為了瞭解銲接造成的殘留應力對結構的影響，本研究利用反射式光彈法觀察金屬銲接後產生之全場應力分佈情形，研究中將建立數值模擬分析方法，利用有限元素軟體建立銲接過程中溫度與應力之變化情形，採用熱彈塑性理論配合熱結構耦合元素及考慮非線性材料參數來進行兩塊尺寸相同之板材對接分析。分析過程中區分為熱學及力學模式兩種分析理論，並使用不鏽鋼(SUS304)及鋁合金(5083)兩種材料進行研究探討。
實驗量測部分採用鑽孔法以貼附應變規方式量測鑽孔釋放之應變，再將應變值利用無窮域平板圓孔理論推導得知未鑽孔前之殘留應力，為單點應力量測方式。另外也進行反射式光彈法獲得全場分佈之殘留應力來相互比較其準確性。反射式光彈法能夠得到元件內部三維應力分佈狀態，除了能得到全域式的應力分佈，屬於非接觸式之力學量測，搭配鑽孔法量測殘留應力為半破壞檢測方法。
本研究為解決因殘留應力較小而不易產生之光彈條紋情形，利用影像處理方式將實驗影像進行高頻雜訊濾波，再結合光彈干涉影像之亮暗場進行相減取絕對值，使條紋增加並作細線化得到明確條紋位置。研究結果顯示實驗量測與理論解析比較有限元素法的分析具有良好的一致性。

In order to determine residual stress caused by welding procedure,the photoelastic coating method was used to observe the full-field stress distribution on structure after the welding process. Using finite element method (FEM) to establish thermal stress for welding analysis,the temperature and stress fields in the welding process were analyzed based on thermo- elasto-plastic theory with thermal structural coupling elements and considering non-linear material parameters. The process is numerically calculated by two FEM modules,including heat transfer and thermal stress. The residual stress of stainless steel (SUS304) and aluminum alloy (5083) are both studied on their thermal and stress field for welding process.
The experimental measurement adopts the hole-drilling method with strain rosette to measure the release of residual strain. Through the inverse calculation, the residual stress is pointwisely obtained from the strain value based on theoretical formula. The photoelastic coating method is also applied to obtain the residual stress of the full-field distribution with the same welding specimen. Image processing methods are used to improve the quality of photoelastic experimentally results. The Fast Fourier Transform was used to filter noise from environment. To increase and sharpen fringe patterns, the absolute value of subtraction from images of the dark field and bright field was processed to obtain a finer fringe. The experimental results are shown in good agreement with the FEM analysis.

[1]N.S. Rossini, M. Dassisti, K.Y. Benyounis, A.G. Olabi,. “Methods of measuring residual stresses in components“,Materials and Design,2012.
[2]ASTM E837-01, “Standard Test Method for Determining Residual Stresses by the Hole Drilling Stress-Gage Method“,2001.
[3]Measurement of residual stresses by the hole-drilling strain gage method. Vishay Precision Group – Teehnote TN-503.
[4]M. Kabiri., Measurement of residual stresses by the hole-drilling method: influences of transverse sensitivity of the gages and relieved strain coefficients. Experimental Mechanics, 1984.
[5]J. Mathar, Determination of initial stresses by measuring the deformation around drilled holes. Trans.,ASME, 1934.
[6]N. J. Renidler and I. Vigness, “Hole-Drilling Strain –Gag Method of Measuring Residual Stress”, Experimental Mechanics, 1966.
[7]M.T. Flaman, Brief investigation of induced drilling stresses in the center-hole method of residual-stress measurement. Experimental Mechanics 1982.
[8]D.C. Drucker, R.D. Mindlin, Stress analysis by three-dimensional photoelasticity methods. Journal of Applied Physics (1940) 724-732.
[9]Y.F. Cheng, New techniques for scattered-lightphotoelasticity. Experimental Mechanics (1963) 275-278.
[10]Y.F. Cheng, A dual-observation method for determining photoelastic parameters in scattered light.Experimental Mechanics (1967) 140-144.
[11]Y.F. Cheng, An automatic system for scattered-light photoelasticity. Experimental Mechanics (1969) 407-412.
[12]L.S. Srinath, Analysis of scattered-light method in photoelasticity. Experimental Mechanics (1969) 463-468.
[13]R.W. Aderholdt, W.F. Swinson, Esablishing the boundary retardation with respect to the observed fringes in scattered-light photoelasticity. Experimental Mechanics (1971) 521-523.
[14]R.J.Sanford, L.A. Beaubien, Stress analysis of a complex part:photoelasticity vs. finite elements. Experimental Mechanics (1977) 441-448.
[15]J. W. Dally, W. F. Rilley, Experimental Stress Analysis, McGraw-Hill, 1978.
[16]A. Katoh, .J. Rao, M. Takashi, T. Kunio, Mode stress intensity factor measurement by scattered-light photoelasticity using digital image processing. Proceedings of Asian Pacific Conference on Fracture and Strength,Japan (1993) 401-406.
