Thermo-mechanical System Research Articles

On Some Forgotten Formulas of L. de Broglie and the Nature of Thermal Time.

From 1948 until around 1965, Louis de Broglie, awarded the Nobel Prize for Physics in 1929 for his fundamental contributions to quantum theory, pursued a systematic study of the formal analogies between wave mechanics and the thermomechanics of Boltzmann and Helmholtz. As part of this line of research, he produced several interesting observations, which were, however, published only in French, and, therefore, had a very limited diffusion. Here, we reconsider, in particular, a result of his relating to the analogy between the internal clock (de Broglie phase) of a free particle and a cyclic isothermal process in a thermomechanical system. We show that the fundamental equivalence obtained by him can be derived under more convenient hypotheses than the original ones, essentially tied to the quantization of the action exchanged by the particle with a suitable thermostat. In this emended formulation, the relations proposed by de Broglie describe the emergence of the particle proper time from a thermal background. They also suggest a specific physical meaning of the Wick rotation, often used in quantum mechanical calculations, and the thermal time that appears in it.

Post-process updating of model parameters to approximate thermal errors of machine tools operating in different configurations

Machine tool (MT) thermal errors induced by external and internal heat sources (e.g. changing environment, friction and power losses in MT components) are an important element in machined workpiece inaccuracies. In the past few decades, indirect software compensation techniques have been used to address thermal errors on account of their economic and ecological aspects. Many slightly different approaches are described in the literature. If thermal error models are properly identified based on experiments with sufficiently varying input parameters, they usually work within similar calibration and verification conditions. As the sensory equipment of machines increases, models can be adapted to regions with higher thermo-mechanical system nonlinearity and inhomogeneity through the introduction of deformation feedback from direct measurements into model structures. However, adaptive functionalities require discrete interruptions of the MT's work cycle, which threaten the integrity of the machined surface and complicate the model structure and thus also implementation and industrial deployment possibilities. In this research, a novel approach of automatic post-process adaptation suitable for repetitive manufacturing, which takes advantage of transfer functions (TF), is proposed for thermal error reduction. The method respects basic heat transfer mechanisms in the MT structure by combining linear parametric models, requires a minimum of additional gauges, and feedback from direct measurements is obtained only during technological pauses in the production process. Post-process adaptation is solved retrospectively by updating model parameters using the heuristic method of genetic algorithms (GA). First, the approach was tuned on a case study of a heavy-duty milling machine with a horizontal headstock for a configuration with an exchangeable spindle head and a configuration with a change in the position of the headstock in the workspace, both of which were different from the initial model's calibration range. Subsequently, the developed approach was applied to repeated production on a medium-sized milling centre. Another goal of the paper is to emphasize the need for quality input information for modelling efforts and the industrial applicability of scientific results.

Themomechanical Response of an Additively Manufactured Hybrid Alloy by Means of Powder Bed Fusion

The laser powder bed fusion (L-PBF) technique was utilized to manufacture a hybrid M789-N709 alloy by depositing M789 steel on wrought N709 steel. The tensile strength of the M789-N709 interface generated during the process has been established to be higher than that of the base materials. In the previous work of the current authors, extensive characterization of the M789-N709 interface (before and after heat treatment) was performed by means of electron backscatter diffraction, electron probe microanalysis, transmission electron microscopy with energy dispersive spectroscopy, and atom probe tomography analyses, to understand the mechanisms associated with its superior strength. In the present work, since the application of the hybrid alloy is targeted towards an elevated temperature environment, the individual high-temperature mechanical properties of M789 and N709 steels were acquired at various temperatures and strain rates using a Gleeble 563 thermomechanical system. Then, based on the flow curves, phenomenological-, and physical-based constitutive material models were established. These constitutive models can be utilized to accurately assess the high-temperature response of the hybrid alloy system using finite element analysis programs. This work demonstrates the application of thermomechanical processing and constitutive modeling in the field of metal additive manufacturing.

