本研究評論過去在文獻中鋁合金鑄造孔洞形成的現象及各學派對孔洞形成機構的理論闡述，嘗試驗證各學派機構的正確性，並加以適當修正，進而將其結合為一完整的孔洞形成理論機構。
第二章根據熱力學模式的公式預測，鑄件中孔洞含量與孔洞內部氣體壓力以及鋁液初始氫含量有關。於熱力學模式凝固進行時氫產生重新分佈，因而影響孔洞的成長，第三章假設氫在凝固時由鑄件冷端往冒口端方向作長距離的重新分佈。Tiller et al.之修正理論足以解釋實驗結果，但理論本身缺乏嚴謹的機構。
第四章導入Ham之理論，重新詮釋氫經由短距離擴散進入析出物之行為是影響孔洞成長動力學的控制因素。前人實驗結果證實氫擴散析出動力學足以解釋鋁合金鑄造孔洞形成之機構。第五章將孔洞形成之現象以更廣義的成核成長動力學加以分析，發現孔洞形成能符合Avrami成核成長動力學理論。由樹枝狀晶體間液體流動補充的影響，凝固補充行為及凝固時氫的重新分配必須同時考慮，才能充分解釋鑄件中孔洞的分布。
第六章更以嚴謹的理論推演，透過假設及數學轉換技巧，使得氫擴散形成孔洞行為轉換成類似單一介質中第二相的析出行為。此推演所獲得的定量預測支持第四章及第五章的半實驗法預測公式。此動力學模式彌補熱力學機構的缺失，能解釋鑄件中孔洞形成時各控制因素的作用，但有別於數值分析法。

In this thesis, the mechanisms of porosity formation in aluminum alloy castings have been reviewed in theoretic. The mechanisms in the literature for porosity formation were re-examined and compared concurrently with the experiments, aiming to derive a more accurate mechanism for porosity formation in aluminum castings.
According to the thermodynamic model for predicting the porosity formation in Chapter 2, the porosity content of the castings is a function of the initial hydrogen content and the gas pressure inside the pore. In order to consider the redistribution of hydrogen during solidification, Chapter 3 adopts the modified theory of Tiller et al. The modified theory can satisfactorily explain the porosity distribution from the chill to the riser end in the castings, however, the modification itself is not on a rigorous scientific basis.
In Chapter 4, the kinetic hydrogen diffusion into the pore has been treated as the controlled factor for the nucleation and growth of pores by the Ham's equation. A good fitting is observed between the experimental result and the prediction by the kinetic model. Thus in Chapter 5, we further assume that the kinetic process of porosity formation is one of the more general phase transformation in materials, and analyzed by the Avrami's equation. By differentiating the factor of the interdendritic feeding resistance, it demonstrates that both the interdendritic feeding behavior by the Darcy's law and the kinetic hydrogen diffusion into the pore have to be taken into consideration to satisfactorily explain the porosity distribution in castings.
In Chapter 6, the mechanism responsible for the occurrence of porosity during the nucleation and growth of pores in alloys has been theoretically derived with a rigorous viewpoint. With some assumptions and transformation, the diffusion problem involving liquid and solid phases during solidification can be treated as a classic problem of solute diffusion in a single-phase matrix of solid during precipitation. The kinetic model supports the prediction by a semi-empirical method in Chapter 4 and 5. This model has an attribute of being capable to address the kinetic factors not treated by thermodynamics and analytically present the functional relationships involved in understanding the mechanism of porosity formation, which is different from the numerical method.

1.J. E. Gruzleski and B. M. Closset, "The Treament of Liquid Aluminum-Silicon Alloys," Book, The American Foundrymen's Society, 1990.
2.Y. S. Kuo, E. Chang and Y. L. Lin, "The feeding Effect of risers on the Mechanical Properties of A201 Al Alloy Plate Castings," AFS Trans., vol. 97, p777, 1989.
3.Y. S. Kuo, "A Study of Riser Feeding Behavior of High Strength A201 Aluminum Alloy," Ph.D. Thesis, National Cheng Kung University, R.O.C., 1990.
4.G. K. Sigworth, C. Wang, "Evolution of porosity during Solidification, Part 1: A Literature Review," AFS Trans., vol. 100, p978, 1992.
