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Optimized plating conditions, included proper designs of insulating shield (IS), auxiliary cathode (AC) and different patterns, contribute to the uniformity enhancement of copper deposition.

Plating experiments were implemented in vertical continuous plating (VCP) line for manufacturing in different conditions. Multiphysics coupling simulation was brought to investigate and predict the plating uniformity improvement of copper pattern. In addition, the numerical model was based on VCP to approach the practical application.

With disproportionate current distribution, different plating pattern design formed diverse copper thickness distribution (CTD). IS and AC improved plating uniformity of copper pattern because of current redistribution. Moreover, optimized plating condition for effectively depositing more uniformed plating copper layer in varied pattern designs were derived by simulation and verified by plating experiment.

The comparison between experiment and simulation revealed that multiphysics coupling is an efficient, reliable and of course environment-friendly tool to perform research on the uniformity of pattern plating in manufacturing.

The purpose of this paper is to develop multi-physics computational model for the conventional gas metal arc welding (GMAW) joining process has been improved with respect to its predictive capabilities regarding the spatial distribution of the mechanical properties (strength, in particular) within the weld.

The improved GMAW process model is next applied to the case of butt-welding of MIL A46100 (a prototypical high-hardness armor-grade martensitic steel) workpieces using filler-metal electrodes made of the same material. A critical assessment is conducted of the basic foundation of the model, including its five modules, each dedicated to handling a specific aspect of the GMAW process, i.e.: first, electro-dynamics of the welding-gun; second, radiation/convection controlled heat transfer from the electric arc to the workpiece and mass transfer from the filler-metal consumable electrode to the weld; third, prediction of the temporal evolution and the spatial distribution of thermal and mechanical fields within the weld region during the GMAW joining process; fourth, the resulting temporal evolution and spatial distribution of the material microstructure throughout the weld region; and fifth, spatial distribution of the as-welded material mechanical properties.

The predictions of the improved GMAW process model pertaining to the spatial distribution of the material microstructure and properties within the MIL A46100 butt-weld are found to be consistent with general expectations and prior observations.

To explain microstructure/property relationships within different portions of the weld, advanced physical-metallurgy concepts and principles are identified, and their governing equations parameterized and applied within a post-processing data-reduction procedure.

Reflow soldering is one of the most significant factors in determining solder joint defect rate. This study aims to introduce an innovative approach for optimizing the multiple performances of the reflow soldering process.

This study aims to minimize the solder joint defect rate of a ball grid array (BGA) package by using the grey‐based Taguchi method. The entropy measurement method was employed together with the grey‐based Taguchi method to compute for the weights of each quality characteristic. The Taguchi L18 orthogonal array was performed, and the optimal parameter settings were determined. Various factors, such as slope, temperature, and reflow profile time, as well as two extreme noise factors, were considered. The thermal stress, peak temperature, reflow time, board‐ and package‐level temperature uniformity were selected as the quality characteristics. These quality characteristics were determined using the numerical method. The numerical method comprises the internal computational flow that models the reflow oven coupled with the structural heating and cooling models of the BGA assembly. The Multi‐physics Code Coupling Interface was used as the coupling software.

The analysis of variance results reveals that the cooling slope was the most influential factor among the multiple quality characteristics, followed by the soaking temperature and the peak temperature. Experimental confirmation test results show that the performance characteristics improved significantly during the reflow soldering process.

The proposed approach greatly reduces solder joint defects and enhances solutions to lead‐free reliability issues in the electronics manufacturing industry.

The findings provide new guidelines to the optimization method which are very useful for the accurate control of the solder joint defect rate within components and printed circuit board (PCB) which is one of the major requirements to achieve high reliability of electronic assemblies.

The purpose of this paper is to develop thermal modelling to investigate the thermal response of sample boards (at board level) during the preheating stage of the reflow process and to validate with experimental measurements.

A thermal‐coupling method that adopted the Multi‐physics Code Coupling Interface (MpCCI) was utilized. A forced‐convection reflow oven was modelled using computational fluid dynamic software (FLUENT 6.3.26), whereas structural heating at the board level was conducted using finite‐element method software (ABAQUS 6.9).

