具變形誘導異向性質之降伏曲面與材料函數的內涵模式

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林希彥(Hsi-Yen Lin) 查詢紙本館藏

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論文名稱

具變形誘導異向性質之降伏曲面與材料函數的內涵模式
(Endochronic Model of Yield Surface and Material Function Accounting for Deformation Induced Anisotropy)

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摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 循環應變硬化
★ 內涵理論
★ 材料函數
★ 記憶消除

關鍵字(英)

★ material function
★ cyclic strain hardening
★ endochronic theory
★ erasure of memory

論文目次

摘要 I
目錄 IV
圖表說明 IX
符號說明 X
第一章緒論 1
1-1前言 1
1-2 文獻回顧 5
1-3 研究動機和方法 15
第二章內涵塑性理論 19
2-1引言 19
2-2內涵本構方程式 20
2-2-1積分式內涵本構方程式 21
2-2-2增量式內涵本構方程式 23
2-2-3微分式內涵本構方程式 24
第三章材料函數 26
3-1材料函數 26
3-2 本文之材料函數模式 28
3-2-1 材料函數之性質 29
3-2-2 材料參數 32
3-3 數值計算 33
3-3-1 積分式內涵本構方程式的數值計算 33
3-3-2 增量式內涵本構方程式的數值計算 35
3-3-3 微分式內涵本構方程式的數值計算 37
第四章降伏曲面模式 40
4-1 降伏曲面 40
4-2 本文之降伏曲面模式 43
頁次
第五章結果與討論 49
5-1 材料函數 49
5-1-1 軸向對稱等應變振幅循環負載 50
5-1-2 軸向非對稱應變振幅循環負載 51
5-1-3 軸向漸增應變振幅循環負載 52
5-1-4 軸向漸變均值應變振幅循環負載 53
5-1-5 軸向漸增均值應變與振幅之循環負載 54
5-1-6 材料記憶消除 55
5-2降伏曲面模式 57
5-2-1 初始降伏曲面 58
5-2-2 隨後降伏曲面 59
5-2-2-1 單軸向負載 59
5-2-2-2 扭向負載 60
5-2-2-3 軸-扭組合負載 61
第六章結論與建議 63
6-1 結論 63
6-2 建議 65
參考文獻 67

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指導教授

葉維磬(Wei-Ching Yeh)

審核日期

2007-1-2

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