本文以含損傷內涵時間黏塑性理論依Zeng及Shang等人對Sn/3.8Ag/0.7Cu銲錫(Equiaxed)於298K、應變率 之單軸循環拉伸實驗數據為對象，以核心函數 及應變率敏感函數 建立不同應變率下穩態循環應力-應變曲線( )，發現 。疲勞壽命除 外，其餘不同應變率壽命對 分佈無明顯不同。以Endochronic疲勞壽命預估公式在 、 不同應變率下以 vs. 作圖得斜率為0.46之直線。因 之試棒製作冷卻速率較快，疲勞壽命較短，其直線截距值較小。
再以Shang等人對同材料於 、不同溫度下(T=298K~393K)之單軸拉伸疲勞實驗為依據，提議內涵時間黏塑性理論之核心函數只有參數 與溫度呈指數函數關係，並利用不同溫度 下穩態之 實驗數據決定其指數。利用循環壽命值隨溫度及 上升而下降之現象，提議循環損傷程度亦隨溫度及 上升而擴大。依此可推導出T-modify損傷乘冪公式及T-modified Lee-Coffin-Manson(T-LCM)壽命預估公式： 。由各溫度下Load-Drop數據決定臨界損傷因子 。發現損傷乘冪指數為常數與溫度無關。各溫度下疲勞壽命以T=298K為基準，依 修正壽命，以 vs. 作圖可得兩直線，在 時C=0.46，其斜率與 之值相同，在 時，其斜率C=0.66大於 之值。各溫度預估結果與實驗數據相當吻合。

In this paper, the damage-coupled endochronic viscoplasticity was used in the cyclic uniaxial tensile test data of the Sn/3.8Ag/0.7Cu solder (equiaxed) at 298K and strain rate . The kernel functions ; and the strain rate sensitivity function were employed to construct the strain rate dependent steady cyclic stress - strain equations： . Except , the fatigue life of all strain rates are not significantly different. Using the endochronic fatigue life prediction formula in and , a straight line drawn in the vs. plot has slope C= 0.46. Due to rapid cooling rate of specimen’s preparation, the line to predict the fatigue life at , has the same slope, but the life is shorter.
The uniaxial tensile fatigue data of the Sn/3.8Ag/0.7Cu solder under different temperatures (T = 298K ~ 393K). were used to determine the exponential function of . By proposing the degree of damage depends on positively N、T and , the T-modify power form damage equation and the T-modified Lee-Coffin-Manson (T-LCM) equation for life prediction: can be derived. From load-drop curves of all temperature, the critical damage factor , and the exponent of damage power form is a constant. Based on T=298K, fatigue life of all temperatures under vs. plot, two straight lines can be drawn in which slope C=0.46 at , and C=0.66 at . The T-LCM equation can predict the experimental data quite well.

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