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In the middle of last century, some scientists discovered grain-boundary anelastic relaxation (GAR) peaks by means of torsional pendulum. Later, various models about the origin of GAR peaks are established through further research. However, its micro-mechanism is still unclear. Recently, according to the results of solute grain boundary segregation or dilution caused by elastic stress, a micro-mechanism of GAR which is grain-boundary absorbing or emitting vacancies has been proposed. Then, the equilibrium equations and the kinetic equations of GAR are established, and the process of GAR is expressed analytically. Furthermore, it has successfully elaborated the intermediate temperature embrittlement peak movement which exists widely in metals. Those developments of GAR theory are reviewed in the present paper.
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Keywords:
- anelastic relaxation /
- grain boundary /
- segregation and depletion /
- intermediate temperature embrittlements
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[2] Ge T S 2000 Foundation of Solid Internal Friction Theory: Grain-Boundary Relaxation and Structure (Beijing: Science Press) p3-481 (in Chinese) [葛庭燧 2000 固体内耗理论基础: 晶界弛豫与晶界结构 第3—481页 (北京: 科学出版社)]
[3] Weber W 1834 Poggendorff's Ann. 35 247
[4] Weber W 1841 Poggendorff's Ann. 24 1
[5] Meyer O 1874 Journ. Rein. U. Angew. Math. 78 130
[6] Voigt W 1892 Ann. D. Phys. 47 671
[7] Poynting J H, Thomson J J 1902 Properties of Matter (London)
[8] Ke T S 1947 phy. Rev. 71 533
[9] Leak G M 1961 Proc. Phys. Soc. 78 1520
[10] Miles G W, Leak G M 1961 Proc. Phys. Soc. 78 1529
[11] Gates R S 1973 Acta Met. 21 855
[12] Ashmarin G M, Zhikharev A I, Shvedov Ye A 1977 Ⅸ Conferencija Metaloznawcka PAN Krakow 391
[13] Sun Z Q, Ke T S 1981 J. de Physique 42 C5-451
[14] Woirgard J, Riviere A 1981 J. De Fouquet, J. De Physique 42 C5-417
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[18] Ke T S 1989/1990 Adv. Sci. China Phys. 3 1
[19] Iwasaki K 1993 Mater. Sci. Forum 119/121 775
[20] Ke T S 1998 J. Mater. Sci. Technol. 14 481
[21] Ke T S 1990 Adv. Sci. China Phys. 3 1
[22] Shinoda T, Nakamura T 1981 Acta Metall. 29 1631
[23] Misra R D K 1996 Acta Mater. 44 885
[24] Xu T D, Cheng B Y 2004 Prog. Mater. Sci. 49 109
[25] Xu T D 2003 Philos. Mag. 83 889
[26] Xu T D 2000 J. Mater. Sci. 35 5621
[27] Xu T D 2002 Scripta. Mater. 46 759
[28] Xu T D 2007 Philos. Mag. 87 1581
[29] Xu T D 2006 Kinetics of Non-equilibrium Grain Boundary Segregation and Intergranular Brittle Fracture (Beijing: Science Press) p112 (in Chinese) [徐庭栋 2006 非平衡晶界偏聚动力学和晶间脆性断裂 第112页 (北京: 科学出版社)]
[30] Xu T D 2009 Sci. China Ser. E-Tech. Sci. 52 1679
[31] Xu T D, Zheng L 2004 Philo. Mag. Lett. 84 225
[32] Kluge M D, Wolf D, Lutsko J F, Phillpot S R 1990 J. Appl. Phys. 67 2370
[33] Xu T D, Zheng L, Wang K, Misra R D K Inter. Mater. Rev. (in press)
[34] Bengough G D 1912 J. Inst. Met. 7 123
[35] Xu T D 2009 10000 Scientific Difficulties: Physics (Beijing: Science Press) p523 (in Chinese) [徐庭栋 2009 "10000个科学难题·物理学卷" (北京: 科学出版社) 第523页]
[36] Horikawa K, Kuramoto S, Kanno M 2001 Acta Mater. 49 3981
[37] Otsuka M, Horiuchi R 1984 J. Jpn. Inst. Met. 48 688 (in Japanese)
[38] Nowosielski R, Sakiewicz P, Mazurkiewicz J 2006 J. Ach. Mater. Manuf. Eng. 17 93
