Al-Mg商用合金在應用時可能遭遇振動破壞的問題，因此本研究探討商用Al-Mg合金(5083及5052)在共振狀態下振動偏移量變化及振動壽命。研究內容包括：(1)以5083為材料探討預應變量(冷軋量)對振動破壞行為影響；(2) 以5083-O及5052-O為材料，探討含Mg量對振動破壞行為影響，探討性質包括制振性(振動阻泥)與裂縫傳播行為等。
實驗結果顯示，所有試片在共振測試過程中，偏移量隨振動次數變化的D-N曲線可分為三區：第一區內試片末端偏移量先隨著振動次數增加而緩慢上升，裂縫主要在此區域在試片表面生成及傳播。此外，第一區的偏移量(起始偏移量)與振動阻泥有一相反的趨勢，即振動阻泥愈大則此區域偏移量愈小；第二區內偏移量可能因振動變形導致制振阻泥降低而急速上升；第三區時因主裂縫傳播至試片內部，試片共振頻率因而下降，導致偏移量急速下降。
預應變量方面的研究顯示，隨著冷軋量的增加，試片起始偏移量降低，共振壽命亦隨之增加。此趨勢在冷軋量超過12.5%時明顯減緩。控制出力以固定試片起始偏移量的振動測試條件下所得到的結果亦類似。經振動試片表面觀察發現，裂縫周圍散佈著滑移帶，隨軋延量增加，此滑移帶量減少，在高冷軋量試片則出現曲折的小裂縫。此外，主裂縫有沿滑移帶或微裂縫成長的傾向。經推測因預應變所導入之差排及晶界可有效消耗振動能量以及提升基地強度，因而增加Al-Mg合金的振動阻泥及振動破壞阻抗。
不同Mg含量拉伸及振動測試結果顯示，高Mg試料(5083-O)之拉伸強度、制振性及等出力、等初始偏移條件下振動壽命均較低Mg試料(5052-O)佳，此現象與基地中Mg固溶量有關。經振動試片表面亦觀察裂縫周圍及前端滑移帶的形成，低Mg試料之生成量明顯較高Mg試料多。振動過程中，差排與固溶Mg原子的交互作用可以消耗振動能量而增加材料的內在阻泥；且Mg固溶強化的效果愈顯著亦有助於提高裂縫傳播阻抗；因此共振壽命隨著含Mg量的增加而改善。
整合以上所述，Al-Mg合金可藉由預先軋延及提升Mg含量，增加基地缺陷密度(差排、晶界及固溶原子等)，來達到提升制振阻泥及共振壽命的效果。而根據等初始偏移條件結果判斷，基地強化對提升共振壽命的貢獻大於制振性。

Given that resonant vibration may occur to accelerate failure when the commercial Al-Mg alloys, such as 5083 and 5052 alloys, are applied in transportation systems. This study investigated the damping capacity and vibration fracture resistance of commercial Al-Mg alloy under resonant vibration conditions. The study items are (a) the effects of prestrain by examining 5083 alloy with different cold rolling reductions, and (b) influences of Mg content, by comparing 5083-O (high Mg) and 5052-O (low Mg) alloys, on the resonant vibration behaviors, including damping capacity and crack growth.
The D-N curves (deflection amplitude vs. numbers of vibration cycles) could be divided into three stages during resonant vibration test of all the samples. In stage I, the initial deflection amplitude is inversely proportional to the damping capacity and the deflection amplitude slightly increases with increasing vibration cyclic number. The cracks propagate mainly within this stage. After Stage I, the deflection amplitude significantly increases with a greater vibration cyclic number. This duration is designated as StageⅡand it may result from a lower damping capacity due to strain hardening. When the vibration proceeds, Stage III with a drastically decreasing deflection begins. The descending deflection in Stage III is due to the deviation of the actual vibration frequency from the resonant frequency caused by the inward propagation of major cracks.
