為利用銲點試片(Solder Joint)尋求受損傷錫球之應力應變行為，本文首先定義材料測試系統之勁度，其值可由穩態循環負荷－位移遲滯曲線量取線性卸(加)載範圍之斜率求得。在前述線性反應下，銲點材料呈線彈性反應其楊氏及剪力模數與塊狀(Bulk)材料相同，故於定循環比例位移(Φ)下可決定銲點試片(彈性)勁度。然後將材料測試系統以彈簧串聯觀念可計算出夾具勁度值，在測試過程(Φ)中設定夾具勁度不變，進而可得銲點試片真實位移，及其負荷－位移遲滯曲線。
本文利用含9顆Sn/3.5Ag/0.75Cu錫球之銲點試片於定溫下不含損傷之單剪實驗為基準找出內涵時間黏塑性理論之核心函數及內涵時間內之材料函數，其值由Φ=90°算起向Φ=0°遞增，但隨非彈性應變振幅增大而變小。依此等向性含損傷內涵時間黏塑性理論在不同循環比例位移路徑下負荷－位移遲滯曲線計算結果與實驗數據比較，兩者相當吻合。依Lee等人提出之循環損傷演化方程式，及非彈性應變振幅隨循環圈數疊加只略微增大，可推導出損傷因子與循環圈數之關係： ，其中參數A由Φ=90°算起向Φ=0°遞增，同時隨等效非彈性應變範圍增大而上升，n則與A趨勢相反。在各種循環比例角度下由D－N及負荷－位移遲滯曲線兩種數據，發現臨界損傷因子0.4<Dc<0.5，並與循環比例位移角度無關。

In order to find stress-strain-damage behavior of solder ball by using solder joint specimen, this thesis defined, at first, the stiffness of material testing system, whose value could be determined from the slope of linear range of loading or unloading of the load-displacement hysteresis loop. Within this range, the solder joints behaved linear elastic with Young’s modulus and shear modulus of bulk material. As a result, the (elastic) stiffness of solder joint specimen under proportional displacement path (Φ) could be determined. Employing the series combination of spring for material testing system, the stiffness of grips could be calculated, whose value was fixed under its corresponding proportional displacement path. Consequently, the load-displacement hysteresis loop of solder joint specimen could be constructed.
In this paper, isothermal undamage simple shear test data of solder joint specimen having 9 Sn/3.5Ag/0.75Cu balls were used as a base to determine the kernel function of endochronic viscoplasticity and the material function in the intrinsic time measure whose values were increased from Φ=90° to 0° but decreased as increased of the effective inelastic strain amplitude. Based on these, the isotropic endochronic viscoplasticity with cyclic damage under various proportional displacement path was used to compute load-displacement hysteresis loops. The computational results were in excellent agreement with data. According to Lee’s evolution equation of cyclic damage and the small increase in effective inelastic strain amplitude with increasing cyclic number, the relationship between damage factor D and the cyclic number N could be derived: , here was increased both from Φ=90° to 0° and the increase of effective inelastic strain amplitude. But the trend of was reversed. Usage of data of D vs. N curves and load-displacement hysteresis loops of various Φ, critical values of damage factor could be determined, 0.4<Dc<0.5 and its value was indepent of Φ.

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