Investigation of intermetallic compound formation, Kirkendall void nucleation and failure in solder joints
Final Report Abstract
The overall goal of the proposed research project was to provide a predictive numerical tool for three-dimensional simulations of long-term aging in solder connections. We derived a comprehensive coupled phase-field model subjected to thermal, mechanical and electrical loadings. Exemplarily, solder joints of microelectronic devices are subjected to such a wide range of loadings. They affect the microstructural evolution of the alloy. Long term investigations are commonly performed under thermally accelerated conditions, but are not available for real-life environmental conditions in literature yet. Therefore, the solder bumps of ten-year-old graphic cards were inspected here. Besides the experiment, the mathematical description of the assigned processes is modeled with the phase-field approach. Phase field methods allow for convenient and efficient moving interface simulations. In this work, phase field approaches had been applied to simulate void growth in binary and multi-component systems, reactive systems subjected to IMC growth, thermal influences on physe decomposition, crack evolution between voids, and higher-order meshing of a solder ball and its binary content. The numerical framework provides a B-spline based finite element method which minimizes the numerical and computational effort without impairing the smoothness required by the problem. In order to demonstrate the possibilities of such general phase field approaches a series of different models from material science and fracture mechanics was investigated. Specifically, a priori unknown crack propagation between two voids of different size in mode-I fracture was presented. The examples show the versatility of the phase field approaches. Standard FEM ansatz functions do not allow to solve high-order PDEs directly, and a natural way to achieve the required continuity is the use of B-splines as finite element basis functions. Such spline-based FEM comes at the expense of a non-intuitive design of the geometrical mesh. Because multi-physics problems, especially with reaction-diffusion terms, require a mesh without distorted elements, we elaborated on a strategy to obtain B-spline-based meshes for curves, surfaces, and volumes. The isoparametric B-spline based meshes are based on homeomorphic transformations which allow us to deduce elementary geometrical shapes from rectangular plate or cuboid solid tensor-product meshes. We present the knot vectors and the control points for a circular plate, a cylinder, and a sphere for practical use. To show our strategy’s versatility, we adapt the presented algorithm to mesh a helix structure and show the chemo-mechanically induced deformation due to phase decomposition.
Publications
- Modeling and numerical simulation of crack growth and damage with a phase field approach. GAMM-Mitteilungen, 39(1), 2016
Kerstin Weinberg, Tim Dally, Stefan Schuss, Marek Werner, and Carola Bilgen
(See online at https://doi.org/10.1002/gamm.201610004) - Void dynamics in lead-free sn-ag-cu solder joints. PAMM, 16(1), 2016
Marek Werner, Thomas Reppel, and Kerstin Weinberg
(See online at https://doi.org/10.1002/pamm.201610296) - Diffusion induced void nucleation in snpb solder joints. PAMM, 17(1), 2017
Marek Werner and Kerstin Weinberg
(See online at https://doi.org/10.1002/pamm.201710256) - A chemo-mechanical model of diffusion in reactive systems. Entropy, 20(2), 2018
Kerstin Weinberg, Marek Werner, and Denis Anders
(See online at https://doi.org/10.3390/e20020140) - A multi-field model for charging and discharging of lithium-ion battery electrodes. Continuum Mechanics and Thermodynamics, 2020
Marek Werner, Anna Pandolfi, and Kerstin Weinberg
(See online at https://doi.org/10.1007/s00161-020-00943-8) - Experimental investigation of microstructural effects in sn-pb solder accumulated during ten years of service life. Micro and Nanosystems, 12, 2020
Marek Werner and Kerstin Weinberg
(See online at https://doi.org/10.2174/1876402912999200518104018)
