Cyclic Stress-Strain Behavior of BGA (Sn/3.5Ag/0.75Cu) Solder Joint under Cyclically Oblique Displacement Tests and Endochronic Viscoplastic Predictions

In this paper, a methodology with workable procedures was proposed and successfully transferred the hysteresis loops of BGA solder joint specimen held by loading-directionally aligned grip system under oblique displacement controlled cyclic tests, into hysteresis loops of “representative” solder ball itself under proportional straining and constant strain rate cyclic tests. Under the elastic unloading during cyclic test, value of elastic modulus of bulk solder specimens and the linear behavior of grip system were used. Following the study of Endochronic cyclic viscoplasticity, the kernel function ρ(Z) = ρ0 exp (−KZ)/Zα was found to be independent of the oblique angle (Φ) of straining paths. However, the steady cyclic behavior of material function f(ξ) ≡ f0 in the definition of intrinsic time Z contained two functions: (1) is the effective inelastic strain amplitude, and (2) f(Φ) Φ(rad) between Φ = 0 (uniaxial) and Φ = π/2 (shear). With (ρ0, α, K) = (4MPa, 0.84, 46) and f0 = [0.24(π/2−Φ)2 − 0.018(π2−Φ) + 1.2] , the endochronic theory predicted experimental hysteresis loops of BGA Sn/3.5Ag/0.75Cu solder joint specimens and Φ = 0°, 27°, 45°, 63°, 90° quite well.Results of ρ(Z) under f0 = 1 were found under independent study based on cyclic tests of bulk specimens under constant uniaxially strain amplitude and various constant strain rates. The values of (ρ0, α, K) = (7.3MPa, 0.84, 30) with f0 = 1.0 were all independent of strain rates. Comparisons of results of both types of specimens revealed that the values of (α, K) were almost the same but (1) ρ0 was smaller for micro-size solder ball, (2) is a material function of Sn/3.5Ag/0.75Cu itself (3) f(Φ) is not a material function, rather it is a special feature to reflect the effects of detail design of solder joint specimen and its connecting methods to the substrates