臺灣博碩士論文加值系統

殘留應力是材料與元件還沒使用或沒受外力時已存在材料結構中的應力。然而釵h機械元件為了改善或變化機械性質，如：表面耐磨、結構強度等，以接觸或非接觸方式輸入瞬間能量在元件表面上，使表面產生相變化或晶粒大小改變，同時也產生不同的體積收縮與擠壓，致使元件表面產生內部的殘留應力，而難以量測。一般量測殘留皆以半破壞性的鑽孔法來檢測，此法對元件整體影響較小，但是常受應變規的限制，因此開始以雲紋干涉法(Moir Interferometry)來量測鑽孔時所釋放的殘留應力，此也大大提高利用鑽孔法量測應力的精度。
現階段本實驗室已能將雲紋干涉術與盲孔鑽孔法之理論與實驗架構結合且實現於單軸向負荷當中。而本研究則針對單軸向負荷下結合雲紋干涉術與盲孔鑽孔法實驗所得到的在雲紋圖做在不同的應力大小、光柵及試片角度以及雷射光的偏振形式對雲紋的影響，同時也推導出雲紋與位移之間的理論關係式來分析雲紋圖形，且實驗與理論分析皆可彼此驗證。
也成戊]計製作雙軸向負荷機構，由單軸向負荷實驗推廣至雙軸向負荷，藉此可以將各種不同平面應力狀態之雲紋呈現於實驗當中。並配合在理論分析中所獲得的應力與位移關係式之等位移線圖，應用於探討試片受力方式與應力狀態，而在最後建立雲紋圖形資料庫的完整性。
同時期已將本技術應用於實際元件上，探討摩擦攪拌銲銲道在銲後各區域的應力狀態，驗證結合雲紋干涉術與盲孔鑽孔法量測殘留應力之正確性與可行。

Residual stress is the stress that already takes place in a component/material even though it hasn’t been subjected to any external forces. Many mechanical components require some specific improvement or mechanical properties like wear resisting ability, toughness etc. In order to achieve those requirements, the components were subjected to an instantaneous energy input either by direct or indirect contact, and this treatment might caused a phase transformation or grain size alteration on its surface, which resulting in volume contraction and expansion that produces residual stress in the component. Hole-drilling is a typical method in residual stress measurement. This method can be grouped as semi-destructive style, which mean that the effect is trivial compared to the entire component. Yet, this method always endured to the limited usage of strain gages. In that case, moir interferometry technique was applied to replace the strain gages for calculating the released residual stress and to increase the accuracy level on hole-drilling method.
Currently, our laboratory had successfully implemented the moir interferometry technique to the blind hole-drilling method. The mechanism of the method also had been established and experimental had been carried out on the mechanism by means of uni-axial loading force. In that case, the present experiment objective is focused on the fringe pattern of blind hole-drilling with moir interferometry technique by means of uni-axial loading under different magnitudes of residual stress, different angles of optical grating and specimen, and various kind of laser beam polarization, and also successfully derived the relation between the fringe orders with displacement in the specimen in order to analyze the fringe pattern of the experiment, which the outcome results are in a good agreement.
Bi-axial loading mechanism which is the expanded version from uni-axial loading had also been established. With this mechanism, we expected the fringes pattern of different planes on the specimen could be observed. Comparing the fringe pattern from the experimental with analytical results, we may have displacement of contour plot which could be use to discuss the residual stress distribution in the specimen under various ways of given loading and also to establish the complete database of those fringe patterns.
We had also applied the blind hole-drilling method with moir interferometry technique to estimate the residual stress on the FSW (Friction Stir Welding) specimen. Blind holes are drilled in several parts of the weld track to examine the accuracy and the feasibility of this method in estimating the residual stress.

