Mathematical models in materials science

Abstract

Modelling has now become a routine part of materials science. It is appropriate therefore to assess some of the successes and failures of the method and to understand how and if modelling differs from ordinary quantitative science. The subject is now sufficiently mature to bear some constructive self-criticism and to temper exaggerated claims. The discussion here of modelling methods and outcomes is intended to be generic, although the examples used come from the author's experience of work on metals.

Keywords

MODELLING VALIDATION REVIEWS MECHANICAL PROPERTIES PHASE DIAGRAMS MICROSTRUCTURE DEVELOPMENT

Get full access to this article

View all access options for this article.

References

Anderson

P. W.

: ‘Local moments and localized states’, Nobel lecture, Bell Telephone Laboratories, Princeton University, Princeton, NJ, December 1977.

Murugananth

, Bhadeshia

H. K. D. H.

, Keehan

, Andrén

H. O.

and Karlsson

: in ‘Mathematical modelling of weld phenomena 6’, (ed. Cerjak

and Bhadeshia

H. K. D. H.

), 205-230; 2002, London, The Institute of Materials.

Keehan

, And Karlsson

, Murugananth

and Bhadeshia

H. K. D. H.

: in ‘Trends in welding research’, (ed. David

S. A.

and DebRoy

), 695-700; 2002, Materials Park, OH, ASM.

Keehan

, L. Karlsson and H.-0. Andrén: Sci Technol. Weld. Join., 2006, 11, 1–8.

Keehan

, Karlsson

, Andrén

H.-O.

and Bhadeshia

H. K. D. H.

: Sci Technol. Weld Join., 2006, 11, 9–18.

Keehan

, Karlsson

, H.-0. Andrén and H. K. D. H. Bhadeshia: Sci Technol. Weld Join., 2006, 11, 19–24.

Bhadeshia

H. K. D. H.

and Honeycombe

R. W. K.

: ‘Steels: microstructure and properties’, 3rd edn; 2006, London, Butterworth-Heinemann.

Miller

M. K.

: Int. Mater. Rev., 1987, 32, 221–240.

Smith

G. D. W.

: in ‘Phase transformations ‘87’, (ed. Lorimer

G. W.

), 365-373; 1988, London, Institute of Materials.

10.

Humphreys

F. J.

: Scr. Mater., 2004, 51, 771–776.

11.

Brough

, Bate

P. S.

and Humphreys

F. J.

: Mater. Sci Technol, 2006, 22, 1279–1286.

12.

Gourgues-Lorenzon

A. F.

: Int. Mater. Rev., 2007, 52, 65–128.

13.

Lauridsen

E. M.

, Schmidt

, Suter

R. M.

and Poulsen

H. F.

: J. Appl Crystallogr., 2001, 34, 744–750.

14.

Poulsen

H. F.

, Bowen

J. R.

and Gundlach

: Scr. Mater., 2004, 51, 783–788.

15.

Chou

T. S.

, Bhadeshia

H. K. D. H.

, McColvin

and Elliott

: in ‘Structural applications of mechanical alloying’, (ed. J. J. de Barbadillo et al), 77-82; 1993, Materials Park, OH, ASM International.

16.

DebRoy

and David

S. A.

: Rev. Mod Phys., 1995, 67, 85–112.

17.

Cottrell

A. H.

: in ‘Electron theory in alloy design’, (ed. Pettifor

D. G.

and Cottrell

A. H.

), Chapter 1; 1992, London, Institute of Materials.

18.

University of Cambridge, NPL: Materials Algorithms Project, available at: www.msm.cam.ac.uk/map/mapmain.html.URL www.msm.cam.ac.uk/map/mapmain.html

19.

Meyer

and Gutte

: Steel Res., 2001, 72, 361–385.

20.

Kaufman

, Clougherty

E. V.

and Weiss

R. J.

: Acta Metall, 1963, 11, 323–335.

21.

Kaufman

and Nesor

: Zietschrift fur Metallkunde, 1973, 64, 249–257.

22.

Hillert

and Staffansson

L. I.

: Acta Chim. Scand, 1970, 24, 3616–3626.

23.

Hillert

: in ‘Hardenability concepts with applications to steels’, (ed. Doane

D. V.

and Krikaldy

J. S.

), 5-27; 1977, Warrendale, PA, The Metallurgical Society of AIME.

24.

Kubachewski

and Evans

E. L.

: ‘Metallurgical thermochemistry’; 1958, Oxford, Pergamon Press.

25.

Pelton

A. D.

, Thompson

W. T.

, Bale

C. W.

and Eriksson

N. G.

: in ‘Advances in phase transitions’, (ed. Embury

J. D.

and Purdy

G. R.

), 52-67; 1988, Oxford, Pergamon Press.

26.

Chart

T. G.

, Counsell

J. F.

, Jones

G. P.

, Slough

and Spencer

P. J.

: Int. Met. Rev., 1975, 20, 57–82.

27.

