Modelling of microstructure evolution during precipitation processes: A population balance approach of the KWN model

Modelling and Simulation in Materials Science and Engineering

Volumn 14, Issue 8, 2006, Pages 1271-1292

  Samaras, S N ^a  

^a UNIVERSITY OF THESSALY   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL LATTICES; GROWTH (MATERIALS); HARDENING; NUCLEATION; PARTICLE SIZE ANALYSIS; PHASE TRANSITIONS; PRECIPITATION (CHEMICAL); SOLID SOLUTIONS; VOLUME FRACTION;

COARSENING; KINETIC MODELS; LATTICE RESISTANCES;

MICROSTRUCTURE;

EID: 33846106796     PISSN: 09650393     EISSN: 1361651X     Source Type: Journal    
DOI: 10.1088/0965-0393/14/8/001     Document Type: Article

References (47)

1. Lifshitz I M and Slyozov V V 1961 The kinetics of precipitation from supersaturated solid solutions J. Phys. Chem. Solids 19 35-50
2. Wagner C 1961 Theorie der alterung von niederschlagen durch Umlosen Z. Elektrochem. 65 581-91
3. Langer J S and Schwartz A 1980 Kinetics of nucleation in near-critical fluids Phys. Rev. A 21 948-58
4. Wagner R and Kampmann R 1991 Materials Science and Technology vol 5 (Weinhein, Germany: VCH) 21
5. Kampmann R, Eckerlebe H and Wagner R 1987 Precipitation kinetics in metastable solid solutions-theoretical considerations and application to Cu-Ti alloys Mater. Res. Soc. Symp. Proc. MRS 57 525-42
6. Myhr O R and Grong O 2000 Modelling of non-isothermal transformations in alloys containing a particle distribution Acta Mater. 48 1605-15
7. Myhr O R, Grong O and Andersen S J 2001 Modelling of the age hardening behavior of Al-Mg-Si Alloys Acta Mater. 49 65-75
8. Robson J D and Prangnell P B 2001 Dispersoid precipitation and process modelling in zirconium containing commercial aluminium alloys Acta Mater. 49 599-613
9. Robson J D and Prangnell P B 2003 Modelling Al3Zr dispersoid precipitation in multicomponent aluminium alloys Mater. Sci. Eng. A 352 240-50
10. Robson J D 2002 Optimizing the homogenization of zirconium containing commercial aluminium alloys using a novel process model Mater. Sci. Eng. A 338 219-29
11. Robson J D 2004 A new model for prediction of dispersoid precipitation in aluminium alloys containing zirconium and scandium Acta Mater. 52 1409-21
12. Robson J D, Jones M J and Prangnell P B 2003 Extension of the N-model to predict competing homogeneous and heterogeneous precipitation in Al-Sc alloys Acta Mater. 51 1453-68
13. Deschamps A, Livet F and Brechet Y 1999 Influence of predeformation on ageing in an Al-Zn-Mg alloy:I. Microstructure evolution and mechanical properties Acta Mater. 47 281-92
14. Deschamps A and Brechet Y 1999 Influence of predeformation and ageing of an Al-Zn-Mg alloy:II. Modeling of precipitation kinetics and yield stress Acta Mater. 47 293-305
15. Nicolas M and Deschamps A 2003 Characterisation and modelling of precipitate evolution in an Al-Zn-Mg alloy during non-isothermal heat treatments Acta Mater. 51 6077-94
16. Kumar S and Ramkrishna D 1997 On the solution of population balance equations by discretization: III. Nucleation, growth and aggregation of particles Chem. Eng. Sci. 52 4659-79
17. Motz S, Mitrovi A and Gilles E D 2002 Comparison of numerical methods for the simulation of dispersed phase systems Chem. Eng. Sci. 57 4329-44
18. Hulburt H M and Katz S 1964 Some problems in particle technology-a statistical mechanical formulation Chem. Eng. Sci. 19 555-74
19. Christian J W 1975 The Theory of Transformations in Metals and Alloys (Part 1) (Oxford: Pergamon)
20. Ratke L and Voorhees P W 2002 Growth and Coarsening: Ripening in Materials Processing 1st edn (New York: Springer)
