the rolled strip. Phase fractions during water cooling are calculated as well. The virtual rolling model minimizes the need for parameter speculation as all parameters are calculated throughout the process. All the input values are read from actual process data and the metallurgical and mechanical state of the strip are computed throughout the whole process. As required by the state-of-art virtual rolling model, this model is based on generally accepted theories and experimentally studied metallurgical and physical phenomena along with the thermo-mechanical response of the actual rolling process.

RESEARCH OF THE THERMAL CYCLE ON THE SURFACE OF THE BILLET AS A CONSEQUENCE OF PLASTIC DEFORMATION DURING MECHANICAL PROCESSING

While the metallurgical characteristics of machined surfaces are constantly improving, there is still a lack of understanding regarding the thermal conditions in which these surfaces are in the process of interaction between the workpiece and the side surface. During machining of high-carbon alloys, very little is known about temperature changes in the internal volume of the machined part, where the workpiece material interacts with the cutting edge of the tool. In this work, the characteristics of the thermal field and the resulting surface metallurgy induced in high carbon alloys for cutting scenarios involving various combinations of thermomechanical boundary conditions were studied. The analysis of the development of the thermal field on the surface of the workpiece made it possible to reveal the heating and cooling rates caused by cutting, allowing to describe two different types of thermal cycle, with the structure Heating-Peak-Cooling and Heating-Quasi-isothermal Deformation-Cooling depending on the aggressiveness of the process. The subsurface thermal zone is found to be related to the deformation caused by cutting because it combines information about the magnitude of the thermal field and the speed of the process. It was found that the highest rate of heat generation caused by plastic deformation occurred in the thin surface layers at the beginning of the contact between the workpiece and the side surface, which was related to the conditions under which the white layers are generated. The analysis of the energy balance indicated the development of a less strong and less impulsive deformation process at greater depths below the surface, which was related to the mechanism of the formation of material resistance layers. Thus, the thermal effect on the processed surfaces was interconnected with their final metallurgical structure, which made it possible to deeply understand the physical conditions that arise when cutting high-carbon alloys.

Thermomechanical Analysis of Steel-to-Timber Connections under Fire and the Material Density Effect

This work presents a thermomechanical numerical analysis of a steel-to-timber connection with dowels in tension when exposed to fire using ANSYS ® software. Three different wood density materials were considered. The connection is built by a three-dimensional model with a thermomechanical boundary condition. A nominal temperature–time curve, ISO 834, was used to simulate the fire effect. Numerical simulation to determine the field of thermal and mechanical stresses was performed using a combined problem. A temperature field was imposed for a given time instant of fire exposure, calculated through a thermal analysis in a transient regime. This temperature profile was coupled to an incremental tensile load, allowing the determination of the maximum mechanical resistance of the connection. According to this methodology, the load-bearing capacity of the connections in each fire rating will be determined. In addition, the numerical results allow verification of the wood density influence on the mechanical resistance of the connection exposed to fire. In conclusion, the load-bearing capacity decreases with fire exposure and with lower material density. With the proposed methodology, the effect of the wood density on the heat transferred through the connection under fire can be verified, and a thermomechanical complex model is proposed to solve and analyze this type of problem, which is the great motivation in this work. The numerical methodology represents well the thermomechanical behavior of the connection under fire. This procedure can be used, considering other different parameters, to improve the design and allow the study of the connection behavior as an alternative to the experimental tests.

Mechanical and Thermal Stress Analysis of Cervical Resin Composite Restorations Containing Different Ratios of Zinc Oxide Nanoparticles: A 3D Finite Element Study.

Due to an increase in prevalence of cervical lesions, it is important to use appropriate restorative materials to reduce the incidence of secondary lesions. Owing to having antibacterial properties, cervical composite restorations containing different ratios of Zinc Oxide nanoparticles (ZnO NPs) have been analyzed using the Finite Element method to determine the optimal incorporation ratio from mechanical and thermal perspectives. A numerical simulation is conducted for a mandibular first premolar with a cervical lesion (1.5 × 2 × 3 mm3) restored with composites containing 0 to 5% wt. ZnO NPs. Subsequently, the samples are exposed to different thermo-mechanical boundary conditions, and stress distributions at different margins are examined. The accumulated stress in the restoration part increases for the 1% wt. sample, whereas the higher percentage of ZnO NPs leads to the reduction of stress values. In terms of different loading conditions, the least and most stress values in the restoration part are observed in central loading and lingually oblique force, respectively. The change in the surface temperature is inversely correlated with the ratio of ZnO NPs. In conclusion, the composite containing 5% wt. ZnO NPs showed the most proper thermo-mechanical behavior among all samples.

