Numerical simulation of vacuum dezincing of lead alloy

Removing zinc by distillation can leave the lead bullion virtually free of zinc and also produces pure zinc crystals. Batch distillation is considered in a hemispherical kettle with water-cooled lid, under high vacuum (50 Pa or less). Sufficient zinc concentration at the evaporating surface is achieved by means of a mechanical stirrer. The numerical model is based on the multiphysics simulation package PHYSICA. The fluid flow module of the code is used to simulate the action of the stirring impeller and to determine the temperature and concentration fields throughout the liquid volume including the evaporating surface. The rate of zinc evaporation and condensation is then modelled using Langmuir’s equations. Diffusion of the zinc vapour through the residual air in the vacuum gap is also taken into account. Computed results show that the mixing is sufficient and the rate-limiting step of the process is the surface evaporation driven by the difference of the equilibrium vapour pressure and the actual partial pressure of zinc vapour. However, at higher zinc concentrations, the heat transfer through the growing zinc crystal crust towards the cold steel lid may become the limiting factor because the crystallization front may reach the melting point. The computational model can be very useful in optimising the process within its safe limits.

Scheduling three-operation jobs in a two-machine flow shop to minimize makespan

This paper considers a variant of the classical problem of minimizing makespan in a two-machine flow shop. In this variant, each job has three operations, where the first operation must be performed on the first machine, the second operation can be performed on either machine but cannot be preempted, and the third operation must be performed on the second machine. The NP-hard nature of the problem motivates the design and analysis of approximation algorithms. It is shown that a schedule in which the operations are sequenced arbitrarily, but without inserted machine idle time, has a worst-case performance ratio of 2. Also, an algorithm that constructs four schedules and selects the best is shown to have a worst-case performance ratio of 3/2. A polynomial time approximation scheme (PTAS) is also presented.

An integrated approach to flow, thermal and mechanical modeling of electronics devices

The future success of many electronics companies will depend to a large extent on their ability to initiate techniques that bring schedules, performance, tests, support, production, life-cycle-costs, reliability prediction and quality control into the earliest stages of the product creation process. Earlier papers have discussed the benefits of an integrated analysis environment for system-level thermal, stress and EMC prediction. This paper focuses on developments made to the stress analysis module and presents results obtained for an SMT resistor. Lifetime predictions are made using the Coffin-Manson equation. Comparison with the creep strain energy based models of Darveaux (1997) shows the shear strain based method to underestimate the solder joint life. Conclusions are also made about the capabilities of both approaches to predict the qualitative and quantitative impact of design changes.

Finite element modelling of crack detection tests

Four non-destructive tests for determining the length of fatigue cracks within the solder joints of a 2512 surface mount resistor are investigated. The sensitivity of the tests is obtained using finite element analysis with some experimental validation. Three of the tests are mechanically based and one is thermally based. The mechanical tests all operate by applying different loads to the PCB and monitoring the strain response at the top of the resistor. The thermal test operates by applying a heat source underneath the PCB, and monitoring the temperature response at the top of the resistor. From the modelling work done, two of these tests have shown to be sensitive to cracks. Some experimental results are presented but further work is required to fully validate the simulation results.

Turbulence modelling and its impact on CFD predictions for cooling of electronic components

This paper will discuss Computational Fluid Dynamics (CFD) results from an investigation into the accuracy of several turbulence models to predict air cooling for electronic packages and systems. Also new transitional turbulence models will be proposed with emphasis on hybrid techniques that use the k-ε model at an appropriate distance away from the wall and suitable models, with wall functions, near wall regions. A major proportion of heat emitted from electronic packages can be extracted by air cooling. This flow of air throughout an electronic system and the heat extracted is highly dependent on the nature of turbulence present in the flow. The use of CFD for such investigations is fast becoming a powerful and almost essential tool for the design, development and optimization of engineering applications. However turbulence models remain a key issue when tackling such flow phenomena. The reliability of CFD analysis depends heavily on the turbulence model employed together with the wall functions implemented. In order to resolve the abrupt fluctuations experienced by the turbulent energy and other parameters located at near wall regions and shear layers a particularly fine computational mesh is necessary which inevitably increases the computer storage and run-time requirements. The PHYSICA Finite Volume code was used for this investigation. With the exception of the k-ε and k-ω models which are available as standard within PHYSICA, all other turbulence models mentioned were implemented via the source code by the authors. The LVEL, LVEL CAP, Wolfshtein, k-ε, k-ω, SST and kε/kl models are described and compared with experimental data.

