Material behavior of steel - Modeling of complex phenomena and thermodynamic consistency

International Journal of Plasticity

Volumn 24, Issue 5, 2008, Pages 746-774

  Wolff, Michael ^a   Böhm, Michael ^a   Helm, Dirk ^b  

^a UNIVERSITY OF BREMEN   (Germany)

^b FRAUNHOFER INSTITUTE FOR MECHANICS OF MATERIALS IWM   (Germany)

Author keywords

Coupling of TRIP and plasticity; Material behavior; Phase transformations; Steel; Thermodynamic consistency; TRIP

Indexed keywords

HEAT TREATMENT; MATHEMATICAL MODELS; PHASE TRANSITIONS; THERMODYNAMICS;

MATERIAL BEHAVIOR; THERMODYNAMIC CONSISTENCY;

STEEL;

EID: 38949132193     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2007.07.005     Document Type: Article

References (89)

1. Aeby-Gautier, E., Cailletaud, G., 2004. N-phase modeling applied to phase transformations in steels: a coupled kinetics-mechanics approach. In: ICHMM-2004 International Conference on Heterogeneous Material Mechanics, Chongqing, Chine.
2. Ahrens, U., 2003. Beanspruchungsabhängiges Umwandlungsverhalten und Umwandlungsplastizität niedrig legierter Stähle mit unterschiedlich hohen Kohlenstoffgehalten. Ph.D. Thesis, Universität Paderborn, Germany.
3. Antretter T., Fischer F.D., and Cailletaud G. A numerical model for transformation induced plasticity (TRIP). J. Phys. IV France 115 (2004) 233
4. Azzouz F., Cailletaud G., Fischer F.D., Pineau A., and Tanaka K. Study of the martensitic transformation on a Cr-Ni-Mo-Al-Ti steel for different thermomechanical paths. J. Phys. IV France 11 (2001) 189
5. Beeuwkes R. Concerning the effect of strain and rate of strain on tensile tests at normal and elevated temperatures. J. Appl. Phys. 5 (1934) 135
6. Bertram A. Elasticity and plasticity of large deformations - an introduction (2005), Springer-Verlag, Berlin, Heidelberg
7. Böck, N., Holzapfel, G.A., 2002. A large strain continuum and numerical method for transformation induced plasticity (TRIP). In: Mang, H.A., Rammerstorfer, F.G., Eberhardsteiner, J. (Eds.), WCCM V, 5th World Congress on Computorial Mechanics, Wien.
8. Böhm, M., Dachkovski, S., Hunkel, M., Lübben, T., Wolff, M., 2003, Übersicht über einige makroskopische Modelle für Phasenumwandlungen im Stahl, Berichte aus der Technomathematik, Universität Bremen, FB 3, Germany, Report 03-09. .
9. Böhm M., Hunkel M., Schmidt A., and Wolff M. Evaluation of various phase-transition models for 100Cr6 for application in commercial FEM programs. J. Phys. IV France 120 (2004) 581
10. Burlet, H., Cailletaud, G., 1987. Modeling of cyclic plasticity in finite-element codes. In: Proceedings of Constitutive Laws for Engineering Materials: Theory and Applications, p. 1157.
11. Cailletaud G., and Sai K. Study of plastic/viscoplastic models with various inelastic mechanisms. Int. J. Plast. 11 (1995) 991
12. Cherkaoui M., Berveiller M., and Lemoine X. Couplings between plasticity and martensitic phase transformation: overall behavior of polycrystalline TRIP steels. Int J. Plast. 16 (2000) 1215
13. Chaboche J.-L. Unified cyclic viscoplastic constitutive equations: development, capabilities, and thermodynamic framework. In: Krausz A., and Krausz K. (Eds). Unified Constitutive Laws of Plastic Deformation (1996), Academic Press 1-68
14. Chaboche J.-L. Viscoplastic constitutive equations for the description of cyclic and anisotropic behavior of metals. Bull. L'Acad. Polonaise Sci. 25 (1977) 33
15. Chaboche J.-L. Thermodynamics of local states: overall aspects and micromechanics based constitutive relations. Tech. Mech. 23 (2003) 113
16. Dalgic M., and Löwisch G. Einfluss einer aufgeprägten Spannung auf die isotherme, perlitische und bainitische Umwandlung des Wälzlagerstahls 100Cr6. Haerterei-Techn. Mitt. 59 (2004) 28
17. Dalgic M., and Löwisch G. Transformation plasticity at different phase transformation of a bearing steel. Material. Werkstofftechnik 37 (2006) 122
18. Denis S. Considering stress-phase transformation interactions in the calculation of heat treatment residual stresses. In: Berveiller M., and Fischer F.D. (Eds). CISM Courses and Lectures - No. 368, Mechanics of Solids with Phase Changes (1997), Springer-Verlag, Wien
