Instantaneous Heat Source Research Articles

Exceptional load-bearing capability of Al FPCB/Cu FPCB lap joints using instantaneous laser-based large area facial soldering: Experimental and numerical investigations

This study introduces a novel method for integrating aluminum flexible printed circuit boards (FPCBs) and copper FPCBs into battery management systems (BMS) using and instantaneous large area facial laser source soldering. Achieving a robust bonding strength of 65 MPa involved applying 600 W of laser power for 2 s, enhancing atom diffusion and promoting intermetallic compound (IMC) growth. Finite Element Method (FEM) simulations revealed variations in heat transfer between Al and Cu, affecting IMC thickness at interfaces. Formation of the (Cu, Ni)3Sn4 phase within solder, and variations in laser output significantly influenced solder joint orientation and Al electrode nucleation. Excessive laser power (>800 W) caused critical damage, such as delamination at the Al-PI interface, altering fracture modes and bonding strength. Furthermore, with a detailed examination of the laser soldering phenomenon through both experimental and numerical investigations, this study provides a thorough understanding of the different soldering mechanisms in conventional reflow soldering compared to instantaneous uniform large-area heat source laser soldering. These insights provide new design and material considerations to replace the conventional wiring harness with Al/Cu FPCB lap joints which optimize the circuitry and reducing BMS volume.

A maximum temperature rise model of the shear band in bulk metallic glasses

Based on mechanisms applicable to bulk metallic glasses (BMGs), such as a superposition principle of an instantaneous finite surface heat source temperature field and a flow model about the shear-band velocity, a maximum temperature rise model of shear bands in BMGs was deduced, ΔTmax=σycpΔupl·vSB2πα. The model describes the dependence of the maximum temperature rise on the yield strength and the shear-band velocity in BMGs. It can be calculated that the maximum temperature rise of BMGs is between 1 K ∼ 30 K at room temperature through these two parameters. A critical temperature, TC, of almost 0.8∼0.9Tg is introduced, at T<TC, the change of the yield strength with temperature in BMGs basically conforms a cooperative shear model (CSM), and at T>TC, a significant reduction of the yield strength in BMGs can be attributed to avoiding failure due to localized material softening.

Transient Temperature Distribution in a Half-Space Due to Local Surface Heating Via Non-Fourier Fractional Dual-Phase-Lag Model

Abstract The non-Fourier heat transfer in a half-space is analyzed under sudden heating or cooling on a local surface. The non-Fourier heat transfer effect is described by the time-fractional dual-phase-lag (DPL) model, where the fractional derivative without singular kernel is used. An axisymmetric mixed initial-boundary value problem is solved by the use of the Hankel and Laplace transforms. Two typical cases of sudden temperature rising on a circular zone of the surface or an instantaneous surface heat source are analyzed. For sudden temperature rises, the heat flux and temperature gradient exhibit an inverse square-root singularity near the boundary of the heating zone and their dynamic intensity factors are computed numerically in the time domain. For the instantaneous surface point heat source, an exact solution of the transient temperature at any position in the Laplace domain is obtained. The effects of the fractional order and relaxation time on the temperature distribution and heat flux response are elucidated. The singular behavior of the transient thermal response and the non-Fourier effect of heat transfer are shown.

Preventing Crack in an Aluminum Alloy Complex Structure during Welding Process Based on Numerical Simulation Technology

