- 學位論文
Mode I圓桿表面裂縫生長性質的探討與應用
A study for evaluating surface crack propagation for Mode Iin circular shaft
摘要
本研究是針對圓軸構件上Mode I表面裂縫的疲勞生長性質，提出評估系統。在圓軸真實疲勞表面裂縫生長是一個非常複雜三維力學問題，主要複雜外力型態、裂縫形狀、軸件邊界因素造成，故一般文獻中只有單一條件分析，並無完整評估模式，本文盡可能提供一套完整數值分析系統與量測疲勞表面裂縫系統，並進而應用到實際工程上金屬疲勞問題上。 首先，對圓軸構件建立一套完整應力強度因子系統，做為研究疲勞裂縫生長基礎，使用有限元素法(finite element method)，針對含裂縫的圓軸桿件承受不同負載下，所相映的應力強度因子解，負載型態包含拉伸(tension)、彎曲(bending)、旋轉彎曲(rotation bending)，並提供大範圍的裂縫形狀分析與沿著裂縫前緣不同位置應力強度因子的解，可涵輓握j部分真實表面裂縫生長使用，避免應用出現不足，並且為了使用方便，亦提供擬合多項式函數以便工程上使用。此外，也使用權函數法(weight function method)估算裂縫面上作用任意應力分佈的應力強度因子解，上述不同應力強度因子解，收集文獻中的結果進行可靠性的驗證，得到不錯吻合，同時也在實驗上得到驗證。對於量測圓桿上表面裂縫尺寸的方法，所以藉由撓度法(compliance method)基礎，發展新的量測圓桿表面裂縫的技術，而量測方法可行性與可靠度，也由有限元素方法與實驗方法得到很好驗證。 當基礎理論與工具具備後，建立一套完整圓軸材料疲勞性質的測試程序，並與標準疲勞CT(Compact 拉伸)試片實驗作比較，得到相當好的吻合。對於真實工程應用，本文提出測試疲勞生長速率之縮小試片技術，與圓桿上表面裂縫進行異物填充修補方法，並且發展三維裂縫修補數值模型，來評估圓桿表面裂縫生長遲滯情形，比較實驗與模型預測結果，皆得到不錯吻合。
並列摘要
This study purposes to understand the surface crack growth for Mode I in a cylindrical rod and provides an assessed system. The true surface crack growth including various loadings, crack shapes and boundary conditions is a complex problem. The most solutions from the literatures consider a single condition and lack completely evaluated system. In the current work, numerical analysis system and predicted the depth of an elliptical surface crack in a cylindrical have been established. Lastly, these have been applied in industrial applications. Finite element analysis has been employed to evaluate the stress intensities along the front of an elliptical surface crack in a cylindrical rod. The finite element solution covers a wide range of crack shapes loaded under end-free and end-constrained axial tension, pure bending and rotation bending. Convenient closed form stress intensity expressions along the whole crack front for each of the loading cases have been given in terms of the crack aspect ratio, crack depth ratio and place ratio. Moreover, weight function method has been used to determine the stress intensities subjected to arbitrary loading on the crack face. The above solutions have been compared against a number of representative solutions collected from the literature. It has been found that different finite element results are generally in good mutual agreement. Simultaneously, experimental backtracking results on the end-constrained axial tension case corroborate well with the closed form solution presented. A Normalized Area-compliance method has been shown to be able to predict the depth of an elliptical surface crack in a cylindrical rod. The new method involves a combination of optical surface crack length measurement and specimen compliance measurement. The accuracy of crack depth prediction using this method has been verified by fractography of fatigue cracked rods. Measurement procedure of fatigue crack propagation behavior using surface crack in a tension rod has been established. Fatigue crack growth behavior from the crack depth and crack surface measurement agrees well with the crack growth data obtained from the standard compact tension specimen. For industrial applications, miniaturized tension specimen testing technique measured fatigue crack growth and surface crack repair in a rod by the infiltration method have been carried out. Evaluation of the retardation phenomenon using 3-D surface crack closure model has been attempted. Growth behavior prediction from the current model agrees well with a number of current experimental results.