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標題: | 半無限軟鐵磁性區域邊緣傾斜裂縫承受均勻磁場作用下所引致之磁漏現象及其破壞力學分析 Magnetic Flux Leakage and Fracture Analysis of Semi-Infinite Soft Ferromagnetic Region with an Oblique Edge Crack subjected to Uniform Magnetic Field |
作者: | Shih-Yuan Chiu 邱士遠 |
指導教授: | 葉超雄(Chau-Shioung Yeh) |
關鍵字: | 磁通量洩漏,邊緣裂縫,馬克斯威爾應力,施瓦茲-克里斯托夫轉換,有理映射,複變函數法, magnetic flux leakage,Maxwell stresses,Schwarz-Christoffel’s transformation,rational mapping,complex variable method, |
出版年 : | 2013 |
學位: | 碩士 |
摘要: | 本文探討半無限域軟鐵磁性區域邊緣斜裂縫承受均勻磁場作用下之破壞力學分析,有鑑於磁通量洩漏技術是一種典型的非破壞型檢測技術之一,用於管線或其他高磁導率物體的現場即時檢測,磁通量洩漏技術方法運用磁化材料由外部接近缺陷時將感知到磁場的特性事實,檢測裂縫,而由其洩漏場得知了裂縫的位置與尺寸,有時甚至知道形狀。
我們考慮一軟鐵磁材料,軟鐵磁材料是一高磁化率材料,以及考慮一有限邊緣斜裂縫在半無限域中受均勻磁場作用產生出磁彈應力及馬克斯威爾應力,當中我們使用一有理函數將一帶有邊緣斜裂縫之半無限域映射到單位圓上,此有理函數的求得是來自於施瓦茲 - 克里斯托夫轉換,而原本施瓦茲 - 克里斯托夫轉換求得之函數為一無理函數。 在考慮靜止的平面問題下,一個帶有邊緣裂縫的半無限區域,受均勻磁場作用下,給定邊界應力及位移條件之磁彈問題我們有一解析方法,在平衡方程式中磁場影響彈性場是以一個類似體力的形式,我們稱之為勞倫茲力。當中我們使用部分分式表示式的疊加來表示原本之映射函數即使用複變解法來解決此問題。而無論在磁場或彈性場中,我們使用複變解法和有理近似技巧加以分析問題,因此我們將獲得精確解,當中近似的部分僅有有理近似時產生的微小誤差,而過程中我們必須先將控制方程式及邊界條件表示成複變函數的形式。最後我們將求得在裂縫端點的應力強度因子,及考慮不同角度的磁場作用下的應力強度因子,同時也研究在同一磁場作用下不同角度的斜裂縫與應力強度因子改變的關係。 In this thesis,we present the fracture analysis of semi-infinite soft ferromagnetic region with an oblique edge crack subjected to uniform magnetic field. In view of the magnetic flux leakage(MFL) technique is one of the basic methods of non-destructive testing used for the in-line inspection of pipelines and other objects made from materials with high magnetic permeability.The MFL methods uses the fact that near a defect in an externally magnetized material the field is forced out of the metal ,which can be detected by field sensors .This leak-field provides information about the location and size. In some case also the shape. The induced magnetoelastic stresses and Maxwell stresses generated by a uniform magnetic field in a semi-infinite soft ferromagnetic medium. The soft ferromagnetic elastic solids with a finite oblique edge crack are considered to be high magnetic susceptibility materials. A rational function that maps a semi-infinite region with an oblique edge crack into a unit circle is formed. The rational mapping function is formed from an irrational mapping function obtained by Schwarz-Christoffel’s transformation. An analytical method for the static plane problem of magnetoelasticity is developed for a semi-infinite medium with an edge crack under stress and displacement boundary conditions in a primary uniform magnetic field. The magnetic field influences the elastic field by introducing a body force called the Lorentz force in the equilibrium equations. The complex variable method in conjunction with the rational mapping function technique is used in the analysis for both magnetic field and mechanical field. The mapping function of the sum of fractional expressions and the complex variable methods are used. Closed solutions are obtained for the problems. Governing equations and boundary conditions are expressed in terms of complex functions. The stress intensity factors at the tips of crack is computed ,and the variation for certain directions of primary magnetic field is shown. The relations between the stress intensity factors and the angle of the oblique edge are also investigated. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/60602 |
全文授權: | 有償授權 |
顯示於系所單位: | 土木工程學系 |
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