第一章 緒論 2
1-1 前言 ……………………………………………………………2
1-2 文獻回顧 ………………………………………………………3
1-2-1 應變規鑽孔法 …………………………………………3
1-2-2 雲紋干涉術 ……………………………………………4
1-2-3 雲紋干涉術結合鑽孔法 ………………………………5
1-3 研究動機與目的 ………………………………………………8
第二章 理論背景介紹 ………………………………………………10
2-1 鑽孔法…………………………………………………………10
2-2 雲紋干涉術 ……………………………………………………14
2-2-1 條紋-位移量關係式推導 ………………………………14
2-2-2 偏振光雲紋干涉 ………………………………………20
2-3 結合雲紋干涉術與盲孔鑽孔法………………………………23
2-4 求取校正係數…………………………………………………26
2-5條紋級數的判別 ………………………………………………28
第三章 研究設備與方法………………………………………………32
3-1 研究流程………………………………………………………32
3-2 結合雲紋干涉術與盲孔鑽孔法設備…………………………34
3-3 試片與負荷機構之製備………………………………………37
3-3-1 試片與光柵之選擇 ……………………………………37
3-3-2 雙軸向負荷機構製備 …………………………………38
第四章 研究結果與討論………………………………………………42
4-1 平面應力狀態下應力-位移關係式之推導 …………………42
4-2 結合雲紋干涉術與盲孔法之單軸向應力的雲紋圖…………57
4-2-1 條W級數之影響 ………………………………………57
4-2-2 單軸向雲紋之角度影響 ………………………………58
4-2-2-1 光柵黏貼角度對雲紋圖的影響分析……………60
4-2-2-2 光柵黏貼角度對理論解等位移線的影響分析…68
4-2-2-3 光柵黏貼角度對雲紋圖與理論解等位移線影響比較………………………………………………76
4-2-2-4 光柵黏貼角度對雲紋應力計算的影響…………79
4-2-3 單軸向應力對雲紋的影響 ……………………………88
4-2-3-1 單軸向應力對雲紋圖的影響分析………………91
4-2-3-2 單軸向應力對理論解等位移線的影響分析……94
4-2-3-3 單軸向應力對雲紋圖與理論解等位移線影響比較 ………………………………………………97
4-2-3-4 單軸向應力對雲紋應力計算的影響……………99
4-2-4 偏振的影響……………………………………………102
4-2-5 單軸向應力雲紋干涉之歸納…………………………108
4-3 平面應力之雲紋圖 …………………………………………109
4-3-1 雙軸向雲紋之應力影響………………………………109
4-3-1-1 雙軸向應力對雲紋圖的影響分析 ……………111
4-3-1-2 雙軸向應力對理論解等位移線的影響分析 …113
4-3-1-3 雙軸向應力對雲紋圖與理論解等位移線影響比較………………………………………………116
4-3-1-4 雙軸向應力對雲紋應力計算的影響 …………118
4-3-1-5 等位移線圖隨雙軸負荷變化之影響 …………121
4-3-2 雙軸向雲紋之角度影響………………………………124
4-3-2-1 等位移線圖隨角度變化之影響 ………………124
4-4 雲紋干涉術結合盲孔鑽孔法於FSW銲道殘留應力的檢測 ……………………………………………………………127
4-4-1 試片之製備與其鑽孔位置……………………………128
4-4-2 雲紋圖的分析…………………………………………130
4-4-3 銲道整體雲紋圖的比對………………………………143
4-4-4 銲道雲紋應力的計算…………………………………145
第五章 結論與未來研究方向 ………………………………………148
5-1 結論 …………………………………………………………148
5-1 未來研究方向 ………………………………………………149
附錄 ………………………………………………………………150
1. 雲紋干涉之幾何繞射原理……………………………………150
2. 繞射與光柵……………………………………………………160
2.1 單狹縫之繞射 …………………………………………161
2.2 雙狹縫之繞射 …………………………………………163
2.3 繞射光柵 ………………………………………………164
3. 光位移量與相位………………………………………………167
參考文獻………………………………………………………………168

