Temperature Dependence Of Material Parameters Research Articles

A density-based topology optimization methodology for thermoelectric energy conversion problems

A density-based topology optimization approach for thermoelectric (TE) energy conversion problems is proposed. The approach concerns the optimization of thermoelectric generators (TEGs) and thermoelectric coolers (TECs). The framework supports convective heat transfer boundary conditions, temperature dependent material parameters and relevant objective functions. Comprehensive implementation details of the methodology are provided, and seven different design problems are solved and discussed to demonstrate that the approach is well-suited for optimizing TEGs and TECs. The study reveals new insight in TE energy conversion, and the study provides guidance for future research, which pursuits the development of high performing and industrially profitable TEGs and TECs.

Numerical modelling approach for the temperature dependent forming behaviour of Ti-6Al-4V

Titanium alloys offer several beneficial characteristics, such as high specific strength, metallurgical stability at elevated temperature, biocompatibility and corrosion resistance. With regard to these superior properties, Ti-6Al-4V is a commonly used titanium alloy for aerospace components and medical products. The production of parts made of Ti-6Al-4V can be done in various ways. One approach is forming at elevated temperature, which requires a focused design of parts, processes and numerical modelling of the forming process. Essential input parameters for the numerical models are temperature dependent material parameters. Since, the yield stress and Young's modulus of the material decrease significantly at elevated temperature, the forming limits are enhanced. For the characterization of the forming behaviour, uniaxial tensile tests at temperatures from 250 °C to 400 °C have been conducted. The samples are heated by conduction in a thermal-mechanical simulator for the tensile test. However, the resulting inhomogeneous temperature distribution along the longitudinal axis of the specimen is a challenge in order to measure proper material properties. Inhomogeneous temperature distribution leads to varying mechanical properties and temperature dependent forming behaviour. To overcome this issue, simple numerical models based on experimental data are necessary, which allow the estimation of the influence of the inhomogeneous temperature distribution. In this paper, therefore, the temperature distribution and the subsequent tensile test are investigated using electrical-thermal and mechanical numerical simulations of the tensile test at elevated temperature. With the combined approach of experimental tests and numerical simulations, the forming behaviour of Ti-6Al-4V can be modelled.

Thermo-mechanical fatigue prediction of a steam turbine shaft

The increasing demands on the flexibility of steam turbines due to the use of renewable energy sources substantially alters the fatigue strength requirements of components of these devices. This paper presents Thermo-Mechanical Fatigue (TMF) design calculations for the steam turbine shaft. The steam turbine shaft is exposed to complex thermo-mechanical loading conditions during the operating cycle of the turbine. An elastic-plastic structural Finite Element Analysis (FEA) of the turbine shaft is performed for the turbine operating cycle on the basis of calculated temperature fields obtained in a previous transient thermal FEA. The temperature dependent material parameters, which are used in the elastic-plastic FEA, are obtained from the uniaxial tests. Consequently, the TMF is predicted for the steam turbine shaft. Several fatigue criteria are used for the identifications of the critical domain and for the TMF damage assessment of the turbine shaft.

Characterization model of thermal shock resistance for fiber reinforced brittle matrix composites over a wide range of cooling environment temperatures

In this study, a thermal shock resistance model over a wide range of cooling environment temperatures for fiber reinforced brittle matrix composites is developed. The model takes into account the combined effects of cooling environment temperature and temperature-dependent material parameters. The critical temperature difference causing matrix cracking of SiC fiber reinforced reaction bonded Si3N4 composite and Nicalon fiber reinforced borosilicate composite are predicted over a wide range of cooling environment temperatures. The results show that the thermal shock resistance of composites is strongly dependent on the cooling environment temperature. Moreover, the quantitative influences of matrix Young's modulus, thermal expansion coefficient of matrix, and interfacial shear stress on thermal shock resistance with increase of cooling environment temperature are studied in detail. And some insights into improving the thermal shock resistance of fiber reinforced brittle matrix composites are obtained.

Modeling and analysis of the effect of thermal losses on thermoelectric generator performance using effective properties

A mathematical model for a thermoelectric generator (TEG) based on constitutive equations has been developed to analyze temperature dependent performance in terms of output power and efficiency. Temperature dependent material properties and thermal losses, which occur as conductive and radiative heat transfer, were considered in the finite element model. Effective material properties were invoked for understanding the influence of temperature dependence of material parameters and related adverse effects on the model TEG. It is shown that analytical equations with effective properties can provide excellent estimation of the performance of a TEG over a broad operating range. The model was simulated, analyzed and validated to examine the effects of different operating conditions and geometry that interact with thermal losses inside the TEG. We believe that this model will further expedite the optimization of TEGs being developed using new material compositions.

