Abstract
This dissertation presents a three-dimensional thermolastic fractureanalysis for a cracked body subjected to thermal loadings. Using conformalmapping technique, the temperature distribution of an infinite solid withan embedded elliptical insulated crack subjected to an uniform heat flowis solved analytically. The elliptical crack region is first mappedconformally onto a penny-shaped crack for which the solution oftemperature on the crack surface is available. The complete analyticalsolution of the temperature field of the entire solid studied is thenobtained by the inverse Fourier transform technique and the singularity oftemperature gradient of the crack surface near the crack front can befound.To deal with three-dimensional thermoelastic fracture behaviors, thethree-dimensional path-independent integrals which are physically theenergy release rates per unit area of crack extension along respectivedirections of crack growth in the volume surrounding the crack frontincrement are presented. To calculate the mixed-mode thermal stressintensity factors, another path-independent integral which denotes theenergy release rate per unit area of crack extension for tearing mode isalso derived. The variation of the integrals along the crack frontincrement is assumed to be linear and a simpler and accurate approachwhich can be employed to calculate three-dimensional thermal stressintensity factors along the crack front indirectly is thus established.To account for the singularities of temperature gradient and thermalstress around the crack front effectively, the collapsed quarter-pointsingular elements are adopted. Based on the aspect of uncoupledthermoelasticity, an three-dimensional finite element model which providesboth heat transfer and thermal stress analysis is performed. The influenceof geometry and Poisson's ratio on the computation of temperaturedistributions and thermal stress intensity factors under various thermalconditions (e. g. prescribed temperature or temperature gradient andconvection cooling etc.) is evaluated. The variations of pure andmixed-mode thermal stress intensity factors along the crack front are alsosutdied for both through and part-through cracks existing in finiteelastic solids.Good agreements between the computed results and referenced solutions showthe validity and accuracy of the pressent analysis.本論文旨在研究三維含裂縫結構的溫度場解析解，並且有系統的發展一三維熱彈性破裂問題之有限單元分析模式，以有效解決一般含平面裂縫之熱彈性力學問題。此外並分別對含貫穿或部分貫穿式裂縫三維體之溫度場及熱應力場做詳盡的探討，計算其熱應力強度因子，以提供含裂縫結構（例如：核能反應器結構組件）安全性之評估。本文首先分析含橢圓形平面絕緣裂縫之無限體於均佈熱流通過下之溫度場，除了成功的得到其溫度場解析解外，並獲致在裂縫平面下靠近裂縫前緣區域其溫度梯度之奇異特性。此外，為考慮裂縫前緣附近溫度梯度和熱應力的奇異性，本文採用崩潰式四分之一點奇異單元配合此區域外等參數二次傳統單元之使用，建立了包含熱傳導及熱應力分析之整體性三維熱彈性有限單元破裂分析模式，而為了能有效且正確的計算熱應力強度因子，本文推導與積分路徑無關之三維能量積分式，配合其與熱應力強度因子間關係的確立，以間接得到熱應力強度因子。為了評估本論文所發展之數值分析模式的正確性，文中分析了含裂縫之厚板、圓柱和圓管等三維結構體受到不同熱負載條件例如定溫、絕緣和熱對流等情況下之數個具代表性的實例。並探討各種不同裂縫、結構幾何形狀及材料係數對破裂行為的影響，由計算結果與既有文獻相較，顯示本文所建立三維有限單元破裂分析模式具有高度之準確性與應用性。