Multilevel refinement for combinatorial optimisation problems

We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (sometimes for the original problem, sometimes the coarsest) and then iteratively refined at each level. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (most notably in the form of multigrid techniques). However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial optimisation problems. In this paper we address the issue of multilevel refinement for such problems and, with the aid of examples and results in graph partitioning, graph colouring and the travelling salesman problem, make a case for its use as a metaheuristic. The results provide compelling evidence that, although the multilevel framework cannot be considered as a panacea for combinatorial problems, it can provide an extremely useful addition to the combinatorial optimisation toolkit. We also give a possible explanation for the underlying process and extract some generic guidelines for its future use on other combinatorial problems.

The effect of thermal cycle profiles on solder joint damage

The relationship between the damage caused at different thermal cycles is very important. The whole of accelerated thermal cycle testing is based on the premise that damage at one cycle is representative of damage at a different cycle. In this paper, the relative damage caused by six thermal cycle profiles are predicted using Finite Element (FE) modelling and the results validated against experiments. Both creep strain and strain energy density were used as damage indicators and creep strain was found to correlate better with experiment. The validated FE model is then used to investigate the effect of altering each of the thermal profile parameters (ramp and swell times, hot and cold temperatures). The components used for testing are surface mount resistors - 1206, 0805 and 0603. The solders investigated are eutectic SnAgCu and eutectic SnAg.

Intermetallic phase detection in lead-free solders using synchrotron X-ray diffraction

The high-intensity, high-resolution x-ray source at the European Synchrotron Radiation Facility (ESRF) has been used in x-ray diffraction (XRD) experiments to detect intermetallic compounds (IMCs) in lead-free solder bumps. The IMCs found in 95.5Sn3.8Ag0.7Cu solder bumps on Cu pads with electroplated-nickel immersion-gold (ENIG) surface finish are consistent with results based on traditional destructive methods. Moreover, after positive identification of the IMCs from the diffraction data, spatial distribution plots over the entire bump were obtained. These spatial distributions for selected intermetallic phases display the layer thickness and confirm the locations of the IMCs. For isothermally aged solder samples, results have shown that much thicker layers of IMCs have grown from the pad interface into the bulk of the solder. Additionally, the XRD technique has also been used in a temperature-resolved mode to observe the formation of IMCs, in situ, during the solidification of the solder joint. The results demonstrate that the XRD technique is very attractive as it allows for nondestructive investigations to be performed on expensive state-of-the-art electronic components, thereby allowing new, lead-free materials to be fully characterized.

Solder life prediction in a thermal analysis software environment

This paper describes recent developments made to the stress analysis module within FLOTHERM, extending its capability to handle viscoplastic behavior. It also presents the validation of this approach and results obtained for an SMT resistor as an illustrative example. Lifetime predictions are made using the creep strain energy based models of Darveaux. Comment is made about the applicability of the damage model to the geometry of the joint under study.

Assessing the scalability of multiphysics tools for modeling solidification and melting processes on parallel clusters

A comprehensive solution of solidification/melting processes requires the simultaneous representation of free surface fluid flow, heat transfer, phase change, nonlinear solid mechanics and, possibly, electromagnetics together with their interactions, in what is now known as multiphysics simulation. Such simulations are computationally intensive and the implementation of solution strategies for multiphysics calculations must embed their effective parallelization. For some years, together with our collaborators, we have been involved in the development of numerical software tools for multiphysics modeling on parallel cluster systems. This research has involved a combination of algorithmic procedures, parallel strategies and tools, plus the design of a computational modeling software environment and its deployment in a range of real world applications. One output from this research is the three-dimensional parallel multiphysics code, PHYSICA. In this paper we report on an assessment of its parallel scalability on a range of increasingly complex models drawn from actual industrial problems, on three contemporary parallel cluster systems.

