Abstract
On a microscopic scale, deformation twinning is carried by the motion of twinning disconnections. A disconnection is an interfacial line defect characterized by a Burgers vector, a line vector, and a step vector. The Burgers vector (dislocation component of the disconnection) carries the deformation while the step vector (ledge component) carries the transformation from one twin variant to the other. On a mesoscopic scale, the deformation produced by twinning is a simple shear. A moving disclination dipole provides a mesoscopic model accounting for the twinning shear. Twin – twin interaction processes including the intersection of twins, the formation of structured twins, and the nucleation of cracks, may feature very complex mechanisms when analyzed on a microscopic scale. It turns out, however, that these mechanisms are controlled by the properties of large disconnection groups containing up to 10 000 disconnections and more. These properties are sufficiently well approximated in the disclination dipole model. The disclination model for twin – twin interaction predicts orientation and volume fractions of secondary twins. The model also predicts the nucleation of cracks and crack growth. The disclination model was used to analyze the ductile-to-brittle transition of austenitic steel deformed at low temperature. The mesoscopic disclination model for twinning is successful because it accounts for the properties and mechanisms of disconnection groups.
References
[1] G. Kostorz, P. Müllner: Z. Metallk. 96 (2005) 703.10.3139/146.101090Search in Google Scholar
[2] H. Heinrich, G. Kostorz, B. Heeb, R. Müller, T. Schweizer, L.J. Gaukler: Ultramicroscopy 49 (1993) 265.10.1016/0304-3991(93)90233-NSearch in Google Scholar
[3] J. Dutkiewicz, G. Kostorz: Mater. Sci. Eng. A 132 (1991) 267.10.1016/0921-5093(91)90383-XSearch in Google Scholar
[4] J. Dutkiewicz, G. Kostorz: Phys. Stat. Sol. (a) 123 (1991) 63.10.1002/pssa.2211230104Search in Google Scholar
[5] H. Heinrich, H.P. Karnthaler, T. Waitz, G. Kostorz: Mater. Sci. Eng. A 272 (1999) 238.10.1016/S0921-5093(99)00474-8Search in Google Scholar
[6] H. Heinrich, P. Szászvári, D. Wilkins, G. Kostorz, in: F. Aldinger, H. Mughrabi (Eds.), Werkstoffwoche 96, DGM Informationsgesellschaft mbH (1997) 447.Search in Google Scholar
[7] P. Szászvári, D.Wilkins, H. Heinrich, G. Kostorz: Mater. Sci. Eng. A 234–236 (1997) 354.10.1016/S0921-5093(97)00228-1Search in Google Scholar
[8] H. Heinrich, V. Abcherli, D.J. Wilkins, G. Kostorz: Mater. Res. Sypm. Proc. 252 (MRS, Warrendale, 1999) KK1.4.1.Search in Google Scholar
[9] M. Terheggen, H. Heinrich, G. Kostorz, A. Romeo, D. Baetzner, A.N. Tiwari, A. Bosio, N. Romeo: Thin Solid Films 431–432 (2003) 262.10.1016/S0040-6090(03)00268-2Search in Google Scholar
[10] V. Nadenau, D. Hariskos, H.-W. Schock, M. Krejci, F.-J. Haug, A.N. Tiwari, H. Zogg, G. Kostorz: J. Appl. Phys. 85 (1999) 534.10.1063/1.369486Search in Google Scholar
[11] M. Krejci, A.N. Tiwari, P. Schwander, H. Heinrich, H. Zogg, G. Kostorz, in: EUREM-11, Vol. 2, edited and published Comm. Europ. Soc. Microsc. (Brussels 1998) 230.Search in Google Scholar
[12] M. Krejci, A.N. Tiwari, H. Zogg, P. Schwander, H. Heinrich, G. Kostorz: J. Appl. Phys. 81 (1997) 6100.10.1063/1.364359Search in Google Scholar
[13] D. Brewster: Edinburgh J. of Sci. 9 (1828) 311.Search in Google Scholar
