Nonlinear Thermal Stress Research Articles

Evaluation of the delamination between resin and metallic components in a power module using nonlinear thermal stress analyses

Evaluation of the delamination between resin and metallic components in a power module using nonlinear thermal stress analyses

Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment

The vibration behavior of the rotating viscoelastic nanobeam embedded in the visco-Pasternak foundation is studied. The governing equation is extracted by using the surface elasticity and the nonlocal elasticity theory. The influence of the humidity on the vibration frequencies of the viscoelastic nanobeam is investigated in the thermal environment. The effects of the linear and the nonlinear thermal stress cases on the vibration frequencies of the viscoelastic nanobeam are studied. The vibration frequencies are obtained based on the differential quadrature method. Also, the numerical results are compared with those which are reported in the literature, and a good correlation is obtained. The results are presented for the different boundary conditions as well as the effect of the torsion spring on the viscoelastic nanobeam ends is investigated. This study focuses on the combined effects of the angular velocity, the internal and external damping, the humidity change, the temperature change, the surface effects (surface density, surface elasticity and surface stress), the nonlocal parameter, the boundary conditions, the visco-Pasternak foundation, the cross section geometry, and the torsion spring. The results of this study could be used to design and manufacture nanosensors, biosensors, atomic force microscope and the NEMS/MEMS devices.

Nonlinear Transient Thermal Stress Analysis of Temperature-Dependent Hollow Cylinders Using a Finite Element Model

In this paper, the nonlinear transient thermal stress analysis is conducted for temperature-dependent hollow cylinders subjected to a decaying-with-time thermal field. By the finite element method, the highly nonlinear governing equations are solved. The time histories of temperature, displacement, and stress due to the decaying-with-time thermal load are computed. A sensitivity analysis includes the effects of exponent of the decayed heat flux and temperature-dependency of density and material properties is carried out. Numerical results show some interesting characteristics of the thermoelastic behaviors of the hollow cylinders studied. In particular, the effect of temperature-dependency of the material properties on the thermoelastic parameters was demonstrated to be significant.

Nonlinear transient thermal stress analysis of thick-walled FGM cylinder with temperature-dependent material properties

In this paper, the problem of generalized thermoelasticity in a thick-walled FGM cylinder with one relaxation time is presented. The material properties are taking as function of temperature and graded in the radial. Due to the nonlinearity of the governing equations, finite element method is adopted to solve such problem. Both the inner and outer curved surfaces of the cylinder are stress free while the inner surface is subjected to thermal shock, while the outer surface is thermally isolated. The effects of temperature-dependent properties, volume fraction parameter and the thermal relaxation time on the physical quantities behavior are evaluated. Results confirm the efficiency of the present algorithm and reveal the significant effects of the temperature-dependent of the material properties.

Thermal Behavior of Cylindrical Buckling Restrained Braces at Elevated Temperatures

The primary focus of this investigation was to analyze sequentially coupled nonlinear thermal stress, using a three-dimensional model. It was meant to shed light on the behavior of Buckling Restraint Brace (BRB) elements with circular cross section, at elevated temperature. Such bracing systems were comprised of a cylindrical steel core encased in a strong concrete-filled steel hollow casing. A debonding agent was rubbed on the core's surface to avoid shear stress transition to the restraining system. The numerical model was verified by the analytical solutions developed by the other researchers. Performance of BRB system under seismic loading at ambient temperature has been well documented. However, its performance in case of fire has yet to be explored. This study showed that the failure of brace may be attributed to material strength reduction and high compressive forces, both due to temperature rise. Furthermore, limiting temperatures in the linear behavior of steel casing and concrete in BRB element for both numerical and analytical simulations were about 196°C and 225°C, respectively. Finally it is concluded that the performance of BRB at elevated temperatures was the same as that seen at room temperature; that is, the steel core yields prior to the restraining system.