The investigation concerning prestrain effect showed that the damping capacity and vibration life increase with increasing the degree of prestrain, but this increasing tendency slows down when the rolling reduction exceeds 12.5%. The results of the vibration tests under the same initial deflection also indicate that vibration life increases with a higher rolling reduction. Observation on the cracks shows that persistent slip bands can be found in the vicinity of the main crack. With an increasing degree of prestrain, the number of slip bands decreases and the tortuous microcracks appear in the sample with a rolling reduction of 50%. Notably, the main cracks tend to propagate along both the slip bands and microcracks. It can be assumed that the higher densities of dislocations and grain boundaries introduced by prestrain can raise the strength and the ability for absorbing the vibration energy, and consequently improve the damping capacity and crack propagation resistance of Al-Mg alloys.
The investigation concerning Mg content showed that high Mg samples possess greater tensile strength, damping capacity and vibration life under constant force or constant ID conditions. Also, the number of slip bands accompanying the crack propagation is reduced with a higher Mg content. This can be ascribed to the interaction between dislocations and dissolved Mg. A higher amount of dissolved Mg can improve the damping capacity and the matrix strength and thus a greater vibration life.
According the results mentioned above, it can be deduced that an increase in the density of defects including dislocations, grain boundaries and dissolved atoms is advantageous to the damping capacity and vibration fracture resistance. And, the matrix strengthening by those defects can be regarded as the main factor affecting vibration life.

1.J. E. Hatch, “Al, Properties and Physical Metallurgy”, ASM, 1984, pp.29.
2.M. Mizuno and H. Nagaoka, International Metal Review, 1979, no.2, pp.68-81.
3.鋁合金構造設計輯覽，日本輕金屬協會原編，賴耿陽譯，復漢出版社，1979，20-40頁。
4.S. M. McGuire, M. E. Fine, O. Buck and J. D. Achenbach, “Nondestructive Detection of Fatigue Cracks in PM 304 Stainless Steel by Internal Friction and Elasticity”, J. Mater. Res., 1993, vol.8, pp. 2216-2223.
5.S. M. McGuire, M. E. Fine and J. D. Achenbach, “Crack Detection by Resonant Frequency Measurements”, Metall. Trans. A, 1995, vol.26A, pp.1123-1127.
6.Mechanical Vibrations, S. S. Rao, Addison-Wesley Publishing Company, Inc., 1990, 2nd ed., pp.4-160.
7.An Introduction to Mechanical Vibration, R. F. Stridel, Jr., John Wiley and Sons, Inc., New York, 1988, 3rd ed., pp.96-226.
8.振動與噪音的阻尼控制，孫慶鴻、張啟軍、姚慧珠編著，機械工業出版社，北京，1992，38-57頁。
9.Dynamic Vibration Absorbers, Theory and Technical Application, B. G. Korenev and L. M. Reznikov, John Wiley and Sons, Inc., England, 1993, pp.1-80.
10.Theory of Vibration, Volume II: Discrete and Continuous Systems, A. A. Shabana, Springer-Verlag, New York, 1991, pp.1-40.
11.洪佳和，「亞共晶鋁-矽(-鎂)合金之共振破壞特性及其冶金影響因素之探討」，國立成功大學材料科學及工程學系，博士論文，民國90年。
12.A. Grannato K. Lucke, “Application of Dislocation Theory to Internal Friction Phenomena at High Frequencies”, J. Appl. Phys., 1956, vol.27, pp.583-593.
13.A. Granato and K. Lucke, “Theory of Mechanical Damping due to Dislocations”, J. of Appl. Phys., 1956, vol.27, pp.583-593.
14.S. E. Urreta De Pereyra, H. Bertorello and A. A. Ghilarducca De Salva, “Precipitation and Grain Boundary Internal Friction Peaks in Al-Mg-Si”, Phys. Stat. Sol., 1988, vol.108, pp.577-586.
15.S. E. Urreta De Pereyra, A. A. Ghilarducca De Salva and F. Louchet, “Precipitation Internal Friction Peaks in Al-Mg-Si”, Phys. Stat. Sol., 1993, vol.139, pp.345-360.
16.E. Carreno-Morelli, S. E. Urreta De Pereyra and A. A. Ghilarducci De Salva, “High Temperature Damping in Al-Mg-Si Industrial Alloys”, Phys. Stat. Sol., 1996, vol.158, pp.449-462.
17.A. Dentsoras and A. D. Dimarogonas, “Resonance Contralled Fatigue Crack Propagation”, Eng. Fract. Mech., 1983, vol.17, no.4, pp.381-386.
