Dislocation Density based Non-local Continuum Plasticity Model
Plastic deformation in metallic materials predominantly attributes to dislocation slip. Although microscale Discrete Dislocation Dynamics models have been used to understand the deformation mechanisms in single crystal, computational expense of such methods restrics the application for large strain simulation for polycrystalline materials. A little effort has been made so far to incorporate dislocation mechanisms to continuum scale polycrystalline plasticity model, rather they have been phenomenological in nature so far. Inherent variability of microstructures in heterogeneous materials manufactured via additive manufacturing and severe plastic deformation process causes unreliable analysis with phenomenological model. Current approach uses dislocation diffusion-reaction based 2-parameter (mobile and immobile dislocation density) continuum dislocation dynamics approach to model non-local plasticity model for advanced materials proven to overcome "strength-ductility trade-off".
Both "intrinsic" and "extrinsic" size effect in plastic deformation known to cause increase in yield strength and hardening in micro-scale metallic structures. Both of this approach has been considered in the current model to develop a generalized framework for wide-range of applications. Grain size based "intrinsic" size effect follows Hall-Petch relationship and has been rationalized as dislocation pile-up against grain boundaries. Interaction between different grain sizes was modeled as stress-gradient based enhancment in hardening while enhanced hardening in bending and torsion of microscale structure was modeled as generation of geometrically necessary dislocation (GND), i.e., plastic strain gradient. An efficient algorithm to calculate stress- and strain-gradient was implemented within LS-DYNA user-defined material subroutine, UMAT. Initial work was submitted to MS&T 2020 Technical Meeting and Exhibition.
Growth Kinetics of Cu/Sn Intermetallics in SAC Microbumps
Intermetallic growth in micro-solder joints has severe effect on the reliability of electronic packaging as it tends to alter the mechanical properties of solders. Interface diffusion between Cu and Sn is responsible for growth Cu6Sn5 and Cu3Sn intermetallic compounds. An analytical model based on Fick's diffusion law and mass conservation principle was develop to model the growth of intermetallics with Cu bond pad was considered as an infinite media and Sn was considered a finite media. Newton-Raphson based iterative solution procedure was adopted to solve the resulting nonlinear system of equations. The model was divided into two distinct stages - in first stage, Sn depletes and both intermetallics grow in volume, and in second stage, Cu6Sn5 depletes and only Cu3Sn grows. This model can be used as a guideline to design microsolder joints for reliable operation of electronic packaging.
Details can be found here: Arafat et el. (2020), "A Model for Intermetallic Growth in Thin Sn Joints Between Cu Substrates: Application to Solder Microjoints", Journal of Electronic Materials, 49, pages 3367–3382. [https://doi.org/10.1007/s11664-020-08019-8]