A study of the radiation thermal boundary conditions influence in three-dimensional thermomechanical contact problems

Any body, by the simple fact of having a certain temperature on its surface, emits heat in the form of electromagnetic radiation. The heat flux emitted is proportional to the fourth power of the temperature of the solid, increasing the inherent non-linearity of the thermomechanical problems. This energy transfer, for systems at high temperatures, has greater relevance than the possible exchange of heat between bodies in contact by conduction or convection processes with a surrounding fluid in the interstitial areas. For this reason, this work presents a robust formulation to study three-dimensional thermomechanical contact problems where radiation boundary and interstitial conditions are simulated. The Boundary Element Method is used to compute the thermomechanical influence coefficients, and a double iterative procedure is used to ensure the achievement of the thermomechanical contact conditions. The final non-linear thermomechanical system of equations is solved using a Newton-Raphson procedure. The proposed formulation is validated with a comparison with some benchmark problems found in the literature and afterward applied to solve different three-dimensional thermomechanical contact problems where the thermomechanical variables are greatly affected by radiation boundary and interstitial conditions.

Phase transitions in porous media

The full quasistatic thermomechanical system of PDEs, describing water diffusion with the possibility of freezing and melting in a visco-elasto-plastic porous solid, is studied in detail under the hypothesis that the pressure-saturation hysteresis relation is given in terms of the Preisach hysteresis operator. The resulting system of balance equations for mass, momentum, and energy coupled with the phase dynamics equation is shown to admit a global solution under general assumptions on the data.

A simple force balance model of subduction initiation

SUMMARY The initiation and development of subduction zones are associated with substantial stress changes both within plates and at plate boundaries. We formulate a simple analytical model based on the force balance equation of a subduction zone, and validate it with numerical calculations of highly non-linear, coupled thermomechanical system. With two kinds of boundary conditions with either fixed velocity or fixed force in the far-field, we quantitatively analyse the role of each component in the force balance equation, including slab pull, interplate friction, plate bending and basal traction, on the kinematics and stress state of a subducting plate. Based on the numerical and analytical models, we discuss the evolution of plate curvature, the role of plastic yielding and elasticity, and how different factors affect the timing of subduction initiation. We demonstrate with the presence of plastic yielding for a plate of thickness, H, that the bending force is proportional to H2, instead of H3 as previously thought. Although elasticity increases the force required to start nucleating subduction it does not substantially change the total work required to initiate a subduction zone when the yielding stress is small. The analytical model provides an excellent fit to the total work and time to initiate subduction and the force and velocity as a function of convergence and time. Plate convergence and weakening rate during nucleation are the dominant factors influencing the force balance of the plate, and 200 km of plate convergence is typically required to bring a nascent subduction zone into a self-sustaining state. The closed-form solution now provides a framework to better interpret even more complex, time-dependent systems in three dimensions.

Microstructure and creep strength of simulated intercritical heat-affected zone of grade 91 steel

ABSTRACT The intercritical heat affected zone (ICHAZ) has been reported as one of the most Type IV cracking susceptible regions in 9Cr creep-resistant steel weldments. However, creep degradation mechanisms within the ICHAZ itself need further clarifications. In this work, two ICHAZ specimens of Grade 91 steel, low-temperature ICHAZ (LT-ICHAZ) and high-temperature ICHAZ (HT-ICHAZ), were simulated using the Gleeble thermomechanical system by exposing to two peak temperatures (860 °C and 900 °C) between AC 1 and AC 3. Dramatically different creep strengths of two simulated ICHAZs were observed and studied. Dilation curve analysis indicates a high fraction of newly transformed martensite formed in the HT-ICHAZ, which results in a much higher hardness (360 HV0.5) of the HT-ICHAZ than 266 HV0.5 of LT-ICHAZ. Precipitates, especially M 23 C 6 carbides, were not fully dissolved in both ICHAZ specimens. After a typical postweld heat treatment (760 °C-2 hours), the faster recovery of low-carbon martensite and reduced precipitation strengthening due to M 23 C 6 carbides coarsening in the HT-ICHAZ led to a significant hardness reduction. These microstructural degradations in the HT-ICHAZ made its creep lifetime about 36 times shorter than that of the LT-ICHAZ tested at 650 °C. The remaining tempered martensite from base metal in the LT-ICHAZ was the primary contributor to maintain its high creep resistance.