5.R. Fuoco, H. Goldenstein and J. E. Gruzleski, "Evaluation of Effect of Modification-Induced Eutectic Undercooling on Microporosity Formation in 356 Al Alloy," AFS Trans., vol. 102, p297, 1994.
6.R. Fuoco, E. R. Correa and A. V. O. Correa, "The Effect of Modification Treatment on Microporosity Formation in 356 Aluminum Alloy Studied By Quenching During Solidification Technique," AFS Trans., Vol. 103, p379, 1995.
7.J. M. Kim and C. R. Loper, Jr., "Effect of Solidification Mechanism on Fluidity of Al-Si Casting Alloys," AFS Trans., vol. 103, p521, 1995.
8.D. R. Poirier, K. Yeum and A. L. Maples, "A Thermodynamic Prediction for Microporosity Formation in Aluminum-Rich Al-Cu Alloys," Metall. Trans. A, vol. 18A, Nov., p1979, 1987.
9.G. K. Sigworth and C. Wang, "Mechanisms of Porosity Formation during Solidification: A Theoretical Analysis," Metall. Trans. B, vol. 24B, Apri., p349, 1993.
10.H. Combeau, D. Carpentier, J. Lacaze and G. Lesoult, "Modeling of Microporosity Formation in Aluminum Alloys Casting," Mater. Sci. and Engi. A173, p155, 1993.
11.J. Huang and J. G. Conley, "Computer Simulation of Pore Size and Shape for Equiaxed Al Alloy Castings," AFS Trans., vol. 106, p265, 1998.
12.A. S. Sabau and S. Viswanathan, "Microporosity Prediction in Aluminum Alloy Castings," Metall. and Mater. Trans. B, vol. 33B, Apri., p243, 2002.
13.N. Chvorinov, "Theory of the Solidification of Castings," Gesserei, vol. 27, p177, 1940.
14.A. F. Faber, Jr. and D. T. Doll, "Feeding of Metal Castings," AFS Trans., vol. 55, p461, 1947.
15.J. B. Caine, "A Theoretical Approach to the Problem of Dimensioning Risers," AFS Trans., vol. 56, p492, 1948.
16.C. M. Adams, Jr. and H. F. Taylor, "Fundamental of Riser Behavior," AFS Trans., vol. 61, p686, 1953.
17.H. F. Taylor, M. C. Flemings and T. S. Piwonka, "Risering-Aluminum Castings," Foundry, May, p217, 1960.
18.W. H. Johnson and J. G. Kura, "Some principles for Producing Sound Al-7Mg Alloy Castings," AFS Trans., vol. 67, p535, 1959.
19.Y. S. Kuo, E. Chang, R. R. Jeng and H. H. Ho, "The Effect of Cooling Rate and Casting Geometry on the Mechanical Property of A201 Aluminum Alloy Plate Castings," AFS Trans., vol. 98, p801, 1990.
20.T. S. Piwonka and M. C. Flemings, "Pore Formation in Solidification," Trans. of the Metall. Soc. of AIME, vol. 236, Aug., p1157, 1966.
21.K. Kubo and R. D. Pehlke, "Mathematical Modeling of Porosity Formation in Solidification," Metal. Trans. B, vol. 16B, p359, 1985.
22.S. Minakawa, I. V. Samarasekera and F. Weinberg, "Centerline Porosity in Plate Castings," Metal. Trans. B, vol. 16B, p823, 1985.
23.E. Niyama, T. Uchida, M. Morikawa and S. Saito, "A Method of Shrinkage Prediction and Its Application to Steel Casting Practice," 49th International Foundry Congress, Apri., p1, 1982.
24.J. A. Spittle, M. Almeshhedani and S. G. R. Brown, "The Niyama Function and Its Proposed Application to Microporosity Prediction," Cast Metal, vol. 7 [1], p51, 1994.
25.C. Y. Liu, K. Murakami and T. Okamoto, "Internal and External Shrinkage in Unidirectionally Solidified Al-4.5wt%Cu Alloy," Mater. Sci. and Engi., A108, p265, 1989.
26.R. A. Entwistle, J. E. Gruzlesi and P. M. Thomas, "Development of Porosity in Aluminum Base Alloys," AFS Trans., vol. 85, p345, 1977.
27.H. Huang and J. T. Berry, "Evaluation of Criteria Function to Minimize Microporosity Formation in Long-Freezing Range Alloys," AFS Trans., vol. 101, p669, 1994.