Aluminum alloy structures are widely used for weight reduction in aviation, shipbuilding, rail vehicles and automotive industries. Fusion welding technology is one of the most important joining methods for lightweight structure assembly due to its advantages such as flexibility in design, high production efficiency, and low cost. However, the local centralized heating during fusion welding inevitably produces residual stress and welding deformation. For actual engineering structures, if the product design is unreasonable or the external restraint is inappropriate, the transient stress or residual stress become a key factor resulting in cracking during the assembly process. In the current study, an effective computational approach was developed based on the MSC Marc software to simulate transient and residual stress fields for complex aluminum alloy structures during the welding process. In the developed computational approach, according to the location and arrangement of welding lines, an instantaneous heat source model was used to replace the traditional moving heat source model, and as a result significanlty improved the calculation efficiency to meet actual engineering needs. The welding stresses, including transient and residual stress, of an A6061 aluminum alloy complex structure were calculated by the developed numerical simulation technology. The simulation results indicated that the cracking was produced by excessive transient stress during welding process. Subsequently, the effect of external restraint intensity on welding stress at the key location was examined numerically. Based on the simulation results, measures to reduce welding stress and cracking risk were put forward based on adjusting the external restraint intensity.

Analytical modeling of temperature distribution in laser powder bed fusion with different scan strategies

This study proposes an analytical model to predict the transient temperature distribution and melt pool size in laser powder bed fusion (LPBF) process with different scan strategies. The scan strategies are divided into discontinuous scan path and continuous scan path. The moving Gaussian surface heat source solution and the instantaneous Gaussian surface heat source transient solution are applied for these two different scan strategies. The residual temperature linear superposition is adopted to consider the multi-track effect on the temperature distribution. The virtual negative power heat source method is utilized to consider the heat diffusion for the tracks that has been scanned of the build part. The image heat source method is used to consider the zero-flux boundary condition at the lateral surface of the build part. The proposed model is validated by the experimental data of the melt pool in single-track LPBF process. The analytical models of these two different scan strategies are verified by the comparison of the melt pool size. Based on the validated analytical model, it is extended for the multiple scan strategies combination processes. The temperature and melt pool predicted by the analytical model show good consistency with the FEM results. The analytical model method is much more efficient than FEM, which is about 120 times faster than FEM for the calculation of round-corner part. Due to the satisfied efficiency and accuracy in the prediction of melt pool size and the thermal history, the proposed analytical model has great potential application in optimization of the scan path planning and avoidance of the undesired residual temperature accumulation in the part.

Numerical simulation of residual stress of butt-welded joint involved in complex column-beam welded structure

The objective of this work is to clarify the effect of the structural restraint and the adjacent welded joints in column-beam welded structure on the final residual stress distribution and its evolution process of the butt-welded joint between the diaphragm and the flange through numerical simulation method. Based on ABAQUS software, a three dimensional thermal-mechanical coupled method was developed to predict the residual stress distribution for multi-pass welded joints. To improve calculation efficiency, an effective computational approach that combines a relatively coarse mesh design and an instantaneous heat source model was proposed to analyze the residual stress distribution for complex welded structures. Firstly, both a fine mesh model with moving heat source and a relatively coarse mesh model with instantaneous heat source were employed to predict the residual stress distribution in the same thick-plate butt-welded joint made of high strength low alloy steel. The computational accuracy of the proposed computational method was verified through comparing the results of the fine mesh model with moving heat source and the corresponding experimental data. Then, the residual stress distributions of the column-beam welded structure, the butt-welded joint under structural restraint condition and free state were calculated using the proposed computational approach. Results suggest that the structural restraint and the adjacent welded joints in the structure have a significant effect on the residual stress distribution.

Memory response in dual-phase-lag thermoelastic medium due to instantaneous heat source

The present work deals with thermoelastic interactions in an isotropic infinite medium with memory-dependent derivative under a dual-phase-lag model. The governing equations are expressed in vector–matrix differential equation (VMDE) form in the Laplace–Fourier transform domain and solved using the eigenvalue approach. Numerical estimations of different thermophysical quantities such as displacement, temperature, and stresses are presented graphically for a coper material by employing the Gaussian quadrature formula and Honig–Hirdes method. Several remarkable points have been mentioned in the graphical representation of the field variables for various kernel functions, time-delay parameters, and magnitude of instantaneous heat source.

Effect of Surface Topology on the Apparent Thermal Diffusivity of Thin Samples at LFA Measurements.