Planar, longitudinal, compressive waves in solids: Thermodynamics and uniaxial strain restrictions

A new tri-axial pressure-based constitutive expression has been found using Cauchy's stress tensor. This stress state emphasizes pressure and shear stress. The description is a pressure plus an effective shear stress allowing for a constitutive law based on atomic solid-state phase changes in crystalline cells due to pressure plus shear-based dislocation motion commonly associated with plasticity. Pressure has a new role in the material's constitutive response as it is separated from plasticity. The thermo-mechanical system describes third-order Gibbs’ expressions without specific volume restrictions placed upon the material. Isothermally, the ratio of heat to shear work in elastic copper is shown to approach zero at a very low temperature and become larger than one as temperature approaches melting. Wave compression models investigated are elastic and plastic: in fully elastic materials, the planar wave is restricted by Poisson's effect although plastic shear changes this constraint. Plastic deformation, dominated by dissipative shear stresses in uniaxial strain, heats the material while excluding phase changes from hydrostatic pressures. The material properties per se across Hugoniot shocks are described with entropy concepts. Shock waves are exceedingly complex since the constitutive laws are linked at extreme temperatures, pressures, and shear stresses. Isothermal, isentropic, isochoric, and iso-shear conditions are used throughout with Jacobian algebra.

Theoretical solution for thermo-mechanical crack-tip stress field for transversely graded materials

The present work deals with the structure of the thermo-mechanical stress field near the crack-tip in a graded material, where properties vary along the crack front in an exponential manner. With assumptions of steady-state conditions and insulated crack faces, expansion of the temperature field around the crack-tip is obtained. Results indicate that the heat flux in the radial and angular direction has inverse square root singularity near the crack-tip. The heat flux in the direction of gradation does not have any singularity. Navier’s equation for a thermo-mechanical system is solved using the Eigenfunction expansion approach to obtain the near crack-tip stress field. The explicit form of the first four terms in the expansion of the displacement field is obtained. It is observed that terms corresponding to in the stress field are directly affected by the temperature or heat flux. Effect of temperature is observed in out-of-plane normal stress only for Considering the first two terms in the asymptotic expansion, a parametric analysis, shows that thermal stresses help relax the constraint ahead of the crack-tip when the structure is constrained in the thickness direction. It helps in the suppression of crack growth mechanisms, which delays the failure of structures.

Finite element model for a coupled thermo-mechanical system in nonlinear strain-limiting thermoelastic body

We investigate a specific finite element model to study the thermoelastic behavior within the context of nonlinear strain-limiting constitutive relation. As a special subclass of implicit relations, the thermoelastic response of our interest is such that stresses can be arbitrarily large but strains remain small, particularly in the neighborhood of crack-tips. In the present communication, we consider a two-dimensional coupled system — linear and quasi-linear partial differential equations for temperature and displacements, respectively. A standard finite element method of continuous Galerkin is then employed to obtain the numerical solutions for the field variables, where two distinct temperature distribution of the Dirichlet type are considered for boundary condition. From a domain with an edge-crack, we find that the near-tip strain growth in the proposed model is slower than the growth of stress, which is the salient feature compared to the predictions of singular strain based on the classical linearized description of the elastic body. In essence, the model can be inherently consistent with the assumption of linearized elasticity and infinitesimal strain theory. This study can provide a theoretical and computational framework to develop physically meaningful models and examine other coupled multi-physics such as an evolution of complex network of cracks induced by thermal shocks.

Experimental Investigation on the Performance of a Novel Thermo-Mechanical Refrigeration System Driven by an Expander-Compressor Unit

Experimental Investigation on the Performance of a Novel Thermo-Mechanical Refrigeration System Driven by an Expander-Compressor Unit

Increase in productivity and quality based on the control of thermodynamic processes during deep profile grinding of the gas-turbine engine blade

The article provides the system of interaction of dynamic processes during deep profile grinding of complex profiles on a multiaxis machine, the influence of dynamic processes on the quality of the surface layer, the endurance limit of the gas-turbine engine blade. The method presented allows to assign corresponding grinding modes based on the forecast of the dynamics of elastic, thermal and working processes in a thermomechanical system. This technique allows to control the process of deep profile grinding to achieve the specified parameters of surface quality, the endurance limit of the blade and increase process efficiency.

