本文探討傾斜位移路徑下，利用BGA銲點試片測試系統負荷-位移修正法及試片夾具勁度值將63Sn/37Pb BGA試片位移-負荷數據修正成錫球位移-負荷數據。 下之拉-扭循環比例位移路徑使用循環內涵時間黏塑性理論之塊材63Sn/37Pb核心函數，預測各 下之循環應力-應變曲線，並建立錫球的等效非彈性應變振幅 與等效應力振幅 關係式為 ，以及BGA試片位移振幅 及對應 之關係式： 。上述方法連結業界BGA試片結果與學界銲錫本構模式之研究結果。
對BGA試片在循環傾斜位移測試下初始壽命預估，本文循環損傷在物理現象下依循環圈數及 上升加大其損傷強度依此，可推導出 -修正之損傷乘冪方程式並決定63Sn/37Pb及Sn/3.5Ag/0.75Cu之損傷指數n。結合損傷演化方程式與前述Endochronic Viscoplasticity 可推導出以 -Modified Lee-Coffin-Manson( -LCM) 方程式： ，及 -LBGA方程式： 。上述方程式對63Sn/37Pb、Sn/3.5Ag/0.75Cu BGA疲勞壽命數據皆有良好之預估結果；再與文獻所提供之預估結果做評論。

In this paper, the force -oblique displacement correction methods of the BGA solder joint specimens and the values of grip stiffness were used to correct the force-oblique displacement curves of the 63Sn/37Pb BGA specimens into the force-displacement data of their solder balls under proportional strain cyclic test. The kernel function of Endochronic cyclic viscoplasticity of 63Sn/37Pb bulk material was employed to predict the cyclic proportional stress-strain curves and then construct the relationship of the effective inelastic strain amplitude and the effective stress amplitude : . Also the BGA oblique displacement amplitude has a relation with of solder ball by . This result connects the research of BGA solder joint specimen in industry and the research of constitutive models in academic.
Based on physical phenomena, dependent damage degree depends positively on N cycle and , then the -modified damage power equation and the -Modified Lee-Coffin-Manson equation( -LCM) for the fatigue initiation life of solder ball: can be derived. Finally the -LBGA equation for the fatigue life of BGA specimens: can be obtained. Using the -LBGA equation, both of 63Sn/37Pb and Sn/3.5Ag/0.75Cu BGA fatigue life can be predicted very well.

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