Bhadeshia

H. K. D. H.

: in ‘Introduction to materials modelling’, (ed. Barber

), 45–72; 2006, London, Maney.

28.

Hack

(ed.): ‘The SGTE casebook: thermodynamics at work’; 1996, London, The Institute of Materials.

29.

Strang

and Vodarek

: Mater. Sci. Technol, 1996, 12, 552–556.

30.

Danielsen

H. K.

and Hald

: in ‘Advances in materials technology for fossil power plants’, (ed. Viswanathan

D. G. R.

and Coleman

), 999–1012; 2005, Materials Park, OH, ASM International; Energ. Mater., 2006, 1, 49–57.

31.

Bhadeshia

H. K. D. H.

: Mater. Sci. Technol., 1989, 5, 131–137.

32.

Babu

S. S.

, Hono

and Sakuri

: Appl Surf Sci., 1993, 67, 321–327.

33.

Thomson

R. C.

and Miller

M. K.

: Appl. Surf Sci, 1995, 87-88, 185–193.

34.

Matsumura

, Sakuma

and Takechi

: Trans. Iron Steel Inst. Jpn, 1987, 27, 570–579.

35.

Matsumura

, Sakuma

and Takechi

: Scr. Metall., 1987, 27, 1301–1306.

36.

Bhadeshia

H. K. D. H.

: ‘Bainite in steels’, 2nd edn; 2001, London, Institute of Materials.

37.

Jacques

P. J.

: Curr. Opin. Solid State Mater. Sci, 2004,8, 259–265.

38.

DeCooman

: Curr. Opin. Solid State Mater. Sci., 2004, 8, 285–303.

39.

Bhadeshia

H. K. D. H.

and Edmonds

D. V.

: Met. Sci, 1980, 14, 41–49.

40.

Bhadeshia

H. K. D. H.

and Edmonds

D. V.

: Met. Sci., 1983, 17, 411–419.

41.

Bhadeshia

H. K. D. H.

and Edmonds

D. V.

: Met. Sci, 1983, 17, 420–425.

42.

Caballero

F. G.

, Bhadeshia

H. K. D. H.

, Mawella

K. J. A.

, Jones

D. G.

and Brown

: Mater. Sci Technol, 2002, 18, 279–284.

43.

Caballero

F. G.

, Bhadeshia

H. K. D. H.

, Mawella

K. J. A.

, Jones

D. G.

and Brown

: Mater. Sci Technol, 2001, 17, 512–516.

44.

Caballero

F. G.

, Bhadeshia

H. K. D. H.

, Mawella

K. J. A.

, Jones

D. G.

and Brown

: Mater. Sci Technol, 2001, 17, 517–522.

45.

Caballero

F. G.

and Bhadeshia

H. K. D. H.

: Curr. Opin. Solid State Mater. Sci, 2005, 8, 186–193.

46.

McLellan

R. B.

and Dunn

W. W.

: J. Phys. Chem. Solids, 1969, 30, 2631–2637.

47.

Dunn

W. W.

and McLellan

R. B.

: Metall Trans., 1970, 1, 1263–1265.

48.

Dunn

W. W.

and McLellan

R. B.

: Metall Trans., 1971, 2, 1079–1086.

49.

Bhadeshia

H. K. D. H.

: Mater. Sci Technol, 1998, 14, 273–276.

50.

Bhadeshia

H. K. D. H.

: J. Mater. Sci., 2004, 39, 3949-3955.

51.

Bhadeshia

H. K. D. H.

: Met. Sci., 1982, 16, 167–169.

52.

Aaronson

H. I.

, Domian

H. A.

and Pound

G. M.

: TMS—AIME, 1966, 236, 753–767.

53.

Aaronson

H. I.

, Domian

H. A.

and Pound

G. M.

: TMS—AIME, 1966, 236, 768–780.

54.

Shiflet

G. J.

, Bradley

J. R.

and Aaronson

H. I.

: TMS—AIME A, 1978, 9A, 999–1008.

55.

Chen

: ‘Ternary quasichemical thermodynamics and first-principles calculations (Fe-C)’, Master's thesis, University of Cambridge, UK, 2004.

56.

Fujii

, MacKay

D. J. C.

and Bhadeshia

H. K. D. H.

: ISIJ Int., 1996, 36, 1373–1382.

57.

Goswami

: ISIJ Int., 1996, 36, 354–360.

58.

Schooling

J. M.

, Brown

and Reed

P. A. S.

: Mater. Sci Eng. A, 1999, A260, 222–239.

59.

Svensson

: Fatigue Fract. Eng. Mater. Struct., 2004, 27, 981–990.

60.

Bhadeshia

H. K. D. H.

, MacKay

D. J. C.

and Svensson

L.-E.

: Mater. Sci Technol., 1995, 11, 1046–1051.

61.

Cool

, Bhadeshia

H. K. D. H.

and MacKay

D. J. C.

: Mater. Sci Eng. A, 1997, A223, 186–200.