This paper deals with the problem of the influence of surface topography on the results of thermal diffusivity measurements when determined using the instantaneous surface heat source method, also called the pulse method. The analysis was based on numerical tests carried out using Comsol Multiphysics software. The results of experimental investigations on the actual material structure using an electron microscope, an optical microscope and a profilometer were used to develop a numerical model. The influence of the non-uniformity of the surface of the tested sample on the determined values of half-time of the thermal response of the sample’s rough surface to the impulse forcing on the opposing flat surface was determined by developing the data for simulated measurements. The effect of the position of the response data reading area on the obtained simulation results was also analyzed. The obtained results can be used to improve the accuracy of experimental heat transfer studies performed on thin-film engineering structures depending on the uniformity and parallelism of the material applied to engineering structures. The difference in half-life determination error results for various analyzed models can be as high as 16.7%, depending on the surface from which the responses of the heating impulse are read. With an equivalent model in which 10% of the material volume corresponds to the rough part as a single inclusion, hemisphere, the error in determining thermal diffusivity was equal to 3.8%. An increase in the number of inclusions with smaller weight reduces an error in the determination of thermal diffusivity, as presented in the paper.

Thermal plane waves in unbounded non-local medium exposed to a moving heat source with a non-singular kernel and higher order time derivatives

In this paper, the thermoelastic characteristics of a nonlocal unbounded viscoelastic medium due to an instantaneous heat source is investigated by considering a modified dual-phase-lag model with higher-order time derivatives. The fractional derivative and Eringen's non-local theory are also applied in the considered model. To extend the application of the classical Kelvin-Voigt model, a fractional derivative operator with non-single kernels based on the Atangana and Baleanu's concept is proposed. After applying the Laplace transform method, the governing systems of equations are expressed as vector-matrix differential form and solved by constructing an eigenvalue problem. Some comparative results are presented to analyze the effects of heat source velocity, nonlocal parameter, structural viscoelastic coefficients, phase lags, fractional and higher-order parameters on the behavior of physical fields.

Silicon Thermal Flow-Sensor Semi-ideal Model

A so-called semi-ideal model has been derived for a pulse-operated MEMS thermal flow sensor by reciprocal numerical mapping of the ideal model of an instantaneous line heat source to the experimental data of the sensor. The novel model not only applies as a precise potential working equation for the sensor but also provides insight into the complete thermal signal transmission chain from the heater to the thermometers of the sensor. It gives answers to prominent peculiarities of the actual heat path of the sensor, prepares ways to improve its design, and offers guidance for a better control of the measuring process. The semi-ideal model was derived in order to replace the so far utilized empirical relations that require multiple calibration measurements. It was found out that the transient temperature profile of the sensor in response to an electrical pulse to the heater is substantially shaped by series thermal conduction of heat. Moreover, it is demonstrated that the impact of the thermal mass of a (practical) line heat source on its transient temperature and released enthalpy can be modeled by considering a virtual cylinder surrounding the source. The same analytical technique also applies for (practical) temperature stations. The findings of the study primarily concern the MEMS sensor. Nevertheless, the presented simple method of numerical mapping can be an effective analytical tool for mathematical modeling by means of numerical data analysis and function evaluation. The concept of a virtual cylinder can help in modeling the dynamics of practical pulsed heating.

Stress intensity factor at the front of 3D-surface crack under transient thermal stress induced by a point heat source

A rectangular surface crack perpendicular to the free surface of a three-dimensional solid is assumed and numerically analyzed when the solid surface is heated by an instantaneous point heat source. In particular, the effect of Poisson’s ratio on the distribution characteristics of the stress intensity factor along the crack front is clarified by the body force method. The present analysis is a numerical model for thermal stress laser cleaving of a brittle materials like Si wafer.

