Temperature-dependent Material Research Articles

Theory-Guided Machine Learning Finds Geometric Structure-Property Relationships for Chemisorption on Subsurface Alloys

Summary Developing physically transparent and quantitatively accurate models that relate the chemical interaction (chemisorption strength) between an adsorbate and a solid surface to the adsorption site's geometry is critical for our understanding of catalysis, corrosion, and electrochemistry. We develop a theory-guided machine-learning (ML) approach, which uses an interpretable class of ML models called generalized additive models (iGAM models), to discover predictive structure-property models that can quantify and explain the link between the geometric structure of an adsorption site and the chemisorption strength. We demonstrate the approach through several case studies, where we analyze the chemisorption strength of chemically distinct adsorbates (O, OH, S, and Cl) on subsurface metal alloy surfaces subjected to various strain- and ligand-induced changes in the local geometric structure. By comparing the ML-derived chemisorption models to previously established electronic-structure models, we clarify the critical physical parameters that control the chemisorption process on metal surfaces.

Static Thermal Coupling Factors in Multi-Finger Bipolar Transistors: Part II-Experimental Validation

In this paper, we extend the model developed in part-I of this work to include the effects of the back-end-of-line (BEOL) metal layers and test its validity against on-wafer measurement results of SiGe heterojunction bipolar transistors (HBTs). First we modify the position dependent substrate temperature model of part-I by introducing a parameter to account for the upward heat flow through BEOL. Accordingly the coupling coefficient models for bipolar transistors with and without trench isolations are updated. The resulting modeling approach takes as inputs the dimensions of emitter fingers, shallow and deep trench isolation, their relative locations and the temperature dependent material thermal conductivity. Coupling coefficients obtained from the model are first validated against 3D TCAD simulations including the effect of BEOL followed by validation against measured data obtained from state-of-art multifinger SiGe HBTs of different emitter geometries.

Static Thermal Coupling Factors in Multi-Finger Bipolar Transistors: Part I—Model Development

In this part, we propose a step-by-step strategy to model the static thermal coupling factors between the fingers in a silicon based multifinger bipolar transistor structure. First we provide a physics-based formulation to find out the coupling factors in a multifinger structure having no-trench isolation (cij,nt). As a second step, using the value of cij,nt, we propose a formulation to estimate the coupling factor in a multifinger structure having only shallow trench isolations (cij,st). Finally, the coupling factor model for a deep and shallow trench isolated multifinger device (cij,dt) is presented. The proposed modeling technique takes as inputs the dimensions of emitter fingers, shallow and deep trench isolations, their relative locations and the temperature dependent material thermal conductivity. Coupling coefficients obtained from the model are validated against 3D TCAD simulations of multifinger bipolar transistors with and without trench isolations. Geometry scalability of the model is also demonstrated.

An inverse meshfree thermoelastic analysis for identification of temperature-dependent thermal and mechanical material properties

In many practical problems, a body is subjected to a thermal load and experience a temperature change. In some cases, the temperature change can be very high and it would be better to consider thermal and mechanical properties as a function of temperature whereas in many cases, temperature-dependent thermal and mechanical properties are unknown. In this article, an inverse method is presented for identification of the thermal conductivity, the specific heat, the coefficient of thermal expansion, and the elastic modulus, where all the properties are considered as functions of temperature. It is assumed that these four material properties are simultaneously unknown. In the proposed method, the unknown parameters of the inverse problem are calculated using measured data from a transient thermomechanical experiment. Sensitivity analysis is carried out by an analytical direct differentiation method and a meshfree technique. Several important factors affecting the identification of the thermal and mechanical properties, such as the error of measuring sensors, the number of sensors, and the number of sampling data are studied in the numerical analyses. The obtained results show that identification of the properties using the proposed inverse method can be achieved with a suitable accuracy even in the cases with measurement errors.

