Thermal Stress Model Research Articles

Thermo-mechanical modeling of thermal stress in metal additive manufacturing considering elastoplastic hardening

The build-up of thermal stress induced by a high-temperature gradient in an additively manufactured part during laser metal additive manufacturing provides significant limitations to the adoption of this process since thermal stress may induce high tensile residual stress and part distortion in the additively manufactured parts. Herein, a thermomechanical analytical model is proposed to predict the in-process elastoplastic hardening thermal stress and strain for single-track scan strategy. The thermal model is validated using experimental results of melt pool geometry. Also, finite element simulation is performed to validate the proposed elastoplastic hardening thermal stress model of the same problem.

Reduced-Order Thermal Modeling for Photovoltaic Inverters Considering Mission Profile Dynamics

Power devices are among the reliability-critical components in the Photovoltaic (PV) inverter, whose failures are normally related to the thermal stress. Therefore, thermal modeling is required for estimating the thermal stress of the power devices under long-term operating conditions of the PV inverter, i.e., mission profile. Unfortunately, most of the thermal models developed for the power device are not suitable for a long-term thermal stress analysis (e.g., days to months), and there is usually a trade-off between the model accuracy and the computational efficiency. To address this challenge, a reduced-order thermal model for PV inverters is proposed in this paper, where the model simplification is based on the thermal impedance characteristic and the mission profile dynamics. The modeling accuracy is evaluated by comparing the estimated thermal stress with the experimental results from a PV inverter test-bench, where daily mission profiles with various dynamics are tested. According to the results, the proposed method offers a relatively high model accuracy (similar to the full-order thermal model) while the computational efficiency is improved significantly, making it suitable for long-term thermal stress modeling applications.

Numerical Modeling of Transient Temperature and Stress in WC–10Co4Cr Coating During High-Speed Grinding

Based on the classical theory of heat conduction and thermoplastic mechanics, the three-dimensional heat transfer and thermal stress models of high-velocity oxygen fuel WC–10Co4Cr coating under the action of a moving heat source during grinding were developed. Considering temperature-dependent material properties, the transient temperature field and the thermal stress field generated in workpiece were simulated by a finite element method (FEM). As both the thermal conductivity and the specific heat capacity of WC–10Co4Cr are larger than 300 M, temperature rise mainly occurred in the coating. The rise in grinding temperature was discontinuous along the depth of the workpiece, and the temperature gradient at the coating–substrate interface was found to be the largest. Due to the large difference in thermal expansion coefficient between coating and substrate material, considerable thermal stress was generated at the bonding surface. Grinding temperature and thermal stresses at the coating–substrate interface started to increase with the decrease in coating thickness. Grinding surface temperatures were measured experimentally for different coating thicknesses, and simulation results were compared with the obtained experimental values. It was found that FEM results were well consistent with experimental observations.

Modeling of thermal stresses destroying the porous coating of heat-exchange surfaces of power plants

Modeling of the low heat conductive low-porous capillary porous coatings and metal (copper, stainless steel) surfaces (base layer) was studied. Heat and mass transfer in the porous coatings moved with excessive liquid due to the combined action of capillary and mass forces. The dynamics of vapor bubble was described along with their heat-dynamic properties, which were observed by the optic research methods. Finding solution for the thermoelasticity allowed to reveal the influence of the specific heat flow and heat tension of compression and stretching depending on time of supply and sizes of pulled particles at the time of the system limit state as to "porous coating - base layer". The theory was confirmed by the trial, which was observed by camcorder SKS-1М.

Modeling of thermal stresses in inorganic matrix composite plates based on the asymptotic theory

A mathematical model has been developed for calculating a temperature non-stationary field and thermal stresses in thin multilayer plates of fabric composite materials on an inorganic matrix based on an alum-chromophosphate binder. The model allows to take into account changes in the microstructure in the matrix and composite fibers during high- temperature heating, taking into account the physical and chemical transformations occurring in them, as well as to calculate thermal stresses in thin plates from the tissue inorganic composite taking into account the kinetics of changes in the characteristics of composites during heating. Methods of multiscale homogenization and finite element modeling of microstresses in periodic cells were used to calculate the characteristics of the inorganic composite, and the method of asymptotic averaging was used to calculate the stresses in the plates. Some results of numerical simulation of the change in stresses in the composite plate during heating are given