Investigation into the performance of turbulence models for fluid flow and heat transfer phenomena in electronic applications

Heat is extracted away from an electronic package by convection, conduction, and/or radiation. The amount of heat extracted by forced convection using air is highly dependent on the characteristics of the airflow around the package which includes its velocity and direction. Turbulence in the air is also important and is required to be modeled accurately in thermal design codes that use computational fluid dynamics (CFD). During air cooling the flow can be classified as laminar, transitional, or turbulent. In electronics systems, the flow around the packages is usually in the transition region, which lies between laminar and turbulent flow. This requires a low-Reynolds number numerical model to fully capture the impact of turbulence on the fluid flow calculations. This paper provides comparisons between a number of turbulence models with experimental data. These models included the distance from the nearest wall and the local velocity (LVEL), Wolfshtein, Norris and Reynolds, k-ε, k-ω, shear-stress transport (SST), and kε/kl models. Results show that in terms of the fluid flow calculations most of the models capture the difficult wake recirculation region behind the package reasonably well, although for packages whose heights cause a high degree of recirculation behind the package the SST model appears to struggle. The paper also demonstrates the sensitivity of the models to changes in the mesh density; this study is aimed specifically at thermal design engineers as mesh independent simulations are rarely conducted in an industrial environment.

Modeling and experiments on an isothermal fatigue test for solder joints

This paper investigates an isothermal fatigue test for solder joints developed at the NPL. The test specimen is a lap joint between two copper arms. During the test the displacement at the ends of the copper are controlled and the force measured. The modeling results in the paper show that the displacement across the solder joint is not equal to the displacement applied at the end of the specimen. This is due to deformation within the copper arms. A method is described to compensate for this difference. The strain distribution in the solder was determined by finite element analysis and compared to the distribution generated by a theoretical 'ideal' test which generates an almost pure shear mode in the solder. By using a damage-based constitutive law the shape of the crack generated in the specimen has been predicted for both the actual test and the ideal pure shear test. Results from the simulations are also compared with experimental data using SnAgCu solder.

Effects of solder reflow on the reliability of flip-chip on flex interconnections using anisotropic conductive adhesives

This work describes the work of an investigation of the effects of solder reflow process on the reliability of anisotropic conductive film (ACF) interconnection for flip-chip on flex (FCOF) applications. Experiments as well as computer modeling methods have been used. The results show that the contact resistance of ACF interconnections increases after the reflow and the magnitude of the increase is strongly correlated to the peak reflow temperature. In fact, nearly 40 percent of the joints are open when the peak reflow temperature is 260°C, while there is no opening when the peak temperature is 210°C. It is believed that the coefficient of thermal expansion (CTE) mismatch between the polymer particle and the adhesive matrix is the main cause of this contact degradation. To understand this phenomenon better, a three-dimensional (3-D) finite element (FE) model of an ACF joint has been analyzed in order to predict the stress distribution in the conductive particles, adhesive matrix and metal pads during the reflow process. The stress level at the interface between the particle and its surrounding materials is significant and it is the highest at the interface between the particle and the adhesive matrix.

On-line algorithms for single machine scheduling with family setup times

The paper considers an on-line single machine scheduling problem where the goal is to minimize the makespan. The jobs are partitioned into families and a setup is performed every time the machine starts processing a batch of jobs of the same family. The scheduler is aware of the number of families and knows the setup time of each family, although information about a job only becomes available when that job is released. We give a lower bound on the competitive ratio of any on-line algorithm. Moreover, for the case of two families, we provide an algorithm with a competitive ratio that achieves this lower bound. As the number of families increases, the lower bound approaches 2, and we give a simple algorithm with a competitive ratio of 2.