[14] F. Pfaff: Pogg. Ann. Phys. Chem. 107 (1859) 333.10.1002/andp.18591830615Search in Google Scholar
[15] E. Reusch: Pogg. Ann. Phys. Chem. 132 (1867) 441.10.1002/andp.18672081106Search in Google Scholar
[16] G. Rose: Abh. Königl. Akad. Wiss. Berlin (1869) 57.Search in Google Scholar
[17] A. Johnson: Fortsch. Min. Kristall. Petrogr. 3 (1913) 93.Search in Google Scholar
[18] J.W. Christian, S. Mahajan: Prog. Mater. Sci. 39 (1995) 1.10.1016/0079-6425(94)00007-7Search in Google Scholar
[19] F.C. Frank, J.H. van der Merwe: Proc. Roy. Soc. London A 198 (1949) 205.10.1098/rspa.1949.0095Search in Google Scholar
[20] A.H. Cottrell, B.A. Bilby: Phil. Mag. (ser. 7) 42/329 (1951) 573.10.1080/14786445108561272Search in Google Scholar
[21] A. Seeger: Z. Metallk. 44 (1953) 247.10.1515/ijmr-1953-440604Search in Google Scholar
[22] J.P. Hirth, R.W. Balluffi: Acta Metall. 21 (1973) 929.10.1016/0001-6160(73)90150-8Search in Google Scholar
[23] A.H. King, Smith: Acta Cryst. A 36 (1980) 335.10.1107/S0567739480000782Search in Google Scholar
[24] A. Brokman: Acta Cryst. A37 (1981) 500.10.1107/S0567739481001198Search in Google Scholar
[25] A.H. King: Acta Metall. 30 (1982) 419.10.1016/0001-6160(82)90222-XSearch in Google Scholar
[26] J.P. Hirth: J. Phys. Chem. Sol. 55 (1994) 985.10.1016/0022-3697(94)90118-XSearch in Google Scholar
[27] R.C. Pond, J.P. Hirth: Solid State Physics 47 (1994) 287.10.1016/S0081-1947(08)60641-4Search in Google Scholar
[28] J.P. Hirth, R.C. Pond: Acta Mater. 44 (1996) 4749.10.1016/S1359-6454(96)00132-2Search in Google Scholar
[29] R.C. Pond, F. Sarrazit: Interface Science 4 (1996) 99.10.1007/BF00200841Search in Google Scholar
[30] R.C. Pond, S. Celotto: Intern. Mater. Rev. 48 (2003) 225.10.1179/095066003225010245Search in Google Scholar
[31] R.W. Armstrong: Science 162 (1968) 799.10.1126/science.162.3855.799Search in Google Scholar
[32] A.E. Romanov, V.I. Vladimirov, in: F.R.N. Nabarro (Ed.), Dislocations in Solids, Vol. 9, (Elsevier, Amsterdam 1992) 191.Search in Google Scholar
[33] F. Kroupa, L. Lejček: Sper. 3, Konf. Čs. Fyzika Olemeuc (1974) 162 (in Czech).Search in Google Scholar
[34] F. Kroupa, L. Lejček: Solid State Phen. 87 (2002) 1.10.4028/www.scientific.net/SSP.87.1Search in Google Scholar
[35] A.E. Romanov, W. Pompe, J.S. Speck: J. Appl. Phys. 79 (1996) 4037.10.1063/1.361866Search in Google Scholar
[36] A.H. King, Y. Zhu: Phil. Mag. A 67 (1993) 1037.10.1080/01418619308213974Search in Google Scholar
[37] A.H. King, F.-R. Chen, L. Chang, J.J. Kai: Interf. Sci. 5 (1997) 287.10.1023/A:1008641103284Search in Google Scholar
[38] P. Pirouz, R. Chaim, U. Dahmen, K.H. Westmacott: Acta Metall. Mater. 38 (1990) 313.10.1016/0956-7151(90)90061-KSearch in Google Scholar
[39] U. Dahmen, K.H. Westmacott, P. Pirouz, R. Chaim: Acta Metall. Mater. 38 (1990) 323.10.1016/0956-7151(90)90062-LSearch in Google Scholar
[40] C. Boulesteix: Phys. Stat. Sol. (a) 86 (1984) 11.10.1002/pssa.2210860102Search in Google Scholar
[41] B.M. Park, S.J. Chung: J. Am. Ceram. Soc. 77 (1994) 3194.Search in Google Scholar
[42] P. Müllner, V.A. Chernenko, D. Mukherji, G. Kostorz: MRS Symp. Porc. Vol. 785 (2004) 415.10.1557/PROC-785-D12.2Search in Google Scholar
[43] A. Coujou, A. Beneteau, N. Clement: Acta Metall. Mater. 40 (1992) 337.10.1016/0956-7151(92)90307-ZSearch in Google Scholar