On the use of LES-based turbulent thermal-stress models for rod bundle simulations

An alternative methodology is proposed here to overcome the excessive cost of large eddy simulations (LES) of full-length heated rod bundle calculations, while improving the inaccurate results typically obtained with Reynolds-averaged Navier–Stokes equations (RANS). While the cost of the full-length LES is generally too high, LES of a small section of a single rod is usually affordable. The idea presented here consists of using the information granted by the small LES calculation to determine the appropriate turbulence viscosity or turbulent thermal diffusivity that can be used to solve only for the temperature field in a pseudo-RANS approach. The study has been performed with single-rod simulations with a P/D of 1.12 and 1.24, considering rod lengths that are representative of reactor applications, for the cases of uniform heat flux and a more realistic cosine-like axial heat distribution. The spectral element code Nek5000 has been used for all LES, RANS, and pseudo-RANS simulations. The recently proposed Nek5000 steady-state solver has been used for solving the temperature field in the pseudo-RANS approach and has proved significantly faster than transient schemes. Prediction of thermal quantities is compared with classical linear and nonlinear RANS models. LES for the full-length rods has also been performed and is used as a reference. Results of the proposed method show significant improvements with respect to those obtained with RANS.

Optimization of the controlling recipe in quasi-single crystalline silicon growth using artificial neural network and genetic algorithm

The thermal field in the seeded directional solidification (DS) of quasi-single crystalline (QSC) silicon needs precise control to preserve the seed and maintain a flat solidification interface. Compared with adjusting the furnace configuration and materials properties, optimizing controlling recipe parameters of the DS process is more convenient and efficient in reality for improving the thermal field. However, controlling elements in the furnace interact with each other and the cooperation effect cannot be estimated by qualitatively deducing, which adds difficulties to the design and improvement of controlling recipe. In this study, an optimization system was built to optimize the controlling recipe during crystal growth and an industrial G6 DS furnace was taken as an application example. Flattening the solidification interface, reducing the thermal stress in the growing crystal and shortening the casting time were chosen as three optimization targets. Two independent heaters and a heat gate were the three controlling elements whose recipe parameters were the optimization variables. A 2D heat transfer model along with a thermal stress model was developed and an Artificial Neural Network (ANN) was trained to study the mapping relationship between optimization variables and targets in order to save computing resource and time. Genetic Algorithm (GA) was employed to yield the optimal recipes of the three controlling elements. The results showed that the optimal recipe achieved better crystal quality compared with the original recipe. The effectiveness and efficiency of this optimization system indicates that it can achieve the optimal result that theoretic analysis may hardly access.

Thermal Fatigue Modelling and Simulation of Flip Chip Component Solder Joints under Cyclic Thermal Loading

Thermal Fatigue of flip chip component solder joints is widely existing in thermal energy systems, which imposes a great challenge to operational safety. In order to investigate the influential factors, this paper develops a model to analyze thermal fatigue, based on the Darveaux energy method. Under cyclic thermal loading, a theoretical heat transfer and thermal stress model is developed for the flip chip components and the thermal fatigue lives of flip chip component solder joints are analyzed. The model based simulation results show the effects of environmental and power parameters on thermal fatigue life. It is indicated that under cyclic thermal loading, the solder joint with the shortest life in a package of flip chip components is located at the outer corner point of the array. Increment in either power density or ambient temperature or the decrease in either power conversion time or ambient pressure will result in short thermal fatigue lives of the key solder joints in the flip chip components. In addition, thermal fatigue life is more sensitive to power density and ambient temperature than to power conversion time and ambient air pressure.

Advances in Modeling of Steel Solidification with IDS

IDS (Inter-Dendritic Solidification) is a thermodynamic-kinetic software package that simulates phase changes, compound formation/dissolution, and solute distribution during solidification of steels as well as during their cooling/heating process after solidification. The software package also simulates solid-state phase transformations related to the austenite decomposition process at temperatures below 900/600 °C, and calculates thermophysical material properties from the liquid state down to room temperature. These data are needed in other models, such as heat transfer and thermal stress models, whose reliability heavily depends on the input data. The software package also features a database for thermodynamic, kinetic and microstructure data, as well as for several material properties. Owing to the short calculation times, the IDS tool is suitable for online applications. This paper presents IDS and its modules with the latest developments and validations, along with examples of modeling results.