Propagation and interference of oppositely traveling generalized multi-fractional-order thermo-viscoelastic waves in discs with fractional-order constitutive and heat conduction models

By extension of the generalized Lord-Shulman (LS) theory to multi-rational-order thermo-viscoelastic spinning annular discs with fractional-order constitutive and heat conduction models, the propagation and interference of the temperature, displacement, and stress waves are studied here under various thermomechanical boundary conditions. A novel finite-element-based numerical iterative time marching technique is developed for the solution of the resulting nonlinear coupled multi-rational-order integrodifferential equations with accumulated terms whose number grows within each time step. The wave interference phenomenon due to simultaneous opposite shocks has not been investigated so far, even for the integer-order thermo-viscoelastic models. Results of the present multi-rational-order thermo-viscoelasticity are compared with those of the integer-order classical and LS thermo-viscoelastic models. Results show that the traction-type tensile and compressive shocks lead to local temperature reduction and rise, respectively, at the wavefront location. Although the thermal and constitutive fractional orders both increase the inertia and damping of the resulting system, the former affects the temperature rise and overshoot, and thermal memory effect and wave lag, whereas the latter affects the mechanical damping and oscillatory nature of the displacements and stresses more remarkably. Indeed, the thermal fractional-order represents an integrated thermal inertia-damping combination whereas the constitutive fractional-order leads to an integrated damping-stiffness combination.

Steady state thermoelastic contact problem of one-dimensional hexagonal quasicrystals

This paper investigates the thermoelastic contact problem of a rigid adiabatic spherical indenter moving on a one-dimensional hexagonal quasicrystal half-space. The frequency response functions of thermoelastic field are derived by considering the thermo-mechanical boundary conditions and thermoelastic governing equations. By using the discrete convolution-fast Fourier transform (DC-FFT) algorithm, the thermoelastic field is calculated numerically, and the distributions of displacements, stresses and temperature rise are obtained. Meanwhile, the influence of different friction coefficients on the thermoelastic field is investigated. The results indicate that, due to the large tangential force and high temperature, the normal phason displacement contour lines tilt to a certain extent in the opposite direction of tangential load, in addition to the slightly larger response at the right end of the contact area. The results of this paper can serve as the theoretical basis for studying the contact problem of one-dimensional hexagonal quasicrystal.

Creep Parameters Determination by Omega Model to Norton Bailey Law by Regression Analysis for Austenitic Steel SS-304

In the material’s creep failure analysis, the difficulty of assessing the applied thermo-mechanical boundary conditions makes it critically important. Numerous creep laws have been established over the years to predict the creep deformation, damage evolution and rupture of the materials subjected to creep phenomena. The omega model developed by the American Petroleum Institute and Material Properties Council is one of the most commonly used creep material models for numerical analysis over the years. It is good in defining the fitness of mechanical equipment for service engineering evaluation to ensure the reliable service life of the equipment. The Omega model, however, is not readily accessible and specifically incorporated for creep evaluation in FEA software codes and creep data is always scarce for the complete analysis. Therefore, extrapolation of creep behavior was performed by fitting various types of creep models with a limited amount of creep data and then simulating them, beyond the available data points. In conjunction with the Norton Bailey model, based on API-579/ASME FFS-1 standards, a curve fitting technique was employed called regression analysis. From the MPC project omega model, different creep strain rates were obtained based on material, stress and temperature-dependent data. In addition, as the strain rates increased exponentially with the increase in stresses, regression analysis was used for predicting creep parameters, that can curve fit the data into the embedded Norton Bailey model. The uncertainties in extrapolations and material constants has highlighted to necessitate conservative safety factors for design requirement. In this case study, FEA creep assessment was performed on the material SS-304 dog bone specimen, considered as a material coupon to predict time-dependent plastic deformation along with creep behavior at elevated temperatures and under constant stresses. The results indicated that the specimen underwent secondary creep deformation for most of the period.

