Undercut是在銲接熔合區邊緣的附近表面上並與進料方向平行的凹陷區域。Undercut會在各種銲接、積層製造、拋光技術等情況廣泛遇到，造成降低靜態、疲勞與斷裂強度並增加在凝固區域應力集中。在本研究中，尺度分析的區域包括在橫截面上自由液面的undercut與bulge。使用尺度分析定律並考慮到楊-拉普拉斯與柏努力方程式，可以成功地將undercut的深度與寬度以及bulge的高度與寬度scale為無因次的能量半徑、馬蘭戈尼數、佩克萊數、普朗特數、損失係數、表面活性溶質濃度、熔點與環境的溫度差與熔點與臨界的溫度差的比值、表面張力係數在undercut與bulge的比值以及金屬固態-液態熱傳導係數的比值。本研究使用COMSOL Multiphsysics 5.6計算二維暫態之流場與熱傳行為造成的金屬表面形貌變化。尺度分析與數值計算或實驗數據的結果吻合。並且也會討論雷射銲接的工作參數對金屬表面形貌的影響。

Undercut, which is the depression region near the fusion zone edge parallel to scanning direction on a solidified surface. Undercuts widely encountered in various welding, additive manufacturing, polishing technologies etc. decrease static, fatigue and fracture strength and increases stress concentration of solidified region. In this work, the domain for scaling includes the undercut and bulge of free surface on transverse cross-section. Utilizing previous scaling law accounting for Young-Laplace and Bernoulli equations for rippling and humping, the depth and width of undercut and height and width of bulge can be successfully scaled to be functions of dimensionless beam power, Marangoni, Peclet and Prandtl numbers, loss coefficient, surface active solute concentration, ratios of surface tension coefficients between undercut and bulge region, ratio between differences in melting and ambient temperatures and critical and melting temperatures, solid-to-liquid thermal conductivity ratio, etc. This work also utilized COMSOL Multiphsysics 5.6 to compute surface deformation affected by unsteady two-dimensional fluid flow and heat transfer. The scaled results are compared well with numerical computation or available experimental data. The effects of laser welding process parameters on surface deformation of undercut and bulge was studied as well.

論文審定書i
摘要ii
Abstractiii
目錄iv
圖次vi
表次vii
符號說明viii
第一章緒論1
1.1研究背景與目的1
1.2文獻回顧2
1.3論文架構4
第二章理論背景6
2.1表面張力(Surface tension)6
2.2馬蘭戈尼效應(Marangoni effect)7
2.3尺度分析(Scale analysis)7
2.3.1無因次量(Dimensionless quantity)8
2.3.2柏努力方程式(Bernoulli's equation)10
2.3.3楊-拉普拉斯方程式(Young–Laplace equation)10
2.3.4尺度分析之推導12
第三章數值方法15
3.1基本假設16
3.2統御方程式17
3.2.1連續方程式17
3.2.2動量方程式18
3.2.3能量方程式19
3.2.4相位場方程式19
3.3邊界條件與初始條件22
3.4網格設定24
3.5材料性質25
3.6參數變換26
第四章結果與討論28
4.1Undercut的成形28
4.2數值與實驗結果之驗證31
4.3不同材料參數的影響38
4.3.1表面活性濃度對表面形貌的影響40
4.3.2液態金屬的熱傳導係數對表面形貌的影響41
4.3.3液態金屬的黏滯係數對表面形貌的影響42
4.4不同工作參數的影響43
4.4.1熱源瓦數對表面形貌的影響43
4.4.2熱源半徑對表面形貌的影響44
4.4.3熱源關閉時間對表面形貌的影響45
第五章結論與未來展望47
參考文獻49

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