Thermal effective stress in shales

Calculating velocities in shales in thermal production settings is important to refine time-lapse reservoir characterization from seismic. The effective stress concept is attractive to potentially reduce the amount of expensive core calibration data required. We propose a formulation for thermal effective stress in shales based on the idea of balancing undrained pore pressure increments from thermal expansion with an increase in the matrix stress to minimize pore deformation. This formulation is motivated by a desire to simplify forward modeling, reduce the number of dimensions that must be experimentally calibrated through core testing, and to leverage existing velocity-stress relations for thermal applications. The concept was tested on data from a well-known set of experiments consisting of two North Sea Kimmeridge shale core samples, which displayed a linear dependence of velocity on pressure and temperature. These data were found to be consistent with the proposed thermal effective stress model with a constant effective stress coefficient when considering elastic changes but do not prove that the concept is universally valid. Thermal effective stress coefficients were calculated for P- and S-wave velocities from the data and were found to lie from 0.66 to 1.22, demonstrating reasonable scaling for the proposed model.

Novel assessment and countermeasure for micro-annulus initiation of cement sheath during injection/fracturing

The excessive changes of downhole pressure and temperature during injection/fracturing could initiate micro-annulus of cement sheath as the leakage pathway of underground fluid, which increases the risk of suspending production and environmental pollution. The investigations on accurate prediction, operational management and new technologies are significant to sustain well integrity and to enhance safety and efficiency in hydrocarbon and geothermal developments. In this work, a novel fully coupled thermal-stress model is proposed, which can predict the micro-annulus initiation and extension in the casing-cement-formation system. The interfaces of cement sheath with casing/formation are simulated using the contact interaction containing cohesive behavior and damage. The surface film condition is set on the internal wall of casing to simulate the heat transfer due to cold-water flow. This model is validated by the laboratory experiment and shows high accuracy. Results indicate that the maximum micro-annulus occurs during depressurization process after injection. It is newly found that the debonding could also emerge at the beginning of cold-water circulation in casing. The thermal effect, compared with pressure, is the dominated factor on micro-annulus initiation and size, while the pressure only causes a small plastic micro-annulus. For countermeasures, enhancing tensile strength is not an effective approach to prevent micro-annulus. By appropriately assigning the injection procedure, the micro-annulus can be eliminated in injection/fracturing operations. The findings can supply the technique support for well integrity assessment and management during hydraulic fracturing or high-pressure injection and production.

Mathematical modelling of thermal dynamic stresses on the basis of a dual – Phase lag model

Using the modified Hooke’s law equation that takes into account the relaxation of stresses and strains, we have obtained the relaxed thermal dynamic stresses equation that includes summands subject to the relaxation properties of materials. An exact analytical solution to a heat conductivity equation derived with the local nonequilibrium of the thermal process in mind was used as a temperature function. An analysis of the exact analytical solution to the thermal dynamic stresses equation for an infinite plate with outer surfaces affected by heat impact indicated the elimination of the abrupt stress variation caused by solutions to classic equations, which do not take into account the relaxation properties of materials. The analysis also showed that in each point of the plate, stresses change following the harmonic law with an oscillation amplitude damped in time. Displacement changes also follow the harmonic law and result in high-frequency harmonic oscillations due to the periodic compression and expansion of the plate in relation to the centre of its thermal symmetry.

Investigation of pinholes in Czochralski silicon ingots in relation to structure loss

In the production of monocrystalline silicon by the Czochralski process, structure loss frequently reduces yield and increases production time. Structure loss means the transition from monocrystalline to multicrystalline structure. It is typically preceded by generation of dislocations and slip. Previous work concluded that a pinhole (i.e. a cavity from gas bubble in the melt) was the main cause of structure loss in an n-type Czochralski ingot. In the present study, seven industrial n-type Czochralski silicon ingots were investigated to assess whether pinholes frequently contribute to cause structure loss. Pinholes were found within 5 cm above the position where dislocations were generated in four out of the seven ingots. Slices were cut with the pinholes at one surface and etched with Sopori etchant. The pinholes did not appear to have affected the arrangements of etch pits in these samples and investigation of pinholes did not reveal the cause of structure loss. Furthermore, there were not significantly higher pinhole frequency before structure loss compared to ingots without structure loss among 4041 industrial ingots. Modeling of thermal stresses showed stress concentration around a pinhole, and it gives new insight into the level of stress the ingot can endure without generating dislocations and slip.