28.G. V. Kutumba Rao and V. Panchanathan, "End Chills Influence on Solidification Soundness of Al-Cu-Si(LM4) Alloy Castings," AFS Trans., vol. 81, p110, 1973.
29.V. de L. Davies, "Feeding Range Determined by Numerically Computed Heat Distribution," AFS Cast Metals Res., J. vol. 11, p33, 1975.
30.V. de L. Davies, "Computed Feeding Range for Gravity Die Castings," Metal Society, p357, 1979.
31.J. Lecomte-Beckers, "Study of Microporosity Formation in Nickel-Base Superalloys," Metal. Trans. A, vol. 19A, p2341, 1988.
32.Y. W. Lee, "A Study on the Mechanism of Porosity Formation in Cast A356 and A206 Aluminum Alloy," Ph.D. Thesis, National Cheng Kung University, R.O.C., 1992.
33.S. T. Kao, E. Chang and Y. W. Lee, "Role of Interdendritic Fluid Flow on the Porosity Formation in A206 Alloy Plate Casting," Mater. Trans., JIM, vol. 35, p632, 1994.
34.S. T. Kao and E. Chang, "The role of the Pressure Index in Porosity Formation in A356 Alloy Castings," Cast Metals, vol. 7, p219, 1995.
35.Kun-Dar Li, Ming-Cheng Cheng and Edward Chang, "Effect of Pressure on the Feeding Behavior of A356 Alloy in Low-Pressure Casting," AFS Trans. vol. 109, p311, 2001.
36.J. Talbot, "Effects of Hydrogen in Aluminum, Magnesium, Copper, and Their Alloy," Inter. Metal. Review, vol. 20, p166, 1975.
37.M. Imabayashi, M. Ichimura and Y. Kanno, "Hydrogen in Pure Aluminum Solidified Unidirectionally," Trans. of J. Inst. Of Metal, vol. 24 [2], p93, 1983.
38.S. N. Tiwari, A. K. Gupta and S. L. Malhotra, "Effect of Hydrogen Gas Content on Shrinkage Defects in Aluminium Alloy Castings," The British Foundryman, Apri., p129, 1986.
39.Q. T. Fang and D. A. Granger, "Porosity Formation in Modified and Unmodified A356 Alloy Castings," AFS Trans., vol. 97, p989, 1987.
40.F. Chiesa, R. Fuoco and J. E. Gruzleski, "Porosity Distribution in Directionally Solidified Test Bars Sand Cast from a Controlled A356 Melt," Cast Metals, vol. 7 [2], p113, 1994.
41.Kun-Dar Li, Ming-Cheng Cheng and Edward Chang, "The Pressure Index of Porosity Formation for A356 Alloy Permanent Mold Castings with Variation of Hydrogen Contents in the Melt," AFS Trans. vol. 109, p301, 2001.
42.W. A. Tiller, K. A. Jackson, J. W. Rutter and B. Chalmers, "The Redistribution of Solute Atoms During the Solidification of Metals," Acta Metal., vol. 1, p428, 1953.
43.W. Eichenauer, K. Hattenbacha and Z. Pebler, Z. Metallk., vol. 52, p682, 1961.
44.W. Eichenauer and J. Markopoulos, "Measurement of the Diffusion Coefficient of Hydrogen in Liquid Aluminum," Z. Metallk., vol. 65 [10], p649, 1974.
45.D. A. Porter and K. E. Easterling, "Phase Transformations in Metals and Alloys," Book, 1992.
46.F. S. Ham, "Theory of Diffusion-Limited Precipitation," J. Phys. Chem. Solids, vol. 6, p335, 1958.
47.J. W. Christian, "The Theory of Transformations in Metals and Alloys, 2nd Ed., Part I: Equilibrium and General Kinetic Theory," Oxford, Pergamon Press, 1975.
48.J. T. Berry, R. P. Taylor and R. A. Overfelt, "Porosity Patterns in A356 Bar and Plate Castings and Their Relation to Riser Design," AFS Trans., vol. 105, p465, 1997.
49.P. D. Lee and J. D. Hunt, "Hydrogen Porosity in Directional Solidified Aluminium-Copper Alloys: In Situ Observation," Acta Mater., vol. 45 [10], p4155, 1997.