[1]Raleigh, “Measurement of Residual Stresses by the Hole-Drilling Strain Gage Method”, Tech. Note 503-4, Measurements Group, NC, 1993.
[2]M. Ya, F. Dai, J. Lu, “Moir interferometry and hole drilling system for residual stress measurement”, The International Society for Optical Engineering, Vol. 5058, pp.400-406, 2003.
[3]J. Mather, “Determination of Initial Stresses by Measuring the Deformation Around Drilled Holes”, Trans. of ASME, Vol. 56, pp. 249-254, 1934.
[4]N. J. Rendler, I. Vigness, “Hole Drilling Strain Gage Method of Measuring Residual Stresses”, Experimental Mechanics, Vol. 6, No.12, pp.577-586, 1966.
[5]R. G. Bthgate, “Measurement of Non-uniform Bi-axial Residual Stresses by the Hole Drilling Method”, Strain, Vol. 4, No. 12, pp. 20-29, 1968.
[6]E. M. Beaney, E. Procter, “A Critical Evaluation of the Centre Hole Technique for the Measurement of Residual Stresses”, Strain, Vol. 10, pp. 7-15, 1974.
[7]M. T. Flaman, “Brief Investigation of Induced Drilling Stresses in the Center-Hole Method of Residual-Stress Measurement”, Experimental Mechanics 22, pp. 26-30, January, 1982.
[8]G. S. Schajer, E. Altus, “Stress Calculation Error Analysis for Incremental Hole-Drilling Residual Stress Measurements”, Transactions of the ASME, Journal of Engineering Materials and Technology, Vol. 118, No. 1, pp. 120-128, 1996.
[9]D. Vangi, “Data Management for the Evaluation of Residual Stresses by the Incremental Hole Drilling Method,” Transaction of the ASME, Journal of Engineering Materials and Technology, Vol. 116, No. 4, pp. 561-566, 1994.
[10]R. A. Kelsey, “Measuring Non-Uniform Residual Stresses by the Hole Drilling Method”, Proceedings of SESA, Vol.14, No.1, pp.181-194, 1956.
[11]G. S. Schajer, ”Measurement of Non-Uniform Residual stresses Using the Hole Drilling Method, Part I – Stress Calculation Procedures”, Trans. of ASME, Journal of Engineering Material and Technology, Vol. 110, No. 4, pp.318-342, 1988.
[12]G. S. Schajer, ”Measurement of Non-Uniform Residual Stresses Using the Hole Drilling Method, Part II – Practical Application of the Integral Method”, Trans. of ASME, Journal of Engineering Material and Technology, Vol. 110, No. 4, pp.344-349, 1988.
[13]Sicot, X. L. Gong, A. Cherouat, J. Lu, “Influence of experimental parameters on determination of residual stress using the incremental hole-drilling method.”, Composites Science and Technology, pp.171-180, 2004.
[14]L. Rayleigh, “On the Manufacture and Theory of Diffraction Grating.”, Phil. Mag. Series4, pp. 81-93, 1874.
[15]J. Guild, “The Interference System of Crossed Diffraction Gratings：Theory of Moir Fringes, Oxford at the Clarendon Press, 1956.
[16]F. M. Gerasimov, V. P. Sergeev, I. A. Teltevskii, V. V. Sergeev, B. V. Marichev, “The Use of Moir Interference Fringes to Control the Ruling of Diffraction Gratings.”, Optical science. 19, pp. 152-156, 1965.