18.J. Zhang, R. J. Perez, M. Gupta and E. J. Lavernia, “Damping Behavior of Particulate Reinforced 2519 Al Metal Matrix Composites”, Scripta Metall. Mater., 1993, vol. 28, pp.91-96.
19.J. Zhang, R. J. Perez and E. J. Lavernia, “Dislocation-Induced Damping in Metal Matrix Composites”, J. Mater. Sci., 1993, vol. 28, pp.835-846.
20.J. Zhang, R. J. Perez and E. J. Lavernia, “Documentation of Damping Capacity of Metallic, Ceramic and Metal-Matrix Composite Materials”, J. Mater. Sci., 1993, vol.28, pp.2395-2404.
21.R. J. Perez, J. Zhang, M. N. Gungor and E. J. Lavernia, “Damping Behavior of 6061Al/Gr Metal Matrix Composites”, Metall. Trans., 1993, vol.24A, pp.701-711.
22.E. J. Lavernia, R. J. Perez and J. Zhang, “Damping Behavior of Discontinuously Reinforced Al Alloy Metal-Matrix composites”, Metall. Mater. Trans., 1995, vol. 26A, pp. 2803-2818.
23.M. Okabe, T. Mori and T. Mura, “Internal Friction caused By Diffusion Around a Second-Phase Particle Al-Si Alloy”, Phil. Mag. A, 1981, vol.44, pp.1-12.
24.M. Hinai, S. Sawaya and H. Masumoto, “Damping Characteristics of Cold-Worked Al-Si Alloys”, Trans. of Japan Inst. Metals, 1986, vol.27, pp.784-788.
25.H. Masumoto, M. Hinai and S. Sawaya, “The influence of Cold-Working in the Damping Capacity of Al-Zn Alloys”, J. Japan Inst. Metals, 1983, vol.24, no.10, pp.681-688.
26.M. Hinai, S. Sawaya and H. Masumoto, “Damping Characteristics of Cold-Worked Al-Si Alloys”, J. Japan Inst. Metals, 1986, vol.27, no.10, pp.784-788.
27.M. Hinai, S. Sawaya and H. Masumoto, “Damping Capacity of Cold-Worked Al-Ni Alloys”, J. Japan Inst. Metals, 1987, vol.28, no.7, pp.600-604.
28.M. Hinai, S. Sawaya and H. Masumoto, “Damping Capacity of Cold-Worked Al-Fe Alloys”, J. Japan Inst. Metals, 1987, vol.28, no.7, pp.595-599.
29.M. Hinai, S. Sawaya and H. Masumoto, “Vibration Damping Characteristics of Al-Ge Alloys”, J. Japan Inst. Metals, 1991, vol.32, no.10, pp.957-960.
30.M. Hinai, S. Sawaya and H. Masumoto, “Effect of Cold Working on Mechanical Damping Capacity of Al-Co Alloys”, J. Japan Inst. Metals, 1993, vol.34, no.4, pp.359-363.
31.S. M. McGuire, M. E. Fine, O. Buck and J. D. Achenbach, “Nondestructive Detection of Fatigue Cracks in PM 304 Stainless Steel by Internal Friction and Elasticity”, J. Mater. Res., 1993, vol.8, pp.2216-2223.
32.S. M. McGuire, M. E. Fine and J. D. Achenbach, “Crack Detection by Resonant Frequency Measurements”, Metall. Trans. A, 1995, vol.26A, pp.1123-1127.
33.林士晴，「球狀石墨鑄鐵之振動破壞特性研究」，國立成功大學材料科學及工程學系，博士論文，民國90年。
34.Fatigue Threshold, D. Taylor, Butterworth and Co. Ltd, 1989, pp.71-91.
35.Fatigue of Materials, S. Suresh, Cambridge University Press. New York, 1991, pp.292.
36.J. J. Mason and R. O. Ritchie, “Fatigue Crack Growth Resistance in SiC Particulate and Whisker Reinforced P/M 2124 Aluminum Matrix Composites”, Mater. Sci. Eng., 1997, vol.A231, pp.170-187.
