本研究以最小二乘法配合有限元素分析與試驗來求得承拉型填角銲十字接頭銲接未滲透部分裂縫尖端Mode I與Mode II之應力強度因子（KI與KII），並將其正規化為應力強度放大係數（MKI與MKII）。在數值分析部份，透過大量的有限元素數值模擬結果、幾何尺寸參數分析與迴歸分析，求得承拉型填角銲十字接頭Mode I與Mode II的放大係數迴歸公式。本研究在試驗部分，共製作了十五支不同幾何尺寸的填角銲十字接頭試體，並以高像素數位照相機記錄試體接頭上裂縫的張開位移(COD)並導入最小二乘法計算其裂縫尖端的Mode I與Mode II的應力強度因子，利用試驗方法所求得的填角銲十字接頭應力強度因子結果與英國標準BS PD-6493中的填角銲十字接頭應力強度因子公式及數值模擬之結果相吻合。由數值分析與試驗結果可得知：承拉型填角銲十字接頭構件，在裂縫長度變小時，x方向COD及y方向COD變小，KI與KII值亦變低，此外，當填角銲腳長變小時，y方向COD變大，KI值亦變高。實際上，此試驗方法可應用於任何對Iwrin 展開式有效的彈性體表面裂縫上。由於此方法易於使用，試驗儀器也方便攜帶，故適合於現場鋼構件接頭裂縫應力強度因子之量測，對於鋼橋或近海結構物之細部的疲勞計算相當有用的方法。

This study is to determine the mixed mode stress intensity factors (SIFs), KI and KII, of load-carrying fillet welded cruciform joints numerically and experimentally by Least-Squares Method, and the SIF results were normalized to magnification factors showing how the geometric dimensional parameters of the fillet welded cruciform joints affect SIFs. In numerical part of the study, numerous numerical examples of various geometric dimensional parameters were analyzed and the SIF results were employed to develop the regression formulas of KI and KII for the cruciform joints. In experimental part of this study, a total of fifteen cruciform joint specimens were tested and analyzed in the digital-camera experiment. The test results showed that the proposed experimental method was able to give satisfactory SIF evaluation for the load-carrying fillet welded cruciform joints, and verified the SIF formula for cruciform joints adopted in British Standard PD-6493 and results of numerical simulation at the same time.

In summary, numerical and experimental results show that the decreasing crack length in the un-penetrated area of a cruciform joint leads to the decreasing KI and KII values for the crack tip, and the decreasing fillet weld leg size for the cruciform joints generates the higher KI value. In fact, the experimental method presented can be applied to determine the SIF of any detail with surface crack where the Irwin’s series solution for crack-tip displacement fields is valid. Due to its simplicity and portability, the experimental method presented is applicable to field measurement of SIFs directly from a detail of interest at the site, which is very useful for fatigue evaluation of details in structures like steel bridges or offshore structures.

Bowness D, Lee MMK. Stress intensity factor solutions for semi-elliptical weld-toe cracks in T-butt geometries. Fatigue & Fracture of Engineering Materials & Structures, 19(6):787-797. (1996).
British Standard PD 6493: Guidance on methods for assessing the acceptability of flaws in fusion welded structures; Appendix E4, British Standard Institution, London, UK. (1991).
British Standard PD 6493: Guidance on methods for assessing the acceptability of flaws in fusion welded structures; Appendix J:29, British Standard Institution, London, UK. (1997).
Frank KH. The fatigue strength of fillet welded connections. PhD thesis, Lehigh University. PA, USA. (1971).
Frank KH, Fisher JW. Fatigue strength of fillet welded cruciform joints. Journal of the Structural Division ASCE; 105(ST9):1727-1740. (1979).
Hobbacher A. Stress intensity factors of welded joints. Engineering Fracture Mechanics; 46(2):173-182. (1993).
Irwin GR. Analysis of stresses and strains near end of a crack transversing a plate. Transactions, ASME. Journal of Applied Mechanics; 24:361. (1957).
Ju SH. Simulating stress intensity factors for anisotropic materials by the least squares method. International Journal of Fracture; 81:283-297. (1996).
Ju SH, Lesniak JR and Sandor BI. Finite element simulation of stress intensity factors via the thermoelastic technique. Experimental Mechanics; SEM 37: 278-284. (1997).
Ju SH. Simulating three-dimensional stress intensity factors by the least-squares Method. International Journal for Numerical Method in Engineering; 43: 1437-1451. (1998).
Ju SH and Rowlands RE. Thermoelastic Determination of KI and KII in an Orthotropic Graphite/Epoxy Composite. Journal of Composite Materials; 37: 2011-2025. (2003).
Kai X, Yong L and Lie ST. Load-carrying welds joints analysis using boundary element method. International Journal of Solids and Structures; 42(9-10): 2965-2975. (2005).
Khodadad Motarjemi A, Kokabi AH, Ziaie AA, Manteghi S and Burdekin FM. Comparison of the stress intensity factor of T and cruciform welded joints with different main and attachment plate thickness. Engineering Fracture Mechanics; 65(4):455-466. (2000).
Lie ST and Bian C. Load-carrying fillet welds using dual boundary element method. Journal of Structural Engineering ASCE; 123(12):1603-1613. (1997).
Lie ST, Zhao Z, Yan SH. Two-dimensional and three-dimensional magnification factors, Mk, for non-load-carrying fillet welds cruciform joints. Engineering Fracture Mechanics; 65(4):435-453. (2000).
Maddox SJ. An analysis of fatigue cracks in fillet welded joints. International Journal of Fracture; 11(2):221-243. (1975).
Pang HLJ. Analysis of weld toe profiles and weld toe cracks. International Journal of Fatigue; 15(1):31-36. (1993).
Usami S and Kusumoto S. Fatigue Strength at Root of Cruciform, Tee and Lap Joints (1st Report). Transactions, Japan Welding Society; 9(1):1-10. (1978).
陳諺輝，＂螺栓孔於高溫下承壓行為之量測與數值模擬”，國立成功大學土木工程學系，碩士學位論文，（2006）。
蔡松木，＂利用數位相機量測裂縫應力集中係數之研究”， 國立成功大學土木工程學系，碩士學位論文，（2004）。