Thermodynamic Analysis of Magnetohydrodynamic Third Grade Fluid Flow with Variable Properties

This article aims to computationally study entropy generation in a magnetohydrodynamic (MHD) third grade fluid flow in a horizontal channel with impermeable walls. The fluids viscosity and thermal conductivity are assumed to be dependent on temperature. The flow is driven by an applied uniform axial pressure gradient between infinite parallel plates and is considered to be incompressible, steady and fully developed. Adomian decomposition method (ADM) is used to obtain series solutions of the nonlinear governing equations. Thermodynamic analysis is done by computing the entropy generation rate and the irreversibility ratio (Bejan number). The effects of the various pertinent embedded parameters on the velocity field, temperature field, entropy generation rate and Bejan number are analysed through vivid graphical manipulations. The analysis shows that an appropriate combination of thermophysical parameters efficiently achieves entropy generation minimization in the thermomechanical system. The analysis shows that entropy generation minimization is achieved by increasing the magnetic field and the third grade material parameters, and therefore designs and processes incorporating MHD third grade fluid flow systems are far more likely to give optimum and efficient performance.

Studying the Dynamic Properties of a Distributed Thermomechanical System and Stability Conditions for Its Control System

Studying the Dynamic Properties of a Distributed Thermomechanical System and Stability Conditions for Its Control System

Modeling and simulations of high and hypervelocity impact of small ice particles

We present a computational model based on the Hot Optimal Transportation Meshfree (HOTM) method and a thermo-visco-elasto-plastic constitutive model for the high-fidelity simulation of high and hypervelocity impact of small ice particles. The competition and combination among various energy dissipation mechanisms in the high energy density event, including plasticity, fracture/fragmentation, and phase change, are predicted by minimizing the thermomechanical system’s potential energy within a variational structure. The variational Eigenerosion algorithm is incorporated in the HOTM method to simulate crack nucleation, propagation, and fragmentation. A multiphase thermo-visco-elasto-plastic model is developed to describe the dynamic response of ice under extreme loading conditions, such as strain and strain-rate hardening, temperature-dependent strength, pressure-dependent viscosity, and phase diagram. The proposed computational framework is validated by comparing to experimental observations and measurements from two ballistic tests at different strain rates. Numerical studies are performed for the impact tests of a microscopic spherical ice particle(⌀800nm) against a Ti-6Al-4V plate at velocities ranging from 250m/s to 5000m/s at an initial temperature of 200K. The evolution of failure modes in the ice projectile is well captured as a result of the energy partitioning explicitly into plasticity, fracture and phase change at different moments. The analysis demonstrates the transition of the dominant failure mechanism due to the increasing input energy density and the nature of stress wave propagation. The competition between fracture and phase change, in the presented configuration of numerical studies, starts when the impact velocity approaching 800m/s and thermal effects play a critical role in determining the local deformation and failure.

Modelovanje zatvaranja uskih okeanskih basena numeričkim simulacijama

Numerical simulations represent an established approach in investigation of geodynamic processes in the Earth's interior and it is applied to a vast variety of geological problems. The closure of a narrow oceanic realm is modelled in this paper. Firstly, a simplified numerical model of a narrow ocean is established. The thermomechanical system is then simulated by solving Navier-Stokes and temperature equations. By imposing boundary conditions for velocity the convergent regime is simulated which leads to a subduction process along a predefined weak shear zone mantle. The subduction subsequently results in development of magmatism, the final closure of the oceanic realm and the onset of continental collision. Considerable amount of ophiolites were successfully obducted onto the overriding continent during the course of the simulation.