Analytical thermal stress modeling in electronics and photonics engineering: Application of the concept of interfacial compliance

Application of the concept of interfacial compliance in analytical thermal stress modeling in electronics and photonics engineering is addressed. The review is based mostly on the author’s research conducted during his tenure with Bell Labs (Basic Research, Area 11, Murray Hill, NJ), University of California (Santa Cruz, CA), Portland State University (Portland, OR), and Small-Business-Innovative-Research (SBIR) ERS Co. The emphasis is on practically important, but often non-obvious and sometime even paradoxical situations.

A neural network approach for determining spatial and geometry dependent Green's functions for thermal stress approximation in power plant header components

The trend in power generation to operate plant with a greater frequency of on/partial/off load conditions creates several concerns for the long term structural integrity of many high temperature components. The Green's function method has been used for many years to estimate the thermal stresses in components such as steam headers by attempting to solve the un-coupled thermal stress problem for a unit temperature step. Once a Green's function for a unit temperature step has been determined, realistic or actual component temperature profiles can be discretised and the time dependent stress profile reconstructed using Duhamel's theorem. Stress fluctuations can therefore be estimated and damage due to fatigue mechanisms can be quantified. A potential difficulty with this method is that Green's function approximations are determined for a single analysis point in a structure. This is because Green's functions are approximated by fitting a trial function to the results of finite element (FE) simulations. While a user can make some judgement on which point in a structure will give the “worst case” (or life limiting) conditions, it is foreseeable that points of interest will be dependent on the specific analysis conditions, such as the stub penetration geometry and the loading condition considered. The neural network approach described in this paper provides a means where transient thermal stress models of complex components (here taken to be steam headers) can be generated relatively quickly and used pro-actively to assess and modify plant operation. A range of header geometries have been considered to make the network applicable over an industry relevant envelope. Coefficients of determination (R2) are typically above 0.92 when reconstructed (from neural network results) unit temperature step stress profiles are compared against “true” FEA results. Mean errors in the stress profiles are, for the majority of cases, less than 10%. Suggestions are also made on possible future improvements to the method through the use of additional constraints on the reconstructed stress profiles.

Mechanical model for the interfacial thermal stress in porous ceramic foam coatings bonded to a substrate

Coatings of porous ceramic foams have potential applications in thermal protection systems of space shuttles. This paper develops a mechanics model for evaluation of thermal stress of porous ceramic foam coating/substrate structures under thermal shock temperature variation. Numerical results show that interfacial stresses exhibit singularity at the edge of ceramic foam coating. Stress intensity factor will reduce when ceramic foam coating has a larger density or a larger thermal conductivity. Comparison between beam model and membrane model is made and it suggests that consideration of bending stiffness is essential for correct evaluation of the thermal stress in the ceramic foams.

Elevated Stand-Off Heights in Solder Joint Interconnections of Surface Mounted IC Packages Result in Appreciable Stress and Warpage Relief

Abstract The “head-in-pillow” (HnP) defects in lead-free solder joint interconnections of IC packages with conventional (small) stand-off heights of the solder joints, and particularly in packages with fine pitches, are attributed by many electronic material scientists to the three major causes: 1) attributes of the manufacturing process, 2) solder material properties and 3)design-related issues. The latter are thought to be caused primarily by elevated stresses in the solder material, as well as by the excessive warpage of the PCB-package assembly and particularly to the differences in the thermally induced curvatures of the PCB and the package. In this analysis the stress-and-warpage issue is addressed using an analytical predictive stress model. This model is a modification and an extension of the model developed back in 1980-s by the first author. It is assumed that it is the difference in the post-fabrication deflections of the PCB-package assembly that is the root cause of the solder materials failures and particularly and perhaps the HnP defects. The calculated data based on the developed analytical thermal stress model suggest that the replacement of the conventional ball-grid-array (BGA) designs with designs characterized by elevated stand-off heights of the solder joints could result in significant stress and warpage relief and, hopefully, in a lower propensity of the IC package to HnP defects as well. The general concepts are illustrated by a numerical example, in which the responses to the change in temperature of a conventional design referred to as ball-grid-array (BGA) and a design with solder joints with elevated stand-off heights referred to as column-grid-array (CGA) are compared. The computed data indicated that the effective stress in the solder material is relieved by about 40% and the difference between the maximum deflections of the PCB and the package is reduced by about 60%, when the BGA design is replaced by a CGA system. Although no proof that the use of solder joints with elevated stand-off heights will lessen the package propensity to the HnP defects is provided, the authors think that there is a reason to believe that the application of solder joints with elevated stand-off heights could result in a substantial improvement in the general IC package performance, including, perhaps, its propensity to HnP defects.