[39] Sun D S, Yamane T, Hirao K 1991 J. Mater. Sci. 26 689
[40] Sun D S, Yamane T, Hirao K 1991 J. Mater. Sci. 26 5767
[41] ASTM International: 'Standard test methods for elevated temperature tension tests of metallic materials', ASTM International, Designation: E21-03a, approved Dec. 1, 2003
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[1] Zener C (Translated by Kong Q P, Zhou B L, Qian Z Q, Ma Y L) 1965 Elastic and Anelastic of Metals (Beijing: Science Press) p3-40 (in Chinese) [C. 甄纳著, 孔庆平, 周本濂, 钱知强, 马应良译 1965 金属的弹性与滞弹性 (北京: 科学出版社) 第3—40页]
[2] Ge T S 2000 Foundation of Solid Internal Friction Theory: Grain-Boundary Relaxation and Structure (Beijing: Science Press) p3-481 (in Chinese) [葛庭燧 2000 固体内耗理论基础: 晶界弛豫与晶界结构 第3—481页 (北京: 科学出版社)]
[3] Weber W 1834 Poggendorff's Ann. 35 247
[4] Weber W 1841 Poggendorff's Ann. 24 1
[5] Meyer O 1874 Journ. Rein. U. Angew. Math. 78 130
[6] Voigt W 1892 Ann. D. Phys. 47 671
[7] Poynting J H, Thomson J J 1902 Properties of Matter (London)
[8] Ke T S 1947 phy. Rev. 71 533
[9] Leak G M 1961 Proc. Phys. Soc. 78 1520
[10] Miles G W, Leak G M 1961 Proc. Phys. Soc. 78 1529
[11] Gates R S 1973 Acta Met. 21 855
[12] Ashmarin G M, Zhikharev A I, Shvedov Ye A 1977 Ⅸ Conferencija Metaloznawcka PAN Krakow 391
[13] Sun Z Q, Ke T S 1981 J. de Physique 42 C5-451
[14] Woirgard J, Riviere A 1981 J. De Fouquet, J. De Physique 42 C5-417
[15] Woirgard J, Amirault J P, 1975 J. de Fouqnet: ICIFUACS-5 392
[16] Bonetti E, Evangelista E, Gondi P, Tognato R 1976 Il Nuovo Cimento 33B 408
[17] Bonetti E, Evangelista E, Gondi P, Tognato R 1977 Phys. Stat. Sol. A 39 661
[18] Ke T S 1989/1990 Adv. Sci. China Phys. 3 1
[19] Iwasaki K 1993 Mater. Sci. Forum 119/121 775
[20] Ke T S 1998 J. Mater. Sci. Technol. 14 481
[21] Ke T S 1990 Adv. Sci. China Phys. 3 1
[22] Shinoda T, Nakamura T 1981 Acta Metall. 29 1631
[23] Misra R D K 1996 Acta Mater. 44 885
[24] Xu T D, Cheng B Y 2004 Prog. Mater. Sci. 49 109
[25] Xu T D 2003 Philos. Mag. 83 889
[26] Xu T D 2000 J. Mater. Sci. 35 5621
[27] Xu T D 2002 Scripta. Mater. 46 759
[28] Xu T D 2007 Philos. Mag. 87 1581
[29] Xu T D 2006 Kinetics of Non-equilibrium Grain Boundary Segregation and Intergranular Brittle Fracture (Beijing: Science Press) p112 (in Chinese) [徐庭栋 2006 非平衡晶界偏聚动力学和晶间脆性断裂 第112页 (北京: 科学出版社)]
[30] Xu T D 2009 Sci. China Ser. E-Tech. Sci. 52 1679
[31] Xu T D, Zheng L 2004 Philo. Mag. Lett. 84 225
[32] Kluge M D, Wolf D, Lutsko J F, Phillpot S R 1990 J. Appl. Phys. 67 2370
[33] Xu T D, Zheng L, Wang K, Misra R D K Inter. Mater. Rev. (in press)
[34] Bengough G D 1912 J. Inst. Met. 7 123
[35] Xu T D 2009 10000 Scientific Difficulties: Physics (Beijing: Science Press) p523 (in Chinese) [徐庭栋 2009 "10000个科学难题·物理学卷" (北京: 科学出版社) 第523页]
[36] Horikawa K, Kuramoto S, Kanno M 2001 Acta Mater. 49 3981
[37] Otsuka M, Horiuchi R 1984 J. Jpn. Inst. Met. 48 688 (in Japanese)
[38] Nowosielski R, Sakiewicz P, Mazurkiewicz J 2006 J. Ach. Mater. Manuf. Eng. 17 93
[39] Sun D S, Yamane T, Hirao K 1991 J. Mater. Sci. 26 689
[40] Sun D S, Yamane T, Hirao K 1991 J. Mater. Sci. 26 5767
[41] ASTM International: 'Standard test methods for elevated temperature tension tests of metallic materials', ASTM International, Designation: E21-03a, approved Dec. 1, 2003
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