Thermo-mechanical stress analysis within a steel exhaust valve of an internal combustion engine

The valves of an internal combustion engine play an essential role in the automobiles and their surroundings significantly affect their thermo-mechanical behavior. The work aims to assess numerically the effect of the real thermo-mechanical boundary conditions on the valves by considering the actual complex surrounding. For this purpose, we have subdivided the valve into seven adequate zones. We have evaluated the average values of the transient heat transfer coefficient, the adiabatic wall temperature and the mechanical load at each subdivision are during the opening and the closing periods. A transient Finite Element Model under ANSYS APDL software is developed and simulations are carried out until reaching the steady state. The temperature distribution and the thermal stresses at each valve position is obtained and then analyzed. The main findings show that the stress intensity distribution is developed in the zones labelled stem guide port and seat local of large temperature gradients, which causes high thermal stresses responsible of cracks or thermal fatigue damage. In addition, knowing the temperature map, the thermal gradient and stress under actual conditions will surely help manufacturers to better design exhaust valve, avoid early failure and enhance the durability of valves.

Towards understanding the thermal history of microstructural surface deformation when cutting a next generation powder metallurgy nickel-base superalloy

Despite the ongoing progress in metallurgical characterisation of machined surfaces, knowledge of the thermal conditions under which they originate during the workpiece-flank interaction is still lacking. When cutting advanced superalloys, little is known about temperature evolution in the machined part volume, where workpiece material interacts with the tool flank. In this work, the characteristics of the thermal field and the resulting surface metallurgy induced in a next generation nickel-base superalloy have been studied for cutting scenarios involving different combinations of thermo-mechanical boundary conditions. Analysis of the thermal field evolution in the workpiece subsurface has allowed the heating and cooling rates induced by cutting to be revealed, allowing description of two distinct types of thermal cycle, with a Heating-Peaking-Cooling (H–P–C) and a Heating-Quasi-isothermal Deformation-Cooling (HQC) structure depending on the process aggressiveness. Subsurface thermal history has been found to relate with the severity of the cutting-induced deformation, as it combines information on thermal field magnitude and on the process rates. Furthermore, thermal balance equations have been applied to study the rate of the heat generation in the machined subsurface due to its own plastic deformation while interacting with the tool flank. This has revealed that the highest rate of heat generation induced by plastic deformation occurred in thin surface layers at the beginning of the workpiece-flank contact, which has been associated to the conditions under which white layers (WLs) are generated. Energy balance analysis has furthermore indicated the development of a less severe and less impulsive deformation process at higher subsurface depths, which has been linked to the formation mechanism of material drag (MD) layers. In this way, the thermal history of machined surfaces has been related to their resulting metallurgical integrity, allowing in-depth understanding of the physical conditions developing when cutting next-generation superalloys.

Implementation of Thermomechanical Multiphysics in a Large-Scale Three-Dimensional Topology Optimization Code

<div class="section abstract"><div class="htmlview paragraph">Due to the inherent computational cost of multiphysics topology optimization methods, it is a common practice to implement these methods in two-dimensions. However most real-world multiphysics problems are best optimized in three-dimensions, leading to the necessity for large-scale multiphysics topology optimization codes. To aid in the development of these codes, this paper presents a general thermomechanical topology optimization method and describes how to implement the method into a preexisting large-scale three-dimensional topology optimization code. The weak forms of the Galerkin finite element models are fully derived for mechanical, thermal, and coupled thermomechanical physics models. The objective function for the topology optimization method is defined as the weighted sum of the mechanical and thermal compliance. The corresponding sensitivity coefficients are derived using the direct differentiation method and are verified using the complex-step method. The design variables are updated using the method of moving asymptotes so that the objective function is minimized resulting in maximum performance of the structure. Solution of the linear systems of equation is scaled across several supercomputer nodes using the Portable, Extensible Toolkit for Scientific Computation (PETSc) developed by Argonne National Laboratory. The finite element models, sensitivity analysis, optimization algorithm, and solver are all implemented in a freeware, density-based, topology optimization code (written in C++) that has been modified for thermomechanical problems. As such, the implementation of the thermomechanical model is provided. The code is applied to solve an example problem under thermal, mechanical, and thermomechanical boundary conditions. The resulting topologies and field variables are shown with a corresponding discussion.</div></div>