Investigation of Thermal Stress of Cement Sheath for Geothermal Wells during Fracturing

Geothermal energy development has increasingly been studied in recently decades because of its renewable and sustainable features. It can be divided into two categories: traditional geothermal (hydrothermal) systems and enhanced geothermal systems (EGS) based on the type of exploitation. The hot dry rock (HDR) in the EGS incorporates about 80% of all thermal energy, and its value is about 100–1000 times that of fossil energy. It is pivotal for geothermal wells to improve the flow conductivity of the HDR mass, enhance the communication area of natural fractures, and constitute the fracture network between injection and production wells by hydraulic treatments. While the wellbore temperature significantly decreases because of fracturing, fluid injection will induce additional thermal stresses in the cement sheath, which will aggravate its failure. Considering the radial nonuniform temperature change, this paper proposes a new thermal stress model for a casing-cement sheath-formation combined system for geothermal wells during fracturing based on elastic mechanics and thermodynamics theory. This model is solved by the Gaussian main elimination method. Based on the analytical model, the thermal stresses of cement sheath have been analyzed. The effects of the main influencing parameters on thermal stresses have also been investigated. Results show that the radial and axial tensile thermal stresses are both obviously larger than tangential tensile thermal stress. The maximum radial and axial thermal stresses always occur at the casing interface while the location of the maximum tangential thermal stress varies. Generally, thermal stresses are more likely to induce radial and axial micro cracks in the cement sheath, and the cement sheath will fail more easily at the casing interface in fracturing geothermal wells. For integrity protection of the cement sheath, a proper decrease of casing wall thickness, casing linear thermal expansion coefficient, cement sheath elasticity modulus, and an increase of the fracturing fluid temperature has been suggested.

An analytical circuit based nonlinear thermal model for capacitor banks

The thermal couplings among capacitors in a bank could significantly alter the reliability performance compared to a single capacitor. The impact of thermal coupling is becoming stronger for high power density systems due to more stringent constraint in volume. Prior-art studies take into account the thermal coupling effects of a capacitor bank by either Finite Element Method (FEM) or experimental characterization, which are case dependent and time-consuming. This paper proposes a nonlinear mathematical model for capacitor banks based on physics of thermal conduction, convection, and radiation. A simplified version of the model is also obtained and represented by an RC circuit network, which enables computational-efficient thermal stress modeling. The proposed models are convenient to use to support model based sizing of capacitor banks and is scalable for multi-cell rectangle layout. A case study with experimental testing is discussed to verify the accuracy of the models.

The performance of concrete filled steel tube columns under post-earthquake fires

In this study, a nonlinear three-dimensional finite element (FE) model was developed and validated to investigate the response of concrete filled tube (CFT) columns subjected to post-earthquake fires. Three steps were considered successively in the modelling, namely, cyclic, thermal and structural analyses. Outputs from the cyclic loading including residual deformations were imposed as an initial condition to the thermal-stress model, imitating the seismic response of the column. Subsequently, a nonlinear sequentially thermal-stress analysis was conducted to simulate the fire response of column after the earthquake. The proposed FE model was validated by comparing the simulation results with the observations of full-scale fire and cyclic tests available in the literature. The validated numerical model was then used to study the behavior of CFT columns under the combined action of earthquake and fire as a multi-hazard event. Three probable seismic damage scenarios were considered in the column, namely, middle length, bottom and top end region damages. The level of damage was assumed as a high damage level, presuming that the column reached 50% of its lateral resistance while still maintaining its overall stability after the earthquake. The results showed that the top and bottom end region damages have not significantly influence the fire response of the damaged column. Besides, the column with the middle span damage performed a lesser fire resistance time owing to the coincidence of damage location to that of onset of global buckling.