TEMPERATURE AND FREQUENCY MODIFIED FATIGUE INITIATION LIFE OF SOLDER ALLOYS PREDICTED BY ENDOCHRONIC CYCLIC DAMAGE-COUPLED VISCOPLASTICITY

In this paper, an evolution equation of cyclically internal damage in the intrinsic damage time scale after the threshold cycles N-0 was extended by employing its damage parameters proposed to be dependent of frequency (v) and temperature (T) under cyclic fatigue loading. The resulting damage-coupled endochronic viscoplasticity can drive v and T modified power form equations of cyclic damage and its fatigue initiation life (N) over bar (I) = N-I + N-0. Under fatigue tests with T effect and N-0 = 0, the power form equation of N-I(T)/(beta) over bar (T-h), named as T-LCM (T modified Lee Coffin-Manson) equation for fatigue initiation life can be derived. The T modified factor (beta) over bar (T-h) depends on the T dependent material elastic modulus, the cyclic stress-strain response and the damage parameters. Theoretical predictions in the life data of Sn/3.8Ag/0.7Cu solder alloy under cyclic strain test with T is an element of [298,393] K were very well. Also under fatigue tests with v effect only, the power form equation of (N) over bar (I) /v(1-k) named as v-LCM (v modified Lee-Coffin-Manson) equation for fatigue initiation life can be derived. The v modified parameter. depends on the v dependent cyclic stress-strain response and the damage parameters. Theoretical predictions in the life data of 96.5Sn/3.5Ag solder alloy with surface cracking effect i. e. N-0 not equal 0 during cyclic strain tests with v is an element of [0.001,1] Hz were quite well. Obviously, the values of power exponents C in the T-LCM and the v-LCM equations can not be determined simply by the least square method as in the Coffin-Manson empirical formulae. Also, they must be justified by constrains imposed in the material parameters defining in the cyclic stress-strain response and the accumulation behavior of cyclic damage. The resultant equations derived here and the Phi-LCM equation derived under Phi angle proportional cyclic strain tests can be combined together to form a T-v-Phi LCM equation for fatigue life studies in the solder alloys using bulk specimens or BGA solider joint specimens.