The simulation showed a complex flow pattern having characteristics of a free‐jet region, stagnation‐flow region, wall jet‐region, recirculation region and vortices. A sharp maximum heat‐transfer coefficient was detected in the stagnation region of the jet, resulting in a spatial variation of local heat transfer on a thermal profile board (TPB). This coefficient affected the temperature distribution in the TPB with different specific heat capacitances and thermal conductivity of the structure. The simulation results were in good agreement with the experimental data and analytical model. The cold region and temperature uniformity (ΔT) increased with increasing complexity of the TPB. The cold region can occur in two possible locations in the TPB. Both occurrences can be related to the flow field of the reflow oven. ΔT of the TPB decreased when the conveyor speed (v) was reduced. A suitable conveyor speed (1.0 cm/s) was determined to maintain ΔT below 10°C, which prevented the thermally critical package from overheating.

The paper provies a methodology for designing a thermal profile for reflow soldering production.

The findings provide fundamental guidelines to the thermal‐coupling method at the board and package levels, very useful for accurate control of ΔT at the board and package levels, one of the major requirements in achieving a high degree of reliability for electronic assemblies.

The purpose of this study is to investigate the effect of electrical and thermal stresses on the void formation of the Sn3.0Ag0.5Cu (SAC305) lead-free ball grid array (BGA) solder joints and to propose a modified mean-time-to-failure (MTTF) equation when joints are subjected to coupling stress.

The samples of the BGA package were subjected to a migration test at different currents and temperatures. Voltage variation was recorded for analysis. Scanning electron microscope and electron back-scattered diffraction were applied to achieve the micromorphological observations. Additionally, the experimental and simulation results were combined to fit the modified model parameters.

Voids appeared at the corner of the cathode. The resistance of the daisy chain increased. Two stages of resistance variation were confirmed. The crystal lattice orientation rotated and became consistent and ordered. Electrical and thermal stresses had an impact on the void formation. As the current density and temperature increased, the void increased. The lifetime of the solder joint decreased as the electrical and thermal stresses increased. A modified MTTF model was proposed and its parameters were confirmed by theoretical derivation and test data fitting.

This study focuses on the effects of coupling stress on the void formation of the SAC305 BGA solder joint. The microstructure and macroscopic performance were studied to identify the effects of different stresses with the use of a variety of analytical methods. The modified MTTF model was constructed for application to SAC305 BGA solder joints. It was found suitable for larger current densities and larger influences of Joule heating and for the welding ball structure with current crowding.

The purpose of this paper is to investigate the added value of using temperature-dependent electric and magnetic properties in high-temperature electromagnetic simulations.

In this work, the electromagnetic properties of Domex 420, SSAB, have been characterized as a function of the temperature, from room temperature to 900°C. The measurement of the electric and magnetic properties was performed inside a vacuum furnace at a number of discrete temperature steps, with particularly small intervals around the Curie temperature. A simple transient multi-physics model was used to investigate the impact of the measured properties in three different representations.

In certain intervals, a simplified approximation of the properties produces accurate results, while fully parametric representation is beneficial when heating above the Curie temperature.

Temperature-dependent electromagnetic properties are rarely found, especially in an easy-to-use form. Using parameterized temperature-dependent approximation of key properties shows noteworthy differences in the outcome of high-temperature electromagnetic modeling.

The purpose of this paper is to address the formulation, implementation, and adaptation of closely coupled multi‐physics problems with h‐ and p‐adaptive finite element methods. A general formulation is chosen allowing for coupled problems of various types. Adaptation algorithms for h‐ and p‐refinement are given.

A generic system of second‐order differential equations is used, where the field of each individual problem is represented as an entry in the list of field variables. Specific problems are implemented by mapping material coefficients to the coefficients of the generic form. An example with four natures is investigated with close coupling between electric, mechanical and thermal fields. h‐ and p‐refinement using a single mesh is considered, where the element order may differ for individual fields.