19. Denis S., Archambault P., Gautier E., Simon A., and Beck G. Prediction of residual stress and distortion of ferrous and non-ferrous metals: current status and future developments. J. Mater. Eng. Perform. 11 (2002) 92
20. Duvaut G., and Lions J.-L. Les inéquations en mechanique et en physique (1972), Dunod, Paris
21. Estrin, Y., 1996. Dislocation-density related constitutive modeling. In: Krausz, A.S., Krausz, K. (Eds.), Unified Constitutive Laws of Plastic Deformation, p. 69.
22. Fischer F.D., Sun Q.P., and Tanaka K. Transformation-induced plasticity (TRIP). Appl. Mech. Rev. 49 (1996) 317
23. Fischer F.D. Modeling and simulation of transformation induced plasticity in elasto-plastic materials. In: Berveiller M., and Fischer F.D. (Eds). Mechanics of Solids with Phase Changes vol. 368 (1997), Springer-Verlag
24. Fischer F.D., Reisner G., Werner E., Tanaka K., Cailletaud G., and Antretter T. A new view on transformation induced plasticity (TRIP). Int. J. Plast. 16 (2000) 723
25. Fischer F.D., Antretter T., Azzouz F., Cailletaud G., Pineau A., Tanaka K., and Nagayama K. The role of backstress in phase transforming steels. Arch. Mech. 52 (2000) 569
26. Fortunier R., Leblond J.B., and Bergheau J.M. A numerical model for multiple phase transformations in steels during thermal processes. J. Shanghai Jiaotong Un. E5 1 (2000) 213
27. Håkansson P., Wallin M., and Ristinmaa M. Comparison of isotropic hardening and kinematic hardening in thermoplasticity. Int. J. Plast. 21 (2005) 1435
28. Hallberg H., Håkansson P., and Ristinmaa M. A constitutive model for the formation of martensite in austenitic steels under large strain plasticity. Int. J. Plast. 23 (2007) 1213
29. Han W., and Reddy B.D. Plasticity - Mathematical Theory and Numerical Analysis (1999), Springer, New York
30. Haupt P. Continuum Mechanics and Theory of Materials (2000), Springer-Verlag, Berlin
31. Heeres O.M., Suiker A.S.J., and de Borst R. A comparison between the Perzyna viscoplastic model and the consistency viscoplastic model. Eur. J. Mech./Solids 21 (2002) 1
32. Helm, D., 1998. Experimentelle Untersuchung und phänomenologische Modellierung thermomechanischer Effekte in der Metallplastizität. In: Hartmann, S., Tsakmakis, C., (Eds.), Aspekte der Kontinuumsmechanik und Materialtheorie, Berichte des Instituts für Mechanik (1, 1998) der Universität Kassel, Germany, pp. 81.
33. Helm, D., 2001. Formgedächtnislegierungen - Experimentelle Untersuchung, phänomenologische Modellierung und numerische Simulation der thermomechanischen Materialeigenschaften, Ph.D. Thesis, Institute of Mechanics, University of Kassel, Germany.
34. Helm D., and Haupt P. Shape memory behavior: modeling within continuum thermomechanics. Int. J. Solids Struct. 40 (2003) 827
35. Helm D. Stress computation in finite thermoviscoplasticity. Int. J. Plast. 22 (2006) 1699
36. Hohenemser K., and Prager W. Über die Ansätze der Mechanik isotroper Kontinua. ZAMM 12 (1932) 216
37. Hömberg D. A mathematical model for induction hardening including mechanical effects. Nonlinear Anal. Real World Appl. 5 (2004) 55
38. Hömberg D., and Weiss W. PID control of laser surface hardening of steel. IEEE Trans. Control Syst. Technol. 14 (2006) 896
39. Houlsby G.T., and Puzrin A.M. A thermodmechanical framework for constitutive models for rate-independent dissipative materials. Int. J. Plast. 16 (2000) 1017
40. Hunkel M., Lübben T., Hoffmann F., and Mayr P. Modellierung der bainitischen und perlitischen Umwandlung bei Stählen. Haerterei-Tech. Mitt. 54 (1999) 365
41. Idesman A.V., Levitas V.I., and Stein E. Structural changes in elastoplastic material: a unified finite-element approach to phase transformation, twinning and fracture. Int. J. Plast. 16 (2000) 893
42. Inoue, T., Tanaka, T., submitted for publication. Unified constitutive equation for transformation plasticity and identification of the TP coefficients. Arch. Mech.
43. Jahnson, W., 1997. Formulierung und Intergration von Stoffgesetzen zur Bescheibung großer Deformationen in der Thermoplastizität und -viskoplastizität. Ph.D. Thesis, Institut für Materialforschung, Forschungszentrum Karlsruhe, Germany.