A study into crack growth in a railway wheel under thermal stop brake loading spectrum

This paper provides a method for solving thermal fatigue crack growth in the rail wheel under stop braking spectrum. The analysis was performed in three stages. In the first stage, a finite element model of the rail wheel is used for all braking applications. For each application, a non-linear thermal stress analysis is performed. The second stage of the sequential analysis is carried out to calculate the stress intensity factor of thermal cracks, by using a semi-analytical solution technique that involves the use of an analytical solution combined with a numerical algorithm to assess fracture strength. In the third stage, a generalised Frost–Dugdale approach has been used to modelling thermal fatigue crack growth.

Thermal Stress and Creep Strain Analyses of a 3D IC Integration SiP with Passive Interposer for Network System Application

In this study, the nonlinear thermal stress distributions at the Cu-low-k pads of Moore's law chips and creep strain energy density per cycle at the solder joints of a 3D IC integration system-in-package (SiP) are investigated. At the same time, the warpage of the TSV interposer and reliability assessment of solder joints in the architecture is examined. The analyzed structure comprises one PCB (printed circuit board), one BT (bismaleimide triazene) substrate, one interposer with through silicon vias (TSVs), two DRAM (dynamic random access memory) chips and one high power ASIC (application specific integrated circuit) chip. The high power chip and DRAM chips are supported, respectively on the top-side and bottom-side of the Cu-filled TSV interposer.

The tool for assessing the damage tolerance of railway wheel under service conditions

This paper aims to provide a prediction of the crack growth in the rail wheel – due to cyclic braking loads, mechanical loads and residual stress from manufacture process. A 3D nonlinear thermal stress analysis model has been used to calculate thermal stress of the rail wheel for all applications in the braking load spectrum. A detailed finite element analysis is performed using the elastic–plastic finite element analysis program for the rail wheel under contact mechanical loads. Computational analysis using a finite element method (FEM) has been used to model and accurately predict distortions and residual stresses during the quenching of pearlitic steels and to compare the results with those of low carbon Bainitic–Martensitic rail wheels. The subsequent analysis is carried out for stress intensity factor of cracks in the rail wheel under service condition by using a semi-analytical solution technique that involves the use of an analytical solution combined with a numerical algorithm to assess fracture strength. The residual life of railway wheel under service conditions has also been predicted.

Nonlinear Thermal Stress/Strain Analyses of Copper Filled TSV (Through Silicon Via) and Their Flip-Chip Microbumps

Most TSVs are filled with copper; siliconpoly and tungsten are the alternatives. The coefficient of thermal expansion (CTE) of copper (~17.5 times 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> /degC) is a few times higher than that of silicon (~2.5 times10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> /degC). Thus, when the copper filled through silicon via (TSV) is subjected to temperature loadings, there is a very large local thermal expansion mismatch between the copper and the silicon/dielectric (e.g., SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ), which will create very large stresses and strains at the interfaces between the copper and the silicon and between the copper and the dielectric. These stresses/strains can be high enough to introduce delamination between the interfaces. In this paper, the nonlinear thermal stresses and strains at the interfaces between the copper, silicon, and dielectric have been determined for a wide-range of aspect ratios (of the silicon thickness and the TSV diameter). One of the major applications of TSV is as an interposer. Because of Moore's (scaling/integration) law, the silicon chip is getting bigger, the pin-out is getting higher, and the pitch is getting finer. Thus, the conventional substrates, e.g., BT (bismaleimide triazine) cannot support these kinds of silicon chips anymore and a silicon interposer (substrate) is needed to redistribute the very fine-pitch and high pin-count pads on the chip to much larger pitch and less pin-count through the silicon vias on the silicon substrate. Depending on the via-size and pitch of the copper filled TSV, the effective CTE of the copper filled TSV interposer could be as high as 10 times 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> /degC. Consequently, the global thermal expansion mismatch between the silicon chip and the copper filled TSV substrate can be very large and the bumps (usually very small, e.g., microbumps) between them may not be able to survive under thermal conditions. In this study, the nonlinear stresses and strains in the microbumps between the silicon chip and copper filled TSV interposer (with and without underfills) have been determined for a wide-range of via sizes and pitches, and various temperature conditions. These results should be useful for 1) making a decision if underfill is necessary for the reliability of microbumps and 2) selecting underfill materials to minimize the stresses and strains in the microbumps.