In coupled problems, the error in each single field is affected by approximation properties of all other field quantities. In order to allow for optimal convergence order in the number of degrees of freedom, the error contributions of all fields have to be considered. Separate error estimation in each field is needed especially in h‐adaptation on a single mesh. Energy coupling coefficients were introduced to derive an adaptation criterion. Convergence analysis of h‐ and p‐adaptation proves the feasibility of the approach.

Piezopyroelectricity considers thermal effects in high‐frequency piezoelectric materials, which is a coupled problem of four natures. The paper introduces an adaptation criterion for such complicated coupled problems and proves feasibility.

The purpose of this paper is to describe main ideas and demonstrate results of the research activities carried out by the authors in the field of design concepts of induction mass heating technology based on multiple-criteria optimization. The main goal of the studies is the application of different optimization methods and numerical finite element method (FEM) codes for field analysis to solve the multi-objective optimization problem that is mathematically formulated in terms of the most important optimization criteria, for example, maximum temperature uniformity, maximum energy efficiency and minimum scale formation.

Standard genetic algorithm (GA), non-dominated sorting genetic algorithm (NSGA) and alternance method of parametric optimization based on the optimal control theory are applied as effective tools for the practice-oriented problems for multiple-criteria optimization of induction heaters’ design based on non-linear coupled electromagnetic and temperature field analysis. Different approaches are used for combining FEM codes for interconnected field analysis and optimization algorithms into the automated optimization procedure.

Optimization procedures are tested and investigated for two- and three-criteria optimization problems solution on the examples of induction heating of a graphite disk, induction heating of aluminum and steel billets prior to hot forming.

Solved problems are based on the design of practical industrial applications. The developed optimization procedures are planned to be applied to the wide range of real-life problems of the optimal design and control of different electromagnetic devices and systems.

The paper describes main ideas and results of the research activities carried out by the authors during past years in the field of multiple-criteria optimization of induction heaters’ design based on numerical coupled electromagnetic and temperature field analysis. Implementing the automated procedure that combines a numerical FEM code for coupled field analysis with an optimization algorithm and its subsequent application for designing induction heaters makes the proposed approach specific and original. The paper also demonstrates that different optimization strategies used (standard GA, NSGA-II and the alternance method of optimal control theory) are effective for real-life industrial applications for multiple-criteria optimization of induction heaters design.

The purpose of this paper is to discuss the recently developed multi-physics computational model for the conventional Gas Metal Arc Welding (GMAW) joining process that has been upgraded with respect to its predictive capabilities regarding the spatial distribution of the mechanical properties controlling the ballistic limit (i.e. penetration resistance) of the weld.

The original model consists of five modules, each dedicated to handling a specific aspect of the GMAW process, i.e.: electro-dynamics of the welding-gun; radiation-/convection-controlled heat transfer from the electric arc to the workpiece and mass transfer from the filler-metal consumable electrode to the weld; prediction of the temporal evolution and the spatial distribution of thermal and mechanical fields within the weld region during the GMAW joining process; the resulting temporal evolution and spatial distribution of the material microstructure throughout the weld region; and spatial distribution of the as-welded material mechanical properties. The model is upgraded through the introduction of the sixth module in the present work in recognition of the fact that in thick steel GMAW weldments, the overall ballistic performance of the armor may become controlled by the (often inferior) ballistic limits of its weld (fusion and heat-affected) zones.

The upgraded GMAW process model is next applied to the case of butt-welding of MIL A46100 (a prototypical high-hardness armor-grade martensitic steel) workpieces using filler-metal electrodes made of the same material. The predictions of the upgraded GMAW process model pertaining to the spatial distribution of the material microstructure and ballistic-limit-controlling mechanical properties within the MIL A46100 butt-weld are found to be consistent with general expectations and prior observations.

To the authors’ knowledge, the present work is the first reported attempt to establish, using computational modeling, functional relationships between the GMAW process parameters and the mechanical properties controlling the ballistic limit of the resulting weld.