本文探討循環比例位移路徑( )下Sn/3.5Ag/0.75Cu BGA銲點試片拉/扭循環負荷之初始疲勞壽命預測。首先利用BGA錫球直立高度0.52mm修正Lee, T. K. 2007年碩士論文中位移-負荷數據，並繼續使用循環內涵時間黏塑性理論之材料參數與核心函數預測各 下之循環應力-應變曲線，利用等效非彈性應變 與等效應力 建立其關係式 。
本文(1)引入損傷等效非彈性應變 於彈性應變密度釋放率和損傷率關係式中之參數 ；(2)在內涵損傷時間定義下建立循環比例位移路徑之內涵損傷演化方程式，並提議損傷累積速率與循環圈數 有乘冪關係。由此可推導出損傷因子 ，並由循環負荷振幅隨 之下降數據獲得 及 並發現 為 、 及 的函數而 與 無關。在 之下Endochronic疲勞壽命預估公式為 ，其 與 無關，但 ，故 vs. 圖中預測結果為與 相關之曲線。此結果在不同範圍 下，可用多段直線表達Coffin-Manson之經驗式。

The purpose of this paper is to investigate the fatigue initiation life prediction of BGA (Sn/3.5Ag/0.75Cu) solder joint specimens under mixed mode cyclic proportional displacement path( ) .First, by using the BGA solder joint standoff 0.52mm to adjust the displacement-loading data of the master's thesis of Lee, T. K. in 2007. And continue with using the material parameters and kernel function of Endochronic cyclic viscoplasticity to simulate cyclic stress-strain curve under proportional displacement path. Then using the effective inelastic strain and effective stress , the relation was established.
This paper(1) aim to employ damage effective strain in parameter that depend on elastic strain energy density release rate and damage rate. (2)Using the definition of intrinsic damage time to establish evolution equation of intrinsic damage under cyclic proportional displacement path. This paper purpose the power form relation between damage accumulate rate and numbers of cycle N. Then damage factor can be derived from the relation, by cyclic loading amplitude vs. N data could compute and n. The results find that depend on , and , n is independence from . Endochronic fatigue life prediction under proportional displacement path , is independence from , but , therefore the result of figure vs. depend on , the result under the different scope of , Coffin-Manson relationship can be expressed by straight lines.

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