Startseite Technik Critical sizes for coherent to semicoherent transition in precipitates
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Critical sizes for coherent to semicoherent transition in precipitates

  • Arun Kumar , Gaganpreet Kaur und Anandh Subramaniam
Veröffentlicht/Copyright: 30. November 2013
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

A coherent precipitate, on growth beyond a critical size, can become semicoherent through the formation of interfacial misfit dislocations. This investigation pertains to the finite element simulation of the state of stress of a coherent precipitate, its growth and the change in state of stress on the formation of an interfacial misfit dislocation loop. Critical radii are determined from the simulations based on: (i) global energy minimum (r*) and (ii) local force balance along the radial direction (rc). The concept of local force balance as existing in literature is extended to the circumferential direction, to calculate a new critical size (rt). Local force balance gives radii at which the interface is the stable position for the dislocation loop. Off-interface stability of the dislocation loops is also investigated. The Cu–γFe system is used as an example to illustrate the new methodology developed and validate the results of the simulation. The power of the methodology is shown by considering a configuration (precipitation in a thin disc), where standard theoretical formulations are inadequate.


* Correspondence address, Dr. Anandh Subramaniam, FB408, Department of Materials Science and Engineering (MSE), Indian Institute of Technology, Kanpur-208016, India, Tel.: (+91) (512) 259 7215, Fax: (+91) (512) 259 7505, E-mail:

References

[1] D.A.Porter, K.E.Easterling: Phase Transformations in Metals and Alloys, Chapman & Hall, London (1992).10.1007/978-1-4899-3051-4Suche in Google Scholar

[2] L.M.Brown, G.R.Woolhouse, U.Valdrè: Philos. Mag.17 (1968) 781. 10.1080/14786436808223029Suche in Google Scholar

[3] J.W.Matthews in: F.R.N.Nabarro (Eds.), Dislocations in Solids, North-Holland Publishing Company, New York (1979).Suche in Google Scholar

[4] L.M.Brown, G.R.Woolhouse: Philos. Mag.21 (1970) 329. 10.1080/14786437008238420Suche in Google Scholar

[5] U.Stigh: Mech. Mater.14 (1993) 179. 10.1016/0167-6636(93)90065-YSuche in Google Scholar

[6] K.Sasaki, M.Kishida, Y.Ekida: Intl. J. Num. Meth. Eng.54 (2002) 671. 10.1002/nme.437Suche in Google Scholar

[7] K.W.Schwarz: J. Appl. Phys.85 (1999) 108. 10.1063/1.369429Suche in Google Scholar

[8] D.Raabe: Z. Metallkd.87 (1996) 493.10.5980/jpnjurol.87.493_2Suche in Google Scholar

[9] S.Sen, R.Balasubramaniam, R.Sethuraman: Scripta Metall. Mater.33 (1995) 527. 10.1016/0956-716X(95)00204-9Suche in Google Scholar

[10] N.Miyano, K.Ameyama, N.Hirano, Y.Takao: Mater. Sci. Eng. A480 (2008) 464. 10.1016/j.msea.2007.08.014Suche in Google Scholar

[11] C.R.Chen, S.X.Li, Q.Zhang: Mater. Sci. Eng. A272 (1999) 398. 10.1016/S0921-5093(99)00507-9Suche in Google Scholar

[12] H.Feng, H.Biermann, H.Mughrabi: Mater. Sci. Eng. A214 (1996) 1. 10.1016/0921-5093(96)10255-0Suche in Google Scholar

[13] K.Nörthemann, A.Pundt: Phys. Rev. B78 (2008) 014105. 10.1103/PhysRevB.78.014105Suche in Google Scholar

[14] S.H.Song, J.B.Kim: KSME J.9 (1995) 351.Suche in Google Scholar

[15] Y.Nakasone, H.Nishiyama, T.Nojiri: Mater. Sci. Eng. A285 (2000) 229. 10.1016/S0921-5093(00)00637-7Suche in Google Scholar

[16] N.Sukumar, D.L.Chopp, N.Moës, T.Belytschko: Comput. Meth. Appl. Mech. Eng.190 (2001) 6183. 10.1016/S0045-7825(01)00215-8Suche in Google Scholar

[17] C.Du, Z.Ying, S.Jiang: IOP Conf. Series: Materials Science and Engineering10 (2010) 012083. 10.1088/1757-899X/10/1/012083Suche in Google Scholar

[18] Anandh Subramaniam: J. Appl. Phys.95 (2004) 8472. 10.1063/1.1745115Suche in Google Scholar

[19] A.Kumar, AnandhSubramaniam: Int. J. Nanosci.10 (2011) 93. 10.1142/S0219581X11007533Suche in Google Scholar