[44] L. Rémy: Metall. Trans. A 12 (1981) 387.10.1007/BF02648536Search in Google Scholar
[45] S. Mahajan, G.Y. Chin: Acta Metall. 22 (1974) 1113.10.1016/0001-6160(74)90066-2Search in Google Scholar
[46] D. Hull: Acta Metall. 8 (1960) 11.10.1016/0001-6160(60)90133-4Search in Google Scholar
[47] P.G. Partridge: Metall. Rev. 12/118 (1967) 169.10.1179/imr.1967.12.1.169Search in Google Scholar
[48] F. Appel: Mater. Sci. Eng. R 22 (1998) 187.10.1016/S0927-796X(97)00018-1Search in Google Scholar
[49] T.H. Blewitt, R.R. Coltman, J.K. Redman: J. Appl. Phys. 28 (1957) 651.10.1063/1.1722824Search in Google Scholar
[50] G.T. Gray III: Acta Metall. 36 (1988) 1745.10.1016/0001-6160(88)90242-8Search in Google Scholar
[51] D.L. Medlin, C.B. Carter, J.E. Angelo, M.J. Mills: Phil. Mag. A 75 (1997) 733.10.1080/01418619708207199Search in Google Scholar
[52] D.L. Medlin, in: S. Ankem, C.S. Pande (Eds.), Advances in Twinning, (TMS, Warrendale, PA 1999) 29.Search in Google Scholar
[53] M. Peach, J.S. Koehler: Phys. Rev. 80 (1950) 436.10.1103/PhysRev.80.436Search in Google Scholar
[54] P. Müllner, K. Ullakko: Phys. Stat. Sol. (b) 208 (1998) R1.10.1002/(SICI)1521-3951(199807)208:1<R1::AID-PSSB99991>3.0.CO;2-4Search in Google Scholar
[55] E. Snoeck, L. Normand, A. Thorel, C. Roucau: Phase Transitions 46 (1994) 77.10.1080/01411599408200317Search in Google Scholar
[56] P. Müllner, W.M. Kriven: J. Mater. Res. 12 (1997) 1771.10.1557/JMR.1997.0244Search in Google Scholar
[57] P. Müllner, V.A. Chernenko, M. Wollgarten, G. Kostorz: J. Appl. Phys. 92 (2002) 6708.10.1063/1.1513875Search in Google Scholar
[58] P. Müllner, V.A. Chernenko, G. Kostorz: J. Magn. Magn. Mater. 267 (2003) 325.10.1016/S0304-8853(03)00400-1Search in Google Scholar
[59] S. Rajasekhara, P.J. Ferreira: Scripta Mater. 53 (2005) 817.10.1016/j.scriptamat.2005.06.003Search in Google Scholar
[60] R.D. James, M. Wuttig: Phil. Mag. A 77 (1998) 1273.10.1080/01418619808214252Search in Google Scholar
[61] Otsuka, T. Ohba, M. Tokonami, C.M. Wayman: Scripta Metall. Mater. 29 (1993) 1359.10.1016/0956-716X(93)90139-JSearch in Google Scholar
[62] P. Müllner, D. Mukherji, M. Aguirre, R. Erni, G. Kostorz: TMS Conf. Proc. Solid→solid phase transformations in inorganic materials (PTM’05), Phoenix, AZ, May 29–June 3, 2005, TMS, in press.Search in Google Scholar
[63] P. Pirouz, J.W. Yang: Ultramicroscopy 51 (1993) 189.10.1016/0304-3991(93)90146-OSearch in Google Scholar
[64] M. Lambrigger, H.A. Calderon, G. Kostorz: Z. Metallkd. 83 (1992) 624.10.1515/ijmr-1992-830810Search in Google Scholar
[65] A.S. Sologubenko, P. Müllner, H. Heinrich, G. Kostorz: Z. Metallkd. 95 (2004) 486.10.3139/146.017981Search in Google Scholar
[66] J.P. Hirth, J. Lothe: Theory of Dislocations, 2nd Edition, Krieger Publ. (Malbar, FL 1992).Search in Google Scholar
[67] G. Kostorz, H. Calderon, J. Martin (Eds.): Fundamental Aspects of Dislocation Interaction: Low Energy Dislocation Structures III, (Elsevier Sequoia, Lausanne 1993, reprinted from Mater. Sci. Eng. A 164).Search in Google Scholar
[68] S.V. Kamat, J.P. Hirth, P. Müllner: Phil. Mag. A 73 (1996) 669.10.1080/01418619608242989Search in Google Scholar
[69] Y.Q. Sun, P.M. Hazzledine, J.W. Christian: Phil. Mag. A 68 (1993) 471.10.1080/01418619308213976Search in Google Scholar
[70] Y.Q. Sun, P.M. Hazzledine, J.W. Christian: Phil. Mag. A 68 (1993) 495.10.1080/01418619308213977Search in Google Scholar