Updating strategy of a domain decomposition preconditioner for parallel solution of dynamic fracture problems

Iterative methods used for analysis of multiphysics problems that result in localized solution features may be highly demanding from a computational standpoint and often require special treatment to be more efficient. Dynamic fracture of metals is one such example in which a nonlinear thermo-mechanical system leads to strain localization, resulting in shear bands and/or cracks, in which iterative solvers may have difficult time converging.In the current paper, we develop a novel updating domain decomposition preconditioner for parallel solution of dynamic fracture problems, in which shearbands are modeled using a temperature-dependent viscoplastic material model and fracture is modeled by the phase-field method. The domain decomposition method is based on the Additive Schwarz Method (ASM).The key idea is to decompose the computational domain into two subdomains, a localized subdomain that includes all localized features of the solution and a healthy subdomain for the remaining part of the domain. In this way, one can apply different solvers in each subdomain, i.e. focus more effort in the localized subdomain. In this work, an LU solver is applied in both subdomains, however, while the localized subdomain is solved exactly at every nonlinear iteration, the healthy subdomain LU operator is reused and only selectively updated. Hence, significant CPU time savings associated with the setup of the preconditioner can be achieved.To this end, we propose a strategy for updating the preconditioner in the healthy subdomain. The strategy is based on an idealized performance-based optimization procedure that takes into account machine on-the-fly execution time. Three dynamic fracture problems corresponding to different failure modes are investigated. Excellent performance of the proposed updating preconditioner is reported in serial and parallel computers.

A dynamic thermo-mechanical actuator system with contact and Barber's heat exchange boundary conditions

AbstractThis work, motivated by the rapid developments in Micro-Electro-Mechanical Systems (MEMS) structures, especially actuators and grippers, analyses the dynamics of a thermo-mechanical system consisting of a horizontal beam joined at one end to a vertical rod. As a result of thermal expansion or vibration of the rod, the other end may come into contact with another part of the MEMS device and that closes an electrical circuit, which is the actuating or switching function of such a beam–rod system. The interaction between the rod's contacting end and the supporting device is described by a normal compliance contact law for the displacements and by an inclusion-type Barber's heat exchange condition for the temperature. The heat-exchange coefficient is a multi-function taking into account the air resistance in the gap when there is no contact and the contact pressure when contact occurs. The model consists of a nonlinear variational inclusion for the temperature coupled with a nonlinear variational equation for the displacements. The existence of a weak solution to the problem is proved by using the Galerkin method, a regularization of Barber's condition with the Yosida approximation of a maximal monotone operator, and a priori estimates.

Sensitivity Analysis of Limit Cycles in an Alpha Stirling Engine: A Bifurcation-Theory Approach

We study a thermo-mechanical system comprised of an alpha Stirling engine and a flywheel from the perspective of dynamical systems theory. Thermodynamics establish a static relation between the flywheel's angle and the forces exerted by the two power pistons that constitute the engine. Mechanics, in turn, provide a dynamic relation between the forces and the angle, ultimately leading to a closed dynamical model. We are interested in the different behaviors that the engine displays as parameters are varied. The temperature of the hot piston and the mechanical phase between both pistons constitute our bifurcation parameters. Considering that energy conversion in the engine can only take place through cyclic motions, we are particularly interested in the appearance of limit cycles.

Prediction of Tempcore Rebar Strength Using a Thermomechanical Simulator with a Designed Hollow Specimen

In the Tempcore process, reinforcing bars are produced by short and intensive cooling. This rapid quenching converts the surface layer of a steel bar to a hardened structure. The exact simulation of the Tempcore process by a thermomechanical system is difficult to achieve because its cooling capacity is generally not sufficient to follow the Tempcore cooling rate. Therefore, herein, a hollow specimen is designed to increase the cooling rate. A series of thermomechanical tests following predetermined cooling curves provided by the thermal model is performed. The measured hardness of the thermomechanical‐tested specimen is used to predict the tensile strength of a Tempcore rebar based on the rule of mixture. The results show that the prediction of the strength of a Tempcore rebar by tailored cooling with a hollow cylindrical specimen is feasible with a high degree of reliability.