A Dual-Probe Heat Pulse Approach using Heated Fiber-Optic Temperature Sensing

The distributed actively heated fiber-optic method is widely used to measure soil thermal conductivity and water content. However, the significant limitations of this technique are that prior soil specific calibration is required, and the measurement of soil volumetric heat capacity, a critical soil thermal parameter, is restricted. This study investigates a novel fiber-optic dual-probe heat pulse method, which utilizes fiber-optics to monitor the temperature response at a certain distance from the heat source to obtain the thermal conductivity and the volumetric heat capacity. Subsequently, the water content can be estimated from its linear relationship with soil volumetric heat capacity. The fiber-optic dual-probe heat pulse method is aimed to overcome the spatial-scale measurement limitations considering the distributed sensing capability of fiber-optic. This requires the sensor to be more robust than the traditional dual-probe method, hence a completely different ratio of the probe diameter to the distance between adjacent cables. Therefore, the applicability of the existing theory needs further verification, and the heating strategies need careful consideration. This study uses a 6 mm diameter fiber Bragg grating (FBG) sensor encapsulated by the alundum tube to conduct laboratory feasibility tests. Two adjacent sensors are fixed in the soil at a distance of 14.60 mm. Different heating powers (30 W/m, 40 W/m, and 50 W/m) and heating durations (10 s, 30 s, 50 s, and 120 s) are implemented. The results showed that the novel approach allows accurate soil volumetric heat capacity and water content estimation with appropriate heating strategies and data interpretation methods. The heating duration below 30 s is a poor fit because of the low-temperature rise, requiring a longer heating duration. For the 120 s heating duration, the measurement error in soil volumetric capacity is less than 2%. On the other hand, the instantaneous line heat source theory overestimates the soil volumetric heat capacity by 5%, while the short-duration line heat source theory performs well in the method.

Thermomagnetic modeling of a nonlocal viscoelastic half-space exposed to an internal heat source through a two-phase delay model

In this article, a thermomagnetic viscoelastic nonlocal model has been introduced that incorporating the nonlocal elasticity theory of Eringen and the Kelvin–Voigt type. In the heat conductivity equation, the dual-phase-lag thermoelastic model (DPL) has been used to account for microstructural effects caused by high-rate heat transfer processes. The proposed DPL thermoelastic model illustrates the effects of material deficiencies and the thermomechanical relationship due to the extremely rapid heating. Within the framework of the nonlocal DPL model, a one-dimensional magneto-thermoelastic problem of half-space whose surface is exposed to an instantaneous heat source and magnetic field has been studied. With the eigenvalue approach technique and Laplace transform method, analytical solutions for the studied physical fields are provided. The transformed expressions to the field quantities are reversed into the physical domain by applying Zakian's algorithm. The effects of the nonlocal parameter, the viscosity and the applied heat source have been shown graphically on the differences in the fields within the medium.

Development of welding simulation technology using general-purpose finite element analysis code

Welding simulation using an instantaneous heat source was performed using ANSYS, which is a general-purpose finite element analysis code, and deformation and residual stress of various test pieces were evaluated. As a result, the effects of the heating region, heating time during welding, number of element divisions in the thickness direction, number of time divisions, etc. on the calculation accuracy were clarified, and the optimum analysis conditions were obtained.

A Study on Fractional Order Thermoelastic Half Space

In this paper, we consider a one dimensional problem on a fractional order generalized thermoelasticity in half space subjected to an instantaneous heat source. The Laplace transform as well as eigen value approach techniques are applied to solve the governing equations of motion and heat conduction. Closed form solutions for displacement, temperature and stress are obtained and presented graphically.

Influence of lumping passes on calculation accuracy and efficiency of welding residual stress of thick-plate butt joint in boiling water reactor

An advanced computing approach based on commercial software ABAQUS was developed to calculate the welding residual stress in a multi-pass butt-welded joint. An equal-density instantaneous heat source model and the lumping-pass method were used to improve the calculation efficiency. According to the numerical and experimental results, the influence of lumping-pass patterns and two-dimensional (2D) model on the calculation accuracy and efficiency of welding residual stress were investigated. The results show that the lumping-pass method can greatly shorten the calculation time. Lumping weld passes along the thickness direction has little effect on the calculation accuracy of welding residual stress while lumping weld passes along the width direction will cause a larger error in calculation accuracy. Using the 2D model can save 97% of the calculation time and is more effective than the lumping-pass method based on 3D model, but it has a certain influence on the calculation accuracy of welding residual stress.