Numerical simulation and validation of a solidification experiment using a continuum mechanical two‐phase/‐scale model

AbstractA numerical simulation of a solidification experiment is presented. The experimental setup consists of an empty screwed up mould, which is filled up with molten steel and cools down due to atmospheric conditions. During the cooling process, the temperature at the centre as well as the shrinkage at the narrow side, respectively, have been recorded. The simulation has been run via the software ANSYS modified by specific provided programmer interfaces, the User Programmable Features (UPFs). All required temperature dependent material parameters have been provided by ThyssenKrupp Steel Europe. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Experimental Characterization and Material Modelling of an AZ31 Magnesium Sheet Alloy at Elevated Temperatures under Consideration of the Tension-Compression Asymmetry

Magnesium sheet alloys have a great potential as a construction material in the aerospace and automotive industry. However, the current state of research regarding temperature dependent material parameters for the description of the plastic behaviour of magnesium sheet alloys is scarce in literature and accurate statements concerning yield criteria and appropriate characterization tests to describe the plastic behaviour of a magnesium sheet alloy at elevated temperatures in deep drawing processes are to define. Hence, in this paper the plastic behaviour of the well-established magnesium sheet alloy AZ31 has been characterized by means of convenient mechanical tests (e. g. tension, compression and biaxial tests) at temperatures between 180 and 230 °C. In this manner, anisotropic and hardening behaviour as well as differences between the tension-compression asymmetry of the yield locus have been estimated. Furthermore, using the evaluated data from the above mentioned tests, two different yield criteria have been parametrized; the commonly used Hill’48 and an orthotropic yield criterion, CPB2006, which was developed especially for materials with hexagonal close packed lattice structure and is able to describe an asymmetrical yielding behaviour regarding tensile and compressive stress states. Numerical simulations have been finally carried out with both yield functions in order to assess the accuracy of the material models.

Modeling and experimental investigation of thermal–mechanical–electric coupling dynamics in a standing wave ultrasonic motor

Ultrasonic motor operation relies on high-frequency vibration of a piezoelectric vibrator and interface friction between the stator and rotor/slider, which can cause temperature rise of the motor under continuous operation, and can affect motor parameters and performance in turn. In this paper, an integral model is developed to study the thermal–mechanical–electric coupling dynamics in a typical standing wave ultrasonic motor. Stick–slip motion at the contact interface and the temperature dependence of material parameters of the stator are taken into account in this model. The elastic, piezoelectric and dielectric material coefficients of the piezoelectric ceramic, as a function of temperature, are determined experimentally using a resonance method. The critical parameters in the model are identified via measured results. The resulting model can be used to evaluate the variation in output characteristics of the motor caused by the thermal–mechanical–electric coupling effects. Furthermore, the dynamic temperature rise of the motor can be accurately predicted under different input parameters using the developed model, which will contribute to improving the reliable life of a motor for long-term running.

Investigation on the effects of temperature dependency of material parameters on a thermoelastic loading problem

The present work is concerned with the investigation of thermoelastic interactions inside a spherical shell with temperature-dependent material parameters. We employ the heat conduction model with a single delay term. The problem is studied by considering three different kinds of time-dependent temperature and stress distributions applied at the inner and outer surfaces of the shell. The problem is formulated by considering that the thermal properties vary as linear function of temperature that yield nonlinear governing equations. The problem is solved by applying Kirchhoff transformation along with integral transform technique. The numerical results of the field variables are shown in the different graphs to study the influence of temperature-dependent thermal parameters in various cases. It has been shown that the temperature-dependent effect is more prominent in case of stress distribution as compared to other fields and also the effect is significant in case of thermal shock applied at the two boundary surfaces of the spherical shell.