Nonlinear transient thermal stress and elastic wave propagation analyses of thick temperature-dependent FGM cylinders, using a second-order point-collocation method

Nonlinear transient thermal stress and elastic wave propagation analyses are developed for hollow thick temperature-dependent FGM cylinders subjected to dynamic thermomechanical loads. Stress wave propagation, wave shape distortion, and speed variation under impulsive mechanical loads in thermal environments are also investigated. In contrast to researches accomplished so far, a second-order formulation rather than a first-order one is employed to improve the accuracy. The FDM method (as a point-collocation FEM method) is used. It is known that other FEM methods cannot show the actual trend jumps due to distributing the abrupt changes in the quantities as the numerical errors and the residuals of the governing equations among the nodal results. Furthermore, the required computational time and allocated computer memory are much reduced by the present solution algorithm. The cylinder is not divided into isotropic sub-cylinders. Therefore, artificial wave reflections from the hard interfaces are avoided. Time variations of the temperatures, displacements, and stresses due to the dynamic or impulsive loads are determined by solving the resulted highly nonlinear governing equations using an iterative updating solution scheme. A sensitivity analysis includes effects of the volume fraction indices, dimensions, and temperature-dependency of the material properties is performed. Results reveal the significant effect of the temperature-dependency of the material properties on the thermoelastic stresses and present some interesting characteristics of the thermoelastic and wave propagation behaviors.

Fire resistance of concrete filled square steel tube columns subjected to eccentric axial load

The fire resistance of concrete filled square steel tube columns (CFT columns) without fire protection under a constant axial load has been previously examined. The purpose of this present study is to investigate the fire resistance of CFT columns when they are subjected to combined loads. This paper presents a nonlinear thermal stress analysis method for predicting the mechanical behavior and fire resistance of CFT columns under eccentric axial load (axial load and flexure moment). This method is based on the stress-strain characteristics of materials at high temperatures and on the mechanics of column deflection curves. From the results of the developed computational technique, it was demonstrated that as the yield stress and rigidity of the steel tube rapidly decreased for approximately 30 minutes, the decrease of flexure moment capacity increased significantly more than that of the axial load capacity. In addition, as the load eccentricity ratio increased, the fire resistance time drastically decreased. However, the time of maximum expansion under eccentric axial load was independent of the load eccentricity ratio.

Finite Element Model Analysis of Thermal Stresses of Thick Airport Concrete Pavement Slabs

Thermal stress caused by temperature distribution in pavement slab is important in the structural design of airport concrete pavements. Airport concrete pavement slab is thick; therefore, temperature in the slab varies nonlinearly throughout its depth. Thermal stress caused by nonlinear temperature distribution differs from that of linear temperature distribution. In this study, thermal stress caused by nonlinear temperature distribution was calculated by using temperatures and restraint strains measured in an experimental concrete pavement with 460-mm-thick slabs. The calculated thermal stress differed from curling stress because of the linear temperature distribution. Temperature distributions in concrete slabs of various thicknesses were computed by solving the heat transfer equation with the control volume method. This calculation revealed that temperature distributions in thick concrete slabs were highly nonlinear. Thermal stress was analyzed to compute the nonlinear thermal stress distributions in concrete slabs from the computed temperature distributions by using a three-dimensional finite element model. On the basis of the analysis, effects of slab thickness and nonlinear temperature distribution on thermal stress were discussed. The effect of nonlinearity was found to be pronounced at a slab thickness greater than 300 mm. In this range, the reduction factor for taking into account the effect of nonlinear distribution was larger than 0.7. It was also found that thermal stresses in summer and spring were relatively large.

Material effect for predicting the fire resistance of concrete-filled square steel tube column under constant axial load

This paper presents a critical review of the performance of the currently available material models with regard to the mechanical behaviour of a concrete-filled steel tube (CFT) column at elevated temperatures. For this purpose, numerical heat transfer analysis and nonlinear thermal stress analysis were carried out by taking into account the existing material properties, such as the thermal and mechanical properties of concrete and steel. In addition, ten CFT column specimens with rectangular cross-sections of 300–350 mm in size were heated for two hours in accordance with KSF 2257 (equivalent to ASTM E119 and JIS A 1304). On comparing the numerical analysis and experimental results, it can be observed that we can validate and employ the existing material models such as EUROCODE, AIJ CODE, Lie’s material model, and Yin’s material model.