A fast reanalysis solver for 3D transient thermo-mechanical problems with temperature-dependent materials

A fast reanalysis solver using linear tetrahedral elements is developed for 3D transient thermo-mechanical problems with temperature-dependent materials. The core idea is to formulate the reanalysis framework of a stable node-based smoothed finite element reanalysis method. In the developed solver, the stable node-based smoothed finite element method (SNS-FEM) is used as the main solver due its accuracy and stability. The combined approximations (CA) method is the auxiliary tool for improving the efficiency of the SNS-FEM. In the developed reanalysis framework, binomial series expressions are used as high-quality basis vectors for the reduced basis method. The transient temperature and displacement fields can then be calculated without solving the complete set of nonlinear or linear system equations. The performance of the developed solver is evaluated through several numerical examples with different kinds of mixed boundary conditions. The results show that the reanalysis framework with two or three basis vectors is 20–50 times faster than the complete analysis and that the solver is much more efficient and stable than other solvers that use the traditional finite element method (FEM) or the smoothed finite element method (NS-FEM). Therefore, the performance of the developed solver is demonstrated.

Elastodynamic Response of a Three-Phase-Lag Model of Orthorhombic Thermoviscoelastic Material with Reference Temperature Dependent Properties

A three-phase-lag model of a homogeneous thermally conducting orthorhombic thermoviscoelastic material under the effect of the dependence of reference temperature on all elastic and thermal parameters is investigated. The Laplace and Fourier transform and eigenvalue approach techniques are used to solve the resulting nondimensional coupled equations. As an application of the problem, harmonically varying and sinusoidal pulse functions are considered. Numerical results for the field quantities are given in the physical domain and illustrated graphically. Comparisons are made for thermoviscoelastic temperature dependent, thermoviscoelastic and thermoelastic materials, respectively, for different values of time, for temperature gradient boundary.

An iterative method for identification of temperature and amplitude dependent material parameters of fiber-reinforced polymer composites

Temperature and amplitude dependent material properties have been observed for fiber-reinforced polymer composites (FRPCs) in previous studies. Accurate identification of the nonlinear material parameters is the basis of evaluation and optimization design of FRPCs. This paper proposes an iterative method based on differential evolution algorithm (DEA) for identifying the amplitude and temperature dependent material parameters of FRPCs. Initially, the expressions of complex elastic and shear moduli of FRPCs involving temperature and amplitude dependent fitting coefficients are proposed, upon which the iterative identification principle for nonlinear elastic and shear moduli and loss factors of FRPCs are clarified. Then, a series of dynamic experiments are conducted on FRPC plate specimens in thermal vibration environment from 20°C to 160°C with the excitation amplitude varied from 0.1g to 1.2g. The experimental data are adopted to identify the unknown fitting coefficients. Finally, the nonlinear elastic and shear moduli as well as loss factors of another specimen are determined via the proposed method, upon which the natural frequencies and damping ratios are achieved and compared to the measured results to validate the proposed identification approach. The effects of DEA key parameters on the iterative accuracy and efficiency are also discussed. From comparisons of identification results and experimental data, it can be seen the calculation errors of natural frequencies and damping ratios associated with the first four modes of FRPC plate are no more than 6.98 % and 13.34 %, respectively, which is acceptable for engineering applications.

A MEMS dynamic mechanical analyzer for in situ viscoelastic characterization of 3D printed nanostructures

Cellular metamaterial structures with sub-micron features have shown the ability to become excellent energy absorbing materials for impact mitigation due to the enhanced mechanical properties of materials at the nanoscale. However, in order to optimize the design of these energy absorbing metamaterial structures we need to be able to measure the dynamic properties of the sub-micron features such as storage and loss moduli and the loss factor. Therefore, at scale testing is required to capture the scale, temperature, and strain rate dependent material properties of these nanoscale materials. This paper presents the design, fabrication, and calibration of a MEMS-based dynamic mechanical analyzer (DMA) that can be directly integrated with the two photon lithography (TPL) process commonly used to fabricate metamaterial structures with nanoscale features. The MEMS-based DMA consists of a chevron style thermal actuator used to generate a tensile load on the structure and two differential capacitive sensors on each side of the structure used to measure load and displacement. This design demonstrated 1.5 ± 0.75 nm displacement resolution and 104 ± 52 nN load resolution, respectively. Dynamic mechanical analysis was successfully conducted on a single nanowire feature printed between the load and displacement stages of the MEMS device with testing frequencies ranging between 0.01–10 Hz and testing temperatures ranging between 22 °C–47 °C. These initial tests on an exemplar TPL part demonstrate that the printed nanowire behaves as a viscoelastic material wherein the transition from glassy to viscous behavior has already set in at the room temperature.