[71] P. Müllner, C. Solenthaler: Phil. Mag. Lett. 69 (1994) 111.10.1080/09500839408241578Search in Google Scholar
[72] P. Müllner, A.E. Romanov: Scripta Metall. Mater. 31 (1994) 1657.10.1016/0956-716X(94)90459-6Search in Google Scholar
[73] P. Müllner, C. Solenthaler: Phil. Mag. Lett. 69 (1994) 171.10.1080/09500839408241588Search in Google Scholar
[74] P. Müllner: Sol. State Phen. 87 (2002) 227.10.4028/www.scientific.net/SSP.87.227Search in Google Scholar
[75] F.C. Frank, in: O.R.N. Washington (Ed.), Proc. Int. Conf. Plastic Deform. of Crstal. Sol., Mellon Inst. Pittsburgh, May 19, 20 (1950) 89.Search in Google Scholar
[76] G. Schöck, in: F.R.N. Nabarro (Ed.), Dislocations in Solids, Vol. 3 (Elsevier, Amsterdam 1980) 63.Search in Google Scholar
[77] P. Müllner: Mater. Sci. Eng. A 234 –236 (1997) 94.10.1016/S0921-5093(97)00196-2Search in Google Scholar
[78] N.A. Pertsev, A.E. Romanov: Mech. Comp. Mater. 19 (1983) 565.10.1007/BF00604454Search in Google Scholar
[79] P. Müllner, P. Pirouz: Mater. Sci. Eng. A 233 (1997) 139.10.1016/S0921-5093(97)00058-0Search in Google Scholar
[80] P. Müllner, C. Solenthaler, M.O. Speidel, in: M.H. Yoo, M.Wuttig (Eds.), Twinning in Advanced Materials (TMS, Warrendale, PA 1994) 483.Search in Google Scholar
[81] L.C. Zhang, G.L. Chen, H.Q. Ye: Mater. Sci. Eng. A 299 (2001) 267.10.1016/S0921-5093(00)01379-4Search in Google Scholar
[82] K. Saito: J. Phys. Soc. Jap. 7 (1969) 1234.10.1143/JPSJ.27.1234Search in Google Scholar
[83] V.S. Litvinov, A.A. Popov, A.A. Elkina, A.V. Litvinov: Phys. Met. Metallogr. 83 (1997) 568.Search in Google Scholar
[84] P. Müllner, C. Solenthaler, M.O. Speidel: Acta Metall. Mater. 42 (1994) 1727.10.1016/0956-7151(94)90382-4Search in Google Scholar
[85] P. Müllner, A.E. Romanov: Acta Mater. 48 (2000) 2323.10.1016/S1359-6454(00)00025-2Search in Google Scholar
[86] P. Müllner, C. Solenthaler, J.P. Uggowitzer, M.O. Speidel: Acta Metall. Mater. 42 (1994) 2211.10.1016/0956-7151(94)90300-XSearch in Google Scholar
[87] W.M. Kriven, in: M.H. Yoo, M. Wuttig (Eds.), Twinning in Advanced Materials (TMS, Warrendale, PA 1994) 435.Search in Google Scholar
[88] E. Snoeck, L. Normand, A. Thorel, C. Roucau: Phase Trans. 46 (1994) 77.10.1080/01411599408200317Search in Google Scholar
[89] K. Wolf, H.-J. Gudladt, H.A. Calderon, G. Kostorz: Acta Metall. Mater. 42 (1994) 3759.10.1016/0956-7151(94)90441-3Search in Google Scholar
[90] F. Laves: Die Naturwissenschaften 39 (1952) 546 (in German).10.1007/BF00593186Search in Google Scholar
[91] F. Laves: Die Naturwissenschaften 39 (1952) 547 (in German).10.1007/BF00593188Search in Google Scholar
[92] A.M. Kosevich, V.S. Boiko: Soviet Physics Usp. 14 (1971) 286 (translated from Usp. Fiz. Nauk. 104 (1971) 201.10.1070/PU1971v014n03ABEH004704Search in Google Scholar
[93] T.E. Mitchell, J.P. Hirth: Acta Metall. Mater. 39 (1991) 1711.10.1016/0956-7151(91)90260-8Search in Google Scholar
[94] A. Zisman, E. Nesterova, V. Rybin, C. Teodosiu: Scripta Mater. 46 (2002) 729.10.1016/S1359-6462(02)00061-1Search in Google Scholar
[95] A. Zisman, C. Teodosiu, V. Rybin: Comp. Mater. Sci. 16 (1999) 307.10.1016/S0927-0256(99)00073-7Search in Google Scholar
[96] A. Zisman, V. Rybin: Sol. State Phen. 87 (2002) 147.10.4028/www.scientific.net/SSP.87.147Search in Google Scholar
© 2006 Carl Hanser Verlag, München