Laterally Penetrative Onset of Convection in a Horizontal Porous Layer

The onset of Darcy–Bénard convection in an unlimited horizontal porous layer is studied theoretically. The thermomechanical boundary conditions of Dirichlet or Neumann type at the lower and upper plane are switched from one type to another, at certain values of the horizontal x-coordinate. A semi-infinite portion of the lower boundary is defined as thermally conducting and impermeable, while the remaining boundary is open and with given heat flux. At the upper boundary, the same thermomechanical conditions are applied, but with a relative spatial displacement L and in the opposite spatial order. A domain of local destabilization around the origin is generated between the lines of discontinuity x = pm ,L/2. The marginal state of convection is triggered centrally, while it is penetrative in the domains exterior to the central domain. The onset problem is solved numerically, with a general 3D mode of disturbance, but 2D disturbances are preferred in most cases. The critical Rayleigh number is given as a function of the dimensionless gap width L and the wavenumber k in the y direction along the lines of discontinuity in the boundary conditions. An asymptotic formula for 2D penetrative eigenfunctions is shown to be in agreement with the numerical results.

Characterization of Thermomechanical Boundary Conditions of a Martensitic Steel for a FAST Forming Process

The present work characterized and modelled the interfacial heat transfer coefficient and friction coefficient of a non-alloy martensitic steel, for a novel Fast light Alloy Stamping Technology (FAST) process. These models were validated through temperature evolution, thickness distribution and springback measurements on experimentally formed demonstrator components, which were conducted on a pilot production line and showed close agreement, with less than 10% variation from experimental results. The developed models and finite element simulations presented in this work demonstrate that non-isothermal processes can be precisely simulated with implementation of the accurate thermomechanical boundary conditions.

Nonlinear thermomechanical vibration mitigation analysis in rotating fractional-order viscoelastic bidirectional FG annular disks under nonuniform shocks

The current article is concerned with the investigation of the formation of the time-dependent three-dimensional distributions and redistributions of the stress and displacement fields of the rotating annular and circular plates/disks under the nonuniform distributions of the dynamic thermomechanical loads or shocks. Redistribution of the stress and displacement fields happens due to the Gerasimov-Caputo-type relaxation kernel of the fractional viscoelastic model of the material in addition to the dynamic nature of the loading. All the mechanical and thermal material properties of the plate or disk may be tailored in both radial and transverse directions. The 3D thermoviscoelasticity theory is employed to develop the governing equations of motion (3D vibration) and heat transfer. Different thermal and mechanical boundary conditions are implemented. The resulting nonlinear time-dependent fractional-order thermoviscoelastic integro-differential equations are solved by proposing and implementing a special procedure that uses numerical evaluation of the singular-kernel Caputo-integral and second-order forward, backward, and central discretization of the spatial and time domains. Eventually, the influences of the bidirectional distribution of the material properties, 2D temperature distribution, fractional order and parameters of the viscoelasticity model, and thermomechanical boundary conditions are investigated on the distributions of the displacement and stress components rigorously and accompanied by 3D demonstrations.

Effects on surface and peripheral zone during single lip deep hole drilling

To adjust the defined surface and peripheral zone properties, such as hardness, residual stresses and surface quality, machining processes are in many cases followed by forming or heat treatment processes. A focused management of the machining process can already adjust the desired properties. The here presented work is part of an interdisciplinary research project in the framework of the priority program "Surface Conditioning in Machining Processes" (SPP 2086) of the German Research Foundation (DFG). This research project has the main objectives to determine the thermo-mechanical as-is state of the drilling peripheral zone during the process by means of a sensor-integrated tool for single lip deep hole drilling as well as to control the process parameters to achieve the aimed peripheral zone properties.Preliminary test series are related to the determination of the thermo-mechanical boundary conditions. From the obtained results, the requirements concerning the sensor-integrated tool can be derived. Further steps include the development of a sensor-integrated tool for the in-process determination of temperature, forces, moments and vibrations, the selection and integration of sensor systems as well as the correlation of process factors with peripheral zone condition. Especially for the determination of the temperature at the affected zone, a multi-sensor approach was chosen. The formulation of a control strategy and its implementation in the deep hole drilling machine of the Institute for Machine Tools (IfW) will finalize the first project phase. Required surface and peripheral zone properties can then be controlled based on measurement and simulation data. Effects on the peripheral zone can then be investigated using process simulations.This contribution gives an overview of the objectives and the planned project steps. Experimental investigations on temperature, feed force and drilling torque during single lip deep hole drilling are described. Also first results of the process simulation and their validation with measured quantities are presented.