An elastic/plastic solution for a hollow sphere subject to thermo-mechanical loading considering temperature dependent material properties

A semi-analytical solution for an elastic/plastic sphere subject to thermo-mechanical loading is given. Material properties are temperature dependent. The solution is valid for any isotropic pressure-independent yield criterion. Even though the general solution in both elastic and plastic regions is rather simple, the solution of the boundary value is cumbersome. The solution is facilitated by using the dimensionless temperature as an independent variable instead of the radial coordinate. A detailed analysis of the solution of the boundary value problem is provided assuming that the pressure and temperature at the inner radius slowly increase whereas the pressure and temperature at the outer radius are kept constant. In particular, qualitative features of the solution are emphasized. Some of these features are useful for the design of spherical vessels subject to thermos-mechanical loading.

Role of fatigue in damage development of refractories under thermal shock loads of different intensity

Refractories insulation of industrial furnaces often fail under repetitive thermal shock. Degradation of silica refractories under thermal shock loads of different intensity was studied. The load variation was achieved by utilisation of geometrically similar samples of different dimensions. Finite element method modelling predicted loads developing during the test. Resulting damage was determined by the ultrasound velocity and crack patterns. Tests involving up to 150 cycles demonstrated the role of fatigue in enabling sub-critical crack formation and countering the crack arrest. Repetitive cycles reduce crack wake friction and intensify loading due to crack debris re-location. Damage saturation, sigmoidal and near-exponential damage growth was typical for low, intermediate and high loads, respectively. Similar trends of damage accumulation were observed in mechanical displacement controlled cyclic fatigue tests performed in wedge splitting set-up. Strain and strain energy based criteria of thermal shock intensity seem to have complimentary value in predicting the crack formation and growth. Thermal shock damage after the first cycle seems to be an effective parameter to predict overall resistance to the degradation in the sample. Load reduction due to previous crack formation related to the fatigue potential for subsequent crack development can explain the crack size variation typically observed in refractories after multiple thermal shocks. For thermal shock tests, the variation of sample size, instead of the temperature interval, is a suitable alternative for refractories with strongly temperature dependant material properties.

Prediction of the behaviour of copper alloy components under complex loadings by electro-thermomechanical coupled simulations

ABSTRACT Electronic devices must be served with electric power for different reasons. A robust and reliable electric connectivity is often realised by electric connectors. For its leading properties, precipitation hardened copper alloys are widely used for designing connectors with high level mechanical or conductance properties. However, copper alloys show a characteristic stress relaxation under mechanical or thermal loads. Finite element analysis is a standard method to design and optimise components with respect to reliability and performance. Hence, a material model considering the characteristic of the mechanical properties and allowing for the simulation of time and temperature dependent elasto-viscoplastic material behavior was developed at the Fraunhofer IWM. The parameters of the model were determined using tensile and relaxation test data of a C19010 alloy. The material model is applied to electro-thermomechanical coupled finite element simulations of connectors with different load histories. The goal of the simulations is the analysis of the impact of stress relaxation on the mechanical properties of systems over time. From the numerical results with the new model it is shown, how stress relaxation influences the connector clamping forces or contact pressure, respectively, in dependence with time or temperature. The simulation results documents that stress relaxation has to be taken into account in finite element simulations during the designing process of electrical devices. This paper is part of a Thematic Issue on Copper and its Alloys.

