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Simulation of complex microstructural geometries using X-FEM and the application to solder joint lifetime prediction

Menk, Alexander (2011) Simulation of complex microstructural geometries using X-FEM and the application to solder joint lifetime prediction. PhD thesis, University of Glasgow.

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Abstract

In electronic devices solder joints form a mechanical as well as an electrical connection between the circuit board and the component (e.g. a chip or a resistor). Temperature variations occurring during field use cause crack initiation and crack growth inside the joints. Accurate prediction of the lifetime requires a method to simulate the damage process based on microstructural properties. Numerical simulation of developing cracks and microstructural entities such as grain boundaries and grain junctions gives rise to several problems. The solution contains strong and weak discontinuities as well as weak singularities. To obtain reasonable solutions with the finite element method (FEM) the element edges have to align with the cracks and the grain boundaries, which imposes geometrical restrictions on the mesh choice. Additionally, a large number of elements has to be used in the vicinity of the singularities which increases the computational effort. Both problems can be circumvented with the extended finite element method (X-FEM) by using appropriate enrichment functions. In this thesis the X-FEM will be developed for the simulation of complex microstructural geometries. Due to the anisotropy of the different grains forming a joint and the variety of different microstructural configurations it is not always possible to write the enrichment functions in a closed form. A procedure to determine enrichment functions numerically is explained and tested. As a result, a very simple meshing scheme, which will be introduced here, can be used to simulate developing cracks in solder joint microstructures. Due to the simplicity of the meshing algorithm the simulation can be automated completely. A large number of enrichment functions must be used to realize this. Well-conditioned equation systems, however, cannot be guaranteed for such an approach. To improve the condition number of the X-FEM stiffness matrix and thus the robustness of the solution process a preconditioning technique is derived and applied. This approach makes it possible to develop a new and fully automated procedure for addressing the reliability of solder joints numerically. The procedure relies on the random generation of microstructures. Performing crack growth calculations for a series of these structures makes it possible to address the influence of varying microstructures on the damage process. Material parameters describing the microstructure are determined in an inverse procedure. It will be shown that the numerical results correspond well with experimental observations.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Keywords: X-FEM, Solder joints, Crack growth, Preconditioner, Numerical enrichment, Meshing, BGA, Lifetime Prediction
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
T Technology > TJ Mechanical engineering and machinery
Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
Colleges/Schools: College of Science and Engineering > School of Engineering > Infrastructure and Environment
Supervisor's Name: Pearce, Professor Chris
Date of Award: 2011
Depositing User: Alexander Menk
Unique ID: glathesis:2011-2519
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 04 May 2011
Last Modified: 10 Dec 2012 13:56
URI: http://theses.gla.ac.uk/id/eprint/2519

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