Thermomechanical modelling of microstructure evolution in solder alloys

The reliability of soldered connections is a very important issue in electronics industry. This project aims to better understand the various factors influencing the lifetimeof solder joints through numerical modelling. Because of the high homologous temperatures at which they operate, the joints exhibit high temperature deformation mechanisms associated with creep and relaxation and are susceptible to lowcycle fatigue. Another issue is that due to the ongoingminiaturisation,microstructural sizes influence the material properties greatly. The project was initiated with the commercial eutectic tin–lead solder in mind. For this alloy the microstructure evolves, coarsens, significantly over time. To accurately capture the various, and sometimes very large, time scales that come into play, accelerated test methods are not suitable and real time testing is too time consuming. This is where numerical simulations can provide more insight and permit a significant reduction in cost and time of the design of highly reliable soldered connections in electronic packages and components. The first part of this thesis deals with the microstructure evolution of tin–lead due to diffusion. In the following two parts the proposed model is extended with respectively viscoplastic material behaviour and a nonlocal damage approach. In the final part attention is given to the tin–silver–copper system, which is one of the most likely replacement candidates of tin–lead in the strive towards a lead-free electronics industry. The evolving microstructure has been taken into account using a phase field model which is solved using the finite element method. The driving force for diffusion has been derived from a macroscopic free energy function, which describes phase segregation in microscopic model systems with long-range interactions evolving according to stochastic Kawasaki dynamics with nearest neighbour exchanges. Simulations of the static ageing process of eutectic tin–lead solder have been performed. The results predict break-up, coalescence, growth, and dissolution of phases, similar to experimental observations. It was also shown that external mechanical loading leads to faster coarsening rates. Quantitative comparison with experiments has been performed using the total interface length as the quantifying parameter and a good agreement was found. To capture the time dependent mechanical behaviour an elasto-viscoplastic material model law been used for the material model. The extensive information on the microstructure found with the phase field model was used to assign different parameter values to the individual phases and interfaces. Results from simulations of mechanical loading of eutectic tin–lead solder showed a strong dependency on the underlying microstructure. Aged microstructures exhibit more pronounced localisation of stresses and strains. To investigate the reliability of the solder, the model has been extended to include damage. The modelling of softening behaviour often leads to bad solutions using the finite element method. Although the viscous nature of the material model is known to regularise the solution, for practical purposes this effect is usually only sufficient for highly rate-sensitive materials or high loading rates and the numerical results still can show a mesh dependency. Therefore, a gradient enhanced nonlocal damage formulation has been implemented. The results of the phase field model are used to assign different damage parameter values to the phases and interfaces. For the tin–lead system the phase boundaries are known to be the crack initiation sites. The cracks next propagate preferably along tin–lead or tin–tin grain boundaries. The approach yields results that are qualitatively comparable with these experimental findings. Because, in the electronics industry, the tin–lead alloy needs to be replaced with a leadfree alternative in the near future, the final chapter deals with one of the most likely candidates, the near eutectic tin–silver–copper. Experiments performed on this ternary alloy revealed a disconcerting feature. Cyclic thermal ageing without any additional mechanical loading was already enough to lead to fracture along grain boundaries. In order to understand and explain this behaviour the experiments have been modelled using a three-dimensional finite element approach. The viscoplastic damage part of the model is extended to account for anisotropy of the material, both in the elastic as well as the thermal properties. Data obtained from Orientation ImageMicroscopy is used to take into account the microstructure at the grain level, which was found not to evolve over time. The results show a good qualitative agreement with the experiments, exhibiting stress concentrations leading to damage along the grain boundaries. The presented modelling approaches have been applied to simulate the complex behaviour of solder alloys. A multiphase alloy who’s mechanical behaviour is determined by its evolving microstructure is modelled and the results are compared with experimental data, showing satisfactory agreement. Furthermore, an industrially interesting material, near eutectic tin–silver–copper, has been successfully investigated, predicting damage in the same areas as seen experimentally, indicating that the elastic and thermal anisotropic properties play an important part in the fatigue life of this alloy.