含邊緣裂縫之纖維複合材料平板在兩種不同纖維走向下之熱應力分析

The Thermal Stress Analysis of a Fiber Composite Material Plate Which Contains Crack in Two Different Fibers Directions

蔡佳豪(Tsai, Nelson)

指導教授 ： 蔣長榮

國立清華大學/工學院/動力機械工程學系/碩士(2012年)

https://doi.org/10.6843/NTHU.2012.00148

摘要

本文之目的在於探討一含裂縫之碳纖維環氧樹酯複合材料平板，在兩側溫度不同情況下，溫度擴散所造成的張裂型裂縫應力集中現象，並利用應力滑順因子反推應力強度因子，進而了解裂縫周圍的行為。本文可應用於航空器、船舶等有殼之機械，當殼之外側溫度低於內側溫度，並產生裂縫時，分析三種裂縫長度與兩種纖維方向一共六種情形，其溫度擴散分布、y方向熱應力分布與應力強度因子的不同。假定平板纖維是垂直或平行裂縫情形下模擬之。為了更貼近裂縫尖端實際的幾何情況及使用應力滑順因子之公式，在裂縫尖端處以一曲率半徑為0.5mm之圓弧模擬之。溫度擴散需要時間，因此時間成為一個重要的參數，所以本文使用暫態(Transient)分析，探討在不同時間點的溫度場下，根據纖維垂直或平行於裂縫的條件及不同裂縫尺寸，所造成之應力強度因子之變化。最後發現，在三種裂縫尺寸與兩種纖維方向時，應力強度因子均會隨著時間而增大。裂縫長度越長，同一時間同纖維方向的應力強度因子也越大。當裂縫走向為x軸，而纖維方向是y軸時，鈍化裂縫前端y方向的應力將會比同一時間，同一裂縫長度，纖維方向是z軸的裂縫前端的應力大；但是，相對應的裂縫，其應力強度因子則有相反趨勢。

關鍵字

熱擴散 ； 熱應力 ； 異向性彈性力學 ； 正交性材料破裂力學 ； 應力滑順因子 ； 應力強度因子

並列摘要

The purpose of this thesis is to research a carbon fiber epoxy composite material plate which contains crack, in the condition of different temperature on two sides, the phenomenon of crack stress concentration cause by the thermal diffusion in opening mode; we used the stress rounding factor to derive the stress intensity factor, and understand the behavior of the area around the crack tip. The thesis can be applied to the shell machine such as the aircrafts and the ships, when the outside temperature of the shell is smaller than the inside temperature of the shell, and there is a crack form on the outside shell, we analyzed three kinds of the crack length and two kinds of fibers direction, so there are total six different situations. In these six situations, we analyze the difference of the distributions of temperature by thermal diffusion, the distributions of y direction thermal stress and the stress intensity factors. We assume that the direction of the fibers in the plate is perpendicular or parallel to the crack and analyze it. In order to be close to the real geometry situation of crack tip and use the equation of stress rounding factor, we use a curve which has a 0.5mm radius on the crack tip to simulate. It takes time for thermal diffusion, so the time become an important parameter; therefore this thesis use transient analysis, to research the situation of different temperature fields at the different time, the variation of stress intensity factor according to the condition of fibers direction which are parallel or perpendicular to the crack and the condition of the different crack length. Finally, we found that in the condition of the three kinds of crack length and two kinds of fibers direction, the stress intensity factors will all become greater as the time increases. At the situation of same fibers direction and the same time, the longer the crack is, the greater the stress intensity factor is. When the direction of crack is x axis, the fibers direction are y axis, the y direction stress on the blunt crack tip will be greater than the y direction stress on the blunt crack tip at the situation of same time and same crack length and the fibers direction are z axis. But, for the corresponding crack, the stress intensity factor showed the opposite tendency.

並列關鍵字

thermal diffusion ； thermal stress ； anisotropic elastic theory ； orthotropic material fracture mechanics ； stress rounding factor ； stress intensity factor

參考文獻

[1] W. E. Anderson, “An engineer views brittle fracture history,” Boeing report, 1969.

[2] D. Broek, Elementary Engineering Fracture Mechanics, Martinus Nijhoff Publishers, Dordrecht, 1986.

[5] M. L. Williams, “Stress Singularities Resulting from Various Boundary Condition in Angular Corners of Plates in Extension,” Journal of Applied Mechanics, Vol. 19, pp. 526-528, 1952.

[8] T.L. Anderson, Fracture Mechanics Fundamentals and Applications, 3rd ed., CRC Press, Boca Raton, 2005.

[10] C. R. Chiang, “The stress field for a blunt crack in an anisotropic material,” International Journal of Fracture, Vol. 68, R41-R46, 1994. (and addendum in International Journal of Fracture, Vol. 70, R99, 1995.)