37.A. Turnbull and E. R. De Los Rios, “The Effect of Grain Size on Fatigue Crack Growth in an Aluminium Magnesium Alloy”, Fatigue Fract. Engng. Mater. Struct., 1995, vol.18, n.11, pp.1355-1366.
38.A. Turnbull and E. R. De Los Rios, “The Effect of Grain Size on Fatigue of Commercially Pure Aluminium ”, Fatigue Fract. Engng. Mater. Struct., 1995, vol.18, n.12, pp.1455-1467.
39.W. Hume-Rothery and G. V. Raynor, The Structure of Metals and Alloys, Institute of Metals, London, 1956, pp.97.
40.L. H. Van Vlack, Elements of Materials Science and Engineering, 6th ed, Addison-Wesley Publishing Co., Reading, MA, 1996.
41.Waldron G. W. J., “A Study by Transmission Electron Microscopy of the Tensile and Fatigue Deformation of Aluminum-Magnesium Alloys”, Acta Metall., 1965, vol.13, pp.897-906.
42.Hideo Yoshida, “Recent Studies in Al-Mg Alloys”, Sumitomo Light Met. Tech., 1988, pp.15-29.
43.M. M. Avedesian and H. Baker, ASM Specialty Handbook-Magnesium and Magnesium Alloys, ASM Metals Park, 1999, pp.13-21.
44.Physical Metallurgy Principles, Robert E. Read-Hill and Reza Abbaschian, PWS Publishing Company, Boston, 1991, pp.227.
45.J. H. Driver and J. M. Papazian, “Dsc and Tem Study of the Cyclic and Monotonic Hardening of Al-5Mg”, Strength of Metal and Alloys (ICSMA 7), Proceeding of the 7th International Conference, 1986, pp.1429-1434.
46.J. H. Driver and J. M. Papazian, “Microstructure Effests of the Cyclic and Monotonic Hardening of Al-5Mg”, Mater. Sci. Eng. 1985, vol.76, pp.51-56.
47.H. Kenji and Y. Toshiro, “Fatigue Strengh of Cold-Worked Al-2.4%Mg Alloy”, J. Mater. Sci., 1981, vol.30, n.329, pp.166-172.
48.G. S. Neshpor, P. G. Miklyaev and V. S. Sinyavskii, “The Effect of Thermomechanical Treatment on the Mechanical Strengh of Sheet of the Aluminum Alloy AlMg6”, Tekhnol. Legk. Splavov. Nauchno-Tekh. Byul., 1977, n.10, pp.3-7.
49.Kunimoto T., Matsumoto Y. and Doi Y., “Fatigue Strength and Crack Propagation of 5086 Alunimum Alloy Pre-Worked by Tension”, J. Jpn. Inst. Light Met., 1987, vol.37, n.7, pp.468-472.
50.K. Ramaraju , Y. V. R. K. Prasad and K. I. Vasu, “Slip Structure and Crack Growth during Fatigue in Aluminum and Aluminum-1% Magnesium”, Metallography, 1972, vol.5, n.3, pp.265-273.
51.Mechanical Vibrations, S. S. Rao, Addison-Wesley Publishing Company, Inc., 1990, 2nd ed, pp.4-160.
52.D. J. Lloyd, “The Deformation of Commercial Aluminum-Magnesium Alloys”, Metall. Trans. A, 1980, vol.11A, pp.1287-1294.
53.T. Takaai and T. Daito, “Observation of Voids and Cracks on Ductile Fracture Process in Tensile Test of 5083 Aluminum Alloy Plate”, J. Japan Inst. of Light Metals, 1983, vol.33, no.2, pp.67-75.
54.T. Y. Tseng, J. R. Su, H. P. Lee, C. M. Liao, “The Exfoliation Corrosion Behavior of Al-Mg Alloy in Variant Rolling Microstructure”, The Chinese Soc. for Mat. Sci., 1990, pp.1269-1272.
55.Physical Metallurgy Principles, Robert E. Read-Hill and Reza Abbaschian, PWS Publishing Company, Boston, 1991, pp.272.
56.G. Screm and F. Gatto, “Changes in Strain-dependent Internal Friction during Fatigue (of Al-Alloys)”, Mater. Sci. Eng., 1975, vol.18, pp.75-80.