Ultrafast x-ray diffraction thermometry measures the influence of spin excitations on the heat transport through nanolayers

We investigate the heat transport through a rare earth multilayer system composed of Yttrium (Y), Dysprosium (Dy) and Niobium (Nb) by ultrafast X-ray diffraction. This is an example of a complex heat flow problem on the nanoscale, where several different quasi-particles carry the heat. The Bragg peak positions of each layer represent layer-specific thermometers that measure the energy flow through the sample after excitation of the Y top-layer with fs-laser pulses. In an experiment-based analytic solution to the nonequilibrium heat transport problem, we derive the individual contributions of the spins and the coupled electron-lattice system to the heat conduction. The full characterization of the spatiotemporal energy flow at different starting temperatures reveals that the spin excitations of antiferromagnetic Dy speed up the heat transport into the Dy layer at low temperatures, whereas the heat transport through this layer and further into the Y and Nb layers underneath is slowed down. The experimental findings are compared to the solution of the heat equation using macroscopic temperature-dependent material parameters without separation of spin- and phonon contributions to the heat. We explain, why the simulated energy density matches our experiment-based derivation of the heat transport, although the simulated thermoelastic strain in this simulation is not even in qualitative agreement.

Life Prediction of Rocket Combustion-Chamber-Type Thermomechanical Fatigue Panels

Thermomechanical fatigue panels represent small actively cooled sections of the hot-gas wall of a regeneratively cooled liquid rocket engine. In combination with cyclic laser heating, the panels are used to study both the fatigue life and thinning and bulging phenomena (the so-called doghouse effect) without the need for testing a full-scale engine. To improve the prediction of the thermomechanical fatigue panel’s fatigue life, a viscoplastic model coupled with isotropic damage and thermal aging was implemented. The temperature-dependent material parameters are determined using experimental data to take into account softening effects due to material degradation. The number of cycles to failure is computed numerically and compared to the results of a thermomechanical fatigue panel test. The damage parameter-based finite element analysis successfully predicts the damage initiation point in the middle cooling channel of the thermomechanical fatigue panel. Critical damage occurs at the 150th cycle, whereas the failure is experimentally observed at the 174th cycle. The effect of the increase of the wall thickness in the fin areas is also obtained by this numerical analysis. This study shows that cost-efficient thermomechanical fatigue panel tests have the potential to validate numerical fatigue life predictions for novel rocket combustion-chamber wall materials.

Efficiency calculation of a thermoelectric generator for investigating the applicability of various thermoelectric materials

Accurate measurement of efficiency for a thermoelectric generator (TEG) is of great importance for materials research and development. Approximately all the parameters of a thermoelectric material (TEM) are temperature dependent, and so we cannot directly apply the ηmax formula for efficiency calculation in the large temperature range. In this work, we have calculated TEG efficiency, and we study the suitability of different TEMs like Bi2Te3, Sb2Te3, PbTe, TAGS ((AgSbTe2)0.15(GeTe)0.85), CeFe4Sb12, SiGe, and TiO1.1 in the estimation of TEG efficiency. The efficiency of TEG made up of Bi2Te3 or Sb2Te3 gives ∼7% in the temperature range of 310 K–500 K. PbTe or TAGS or CeFe4Sb12 generates ∼6% in the temperature range of 500 K–900 K and SiGe or TiO1.1 also have remarkable efficiency in the higher temperature range, i.e., ∼1200 K. The calculated efficiency obtained is close to experimental results. Here, we report the enhancement of efficiency by using the segmented technique for different combinations of the above-mentioned materials. To this end, the proposed values of overall efficiency of TEG by segmenting Bi2Te3 and PbTe; Bi2Te3 and TAGS; Bi2Te3 and CeFe4Sb12 are 12%, 14%, and 11.88%, respectively, for the temperature range of 310 K–900 K. For automobiles, the efficiency of TEG having fixed exhaust temperature with varying sink temperature is also discussed. For the steel industry and spacecraft applications (up to 1200 K), either segmentation is done by comprising Bi2Te3, PbTe and SiGe, or Bi2Te3 and TiO1.1, which yields an efficiency of ∼15.2% and ∼17.2%, respectively. The relative change in efficiency by considering loss at the interface surface is found to be 10.5%. The proposed methodology and results can be treated as a viable option for engineers who are looking to fabricate TEG in real life by using the temperature dependent material's parameters such as thermal conductivity, electrical conductivity, and Seebeck coefficient on which zT¯ depends.