Eigenfunction approach to generalized thermo-viscoelasticity with memory dependent derivative due to three-phase-lag heat transfer

The present article investigates a new mathematical model of generalized thermo-viscoelasticity based on memory-dependent derivative in the context of three-phase-lag heat transfer subjected to an instantaneous point heat source. The governing coupled equations associated with kernel function and time delay are constituted for a two-dimensional problem of semi-infinite space in an isotropic medium. The bounding surface of the half-space is assumed to be subjected to a time-dependent thermal shock and rigidly fixed. The Eigenfunction expansion approach is proposed to analyze the problem and, consequently, the analytical solutions of the thermodynamic field variables viz. temperature, displacement and stresses are obtained in the Laplace-Fourier transformed domain. The effects of the kernel function and time-delay factor on the distributions of the non-dimensional thermodynamic field variables are presented graphically and compared with the several well-known generalized thermoelasticity theories present in the literature. Finally, some remarkable points are mentioned in conclusion.

Thermo-viscoelastic interaction under dual-phase-lag model with memory-dependent derivative

This article deals with the thermo-viscoelastic interaction in a two-dimensional homogeneous, isotropic, infinite space subjected to an instantaneous heat source. The problem is considered in the domain of dual-phase-lag (DPL) model of generalized thermo-viscoelasticity with memory-dependent derivative (MDD). The joint Laplace–Fourier transform is used as mathematical tool to obtain vector matrix differential equation and it is then solved by utilizing eigenvalue approach. Numerical estimation of displacements, stresses, and temperature are figured for a certain material by utilizing Bellman method and Gaussian quadrature formula. At last, the impact of space variable, time, kernel function, time-delay, and phase-lag parameters on the thermophysical quantities is analyzed graphically.

Theory and Solutions of Heat Pulse Method for Determining Soil Thermal Properties

Information on thermal properties of soil is of paramount importance for environmental and earth science, and engineering. The heat pulse (HP) method has become the key technology for accurate determination of soil thermal properties and a variety of other physical properties (e.g., water content, bulk density, and water flux) in both laboratory and field environments. The HP method is a transient method that is commonly based on the analytical solutions to the radial heat flow equation when a line-heat source is applied. Over the past few decades, great endeavors have been devoted to advance the HP method. For example, the evolution and development in probe design, data logging equipment, data interpretation and computing capability has remarkably improved the accuracy and ease of use for determining soil thermal properties. However, there is a lack of study collating and synthesizing the development of the theory/solutions to obtain thermal properties of soil using the HP method. In this paper, we review the fundamental theories and solutions of the HP method, including differences and similarities of theories and applications between instantaneous line heat source (ILHS) and short-duration line heat-source (SLHS), between dual-probe heat-pulse (DPHP) and single-probe heat-pulse (SPHP) methods, and between the non-linear model fit (NMF) method and single point (SPM) method for data interpretation. In addition, the numerical solutions and semi-analytical solutions are also presented to provide heat pulse users information for selecting the best-fit method to meet their goals.

On thermoelastic problem of a thermosensitive functionally graded rectangular plate with instantaneous point heat source

The present article attempts to investigate transient thermoelastic problem of a functionally graded thin rectangular plate with thermosensitive and spatial variable dependent material properties. All the material properties are assumed to be isotropic. Kirchhoff’s variable transformation is used to deal with the nonlinearity of the three dimensional heat conduction equation and that equation is solved by the integral transform method considering an instantaneous point heat source. The thermoelastic behavior of the rectangular plate is studied together with the thermal deflection and thermally induced resultant moments. Numerical computations are carried out for ceramic-metal-based functionally graded material, in which alumina is selected as ceramic and nickel as metal. The results are illustrated graphically.