50.R. C. Atwood, S. Sridhar, W. Zhang and P. D. Lee, "Diffusion-Controlled Growth of Hydrogen Pores in Aluminium-Silicon Castings: In Situ Observation and Modelling," Acta Mater., vol. 48, p405, 2000.
51.P. D. Lee and J. D. Hunt, "Hydrogen Porosity in Directionally Solidified Aluminium-Copper Alloys: A Mathematical Model," Acta Mater., vol. 49, p1383, 2001.
52.R. C. Atwood, S. Sridhar and P. D. Lee, "Equations For Nucleation of Hydrogen Gas Pores During Solidification of Aluminium Seven Weight Percent Silicon Alloy," Scripta Mater., vol. 41 [12], p1255, 1999.
53.P. D. Lee and S. Sridhar, "Direct Observation of the Effect of Strontium on Porosity Formation During the Solidification of Aluminium-Silicon Alloy," Int. J. Cast Metals Res., vol. 13, p185, 2000.
54.M. Avrami, "Kinetics of Phase Chang. I General Theory," J.Chem. Phys., vol. 7, p1103, 1939.
55.W. A. Johnson and R. F. Mehl, Trans. AIME, vol. 135, p416, 1939.
56.S. T. Kao, "Modeling of Porosity Prediction in Aluminum Alloys," Ph.D. Thesis, National Cheng Kung University, R.O.C., 1996.
57.L. Backerud, G. Chai and J. Tamminen, "Solidification Characteristics of Aluminum Alloys Volume 2: Foundry Alloys," American Foundrymen's Society, Inc., Illinois, p136-139, 1990.
58.C. E. Ransley and H. Neufeld, J. Inst. Metals, vol. 74, p599-620, 1948.
59.M. C Flemings, "Solidification Processing," Mcgraw-Hill Book Company, New York, 1974.
60.P. Shewmon, "Diffusion in Solids, 2nd ed.," The Minerals, Metals & Materials Society, Pennsylvania, p37-38, 1989.
61.Alscan model "F", User's Manual Ver. 1.2, Bomem Inc., 1994.
62.L. Arnberg, L. Backerud and G. Chai, "Solidification Characteristics of Aluminum Alloys Volume 3: Dendrite Coherency," American Foundrymen's Society, Inc., Illinois, p93-95, 1996.
63.W. Kurz and D. J. Fisher, "Fundamentals of Solidification," Trans. Tech. Publications Ltd, Switzerland, p83, 1989.
64.K. P. Young and D. H. Kirkwood, "The Dendrite Arm Spacings of Aluminum-Copper Alloys Solidified Under Steady-State Conditions," Metall. Trans. A, vol. 6A, p197-205, 1975.
65.R. E. Reed-Hill, "Physical Metallurgy Principles, 3rd Ed.," PWS-Kent Publishing Co., Boston, p. 469, 1992.
66.D. See, R. C. Atwood and P. D. Lee, "A Comparison of three modeling approaches for the prediction of microporosity in aluminum-silicon alloys," J. of Materials Science, vol. 36, p3423, 2001.
67.J. Markworth: J. Mater. Sci. Letter, vol. 12, p1487-1489, 1993.
68.S. F. Jones, G. M. Evans and K. P. Galvin, Adv. Colloid Interface Sci., vol. 80, p27, 1999.
69.W. LaOrchan and J. E. Gruzleski, "Grain Refinement, Modification and Melt Hydrogen-Their Effects on Microporosity, Shrinkage and Impact Properties in A356 Alloy," AFS Trans., vol. 100, p415-424, 1992.
70.J. M. Kim, H. W. Kwon, D. G. Kim and C. R. Loper, Jr., "Porosity Formation in Relation to the Feeding Behavior of Al-Si Alloys," AFS Trans., vol. 105, p825-831, 1997.
71.R. Fuoco, E. R. Correa and M. de Andrade Bastos, "Effects of Grain Refinement on Feeding Mechanism in A356 Aluminum Alloy," AFS Trans., vol. 106, p401-409, 1998.
72.J. G. Conley, J. Huang, J. Asada and K. Akiba, "Modeling the Effects of Cooling Rate, Hydrogen Content, Grain Refiner and Modifier on Microporosity Formation in Al A356 Alloys," Materials Science and Engineering, vol. A285, p49-55, 2000.
73.Procast Build-in Database, Procast The Professional Casting Simulation System, UES, Inc., 1988.