Influence of die geometric structure on flow balance in complex hollow plastic profile extrusion

The unbalanced flow problem often occurs at die exit in the extrusion process of plastic profile, which directly influences the performance of final products. For the lack of corresponding theoretical basis, reasonable extrusion die design is still a difficult task, especially for the complex hollow profile. With the development of computational fluid dynamics theory, numerical method becomes an effective way to investigate the complex material forming problems. In the present study, a design strategy for complex hollow profile extrusion die was proposed based on the principles of flow balance. The mathematical model for three-dimensional non-isothermal polymer melt flow within complex extrusion die runner was developed based on the computational fluid dynamics (CFD) theory. The governing equations were deduced based on the finite volume method, and the pressure-velocity coupling problem was solved by using the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The Arrhenius equation was employed to involve the temperature dependence of material parameters. The flow characteristics of PVC polymer melts in the extrusion process of complex hollow profile were investigated. The distributions of principal field variables including flow velocity, melt temperature, and pressure drop were obtained. The effects of die geometric parameters on the velocity distribution uniformity were further analyzed, and a design strategy was proposed to achieve the flow balance in complex plastic profile extrusion process.

Theoretical modeling on the laser induced effect of liquid crystal optical phased beam steering

Non-mechanical laser beam steering has been reported previously in liquid crystal array devices. To be one of the most promising candidates to be practical non-mechanical laser deflector, its laser induced effect still has few theoretical model. In this paper, we propose a theoretical model to analyze this laser induced effect of LC-OPA to evaluate the deterioration on phased beam steering. The model has three parts: laser induced thermal distribution; temperature dependence of material parameters and beam steering deterioration. After these three steps, the far field of laser beam is obtained to demonstrate the steering performance with the respect to the incident laser beam power and beam waist.

Determination of temperature dependency of material parameters for lead-free alkali niobate piezoceramics by the inverse method

Sodium potassium niobate (NKN) piezoceramics have been paid much attention as lead-free piezoelectric materials in high temperature devices because of their high Curie temperature. The temperature dependency of their material parameters, however, has not been determined in detail up to now. For this purpose, we exploit the so-called Inverse Method denoting a simulation-based characterization approach. Compared with other characterization methods, the Inverse Method requires only one sample shape of the piezoceramic material and has further decisive advantages. The identification of material parameters showed that NKN is mechanically softer in shear direction compared with lead zirconate titanate (PZT) at room temperature. The temperature dependency of the material parameters of NKN was evaluated in the temperature range from 30 °C to 150 °C. As a result, we figured out that dielectric constants and piezoelectric constants show a monotonous and isotropic increment with increasing temperature. On the other hand, elastic stiffness constant c44E of NKN significantly decreased in contrast to other elastic stiffness constants. It could be revealed that the decrement of c44E is associated with an orthorhombic-tetragonal phase transition. Furthermore, ratio of elastic compliance constants s44E/s33E exhibited similar temperature dependent behavior to the ratio of piezoelectric constants d15/d33. It is suspected that mechanical softness in shear direction is one origin of the large piezoelectric shear mode of NKN. Our results show that NKN are suitable for high temperature devices, and that the Inverse Method should be a helpful approach to characterize material parameters under their practical operating conditions for NKN.

Numerical modeling of inelastic structures at loading of steady state rolling

In order to gain a deeper knowledge of the interactions in the coupled tire-pavement-system, e.g. for the future design of durable pavement structures, the paper presents recent results of research in the field of theoretical-numerical asphalt pavement modeling at material and structural level, whereby the focus is on a realistic and numerically efficient computation of pavements under rolling tire load by using the finite element method based on an Arbitrary Lagrangian Eulerian (ALE) formulation. Inelastic material descriptions are included into the ALE frame efficiently by a recently developed unsplit history update procedure. New is also the implementation of a viscoelastic cohesive zone model into the ALE pavement formulation to describe the interaction of the single pavement layers. The viscoelastic cohesive zone model is further extended to account for the normal pressure dependent shear behavior of the bonding layer. Another novelty is that thermo-mechanical effects are taken into account by a coupling of the mechanical ALE pavement computation to a transient thermal computation of the pavement cross-section to obtain the varying temperature distributions of the pavement due to climatic impact. Then, each ALE pavement simulation considers the temperature dependent asphalt material model that includes elastic, viscous and plastic behavior at finite strains and the temperature dependent viscoelastic cohesive zone formulation. The temperature dependent material parameters of the asphalt layers and the interfacial layers are fitted to experimental data. Results of coupled tire-pavement computations are presented to demonstrate potential fields of application.

A Comparison of Simple Methods to Incorporate Material Temperature Dependency in the Green's Function Method for Estimating Transient Thermal Stresses in Thick-Walled Power Plant Components.

