https://scholars.lib.ntu.edu.tw/handle/123456789/169096
標題: | 冪定律用於循環彈塑性與黏彈性之建模(1/2) The power law for modeling cyclic elastoplasticity and viscoelasticity |
作者: | 洪宏基 | 關鍵字: | 黏彈性;彈塑性;冪定律;分數導數;棘齒行為;對稱零均值應力循環;真實應力控制;拉壓硬化不對稱;徑向位移;viscoelasticity;elastoplasticity;power law;fractional derivative;ratchetting;cyclic loading with zero mean stress;true stress control;asymmetry of hardening between tension and compression | 公開日期: | 2003 | 出版社: | 臺北市:國立臺灣大學土木工程學系暨研究所 | 摘要: | 本計畫以兩年為期,以實驗的、理論的、計 算的方式探索固態系統之黏彈性與彈塑性行為反 應規律,嘗試找出其共通的共性,歸結基本原理, 以適當的數學語言表達之。以此共性、原理、數學 模式為平台,具體引入黏彈性時間冪定律及塑性當 量冪定律的觀念,藉由冪定律與分數導數及積分組 成律核函數的關係來系統化地模擬黏彈性與彈塑 在黏彈性及彈塑性的各種應力應變關係中,循 環棘齒行為是極難妥適建模描述的。一般認為唯有 在應力均值不為零的循環負載下才會發生棘齒,但 由實際的文獻與實驗卻發現即使在應力均值為零 的對稱等振幅應力循環負載下,也能觀察到拉伸向 的棘齒現象。本計劃第一年在實驗部分嘗試把實驗 分為真實應力控制與標稱應力控制來分析在應力 均值為零的循環負載下所觀察到的棘齒現象。經比 較分析後證實:不論是真實應力控制或標稱應力控 制的實驗,在應力均值為零的循環負載下都會往拉 由進一步分析顯示,上述在應力均值為零時 所觀察到的拉伸向棘齒現象是由拉、壓硬化不對稱 所造成,壓硬化大於拉硬化,因此隨著實驗循環圈 數的累積,會逐漸往拉伸向產生棘齒。而且先拉或 先壓不同的控制歷時會影響拉、壓硬化不對稱的程 度,先壓的控制歷時會讓壓硬化加劇,因此往拉伸 向的棘齒會較先拉控制歷時還快出現,棘齒現象也 較明顯。對於循環硬化材料,如鋁7075,拉伸向的 棘齒現象在一開始的幾圈循環裡會被循環硬化所 隱蔽。但隨著循環硬化的影響逐漸變小,便可觀察到拉伸向棘齒。 另外,為了讓實驗達到真實應力控制,本研 究也導出徑向位移的理論公式,並以自製的環向伸長計驗證其精確度。 The present project was proposed to study in a two-year period common characteristics and basic principles underpinning viscoelasticity and elastoplasticity. The power law is specifically introduced into the stress-strain relationship by converting the power law to the fractional derivative and to the kernel of the stress functional of the plastic strain increment. Ratchetting is one of the most difficult behavior to model among the viscoelastic and elastoplastic stress-strain relations. Generally speaking, ratchetting can be found under cyclic loading with non-zero mean stress. However, some experiments showed that even under cyclic loading with zero mean stress, ratchetting in the direction of tension can still be found. The first year experimental part of this project analyzed the phenomena of ratchetting under nominal-stress -controlled cyclic loading and true-stress-controlled cyclic loading with zero mean stress. The results show that ratchetting in the direction of tension can be found in true-stress-controlled experiments as well as in nominal-stress-controlled experiments. The results of analysis also show that the ratchetting in the direction of tension as mentioned above was caused by the asymmetry of hardening between tension and compression, the hardening of compression being larger than the hardening of tension and hence the tensile strain being larger than the compressive strain in each cycle. As the cyclic contributions accumulated, the ratchetting in the direction of tension gradually developed. Furthermore, the difference of controlled path would also affect the asymmetry of hardening between tension and compression. If the controlled path started in the compression direction, the asymmetry of hardening between tension and compression would be more apparent than that of the controlled path starting in the direction of tension; therefore, ratchetting is more apparent. For cyclic hardening materials, e.g. Al 7075, the phenomenon of ratchetting in the direction of tension was shadowed in the first few cycles. Once the cyclic hardening effect phased out, ratchetting manifested itself. In order to conduct true-stress-controlled experiments, we developed formulae to calculate the theoretical value of radial strain, and checked its accuracy by a self-developed radian strain extensometer. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/2813 | 其他識別: | 912211E002077 | Rights: | 國立臺灣大學土木工程學系暨研究所 |
顯示於: | 土木工程學系 |
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912211E002077.pdf | 920.33 kB | Adobe PDF | 檢視/開啟 |
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