2001-08-012024-05-18https://scholars.lib.ntu.edu.tw/handle/123456789/697594摘要：彈塑性組成模式可用以描述固態系統諸多宏觀現象，如彈塑性、循環塑性、遲滯、摩擦、塑鉸等。這些現象不止存在於材料、也存在於構件、介面、元件，甚至整體結構。 本三年期研究計畫由動態系統學的觀點，研究彈塑性組成模式之對稱群、建模、模式架構、模式識別、參數估測、實驗觀察等主題。 本期為第三年，在對稱群方面，由閔氏時空之羅倫茲群、龐卡萊群，擴展至共形群，得到偽歐空間之群表示，了解李代數與應變輸入之關係。在建模與模式架構方面，為解決循環塑性回應力循環振盪及反向降伏時應力應變曲線過方的難題，引入了降伏厚面的觀念，導出其塑性開關充要條件及組成方程式，也進行模式層級架構之探討，並與其他模式比較。另一方面以積分形式組成律，代入指數函數與冪函數的核函數，從最初的模式建構至參數估測時的實驗設計、估計之數值方法、以及最後的模式模擬，發展系統化的實驗數據處理方法。 在實驗觀察方面，針對單向對稱等振幅應力循環下之棘齒行為進行研究。根據一連串的實驗以及數據分析發現，鋁7075及鋁6061於單向對稱等振幅循環下竟有拉壓硬化不對稱之現象，因此當其循環硬化趨於飽和時，每一圈應力循環下總是會產生拉伸向的應變累積，導致所謂<br> Abstract: Constitutive models of elastoplasticity may be em- ployed to describe more macroscopic phenomena than people thought. In addition to elastoplasticity, they include cyclic plasticity, hysteresis, friction, plastic hinge, etc. These phenomena appear not only in materials, but also in members, interfaces, devices, and even in a whole engineering structure. In other words they appear in a variety of solid state systems. This three-year project was proposed to study elastoplastic models from a dynamical-system- theoretic point of view, focusing on the issues of symmetry groups, modeling and model hierarchy, model identification and parameter estimation, and experimental observation. In the third year we have, in the symmetry groups aspect, expanded from the Lorentz and Poincare groups acting on Minkowski spacetime to conformal group, obtaing its group representations in pseudo- Euclidean space and relating its Lie algebra to the strain input. In the medeling and model hierarchy aspect, we have postulated a comprehensive model with yield thick-surface to circumvent the problems of back stress oscillation and over-square elastic- plastic transition. In the model identification and parameter estimation aspect we have developed a sys- tematic procedure for experimental design, data processing and parameter estimation for models of the integral-equation type with exponential and power function kernels. In the experimental observation aspect we have found that annealed Aluminum alloys 7075 and 6061 in uniaxial tension-compression cyclic stress-con- trolled tests exhibited ratchetting even with zero mean stress and equal amplitudes at room temperature and that the ratchetting was all in the direction of elon- gation no mather the cyclic tests began in tension or in compression. The initail few cycles were dominated by cyclic hardening, and once the effect of cyclic hard- ening saturated, ratchetting manifest itself. Careful comparisons of the stress-strain loops after saturation showed that there were clear evidences of tension- compression asymmetry of strain hardening, namely strain accumulation in the tensile half-cycle of each cycle being larger than that in the compressive half- cycle of the cycle, and hence ratchetting tended to elongate (even with zero mean stress). The observa- tion was further confirmed by true stress-controlled tests.彈塑性組成律循環塑性閔氏時空偽歐空間龐卡萊群共形群降伏厚面模式識別參數估測冪定律實驗設計循環硬化鋁7075。elastoplasticityconstitutive lawcyclic plasticity Minkowski spacetimepseudo-Euclidean spacePoincare groupconformal groupyield thick-surfacemodel identificationparameter estimationpower lawexperimental designcyclic hardeningAl 7075.