[17]N. Wadsworth, M. Marchant, B. Billing. ”Real-time Observation of In-Plane Displacement of Opaque Surface”, Opt. Laser Technol. Vol. 5, pp.119-123, 1973.
[18]R. Czarnet, “New Methods in Moir Interferometry”, PHD Dissertation Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA, 1984.
[19]Z. Wu, J. Lu, B. Han, “Study of Residual Stress Distribution by a Combined Method of Moir Interferometry and Incremental Hole Drilling, Part I: theory.” Transaction of the ASME Journal of Applied Mechanics, Vol. 65, pp. 837-843, December, 1998.
[20]Z. Wu, J. Lu, B. Han, “Study of Residual Stress Distribution by a Combined Method of Moir Interferometry and Incremental Hole Drilling, Part II: experimental.” Transaction of the ASME Journal of Applied Mechanics, Vol. 65, pp.844-850, December, 1998.
[21]陳浩民, “結合雲紋干涉及鑽孔法之殘留應力分析”, 國立中正大學碩士論文, 民國92年。
[22]Z. Wu, G. Montay, J. Lu, “High Sensitivity Moir Interferometry and Incremental Hole Drilling Method for Residual Stress Measurement”, Comptes Rendus de I Academie des Sciences Series IIB, Vol. 329, No. 8, pp. 585-593, 2001.
[23]Z. Wu, J. Lu, Y. Guo, “A Study of Process-Induced Residual Stress in PBGA Packages”, Trans. of ASME, Vol. 122, pp.262-266, 2000.
[24]M. Ya, F. Dai, J. Lu, “Study of Nonuniform In-Plane and In-Depth Residual Stress of Friction Stir Welding. ”, Journal of Pressure Vessel Technology, pp.201-208, 2003.

[25]李驊登, 胡永祥, 邴兆齊, “盲孔法量測殘留應力應用”,國立成奶j學機械研究所報告。
[26]M. Ya, P. Marquette, F. Blahcene, J. Lu. ”Residual stresses in laser welded aluminium plate by use of ultrasonic and optical methods”, Materials Science and Engineering A 382, pp.257-264, 2004.
[27]Y. M. Xing, J. Lu. ”An experimental study of residual stress induced by ultrasonic shot peening.”, Journal of Materials Processing Technology 152, pp.56-61, 2004.
[28]G. Montay, A. Cherouat, C. Garnier, J. Lu, “Determining Residual Stress in Spherical Components：A New Application of the Hole-Drilling Method.”, Journal of Testing and Evaluation, pp.73-79, 2004.
[29]S. T. Lin ”A New Moir Interferometer for Measuring In-plane Displacement.”, Experimental Mechanics, Vol. 41, No.2, pp.140-143, 2004.
[30]S. T. Lin ”Blind-hole Residual Stress Determination Using Optical Interferometry”, Experimental Mechanics, Vol. 40, No.1, pp.60-67, 2000.
[31]R. C. Schwarz, L. M. Kutt, J. M. Papazian, “Measurement of Residual Stress Using Interferometry Moir: A New Insight.” Experimental Mechanics, Vol. 40, No. 3, pp. 271-281, September 2000.
[32]陳揚世，“孔洞底部幾何形狀對盲孔法之殘留應力分析之影響”，國立中正大學碩士論文，民國93年。
[33]黃正ㄧ, “結合雲紋干涉術及盲孔鑽孔法量測殘留應力”, 國立中正大學碩士論文, 民國94年。


[34]D. Post, B. Han, P. Ifju, “High Sensitivity Moir (Experimental Analysis for Mechanics and Materials)”, Springer-Verlag, New York USA, 1994.
[35]G. S. Schajer, “Application of Finite Element Calculation to Residual Stress Measurements”, J. Eng. Mater. Tech., Vol. 103, pp.157-163, 1981.
[36]W. Soete, and R. Vancrombrugge, “An Industrial Method for the Determination of Residual Stresses”, Proc. SESA , No. 1, pp. 17-28, 1950.
[37]張維麟, “6061鋁合金及其顆粒強化銲道之摩擦攪拌銲接研究”, 國立中正大學碩士論文, 民國94年。
[38]李冠卿, “近代光學”, 初版, 聯經出版事業公司發行, 民國77年。
[39]Eugene Hecht, “Optics”, 4th Ed., International Editon, Addison Wesley, Pub. Co Ltd., New York USA, 2002.
[40]G. S. Schajer, E. Altus, “Stress Calculation Error Analysis for Incremental Hole-Drilling Residual Stress Measurements”, Transactions of the ASME, Journal of Engineering Materials and Technology, Vol. 118, No. 1, pp. 120-128, 1996.
[41]S. Timoshenko, J. M. Goodier, “Theory of Elasticity”, New York : McGraw-Hill, 1951.