Determination of thermo-mechanical quantities with a sensor-integrated tool for single lip deep hole drilling

To adjust the subsurface workpiece properties, such as hardness and residual stresses as well as surface quality, machining processes are often followed by forming, peening or heat treatment processes. An appropriate setup of the machining process can adjust the desired properties. The work presented here is part of an interdisciplinary research project in the framework of the priority program "Surface Conditioning in Machining Processes" (SPP 2086) of the German Research Foundation (DFG). This research project has the main objectives to determine the actual thermo-mechanical state of the surface and subsurface in single lip deep hole drilling during the process by means of a sensor-integrated tool as well as to control the process parameters to achieve the desired workpiece properties.Preliminary test series are related to the determination of the thermo-mechanical boundary conditions with thermal, material and machining models. From the obtained results, the requirements concerning the sensor-integrated tool can be derived. Further steps include the development of a tool for the in-process determination of the real cutting conditions, the selection and integration of sensor systems as well as the correlation of process states with workpiece conditions. The single lip deep hole drilling tool will be equipped with sensor systems for the acquisition of temperatures, forces, torques and vibrations close to the affected zone. In particular, for the determination of the process temperature close to the cutting zone, a multi-sensor approach was chosen. Effects on the workpiece can then be investigated using material simulations. The elaboration of a control strategy and its implementation in a deep hole drilling machine will finalize the current project phase. The final goal is that the required workpiece surface and subsurface properties can be controlled based on measurement and simulation data.

Investigation of the thermal-elastic problem in cracked semi-infinite FGM under thermal shock using hyperbolic heat conduction theory

In this paper, a thermoelastic analytical model is established for a functionally graded half-plane containing a crack under a thermal shock in the framework of hyperbolic heat conduction theory. The moduli of functionally graded materials (FGMs) are assumed to vary exponentially with the coordinates. By employing the Fourier transform and Laplace transform, coupled with singular integral equations, the governing partial differential equations under mixed, thermo-mechanical boundary conditions are solved numerically. For both the temperature distribution and transient stress intensity factors (SIFs) in FGMs, the results of hyperbolic heat conduction model are significantly different than those of Fourier’s Law, which should be considered carefully in designing FGMs.

A multiscale two-way thermomechanically coupled micromechanics analysis of the impact response of thermo-elastic-viscoplastic composites

A dynamic multiscale micromechanics model that accounts for two-way thermomechanical coupling in composites is presented. It predicts not only the standard deformation that results from a temperature change, but also the temperature change that results from mechanical deformation. In addition, viscoplastic material behavior is included at the scale of the fiber/matrix constituents in a local High-Fidelity Generalized Method of Cells analysis, which is conducted at each material point of a global analysis on a composite specimen. The global analysis of the composite considers time-dependent thermomechanical boundary conditions capable of simulating impact loading while solving the coupled transient thermal problem and the dynamic mechanical problem. Effective thermoelastic and physical properties, as well as homogenized inelastic strains are provided to the global model from the local scale. The multiscale model was employed to examine the impact response of carbon/epoxy and SiC/Ti composites with emphasis on the temperature changes and inelastic strains induced by the impact loading. It was found that the behavior of the two types of composites was quite different, with the differences traceable to the effect of the matrix material properties on the terms within the energy equation, which governs the heat generation.

Thermo-viscoelastic response of a cracked, functionally graded half-plane under a thermal shock

In this paper, a thermo-viscoelastic model is developed for the crack problem in an infinite, functionally graded half plane under a thermal shock. The moduli are assumed to be separable forms of both spatial coordinates and time, and two types of relaxation function of viscoelasticity are considered in this paper. By employing the Fourier transform and Laplace transform, coupled with the singular integral equations, the governing partial differential equations under mixed thermo-mechanical boundary conditions are solved numerically. The results show that the variations of stress intensity factors (SIFs) in viscoelastic functionally graded materials (FGMs) are significantly different than those in the elastic ones, which cannot be neglected in designing FGMs.