62.

Lalam

S. H.

, Bhadeshia

H. K. D. H.

and MacKay

D. J. C.

: Sci Technol. Weld Join., 2000, 5, 135–147.

63.

Dunne

, Tsuei

and Sterjovski

: ISIJ Int., 2004, 44, 1599–1607.

64.

Cai

, Cottis

R. A.

and Lyon

S. B.

: Corros. Sci, 1999, 41, 2001–2030.

65.

Evans

: Mater. Sci Technol., 1999, 15, 647–658.

66.

Brun

, Yoshida

, Robson

J. D.

, Narayan

, Bhadeshia

H. K. D. H.

and MacKay

D. J. C.

: Mater. Sci. Technol, 1999, 15, 547–554.

67.

Cole

, Martin-Moran

, Sheard

, Bhadeshia

H. K. D. H.

and MacKay

D. J. C.

: Sci Technol. Weld. Join., 2000, 5, 81–89.

68.

Yoo

Y. S.

, Jo

C. Y.

and Jones

C. N.

: Mater. Sci Eng. A, 2002, A336, 22–29.

69.

MacKay

D. J. C.

: ‘Information theory, inference, and learning algorithms’; 2003, Cambridge, Cambridge University Press.

70.

MacKay

D. J. C.

: Neural Comput., 1992, 4, 448–472.

71.

Sumpter

B. G.

and Noid

D. W.

: Ann. Rev. Mater. Sci, 1996, 26, 223–277.

72.

Bhadeshia

H. K. D. H.

: ISIJ Int., 1999, 39, 966–979.

73.

Murugananth

: ‘Design of welding alloys for creep and toughness’, PhD thesis, University of Cambridge, Cambridge, UK, 2002.

74.

Chang

L. C.

and Bhadeshia

H. K. D. H.

: Mater. Sci Technol., 1996, 12, 233–236.

75.

Chakraborti

: Int. Mater. Rev., 2004, 49, 246–260.

76.

Chatterjee

, Murugananth

and Bhadeshia

H. K. D. H.

: Mater. Sci Technol., 2007, 23, (7), 819–827.

77.

Saha

and Olson

G. B.

: J. Comput. Aided Mater. Des., 2007, 14, 177–200.

78.

Saha

, Jung

and Olson

G. B.

: J. Comput. Aided Mater. Des., 2007, 14, 201–233.

79.

Bhadeshia

H. K. D. H.

: Mater. Sci. Technol, 2005, 21, 1293–1302.

80.

Irvine

K. J.

and Pickering

F. B.

: in ‘Physical properties of martensite and bainite, special report 93’, 110-125; 1965, London, Iron and Steel Institute.

81.

Hawkins

M. J.

and Barford

: J. Iron Steel Inst., 1972, 210, 97–105.

82.

Singh

S. B.

and Bhadeshia

H. K. D. H.

: Mater. Sci Eng. A, 1998, A245, 72–79.

83.

Fujita

: Adv. Mater. Process., 1992, 4, 42–47.

84.

Metcalfe

, Bakker

W. T.

, Blum

, Bygate

R. P.

, Gibbons

T. B.

, Hald

, Masuyama

, Naoi

, Price

and Sawaragi

: in ‘New materials and plant designs and their practical implications for future CCGT and conventional power stations’, (ed. Metcalfe

), 189-199; 1997, London, Mechanical Engineering Publishers.

85.

Cerjak

, Hofer

and Schaffernak

: ISIJ Int., 1999, 39, 874–888.

86.

Bhadeshia

H. K. D. H.

: ISIJ Int., 2001, 41, 621–640.

87.

Blum

H. J. R.

and Hald

: in ‘Advanced steam plant’, 3-18; 1997, London, Institution of Mechanical Engineers.

88.

Masuyama

, Komai

, Yokoyama

, Yamamoto

, Miyata

and Igarashi

: JSME Int. J., 1998, 41, 1098–1104.

89.

Ducastelle

: in ‘Electron theory in alloy design’, (ed. Pettifor

D. G.

and Cottrell

A. H.

), 122-157; 1992, London, Institute of Materials.

90.

Thomas

W. M.

and Dolby

R. E.

: Proc. 6th Int. Trends in Welding Research Conf., (ed.

David

S. A.

.), 203-211; 2003, Materials Park, OH, USA, ASM International.

91.

Yin

Y. F.

and Faulkner

R. G.

: Proc. 6th Int. Charles Parsons Turbine Conf., (ed.

Strang

.), 457-471; 2003, London, Institute of Materials.

92.

Yamasaki

and Bhadeshia

H. K. D. H.

: Mater. Sei. Technol., 2003, 19, 723–731.

93.

Robson

J. D.

and Bhadeshia

H. K. D. H.

: Mater. Sei. Technot, 1997, 13, 631–639.

94.

Robson

J. D.

and Bhadeshia

H. K. D. H.

: Mater. Sei. Technot A, 1997, 28A, 640–644.