[20] K.Tillmann, A.Förster: Thin Solid Films368 (2000) 93. 10.1016/S0040-6090(00)00858-0Suche in Google Scholar

[21] R.Sankaran, C.Laird: J. Mech. Phys. Solids24 (1976) 241. 10.1016/0022-5096(76)90006-5Suche in Google Scholar

[22] J.K.Lee, W.C.Johnson: Acta Metall.26 (1978) 541. 10.1016/0001-6160(78)90106-2Suche in Google Scholar

[23] M.E.Thompson, C.S.Su, P.W.Voorhees: Acta Metall. Mater.42 (1994) 2107. 10.1016/0956-7151(94)90036-1Suche in Google Scholar

[24] F.J.Humphreys: Acta Metall.16 (1968) 1069. 10.1016/0001-6160(68)90095-3Suche in Google Scholar

[25] R.S.Herrick, J.R.Weertman, R.Petkovic-Luton, M.J.Luton: Scripta Metall.22 (1988) 1879. 10.1016/S0036-9748(88)80230-8Suche in Google Scholar

[26] J.Douin, P.Donnadieu, F.Houdellier: Acta Mater.58 (2010) 5782. 10.1016/j.actamat.2010.06.053Suche in Google Scholar

[27] G.C.Weatherly: Philos. Mag.17 (1968) 791. 10.1080/14786436808217753Suche in Google Scholar

[28] F.D.Fischer, H.J.Böhm, E.R.Oberaigner, T.Waitz: Acta Mater.54 (2006) 151. 10.1016/j.actamat.2005.08.039Suche in Google Scholar

[29] S.S.Quek, Y.Xiang, D.J.Srolovitz: Acta Mater.59 (2011) 5398. 10.1016/j.actamat.2011.05.012Suche in Google Scholar

[30] F.R.N.Nabarro: Theory of crystal dislocations, Clarendon Press, Oxford (1967) 75.Suche in Google Scholar

[31] G.S.Was: Fundamentals of Radiation Materials Science, Springer, New York (2007).Suche in Google Scholar

[32] J.P.Hirth, J.Lothe: Theory of Dislocations, McGraw-Hill, New York (1968).Suche in Google Scholar

[33] W.Bollmann: Crystal Defects and Crystalline Interfaces, Springer-Verlag, Berlin (1970). 10.1007/978-3-642-49173-3Suche in Google Scholar

[34] A.Reuss: J. Appl. Math. Mech.9 (1929) 49.10.1002/zamm.19290090104Suche in Google Scholar

[35] G.R.Woolhouse, M.Ipohorski: Proc. R. Soc. A324 (1971) 415. 10.1098/rspa.1971.0147Suche in Google Scholar

[36] W.A.Jesser: Philos. Mag.19 (1969) 993. 10.1080/14786436908225864Suche in Google Scholar

[37] H.Brooks: Metal Interfaces, American Society of Metals, Cleveland (1952) 20.Suche in Google Scholar

[38] T.Mura: Micromechanics of Defects in Solids, Martinus Nijhoff Publishers, The Hague (1982). 10.1007/978-94-011-9306-1Suche in Google Scholar

[39] E.A.Brandes (Ed.): Smithells Metals Reference Book, Butterworths, London (1983).Suche in Google Scholar

[40] K.E.Easterling, H.M.Miekk-Oja: Acta Metall.15 (1967) 1133. 10.1016/0001-6160(67)90388-4Suche in Google Scholar

[41] D.Watanabe, C.Watanabe, R.Monzen: J. Mater. Sci.43 (2008) 3946. 10.1007/s10853-007-2159-8Suche in Google Scholar

[42] R.Abeyaratne, J.K.Knowles: Evolution of Phase Transitions, Cambridge University Press, Cambridge (2006). 10.1017/CBO9780511547133Suche in Google Scholar

[43] M.E.Gurtin: Configurational Forces as Basic Concepts of Continuum Physics, Springer-Verlag, New York (2000).Suche in Google Scholar

[44] G.Dehm, T.Wagner, T.J.Balk, E.Arzt: J. Mater. Sci. Technol.18 (2002a) 113.Suche in Google Scholar

[45] L.B.Freund, S.Suresh: Thin Film Materials, Cambridge University Press, Cambridge (2003).Suche in Google Scholar

[46] S.C.Abrahams, L.Guttman, J.S.Kasper: Phys. Rev.127 (1962) 2052. 10.1103/PhysRev.127.2052Suche in Google Scholar

Received: 2012-12-12
Accepted: 2013-7-10
Published Online: 2013-11-30
Published in Print: 2013-12-12

© 2013, Carl Hanser Verlag, München

Heruntergeladen am 2.2.2026 von https://www.degruyterbrill.com/document/doi/10.3139/146.110979/html
Button zum nach oben scrollen