本文以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 之實驗數據為對象，利用2008年歐士豪碩士論文中之核心函數及本文建立之應變率敏感函數 ，計算循環穩態應力-應變遲滯曲線其結果與實驗相當吻合，其循環應力-非彈性應變曲線，隨應變率上升往高應力值向上平移。疲勞壽命除 外，其餘壽命對 之分佈無明顯之不同。以Endochronic疲勞壽命預估公式在 、不同應變率下以 vs. 作圖可得一曲線，並在 下可以三段Coffin-Manson直線表示。在 下，進行循環損傷參數( 、n)之外插，以直線方式將壽命預估推廣至 。由於 之試棒製作冷卻速率較快，疲勞壽命較短，壽命預估時 對應 之值向上平移修正，即可得理想之結果。
本文再以Shang等人對上述銲錫於 、不同溫度下(T=298K~393K)之實驗為依據，擴大內涵時間黏塑性理論中核心函數與溫度的關係，其模擬結果與實驗數據相當貼合。在 、各溫度下，以 及 決定參數n為0.7。在動態再結晶影響下，晶粒細化而導致微裂紋增加，溫度從298K升高， 之值亦隨之上升，但對 分佈之趨勢與298K時相同。以Endochronic疲勞壽命預估公式在 及各溫度下進行預估，以 vs. 作圖可得一曲線，結果與實驗數據相當吻合，且各溫度趨勢一致。

In this paper, the kernel function and the strain rate sensitive function in the Endochronic viscoplasticity was established by using the paper of Ou and Sn/3.8Ag/0.7Cu (equiaxed structure) experimental data of Zeng and Shang et. al., in the room temperature 298K and strain rate . The cyclic stress-strain hysteresis loops and the experimental data were in very good agreement, and the stress raised with increased strain rate in the cyclic stress-inelastic strain curve. Then, the Endochronic fatigue life relationship was used to predict the fatigue initiation life of different strain rate, and the results could represented by Coffin-Manson relationship at . The cyclic damage parameter of ( , n) were extrapolated at , and the fatigue life would be extend to in linearly. The specimen of has shorter fatigue life cause of the faster cooling rate, then the ideal results would be shift the parameter under fatigue life prediction.
The kernel function with temperature relationship in Endochronic viscoplasticity was broadened by using experimental data of Shang et. al., in different temperature and strain rate , then the results and the experimental data were in very good agreement. The parameter n=0.7 determinated by and under and at different temperature. Microcracks increasing resulted from finer grain under dynamic recrystallization. As the temperature raising from 298K, will increases as well, but the trends of distribution were as the same as it was at 298K. The Endochronic fatigue life relationship was used to predict the fatigue initiation life under different temperature. The fatigue life can be shown by vs. plot, then the results and the experimental data were in very good agreement, and the trend was the same at different temperature.

[1]Zeng Q. L., Wang Z. G., Xian A. P., and Shang J. K., “Cyclic Softening of the Sn-3.8Ag-0.7Cu Lead-Free Solder Alloy with Equiaxed Grain Structure,” Journal of Electronic Materials, Vol. 34, No.1, pp.62-67, 2005.
[2]Shang J. K., Zeng Q. L., Zhang L., and Zhu Q. S., “Mechanical Fatigue of Sn-rich Pb-free Solder Alloys,” J. of Mater. Sci : Mater. In Electron., Vol. 18(1-3), pp. 211-227, 2007.
[3]Zeng Q. L., Wang Z. G., and Shang J. K., “Microstructural Effects on Low Cycle Fatigue of Sn-3.8Ag-0.7Cu Pb-free Solder,” Key Engineering Materials, Vols. 345-346, pp.239-242, 2007.
[4]Kanchanomai C., Miyashita Y., Mutoh Y., and Mannan S. L., “Influence of Frequency on Low Cycle Fatigue Behavior of Pb-Free Solder 96.5Sn–3.5Ag,” Material Science and Engineering A 345, pp.90-98, 2003.
[5]Kanchanomai C., Mutoh Y., “Effect of Temperature on Isothermal Low Cycle Fatigue Properties of Sn-Ag Eutectic Solder,” Material Science and Engineering A 381, pp.113-120, 2004
[6]Zhu Q. S., Wang Z. G., Zeng Q. L., Wu S. D., and Shang J. K., “Rapid Cycle-Dependent Softening of Equal Channel Angularly Pressed Sn-Ag-Cu Alloy,” Journal of Material Research., Vol. 23, No. 10, pp.2630-2638, 2008.
[7]Zhu Q. S., Wang Z. G., Wu S. D., and Shang J. K, “Enhanced Rate-Dependent Tensile Deformation in Equal Channel Angularly Pressed Sn-Ag-Cu Alloy,” Material Science and Engineering A 502, pp.153-158, 2009.
[8]Lee C. F., and Shieh T. J., “Theory of Endochronic Cyclic Viscoplasticity of Eutectic Tin/Lead Solder Alloy,” J. of Mech., Vol. 22, No.3, pp.181-191, 2006.
[9]Lee C. F., and Chen Y. C., “Thermodynamic Formulation of Endochronic Cyclic Viscoplasticity with Damage-Application to Eutectic Sn/Pb Solder Alloy,” J. of Mech., Vol. 23, No.4, pp. 433-444, 2007.
[10]歐士豪，含損傷內涵時間黏塑性理論對Sn/Ag/Cu銲錫低應變率疲勞及熱循環耦合循環熱-力行為及不同應變率疲勞初始壽命預估，
碩士論文-國立成功大學工程科學系，2008。
[11]Valanis K. C., “A Theory of Viscoplasticity without a Yield Surface, PartⅠ. General Theory,” Archives of Mechanics, pp. 517-533, 1971.
[12]Valanis K. C., “A Theory of Viscoplasticity without a Yield Surface, PartⅡ. Application to Mechanical Behavior of Metal,” Archives of Mechanics, pp. 535-551, 1971.
[13]Lee C. F., “Recent Finite Element Applications of the Incremental Endochronic Plasticity,” International Journal of Plasticity, Vol. 11, No.7, pp. 843-865, 1995.
[14]Lee C. F., “Numerical Method of the Incremental Endochronic Plasticity,” The Chinese Journal of Mechanics, Vol.8, No.4, pp. 377-396, 1992.
[15]Stolkarts, V., Keer, L. M., Fine, and M. E., “Damage Evolution Governed by Microcrack Nucleation with Application to the Fatigue of 63Sn-37Pb Solder,” J. Mech. Phys. Solids Packaging, Vol. 47, pp.2451-2468, 1999.
[16]Lau J. and Dauksher W., “Effects of Ramp-Time on the Thermal-Fatigue Life of SnAgCu Lead-Free Solder Joints,” IEEE Electronic Components and Technology Conference, pp. 1292-1298, 2005.
[17]Lee C. F., Lee Z. H., and Ou S. H., “The Endochronic Viscoplasticity for Sn/3.9Ag/0.6Cu Solder Under Low Strain Rate Fatigue Laoding Coupled Thermal Cycling,” J. of Mech., Vol. 25, No.3, pp. 261-270, 2009.
[18]Zeng Q. L., Wang Z. G., Xian A. P., and Shang J. K., “Low Cycle Fatigue Behavior of Sn-3.8Ag-0.7Cu Lead-Free Solder,” Chinese J. Material Research., Vol. 18, pp. 11-17, 2004.