Code-to-code verification for thermal models of melting and solidification in a metal alloy: comparisons between a Finite Volume Method and a Finite Element Method

Abstract. Verification, the process of checking a modelling output against a known reference model, is an important step in model development for the simulation of manufacturing processes. This manuscript provides details of a code-to-code verification between two thermal models used for simulating the melting and solidification processes in a 316 L stainless steel alloy: one model was developed using a non-commercial code and the Finite Volume Method (FVM) and the other used a commercial Finite Element Method (FEM) code available within COMSOL Multiphysics®. The application involved the transient case of heat-transfer from a point heat source into one end of a cylindrical sample geometry, thus melting and then re-solidifying the sample in a way similar to an autogenous welding process in metal fabrication. Temperature dependent material properties and progressive latent heat evolution through the freezing range of the alloy were included in the model. Both models were tested for mesh independency, permitting meaningful comparisons between thermal histories, temperature profiles and maximum temperature along the length of the cylindrical rod and melt pool depth. Acceptable agreement between the results obtained by the non-commercial and commercial models was achieved. This confidence building step will allow for further development of point-source heat models, which has a wide variety of applications in manufacturing processes.

Structural and electrical properties of dipole-like substituted barium titanate

Structural and electrical properties of Ba[(Ga0.05,Ta0.05)Ti0.9]O3 (BGT) and Ba0.8Sr0.2[(Ga0.05,Ta0.05)Ti0.9]O3 (BSGT) have been characterized to determine the effects of charge compensated dipole-like substitutions on temperature dependent material properties. BGT has a maxima in the relative permittivity curve that corresponds to a tetragonal (P4/mmm) to cubic () phase transition which is consistent with the Rietveld refinement of XRD data. The ɛr value for BGT is 600 at 100 °C and varies by ∼25% over the temperature range [RT, 170 °C]. Sr addition in the B site of ABO3 is performed to increase the relative permittivity value while maintaining the same trend of temperature insensitivity of relative permittivity.

Estimating sensor number and spacing for inverse calculation of thermal boundary conditions using the conjugate gradient method

The conjugate gradient method is a popular tool for solving inverse heat transfer problems which arise for example from the estimation of unknown thermal boundary conditions or temperature dependent material properties. Depending on the desired accuracy of the results, input data of numerous temperature sensors need to be considered. However, due to limited access and available space many systems offer only a few temperature measurement spots. Therefore, this paper focuses on the question how changes in the number of temperature measurements affect the inversely estimated boundary condition. This behavior is studied by two numerical test cases with different boundary conditions, thermal properties and geometries, investigating also varying resolutions of the boundary condition and the effect of measurement errors. The results of both test cases show, that for undisturbed measurement data as well as superimposed measurement errors, fewer temperature readings than unknowns are sufficient to accurately estimate the boundary condition. Also, after exceeding a threshold in sensor number, only little improvement of inverse estimated results can be observed in both test cases. To transfer these findings on further inverse heat transfer scenarios, the key heat conduction parameters are summarized in a characteristic parameter, the Fourier number. This number supports the estimation of necessary sensor count in future inverse investigations with varying thermal parameters, geometries and investigation time.

Damped dynamic behavior of an advanced piezoelectric sandwich plate

In this paper, damped dynamic deflections of an advanced piezoelectric sandwich plate (APSP) subjected to thermo-electro-mechanical loads have been studied using a meshless method. In the considered APSP, two active piezoelectric layers are attached on to the faces of a passive advanced structure consisting of two thin graphene reinforced nanocomposite (GRNC) layers and a thick porous polymeric core. In GRNC layers, graphene content is assumed to be varied according to functional distribution profiles. Using modified Halpin-Tsai’ equations, temperature dependent material properties of nanocomposite layers have been determined. Reddy’s third order theory of plates (called TSDT) is utilized to obtain the coupled governing equations, and MLS shape functions are adopted in the meshless solution. The influences of graphene content, porosity, temperature, electro-mechanical loading and structural damping on dynamic deflection behavior have been investigated. The results reveal that adding graphene volume fraction from 3% to 7% significantly affects the damping ratio, settling time and dynamic response of APSPs. However, further addition of graphene content has little effect on those responses. Moreover, embedding more pores in the core layer remarkably changes the damped dynamic behavior of APSPs due to a significant reduction in structural weight and a slight decrease in structural stiffness.

