Expected stress relief in a bi-material inhomogeneously bonded assembly with a low-modulus-and/or-low-fabrication-temperature bonding material at the ends

It is shown, based on the developed analytical predictive model, that a significant thermal stress relief can be achieved in an optimized design of an inhomogeneously bonded bi-material assembly, if its bonding system is designed in such a way that the interfacial shearing stress at the ends of the high-modulus-and-high-bonding-temperature mid-portion of the assembly at its boundary with the low-modulus-and-low-bonding-temperature peripheral portion is made equal to the stress at the assembly ends. The numerical example carried out for such an optimized ball-grid-array (BGA) or a column-grid-array (CGA) electronic assembly indicates that the above measure enables one to design an assembly, in which the induced interfacial stresses are about half of the stresses in a regular, non-optimized, but still inhomogeneously bonded assembly with a low-modulus-and/or-low-bonding-temperature material at its ends. The predicted maximum stress in an optimized assembly is only about 41 % of the maximum stress in a homogeneously bonded BGA assembly and about 46 % of the maximum stress in a homogeneously bonded CGA assembly. The numerical data indicated also that the application of the CGA technology in a non-optimized inhomogeneously bonded assembly enables one to achieve a 19 % stress relief in the case of an application of the epoxy adhesive at the peripheral portions of the assembly, and that a 34 % stress relief could be expected in the case of the use of a low modulus solder at the assembly ends. When a BGA technology is considered, the application of an epoxy or a low modulus solder at the peripheral portions of the assembly leads to approximately the same stress relief effect: about 14 % in the case of an epoxy adhesive and about 13 % in the case of a low modulus solder. When a CGA technology is considered, the application of an epoxy at the peripheral portions of the non-optimized assembly leads to about 9.0 % stress relief, while the application of a low modulus solder results in about 24 % stress relief. If, e.g., the yield stress in shear is 1.85 kg/mm² for the solder in the assembly’s mid-portion and 1.35 kg/mm² for the peripheral solder material, the application of the CGA technology in combination with an inhomogeneous bond with an epoxy adhesive or a low modulus solder at the assembly ends might enable one to avoid inelastic strains in the solder, weather in the mid-portion or in the peripheral portion, thereby increasing dramatically the fatigue lifetime of the bond. It is even easier to achieve this goal with the use of the suggested optimized design of an inhomogeneous bond.