The threat of thermal fatigue is an increasing concern for thermal power plant operators due to the increasing tendency to adopt “two-shifting” operating procedures. Thermal plants are likely to remain part of the energy portfolio for the foreseeable future and are under societal pressures to generate in a highly flexible and efficient manner. The Green’s function method offers a flexible approach to determine reference elastic solutions for transient thermal stress problems. In order to simplify integration, it is often assumed that Green’s functions (derived from finite element unit temperature step solutions) are temperature independent (this is not the case due to the temperature dependency of material parameters). The present work offers a simple method to approximate a material’s temperature dependency using multiple reference unit solutions and an interpolation procedure. Thermal stress histories are predicted and compared for realistic temperature cycles using distinct techniques. The proposed interpolation method generally performs as well as (if not better) than the optimum single Green’s function or the previously-suggested weighting function technique (particularly for large temperature increments). Coefficients of determination are typically above , and peak stress differences between true and predicted datasets are always less than 10 MPa.

Modeling of Friction Self-Piercing Riveting of Aluminum to Magnesium

In recent years, higher requirements on vehicle performance and emission have been posing great challenges to lightweighting of vehicle bodies. Mixed use of lightweight materials, e.g., aluminum alloys and magnesium alloys, is one of the essential methods for weight reduction. However, the joining of dissimilar materials brings about new challenges. Self-piercing riveting (SPR) is a feasible process to mechanically join dissimilar materials, however, when magnesium alloy sheet is put on the bottom layer, cracks occur inevitably due to the low ductility of the magnesium alloy. Friction self-piercing riveting (F-SPR) process is a newly proposed technology, which combines the SPR with friction stir spot welding (FSSW) and has been validated being capable of eliminating cracks and improving joint performance. However, in the F-SPR process, the generation of the transient friction heat and its effect on interaction between the rivet and the two sheets are still unclear. In this paper, a three-dimensional thermomechanical-coupled finite-element (FE) model of F-SPR process was developed using an ls-dyna code. Temperature-dependent material parameters were utilized to calculate the material yield and flow in the joint formation. Preset crack failure method was used to model the material failure of the top sheet. The calculated joint geometry exhibited a good agreement with the experimental measurement. Based on the validated model, the transient formation of F-SPR mechanical joint, stress distribution, and temperature evolution were further investigated.

Partitioned coupling strategies for multi-physically coupled radiative heat transfer problems

This article aims to propose new aspects concerning a partitioned solution strategy for multi-physically coupled fields including the physics of thermal radiation. Particularly, we focus on the partitioned treatment of electro–thermo-mechanical problems with an additional fourth thermal radiation field. One of the main goals is to take advantage of the flexibility of the partitioned approach to enable combinations of different simulation software and solvers. Within the frame of this article, we limit ourselves to the case of nonlinear thermoelasticity at finite strains, using temperature-dependent material parameters. For the thermal radiation field, diffuse radiating surfaces and gray participating media are assumed. Moreover, we present a robust and fast partitioned coupling strategy for the fourth field problem. Stability and efficiency of the implicit coupling algorithm are improved drawing on several methods to stabilize and to accelerate the convergence. To conclude and to review the effectiveness and the advantages of the additional thermal radiation field several numerical examples are considered to study the proposed algorithm. In particular we focus on an industrial application, namely the electro–thermo-mechanical modeling of the field-assisted sintering technology.

Effect of Temperature Rate Term while Predicting Thermal Ratcheting of a Thin Cylinder due to Cyclic Temperature Variation

The occurrence of progressive plastic deformation due to ratcheting under thermal cycling governs the integrity and life of industrial components such as the main vessel of sodium cooled fast reactors (SFR). Present work firstly discussed a constitutive model with temperature rate terms (TRT) to highlight the effect of thermal load rate (TLR) during the ratcheting behavior of the two-bar mechanical system (SS 316 LN). The influence of TLR is studied for various stress controlled cyclic thermo-mechanical loadings considering temperature dependent material parameters. Secondly, the approach is used to reveal the effect of TRT while predicting thermal ratcheting of a thin cylinder caused by change in peak temperature during temperature front movement. Such loading situations are more relevant to the SFR when the pool temperature varies with free-level variations. Visco-plastic formulation with and without TRT is used for analysis, which is validated by comparing the published experimental and numerical results.