[17]K. Ramesh, A.K. Yadav, V.A. Pankhawalla, Plotting of fringe contours fromfinite element results.communications in numerical methods. Communications in Numerical Methods in Engineering(1995) 839-847.
[18]K. Ramesh, P.M. Pathak, Validation offinite element modelling through photoelastic fringe contours. Communications in Numerical Methods in Engineering (1999) 229-238.
[19]P.R.D. Karthick Babu, K. Ramesh, Development of photoelastic fringe plotting scheme from 3D FE results. Communications in Numerical Methods in Engineering (2006) 809-821.
[20]G. Singh, D. Singh Mehta, Residual and induced birefringence measurement of ito-coated pet substrate by photoelastic method. Journal of Display Technology (2015) 11(12): 1035-1041.
[21]H. Fessler and C. Pappalettere, “Plastic-Elastic Strains in Two_Dimensional Sections of Partial-Penetration Fillet Welds”, Journal of Strain Analysis, (1989) V 24, N 1, pp15-21.
[22]S.C. Gambrell, Jr., “Use of Photostress to Characterize the Mechanical Behavior of Weldments “,Experimental Techniques, January/February 1993, pp15-18.
[23]S.C Gambrell, Jr.,“Yield Detection in Aluminum Welded Joints Using Photostress “, Experimental Techniques, March/April 1994, pp11-14.
[24]N.S. Raghavendran and M.E. Fourney,”Stress Analysis of a Welded Joint” , Engineering Fracture Mechanics, (1994) V48, N5, pp619-627.
[25]郭錦龍、徐澤志、邵清安，金屬薄板之殘留應力量測，元智工學院機械工程研究所，1994年，碩士論文。
[26]Ueda, Y., Yamakawa, T., "Analysis of thermal elastic-plastic stress and strain during Welding by finite element method", Transactions of the Japan-Welding Society 2 September 21, 90-100, (1971).
[27]J.K. Sharplesa, L. Gardnera, S.K. Batea, M.R. Goldthorpeb, J.R. Yatesc, H. Bainbridge, Project to evaluate the integrity of repaired welds. International Journal of Pressure Vessels and Piping (2005) 82:319–338.
[28]Dean, D., Hidekazu, M., "Prediction of welding residual stress in multi-pass butt-welded modified 9Cr-1Mo steel pipe considering phase transformation effects", Computational Materials science 37 (2006) 209-219-34.
[29]劉如峯、黃金城，核能電廠組件多層銲接之有限元素分析，中國機械工程學會第二十四屆全國學術研討會論文集，2007 年，A01-0060。
[30]許志民、李驊登，材料物理特性對放電加工鑽孔法引進殘留應力之影響，國立成功大學機械工程研究所，2006 年，碩士論文。
[31]林德超、史耀武，銲缝匹配影响銲接残余应力的研究材料工程，1999 年，6: 24-29。
[32]K.K. Tang, Z.X. Li, D.D. He, Z.H. Zhang, Evolution of plastic damage in welded joint of steel truss with pre-existing defects. Theoretical and Applied Fracture Mechanics (2010) 54: 117–126.
[33]洪光民、黃國興、林文輝，ㄧ維傅利葉分析應用在光弾影像上的相位擷取，二十六屆中國機械工程師學會年會，2009年。
[34]Toll, S., Tang, S., and Hovanesian, J., "Computerized photoelastic fringe multiplication," Experimental Techniques, 14(4), 21-23 (1990)
[35]Han, B., “Interferometric methods with enhanced sensitivity by optical/digital fringe multiplication,” Applied Optics, 32(25), 4713−4718 (1993)
[36]Han, B., and L. Wang, “Isochromatic fringe sharpening and multiplication,” Experimental Techniques, 18(6), 11−13 (1994)
[37]Han, B., and L. Wang, “Isochromatic fringe sharpening and interploation along an isoclinic contour, with application to fracture mechanics,” Experimental Mechanics, 36(4), 305−311 (1996)
[38]蔡曜隆、周長彬，銲接溫度與應力之分析實驗，國立交通大學機械工程研究所，2001年，碩士論文。
[39]G. S. Schajer, “Application of Finite Element Calculation to Residual Stress Measurement”, Journal of Engineering Materials and Technology,pp.205~207,1985.
[40]Dally J. W. , Riley W.F. “Experimental Stress Analysis”McGraw-Hill Companies, N.Y, 1978.
[41]張朝銑、敖仲寧，電子光斑干涉術結合應變規鑽孔法之平板內應力場分析，國立中正大學機械工程系，2012年，碩士論文。
[42]楊婷雅、黃育熙，利用光彈法研究光學薄膜之應力光學係數，國立臺灣科技大學機械工程研究所，2017年，碩士論文。
[43]吳彥熹、張奇偉，應用數位反射式光彈法量測腐蝕鋼筋混凝土構件之應力行為，中華大學土木與工程資訊學系，2010年，碩士論文。
[44]程翊峰、王偉中，應用正向反射式顯微光彈儀於雷射鑽孔後玻璃試片殘留應力之研究，國立清華大學動力機械工程學系，2016年，碩士論文。