結構鋼材在循環載重下之彈塑性行為研究

本研究主要係建立有限元素模型和模擬結構鋼材在循環載重下之彈塑性行為。在循環載重下，材料會呈現循環完全彈性、循環彈性安定性、循環塑性安定性或棘輪的行為模式。本論文主要容分為三部份，首先，建立線性等向性硬化和線性運動硬化組合模型，以簡單懸臂樑受反覆載重作用為例，分析結果與ANSYS比較，以驗證有限元素分析程式之準確性。其次，採用Chaboche非線性運動硬化模型，探討金屬材料在單軸循環拉伸壓縮作用下之塑性行為。由實驗觀察發現，在非對稱應力控制條件下，材料會發生循環棘輪行為，並隨著循環載重週期累加。有限元素分析結果顯示，Chaboche模型能有效分析材料之棘輪反應，並與實驗結果相符。最後，建立彈塑性接觸有限元素模型，分析接觸表面受循環滾滑動接觸作用之彈塑性反應。本研究採用Prager模型和Chaboche模型模擬軌道鋼和CS1026碳鋼之金屬材料於循環載重週期之塑性變形。研究結果發現，Prager模型對於安定性分析能得到良好的預測結果，但無法有效模擬材料棘輪反應，而Chaboche能有效預測材料之棘輪行為。另外，由安定性極限分析結果發現，接觸應力於安定性極限範圍內，因塑性變形、殘留應力和應變硬化之影響，材料內部降伏強度會隨載重週期增加而提升，並抑制材料進一步塑性變形的發生。當接觸應力超過安定性極限，殘留應力並不影響材料塑性流動的累積，在循環載重過程，塑性應變會呈現循環棘輪反應，而棘輪應變率隨著週期數的增加遞減。

關鍵字

有限元素、循環載重、安定性現象、棘輪現象、非對稱應力控制、循環滾滑動接觸、安定性極限

並列摘要

The purpose of this research is to develop a finite element model to study the elastic-plastic deformation of structural steel under cyclic loading. The finite element analysis is applied to investigate the elastic-plastic behavior of structural steel with cyclic elastic-entirely, cyclic elastic shakedown, cyclic plastic shakedown or ratcheting under cyclic loading. First, the constitutive law for linear isotropic hardening and kinematic hardening model with Von-Mises yield surface and associated flow rule is developed. Numerical solutions of a cantilever beam under reversed of loading are compared with ANSYS solutions and there is a good agreement between two solutions. Next, the constitutive model of nonlinear kinematic hardening rule proposed by Chaboche is used to investigate the ratcheting response of CS1026 carbon steel with uniaxial loading history for an unsymmetrical stress controlled system. Finally, the finite element analysis is applied to investigate the elastic-plastic response of rail steel and CS1026 carbon steel under rolling and sliding line contact. Numerical results show that the Prager’s model can give a good prediction on the shakedown limit and the Charboche model can effectively simulate the ratcheting behavior of materials under cyclic contact loading. The shakedown limits are also calculated for various combination of contact loading to assess the plastic flow that occurs when the shakedown limit is exceeded. When the contact loading exceeds the shakedown limit, the plastic strain can accumulate with increasing number of contact cycles.