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Between microscopic and mesoscopic descriptions of twin–twin interaction

  • Peter Müllner EMAIL logo
Published/Copyright: January 11, 2022
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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.


Prof. Peter Müllner Department of Materials Science and Engineering Boise State University 1910 University Dr., MS 2075 Boise, ID 83725, USA Tel.: +1 208 426 5136 Fax: +1 208 426 2470

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

Received: 2005-11-21
Accepted: 2005-12-13
Published Online: 2022-01-11

© 2006 Carl Hanser Verlag, München

Articles in the same Issue

  1. Frontmatter
  2. Professor Dr. Gernot Kostorz 65 years
  3. Dislocation micromechanisms under single slip conditions
  4. Characterisation of short-range order using dislocations
  5. Between microscopic and mesoscopic descriptions of twin–twin interaction
  6. Influence of the thermoelastic effect on the acoustic properties of pure metals at low temperatures
  7. Recent progress in the area of bulk metallic glasses
  8. Formation of the ABC6-type ordered structure in fcc alloys
  9. Short-range order in Fe-21.9 at.% Al
  10. Criteria for developing castable, creep-resistant aluminum-based alloys – A review
  11. Phase decomposition and precipitation of metastable A2 phase in B2 ordered Co–Al–Fe alloys
  12. Atomic migration and ordering phenomena in bulk and thin films of FePd and FePt
  13. Late-stage coarsening of oil droplets of excess oil in microemulsions following a temperature quench
  14. Small-angle scattering from spherical particles on randomly oriented interfaces
  15. Ripening of L12 Ni3Ti precipitates in the framework of the trans-interface diffusion-controlled theory of particle coarsening
  16. Texture evolution in equiaxed polycrystalline L10-ordered FePd during coarsening at 600 °C
  17. Modulated structures in amorphous films of Cr-silicide prepared by electron-beam-deposition
  18. Early stages of nucleation and growth of Guinier –Preston zones in Al–Zn–Mg and Al–Zn–Mg–Cu alloys
  19. Experimental and theoretical characterization of Al3Sc precipitates in Al–Mg–Si–Cu–Sc–Zr alloys
  20. Ag2Al plates in Al–Ag alloys
  21. A critical analysis of the composite model as applied to high-temperature creep of Al and an Al–Mg alloy
  22. Damage behaviour of an Al2O3 particle-reinforced 6061 alloy induced by monotonic and cyclic deformation
  23. Deformation behaviour of ultrafine-grained magnesium with 3 vol.% graphite
  24. Press/Presse
  25. Conferences/Konferenzen
  26. Frontmatter
  27. Editorial
  28. Professor Dr. Gernot Kostorz 65 years
  29. Articles BBasic
  30. Dislocation micromechanisms under single slip conditions
  31. Characterisation of short-range order using dislocations
  32. Between microscopic and mesoscopic descriptions of twin–twin interaction
  33. Influence of the thermoelastic effect on the acoustic properties of pure metals at low temperatures
  34. Recent progress in the area of bulk metallic glasses
  35. Formation of the ABC6-type ordered structure in fcc alloys
  36. Short-range order in Fe-21.9 at.% Al
  37. Criteria for developing castable, creep-resistant aluminum-based alloys – A review
  38. Phase decomposition and precipitation of metastable A2 phase in B2 ordered Co–Al–Fe alloys
  39. Atomic migration and ordering phenomena in bulk and thin films of FePd and FePt
  40. Late-stage coarsening of oil droplets of excess oil in microemulsions following a temperature quench
  41. Small-angle scattering from spherical particles on randomly oriented interfaces
  42. Ripening of L12 Ni3Ti precipitates in the framework of the trans-interface diffusion-controlled theory of particle coarsening
  43. Articles AApplied
  44. Texture evolution in equiaxed polycrystalline L10-ordered FePd during coarsening at 600 °C
  45. Modulated structures in amorphous films of Cr-silicide prepared by electron-beam-deposition
  46. Early stages of nucleation and growth of Guinier –Preston zones in Al–Zn–Mg and Al–Zn–Mg–Cu alloys
  47. Experimental and theoretical characterization of Al3Sc precipitates in Al–Mg–Si–Cu–Sc–Zr alloys
  48. Ag2Al plates in Al–Ag alloys
  49. A critical analysis of the composite model as applied to high-temperature creep of Al and an Al–Mg alloy
  50. Damage behaviour of an Al2O3 particle-reinforced 6061 alloy induced by monotonic and cyclic deformation
  51. Deformation behaviour of ultrafine-grained magnesium with 3 vol.% graphite
  52. Notifications/Mitteilungen
  53. Press/Presse
  54. Conferences/Konferenzen
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