44. Johnson G., and Cook W. Fracture characteristic of three metals subjected to various strains, strain rates, temperatures and pressures. Eng. Fract. Mech. 21 (1985) 31
45. Kim J., Im S., and Kim H.-G. Numerical implementation of a thermo-elastic-plastic constitutive equation in consideration of transformation plasticity in welding. Int. J. Plast. 21 (2005) 1383
46. Kratochvil J., and Dillon O.W. Thermodynamics of crystalline elastic-visco-plastic materials. J. Appl. Phys. 41 (1970) 1470
47. Krempl E. A small-strain viscoplasticity theory based on overstress. In: Krausz A.S., and Kraus K. (Eds). Unified Constitutive Laws of Plastic Deformation (1996), Academic Press 281
48. Leblond J.B., and Devaux J. A new kinetic model for anisothermal metallurgical transformations in steels including effect of austenite grain size. Acta Metall. 32 (1984) 137
49. Leblond J.B., Mottet G., and Devaux J.C. A theoretical and numerical approach to the plastic behavior of steels during phase transformations - I. J. Mech. Phys. Solids 34 (1986) 395
50. Leblond J.B., Mottet G., and Devaux J.C. A theoretical and numerical approach to the plastic behavior of steels during phase transformations - II. J. Mech. Phys. Solids 34 (1986) 411
51. Leblond J.B., Devaux J., and Devaux J.C. Mathematical modeling of transformation plasticity in steels - I. Int. J. Plast. 5 (1989) 551
52. Leblond J.B. Mathematical modeling of transformation plasticity in steels - II. Int. J. Plast. 5 (1989) 573
53. Lemaitre J. Handbook of Materials Behavior Models (2001), Academic Press, San Diego, USA (Chapter 9.11-9.14)
54. Lemaitre J., and Chaboche J.-L. Mechanics of Solid Materials (1990), Cambridge University Press, Cambridge
55. Levitas V.I. Thermomechanical theory of martensitic phase transformation in inelastic materials. Int. J. Solids Struct 35 (1998) 889
56. Levitas V.I. Structural changes without stable intermediate state in inelastic material. Part I. General thermomechanical and kinetic approaches. Int. J. Plast. 16 (2000) 805
57. Levitas V.I. Structural changes without stable intermediate state in inelastic material. Part II. Applications to displacive and diffusional-displacive phase transformations, strain-induced chemical reactions and ductile fracture. Int. J. Plast 16 (2000) 851
58. Lion A. Constitutive modeling in finite thermoviscoplasticity: a physical approach based on nonlinear rheological models. Int. J. Plast. 16 (2000) 469
59. Maugin G.A. The Thermodynamics of Plasticity and Fracture (1992), Cambridge University Press, Cambridge
60. Mielke A., Theil F., and Levitas V. A variational formulation of rate-independent phase transformations using an extremum principle. Arch. Ration. Mech. Anal. 162 (2002) 137
61. Meftah S., Barbe F., Taleb L., and Sidoroff F. Parametric numerical simulations of TRIP and its interaction with classical plasticity in martensitic transformation. Eur. J. Mech. A: Solids 26 (2007) 688
62. Müller I. Thermodynamik - Grundlagen einer Materialtheorie (1972), Bertelsmann Universitätsverlag
63. Nagayama K., Kitajima Y., Kigami S., Tanaka K., Fischer F.D., and Cailletaud G. Transformation induced plasticity in maraging steel: an experimental study. Key Eng. Mater. 177-180 (2000) 443
64. Nagayama K., Terasaki T., Tanaka K., Fischer F.D., Antretter T., Cailletaud G., and Azzouz F. Mechanical properties of a Cr-Ni-Mo-Al-Ti maraging steel in the process of martensitic transformation. Mater. Sci. Eng. A A308 (2001) 25
65. Nagayama K., Terasaki T., Goto S., Tanaka K., Antretter T., Fischer F.D., Cailletaud G., and Azzouz F. Back stress evolution and iso-volume fraction lines in a Cr-Ni-Mo-Al-Ti maraging steel in the process of martensitic transformation. Mater. Sci. Eng. A A336 (2002) 30
66. Patoor E., and Berveiller M. Micromechanical modeling of the thermomechanical behavior of shape memory alloys. In: Bergveiller M., and Fischer F.D. (Eds). Mechanics of Solids with Phase Changes vol. 368 (1997), Springer-Verlag
67. Perzyna P. The constitutive equations for rate sensitive plastic materials. Quater. Appl. Math. 20 (1963) 321
