本文主要探討內涵塑性理論之材料函數（material function） ，藉由適當地選擇材料函數中之材料參數，可將該材料函數區分成六種類型之態樣，以期更適切地描述材料在非對稱振幅循環負載下之材料行為，包括包辛格效應（Bauschinger effect）、循環硬化(軟化)、應力穩定飽和（saturation）、循環應力峰值（peek stress）的變化以及材料記憶消除（erasure of memory）行為，並以Shiao [1]及Lamba and Sidebottom [2]之實驗結果驗證本文之材料函數模式；另外本文提出一組與隨後降伏曲面(sequencent yield surface)之形狀特徵比 (aspect ratio)相關的材料函數，建立一降伏曲面的內涵模式，藉以模擬材料在小變形(small pre-strain range)下因變形誘導異向性（deformation induced anisotropy）而表現在其隨後降伏曲面呈前凸後扁狀( sharp front and blunt rear)的演化行為，另以Wu and Yeh [3] 對AISI 304 不銹鋼施以軸向、扭向以及軸扭雙向應變作用之實驗結果驗證本文之降伏曲面模式；採用本文之材料函數及降伏曲面模式預測材料循環塑性行為及降伏曲面的演化行為與實驗結果比對相當吻合。 In this article, a material function of endochronic theory is proposed for investigating the plastic behaviors of material. Depending on the material parameters properly chosen, the present model can be classified into six categories, and is appropriate for describing various materials behaving cyclic strain hardening inherently with respect to the deformation history. Experimental verification of the theory was demonstrated using the experimental results of Shiao [1] and Lamba and Sidebottom [2]. The theory is in good agreement with experimental results obtained by Shiao [1] through comparing the stress-strain hysteresis loops of SAE 4340 steel under axisymmetrically cyclic loading condition with various amplitudes. In addition, the present model is shown to be capable of describing the behavior of erasure of memory of materials, as experimentally observed by Lamba and Sidebottom [2]. In addition, an endochronic model of yield surface is proposed. Based on this model, the yield surface is simulated such that the forward and rear parts of the yield surface are described by different ellipses which are characterized by corresponding aspect ratio functions, respectively. Verification of the endochronic theory used the experimental results of yield surfaces obtained by Wu and Yeh [3] for AISI 304 stainless steel. The experiments were performed cyclically under uniaxial, torsional, and combined axial-torsional loading conditions. The result has shown that the agreement between the prediction and experiments is quite satisfactory. In addition to the distortion of the yield surface plastically behaving a sharp front accompanied by a blunt rear, the anisotropic kinematic hardening effect has been addressed in this investigation.