21. Russell K C 1980 Nucleation in solids: the induction and steady state effects Adv. Colloid Interface Sci. 13 205-318
22. Stowell M J 2002 Precipitate nucleation: does capillarity theory work? Mater. Sci. Technol. 18 139-144
23. Cerri E and Leo P 2005 Influence of severe plastic deformation on aging of Al-Mg-Si alloys Mater. Sci. Eng. A 410-11 226-9
24. Rack H J 1977 The influence of prior strain upon precipitation in a high-purity 6061 aluminum alloy Mater. Sci. Eng. 29 179-88
25. Dutkiewicz J and Litynska L 2002 The effect of plastic deformation on structure and properties of chosen 6000 series aluminium alloys Mater. Sci. Eng. A 324 239-43
26. lsmail Z H 1995 Microstructure and mechanical properties developed by thermomechanical treatment in an AlMgSi alloy Scr. Metall. Mater. 32 457-62
27. Rack H J 1978 Elevated temperature behavior of thermomechanically treated 6061 aluminum Scr. Metall. 12 777-9
28. Rack H J and Krenzer R W 1977 Thermomechanical treatment of high purity 6061 aluminum Metall. Mater. Trans. A 8A 335-46
29. Glicksman M E 2000 Diffusion in Solids 1st edn (New York: Wiley)
30. David R, Villermaux J, Marchal P and Klein J P 1991 Crystallization and precipitation engineering-IV. Kinetic model of adipic acid crystallization Chem. Eng. Sci. 46 1129-36
31. Hounslow M J, Ryall R L and Marshall V R 1988 A discretized population balance for nucleation, growth, and aggregation AIChE J. 34 1821-32
32. Marchal P, David R, Klein J P and Villermaux J 1988 Crystallization and Precipitation Engineering-I. An efficient method for solving population balance in crystallization with agglomeration Chem. Eng. Sci. 43 59-67
33. Martin J W 1998 Precipitation Hardening 2nd edn (Oxford: Butterworth-Heinemann)
34. Nembach E 1997 Particle Strengthening of Metals and Alloys 1st edn (New York: Wiley)
35. Kocks U F, Argon A S and Ashby M F 1975 Thermodynamics and kinetics of slip Prog. Mater. Sci. 19 1-278
36. Shercliff H R and Ashby M F 1990 A process model for age hardening of aluminum alloys-I. The model Acta Metall. Mater. 38 1789-802
37. Shercliff H R and Ashby M F 1990 A process model for age hardening of aluminum alloys: II. Applications of the model Acta Metall. Mater. 38 1803-12
38. Gandin C A, Bréchet Y, Rappaz M, Canova G, Ashby M and Shercliff H 2002 Modelling of solidification and heat treatment for the prediction of yield stress of cast alloys Acta Mater. 50 901-27
39. Esmaeili S, Lloyd D J and Poole W J 2003 Modelling of precipitation hardening for the naturally aged Al-Mg-Si-Cu alloy AA6111 Acta Mater. 51 3467-81
40. Esmaeili S, Lloyd D J and Poole W J 2003 A yield strength model for the Al-Mg-Si-Cu alloy AA6111 Acta Mater. 51 2243-57
41. Anderson W A 1959 Precipitation from Solid Solution (Metals Park OH: ASM)
42. Grong O 1997 Metallurgical Modeling of Welding of Aluminum Alloys 2nd edn (London: The Institute of Materials)
43. Borgenstam A, Engström A, Höglund L and gren J 2000 DICTRA, a tool for simulation of diffusional transformations in alloys J. Phase Equilib. 21 269-80
44. Trivedi R 1981 Volume diffusion-controlled growth kinetics and mechanisms in binary alloys Proc. Int. Conf. on Solid-Solid State Transformations (Pittsburgh, PA, USA: Carnegie Mellon University) pp 477-502
45. Sundman B, Jonsson B and Andersson J O 1985 The thermo-calc databank system Calphad 9 153-90
46. Hornbogen E 2001 Hundred years of precipitation hardening J. Light Met. 1 127-32
47. Edwards G A, Stiller K, Dunlop G L and Couper M J 1998 The precipitation sequence in Al-Mg-Si alloys Acta Mater. 46 3893-904