利用1045鋼在 及 Yang的實驗建立內涵時間循環塑性理論核心函數 及材料函數 。依含(或不含)大平均應變循環應變下之應力振幅實驗數據，材料函數 之值會隨循環圈數變動而有循環軟化至穩態之反應。本文以 表示 在N循環下之值，配合本構方程式，對在循環應變振幅0.5%、0.7%、0.8%和1.0%及 下計算應力振幅，其結果與實驗數據吻合。且發現不含平均應變下並無平均應力，而在平均應變 時，平均應力( )隨N之增加而下降之反應，當 時 下降趨勢較緩，當 時 下降較急，特別是 下降非常急速。從 下降圖中， 均會下降到 。
再對循環降伏應力內蠕變行為分析。由於循環應力下之增量形式內含時間本構方程式無法預估出在不同圈數時所對應之累積平均應變值，故本文提議使用蠕變率計算法來預估不同平均應力及應力振幅下的蠕變，其計算結果與數據相當吻合。

關鍵字:內涵時間循環塑性理論，大平均應變之平均應力鬆弛，不對稱之循環降伏應力衍生之蠕變，蠕變率

In this paper, experimental data of 1045 steel under and provided by Yang was employed to establish the kernel function and the material function in the Endochronic cyclic plasticity. According to data of stress amplitudes under cyclic strain amplitude with/without large mean strain , the value of were changed with the cycle of N from cyclic softening to steady response .In this paper, denote to represent under N in the constitutive equation and then compute stress amplitudes, under cyclic strain amplitudes of 0.5, 0.7, 0.8 and 1.0% with 8% mean strain. The results were in good agreement with the experimental data. It found that without mean strain, there were no mean stress , however in the ,mean stress was decreased with the increase of N . When decreased slowly，when decreased rapidly, especially decreased very rapidly. All was dropped to 。
In the analysis of ratcheting behavior within the cyclic yield stress, since the incremental form of Endochronic plasticity under cyclic stress was unable to predict the cumulative mean strain, the ratcheting rate was proposed to use in the computation of the ratcheting strain under various stress amplitudes with mean stress. The results computed were in good agreement with the experimental data.

[1] Valanis, K.C.,“A Theory of Viscoplasticity Without a Yield Surface, Part I. General Theory”, Archives of Mechanics, pp.517-533, 1971.
[2] Valanis, K.C., “Fundamental Consequences of a New Intrinsic Time Measure : Plasticity as a Limit of The Endochronic Theory”, Archives of Mechanics, Vol.32, pp.171-191, 1980.
[3] Lee, C.F., “A Simple Endochronic Creep Modelling and Its Computational Implementation,” The Chinese J. Mechanics, Vol.7, No. 1,pp.21-32(1991).
[4] Lee, C. F.,“Numerical Method of The Incremental Endochronic Plasticity”, The Chinese Journal of Mechanics, Vol.8, No.4, pp.377-396, 1992.
[5] Lee, C.F., Shen, H.T., and Pen, W.T., “A Unified Creep-Cyclic plasticity Theory of Endochronic Viscoplasticity with Applications in 304 Stainless Steel,” The Chinese J. Mechanics, seriesA, 19, pp.443-453(2003).
[6] Rider,R.J., “Fatigue and ratcheting interactions”, Int. J. Fatigue, Vol. 17, No. 7, pp. 507-511, 1995.
[7] Van,K.Dang, , “Evaluation of fatigue-ratcheting damage of a pressurised elbow undergoing damage seismic inputs”,Nuclear Engineering and Design ,Vol.196, pp. 41–50,2000.
[8] Yang, X, “Low Cycle Fatigue and Cyclic Stress Ratcheting Failure Behavior of Carbon Steel 45 under Uniaxial Cyclic Loading”, International Journal of Fatigue,Vol.27,pp1124-1132,2005.
[9] Wei,E., “Simulation of Ratcheting and Low Cycle Fatigue”, International Journal of Pressure Vessels and Piping, No. 81, pp.235-242,2004.
[10] Lee,C.F., “A Systematic Method of Determining Marerial Function in Endochronic Plasticity”, The Chinese Journal of Mechanics, Vol.8, No.6, pp.419-430,1987.
[11] Valanis, K.C. and Fan, J.,“Endochronic Analysis of Cyclic Elastoplastic Strain Fields in a Notched Plate ”, ASME Journal of Applied Mechanics, Vol.50, pp.789-794, 1983.
[12] Lee, C. F. and Shieh, T. J.,“Theory of Endochronic Cyclic viscoplas- ticity of Eutectic Tin/Lead Solder Alloy”, J. of Mechanics,Vol.22,pp. 181-191,2006
[13] 吳宗益, “1070鋼受拘束熱循環下增量式內涵時間循環黏塑性計算法之評估,” 成功大學工程科學系碩士畢業論文,2005.
[14] 陳柏宏, “利用內涵時間黏塑性與穩態潛變理論之計算法對1070鋼受拘束熱循環應力應變行為之評估,” 成功大學工程科學系碩士畢業論文,2005.
[15] 郭長信, “內涵時間有限元素法之潛變分析,” 成功大學工程科學系碩士畢業論文,2006.