本文利用內涵時間黏塑性理論模擬Wei等人對Sn/3.9Ag/0.6Cu銲錫材料於低應變率疲勞及熱循環耦合之熱-力負載實驗，考慮銲錫材料於熱循環情況下晶粒因而成長，對核心函數做適當修正，則在In-phase模式下計算之循環應力-應變行為與實驗數據相當吻合，在Out-phase模式下之模擬結果與Wei等人Damage-Coupled Constitutive Model之模擬結果趨勢一致。本文再以Zeng等人對Sn/3.8Ag/0.7Cu(equiaxed)銲錫材料之實驗，利用內涵時間黏塑性理論模擬其應力-應變行為，並由實驗之應力振幅-壽命圖求得損傷D與循環圈數N之關係，再以含損傷內涵時間黏塑性理論計算銲錫受損傷之應力-應變行為，於材料發生buckling前皆能吻合實驗數據，接著以Coffin-Manson修正式預估D=0.25時之疲勞壽命，對不同應變率之疲勞壽命皆能有效預估，進而得知即使相同材料但微結構不同，疲勞壽命之趨勢也有差異，與Zeng等人觀察不同微結構(equiaxed/dendritic)之破壞機制有所區別符合。

Sn/3.9Ag/0.6Cu experimental at low strain rate and thermal cycling coupled of Wei et. al., in this paper, using Endochronic viscoplasticity established cyclically hysteresis loops. Consider material will age under thermal cycle, the kernel function must be modified. The results and the experimental data were in very good agreement under In-phase condition, and had almost the same trend with that of the Damage-Coupled Constitutive Model of Wei et. al. under Out-phase condition.Sn/3.8Ag/0.7Cu(equiaxed) experimental of Zeng et. al., the Endochronic viscoplasticity was used to simulate cyclic stress-strain hysteresis loops. By stress amplitude vs. life data could compute D-N relation, the Endochronic viscoplasticity with damage was used to simulate Sn/3.8Ag/0.7Cu(equiaxed) cyclic stress-strain hysteresis loops with damage under strain amplitude 0.8% provided by Zeng et. al. in temperature 298K. The results were in very good agreement with data before the material buckling. Modified Coffin-Manson relationship was derived and used to predict the data of fatigue initiation life very effectively, and then fatigue initiation life was distinction under different microstructure. This result was to conform to the fracture mechanism under different microstructure

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