A Data-Driven Machine Learning Model for the Stress-Strain Behavior of Single Grain SAC305 Solder Joints

Sn-Ag-Cu (SAC) alloys are a type of lead-free solder that are commonly used in microelectronic packaging. These materials typically contain more than 95% β-Sn, which is a highly anisotropic material with different elastic moduli and coefficients of thermal expansion depending on the crystal direction. In particular, a set of 6 unique elastic compliances are needed to model the elastic behavior. When β-Sn is plastically deformed beyond its elastic limit, the deformations are governed by the movement of dislocations on specific crystallographic planes and directions. There are 10 different slip families with 32 slip systems that have been identified for β-Sn body-centered tetragonal (BCT) crystals. In our current work, we are developing approaches to modeling the mechanical response of SAC solder joints made up of a small number of β-Sn grains reinforced with Ag3Sn and Cu6Sn5 intermetallic particles. Anisotropic elasticity theory for a BCT crystal is being used to model the elastic behavior of the grains, while Crystal Plasticity (CP) theory is being used to predict the post yielding material response by considering the crystallographic deformation mechanisms.In the study reported in this paper, a data-driven machine learning (ML) model was developed to predict the mesoscale deformation behavior of single crystal SAC samples. The ML model was trained using a large number of solder stress-strain curves for various crystal orientations obtained using simulations performed with the crystal plasticity-based DAMASK code. The constants in the CP code were first calibrated with experimental solder stress-strain data (both elastic and plastic regions) to obtain the model constants that describe the overall material deformation of SAC305 alloy from a crystallographic standpoint. For a single crystal SAC sample, there are an infinite number of possible orientations for uniaxial loading that can lead to an infinite number of different overall mechanical deformation behaviors. To account for this, a large number of CP simulations (10,000) were performed using the DAMASK code for samples with various single crystal orientations. A time-series based machine learning model was then trained on simulated stress-strain plots for the 10,000 known orientations. At first, the simulation data were categorized as inputs (crystal orientations and strains) and corresponding outputs (stress) considering data normalization and proper sequencing. During training, mean squared error (MSE) loss function was observed based on the number of epochs of the training process. Adam, which is a variant of stochastic gradient descent (SGD), was used as an optimization algorithm. To obtain and efficient and reliable model, tuning was performed based on hyperparameter and batch size and eventually cross-validation was considered to estimate the model performance.Finally, the accuracy of the trained ML model was evaluated by predicting the stress-strain behavior of a set of 2500 additional orientations that were not in the training set. The accuracy of the ML predictions were shown to be very good, so that the ML model can be used in the future without the need to perform computationally expensive and time-consuming CP simulations. In particular, the machine learning model can help to bypass the complicated pre-processing, computation, and post-processing aspects of numerical crystal plasticity modeling.