Numerical investigation on plume expansion, components evolution and ionization of polytetrafluoroethylene (PTFE) irradiated by nanosecond laser

To investigate the plume expansion, components evolution and ionization in the laser ablation pulsed plasma thruster, which is difficult to obtain from experiments, the non-Fourier heat conduction model, fluid dynamics model and thermochemical model are established. The non-Fourier heat conduction model is established to calculate the propellant ablation, taking into account temperature dependent material properties, phase transition, depolymerization of polytetrafluoroethylene propellant, the reflection of the laser beam at the surface of the propellant, and non-Fourier effect. The fluid dynamics model is established to calculate the plume expansion, taking into account plume absorption and shielding. The thermochemical model is established to calculate the components evolution and ionization, taking into account nine chemical and ionization reactions with 12 components. By coupling the three models, the thermochemical characteristics, plume expansion and ionization of polytetrafluoroethylene irradiated by a nanosecond laser are numercially calculated.

Determination of relevant mechanical properties for the production process of polyethylene by using mesoscale molecular simulation techniques

ABSTRACT In this study, we determine the strain rate and temperature-dependent mechanical material behavior as well as the glass transition temperature and coefficient of thermal expansion of polyethylene melts using molecular dynamics simulation. In order to achieve realistic chain lengths polyethylene was simulated by three different coarse-grained models of various bead sizes. All simulations are performed by using the simulation package ESPResSo++, which we extended with a regulation procedure for the simulation of tensile tests on the micro-scale. The process-relevant observables, such as the elastic modulus, yield stress, and Poisson’s ratio are investigated at the meso-level. The chain orientation and entanglement behavior show effects that precisely illuminate the experimental stress strain response, giving important hints for production process control. Summarized, we are able to successfully reproduce the characteristic stress strain response for polyethylene as observed in experiments. Thus, we establish a closer link between microscopic and macroscopic system descriptions in order to provide a deeper understanding of material properties in their production process, i.e. for changing external conditions.

Dynamic responses of bidirectional functionally graded rotor shaft

This article deals with the finite element (FE) modeling and dynamics analysis of bidirectional functionally graded (2D-FG) rotating shaft system considering temperature-independent (TID) and temperature-dependent (TD) material properties of shafts. Time-dependent two-dimensional (2D) temperature distribution of such shaft has been found using the finite difference method (FDM). Based on the first-order shear deformation theory, a three noded beam elements has been developed for the finite element (FE) modeling and dynamic analysis of such shaft systems. It has been observed from obtained results that dynamic responses have significantly been influenced by temperature variation, power-law index, and internal viscous and hysteretic damping.

Investigating the effects of cooling rate on distortion of asymmetric composite laminates

Predicting the final shape of composite laminates after the curing cycles is crucial. An experimental and two numerical (with constant and temperature dependent material properties) studies have been presented. The purpose of this study is to investigate the effects of different cooling rates on the distortion of thin asymmetric composite laminates with different lay-ups after the curing cycle. Properties of a UD layer in different temperature have been obtained using TMA, DMA and micromechanical formulation. The samples were subjected to three different cooling stages. Results indicated that the distortion of the asymmetric composite laminate was significantly depending on the cooling rate and lay-up configurations. Accelerating the cooling rate can significantly enhance the out of plane deformation of the asymmetric laminates. In the slowest cooling rate, the effects of thermal residual stresses due to temperature change are minimum and consequently the results of both numerical analyses are closer to experimental observations. The analysis with temperature dependent material can predict the deformation of specimens with slowest cooling rate better than the analysis with constant material properties. Because of the sudden change in temperature, for prediction of distortion after the higher cooling rates, a transient analysis will be needed.

A Temperature-Control System for Continuous-Flow Microwave Heating Using a Magnetron as Microwave Source

A real-time temperature control system is designed for microwave heating of a continuous-flow substance. In this system, a magnetron is used as the microwave source, and its output power can be continuously adjusted though circuit design. A programmable logic controller (PLC) is used to procedure the temperature and power data as well as lead the whole control decision. The sample temperature can be controlled by regulating the output power of the magnetron though the control signal from the PLC during the heating process. The complete system is finally assembled into a user-friendly device, where the users can operate and monitor the heating process conveniently though a touch screen. A temperature-dependent material (Phosphoric acid) is used in system tests. The results show that the designed system can successfully achieve the desired temperature with an acceptable accuracy and stability.