Thermal stress analysis of 1 MW gyrotron collector

During 2004 and 2005, collectors on three of the gyrotrons used at DIII-D failed due to stress cracks. In order to investigate reasons for these failures, a nonlinear elastic plastic thermal stress analysis of the collector/design was undertaken. The thermal stress analysis results indicated that the effective strain for oxygen free high conductivity copper material under the operating conditions limited the cycle life of the collector due to fatigue, resulting in failures. The desired service life of more than 10 5 thermal cycles can be obtained by: (1) operational changes, such as increasing the frequency and amplitude of sweeping to reduce the effective heat flux, (2) design changes, such as: increasing the height and/or diameter of collector, enhancing the heat transfer coefficient by roughening the coolant channel walls, or (3) changing the material of the collector to dispersion strengthened copper such as Glidcop. The analysis and conclusions are presented.

Nonlinear behaviors of a comb drive actuator under electrically induced tensile and compressive stresses

A theory with experimental verifications has been developed to investigate the nonlinear behavior of comb drive actuators under applied external electrical potential and Joule heating effects. The nonlinear behavior originates from coupled effects of the beam structure under applied electrical potential with electrostatically induced tensile stress and thermally induced compressive stress. Detailed analyses have been conducted to study the nonlinear spring force, residual and thermal stresses, as well as the dynamic behaviors of the actuator. Experimental and numerical simulation results based on an energy model have been proposed to analyze the linear and cubic stiffness as well as frequency changes of the comb drive actuators. Theories and models developed on the comb drive actuator in this work could be extended to explain nonlinearity and dynamic behaviors of more complicated microsystems encountering other force-induced nonlinear sources.

Geometrical non-linear thermal stress analysis of threaded-adhesive joints applied in non-magnetic dewar

The geometrical non-linear thermal stress analysis of the threaded-adhesive joints for non-magnetic Dewar was carried out. The stress analysis shows that the serious stress concentration occurs around the adhesive fillet at the adhesive free end of the lower threaded–adhesive joint of the inner shell. The glass fiber reinforced plastics (GFRP) around the roots of the first and last threads of the internal thread of the joint are also critical regions. In addition, the effects of the thread length and the thread pitch on the von Mises stress distribution were discussed. Decrease of the thread length and increase of the thread pitch will decrease the maximum von Mises stress at the critical locations of the adhesive and GFRP.

Steady-state thermal and geometrical non-linear stress analysis of an adhesively bonded tee joint with double support

The adhesive joints consist of adhesive layer and adherends with different mechanical and thermal properties. In case the adhesive joint is subjected to a temperature difference, thermal stresses arise in the adhesive joint due to the thermal and mechanical mismatches of the adhesive layer and the adherends. If the thermal expansion of the adhesive joint is restrained the stresses in the adhesive and adherends can reach considerable levels. In this study, the geometrically non-linear thermal stress analysis of an adhesively bonded tee joint with double support was carried out using the finite element method. The configurations of the adhesive tee joint bonded to a rigid base and to a flexible horizontal plate were considered. It was assumed that the adhesive tee joint is subjected to variable thermal boundary conditions, that is, air flows with different temperature and velocity parallel and perpendicular to outer surfaces of the tee joint. In order to determine the thermal strains with respect to a reference temperature, it is necessary to know the final temperature distributions through the adhesive tee joint. The heat transfer analysis of the tee joint showed that high heat fluxes occurred inside the adhesive fillets at the adhesive free ends whereas the vertical and horizontal plates experience uniform low-temperature distributions. Based on the final temperature distribution of the adhesive tee joint its geometrical non-linear stress analysis was carried out considering large displacement effects for two plate edge conditions in which the edges of the vertical and horizontal plates were fully or partly constrained. The stress analyses showed that high stress concentrations occurred inside the adhesive fillets around the adhesive free ends. The surfaces of the vertical and horizontal plates near the free ends of the adhesive–plate interfaces and the adhesive–support interfaces also experience stress concentrations. The adhesive tee joint was subjected to the highest stresses in the adhesive layer and plates when the edges of the horizontal and vertical plates were fully fixed. In addition, increasing the effect of the support length resulted in increases in the peak stresses at the critical locations of the adhesive layer and the plates.

