A generalized multi-domain Rayleigh Ritz (MDRR) stress analysis model has been proposed earlier by the authors [Ling et. Al. 1996] to obtain the stress and strain field in surface-mount solder joints, under the cyclic thermal loading condition. Elastic, plastic and time dependent visco plastic analysis has been demonstrated a BGA solder joints. The analysis results confirm that the MDRR technique is capable of providing stress, strain analysis with adequate accuracy, without time consuming finite element model generation and analyses.
The MDRR stress analysis approach is general in principle for various
surface-mount interconnects. By choosing appropriate mapping function,
different physical configurations are replaced by identical fictitious
domains. The rest of the analysis thus can be carried out in an invariant
manner. In the current paper, the MDRR technique is applied to BGA solder
joints, under the thermomechanical loading environments. Specific isoparametric
mapping functions are chosen to map the unique geometry outline of a BGA
electronic package assembly. The eutectic solder joint and high lead solder
joint material properties are assigned at different solder joint regions
accordingly. Polynomial displacement fields are assumed in the fictitious
domain and the total potential energy is calculated and minimized in the
same fashion as for J-leaded solder joint stress analysis. Stress contours
are generated in the BGA solder joints under thermomechanical loading.
All results are compared with finite element analysis results for the same
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