68. Petit-Grostabussiat S., Taleb L., and Jullien J.-F. Experimental results on classical plasticity of steel subjected to structural transformations. Int. J. Plast. 20 (2004) 1371
69. Réti T., Horváth L., and Felde I. A comparative study of methods used for the prediction of nonisothermal austenite decomposition. J. Mater. Eng. Perform. 6 4 (1997) 433
70. Réti T., and Felde I. A non-linear extension of the additivity rule. Comput. Mater. Sci. 15 (1999) 466
71. Réti T., Fried Z.L., and Felde I. Computer simulation of steel quenching process using a multi-phase transformation model. Comput. Mater. Sci. 22 (2001) 261
72. Schmidt A., Suhr B., Moshagen T., Woff M., and Böhm M. Adaptive finite element simulations for macroscopic and mesoscopic models. Mater. Werkstofftechnik 37 (2006) 142
73. Shi W., Zhang X., and Liu Z. Model of stress-induced phase transformation and prediction of internal stresses of large steel work-pieces during quenching. J. Phys. IV France 120 (2004) 473
74. Simo J.C., and Hughes T.J.R. Computational Inelasticity (2000), Springer-Verlag, New York
75. Taleb L., and Petit-Grostabussiat S. Elastoplasticity and phase transformations in ferrous alloys: some discrepancies between experiments and modeling. J. Phys. IV France 12 11 (2002) 187
76. Taleb L., and Sidoroff F. A micromechanical modeling of the Greenwood-Johnson mechanism in transformation induced plasticity. Int. J. Plast. 19 (2003) 1821
77. Taleb L., and Petit S. New investigations on transformation-induced plasticity and its interaction with classical plasticity. Int. J. Plast. 22 (2006) 110
78. Taleb L., Cailletaud G., and Blaj L. Numerical simulation of complex ratcheting tests with a multi-mechanism model type. Int. J. Plast. 22 (2006) 724
79. Tanaka K., Teresaki T., Goto S., Antretter T., Fischer F.D., and Cailletaud G. Effect of back stress evolution due to martensitic transformation on iso-volume fraction lines in a Cr-Ni-Mo-Al-Ti maraging steel. Mater. Sci. Eng. A341 (2003) 189
80. Videau J.-Ch., Cailletaud G., and Pineau A. Modélisation des effets mécaniques des transformations de phases pour le calcul de structures. J. Phys. IV 4 (1994) 227 (Colloque C3, supplément au J. de Physique III)
81. Videau J.-Ch., Cailletaud G., and Pineau A. Experimental study of the transformation-induced plasticity in a Cr-Ni-Mo-Al-Ti steel. J. Phys. IV 6 (1996) 465 (Colloque C3, supplément au J. de Physique III)
82. Wang W.M., Sluys L.J., and de Borst R. Viscoplasticity for instabilities due to strain-rate softening. Int. J. Numer. Methods Eng. 40 (1997) 3839-3864
83. Wolff M., Böhm M., Löwisch G., and Schmidt A. Modeling and testing of transformation-induced plasticity and stress-dependent phase transformations in steel via simple experiments. Comput. Mater. Sci. 32 (2005) 604
84. Wolff, M., Böhm M., Schmidt, A., 2005b. A thermodynamically consistent model of the material behavior of steel including phase transformations, classical and transformation-induced plasticity. In: Wang, Y., Hutter, K., (Eds.), Trends in Applications of Mathematics to Mechanics, Shaker Verlag, Aachen, Germany, p. 591.
85. Wolff M., Böhm M., and Schmidt A. Modeling of steel phenomena and its interactions - an internal-variable approach. Material. Werkstofftechnik 37 (2006) 147
86. Wolff, M., Böhm, M., 2006. Transformation-induced plasticity in steel - general modeling, analysis and parameter identification, University of Bremen, report Berichte aus der Technomathematik 06-02. .
87. Wolff, M., Böhm, M., Dalgic, M., Hüßler, I., 2007. Evaluation of models for TRIP and stress-dependent transformation behaviour for the martensitic transformation of the steel 100Cr6. Comput. Mater. Sci., in press, doi:10.1016/j.commatsci.2007.07.40.
88. Wolff M., Böhm M., Dalgic M., Löwisch G., and Rath J. Validation of a TRIP model with backstress for the pearlitic transformation of the steel 100Cr6 under step-wise loads. Comput. Mater. Sci. 39 (2007) 49
89. Wolff, M., Boettcher, S., Böhm, M., 2007b. Phase transformations in steel in the multi-phase case - general modeling and parameter identification. University of Bremen, report Berichte aus der Technomathematik 07-02. .