Thermal non-linear elastic stress analysis of an adhesively bonded T-joint

Adhesive joints consist of adherends and an adhesive layer having different thermal and mechanical properties. When they are exposed to uniform thermal loads the mechanical-thermal mismatches of the adherends and adhesive layer result in uniform but different thermal strain distributions in the adhesive and adherends. The thermal stresses arise near and along the adherend-adhesive interfaces. The present thermal stress analyses of adhesively bonded joints assume a uniform temperature distribution or a constant temperature imposed along the outer boundaries of adhesive lap joints. This paper outlines the thermal analysis and geometrically non-linear stress analysis of adhesive joints subjected to different plate edge conditions and varying thermal boundary conditions causing large displacements and rotations. In addition, the geometrically non-linear thermal stress analysis of an adhesively bonded T-joint with single support plus angled reinforcement was carried out using the incremental finite element method, which was subjected to variable thermal boundary conditions, i.e. air streams with different temperatures and velocities parallel and perpendicular to its outer surfaces. The steady state heat transfer analysis showed that the temperature distribution through the joint members was non-uniform and high heat fluxes occurred inside the adhesive fillets at the adhesive free ends. Based on the geometrically non-linear stress analysis of the T-joint bonded to both rigid and flexible bases for different plate edge conditions, stress concentrations were observed at the free ends of adhesive-adherend interfaces and inside the adhesive fillets around the adhesive free ends, and the horizontal and vertical plates also experienced considerable stress distributions along outer surfaces. In addition, the effect of support length on the peak thermal adhesive stresses was found to be dependent on the plate edge conditions, when a support length allowing moderate adhesive stresses was present.

Geometrically non-linear thermal stress analysis of an adhesively bonded tubular single lap joint

In this study, the geometrically non-linear thermal stress analysis of an adhesively bonded tubular single lap joint subjected to airflows having different temperature and velocity outside and inside its inner and outer tubes was carried out using the incremental finite element method. Since the thermal expansion coefficients of tubes and adhesive were different the thermal strains arising along the adhesive–tube interfaces resulted in high thermal stresses in the adhesive layer and tubes for different end conditions applied to the ends of its outer and inner tubes. The joint region was considerably deformed, and serious stress concentrations occurred around the adhesive free ends. This effect became more evident in cases the tube edges were fully restrained. The peak thermal adhesive and tube stresses occurred at the free ends of the adhesive–tube interfaces. In addition, increasing the overlap length had an effect of reducing the peak adhesive and tube stresses, and an optimum overlap length/joint length ratio of 0.2 was determined.

On non-linear thermal stresses in an adhesively bonded single lap joint

Since adhesive joints consist of adhesive and adherends with different mechanical and thermal properties, the adhesive and adherends present different stress and strain states under thermal loads due to the thermal–mechanical mismatches. Thermal strains result in serious stresses even though the adhesive joints are not restrained. In this study, the thermal stress analysis of an adhesively bonded single lap joint (SLJ) was carried out considering the large displacement effects. In the thermal analysis, the outer surfaces of the SLJ are assumed to be subjected to air flows with different temperature and velocity. The final temperature distribution in the adhesive joint was used to compute thermal strains. Later, the geometrical non-linear stress analysis of the SLJ was carried out for four adherend edge conditions using the incremental FEM. Thermal strain concentrations were observed inside the adhesive fillets around the free ends of the adhesive layer. The top and bottom surfaces of the adherends also experienced high thermal stresses. The detailed analysis showed that the most critical adhesive regions were the free ends of the adhesive–adherend interfaces. It was observed that thermal loads caused serious stress and strain concentrations in joint members as well as the structural loads (Structural adhesive joints in engineering. London: Elsevier Applied Science; 1984). In order to reduce the peak stresses at the critical adhesive and adherend regions increasing the overlap length was not beneficial for all adherend edge conditions.