A New Description of Yield Loci Based on Polycrystal Plasticity for High Strength Steels

Abstract:

Recently, many flexible constitutive equations have been proposed for sheet forming simulations. However, various mechanical tests are required to determine the many material parameters needed for such models. In the present work, effort has been made to investigate the correlation between the polycrystal plasticity based yield loci and those determined from mechanical tests, in order to define yield functions easily and accurately with minimum amount of experimental work. The results for different materials indicate that, in many cases, the Hill’48 deviates significantly from the measured yield loci. The yield loci derived from measured texture and polycrystal plasticity perform better than the Hill’48 yield function in general. Based on the two yield loci derived from the Taylor full constraint model and the Pancake model, a new combined model is proposed. The new model uses the averaged biaxial points of the two models but keeps the shape of the yield loci derived from the Taylor full constraint model in the stretching regime. The stress factors in the uniaxial and shear mode are calculated by averaging the stress factors of the two models. The proposed new description has been validated using several steel grades.

• Periodical: Key Engineering Materials (Volumes 410-411)
• Pages: 543-553
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.410-411.543
• Online since: March 2009
• Authors: Yu Guo An, Henk Vegter, Louisa Carless
• Keywords: Crystal Plasticity, Plastic Anisotropy, Yield Loci

References

[1] R. von Mises: Mechanik der plastischen Formanderung von Kristallen. Z. Angew. Math. Mech. 8 (1928) p.161.

DOI: 10.1002/zamm.19280080302

[2] R. Hill: A theory of the yielding and plastic flow of anisotropic metals. Proc. Royal Soc. London A 193 (1948), p.281.

[3] W.F. Hosford: A generalized isotropic yield criterion. J. Appl. Mech. Trans. ASME 39 (1972), p.607.

DOI: 10.1115/1.3422872

[4] W.F. Hosford: On yield loci of anisotropic cubic metals. In: Proceedings of the Seventh North American Metalworking Conference, Dearborn (1979), p.191.

[5] F. Barlat, J. Lian: Plastic behaviour and stretchability of sheet metals. Part I: a yield function for orthotropic sheets under plane stress conditions. Int. J. Plasticity 5 (1989) p.51.

DOI: 10.1016/0749-6419(89)90019-3

[6] F. Barlat, D.J. Lege, J.C. Brem: A six-component yield function for anisotropic materials. Int. J. Plasticity 7 (1991) p.693.

DOI: 10.1016/0749-6419(91)90052-z

[7] F. Barlat, R.C. Becker, Y. Hayashida, Y. Maeda, M. Yanagawa, K. Chung, K., J.C. Brem, D.J. Lege, K. Matsui, S.J. Murtha, S. Hattori: Yielding description for solution strengthened aluminium alloys. Int. J. Plasticity 13 (1997), p.385.

DOI: 10.1016/s0749-6419(97)80005-8

[8] F. Barlat, J.C. Brem, J.W. Yoon, K. Chung, R.E. Dick, D.J. Lege, F. Pourboghrat, S.H. Choi, E. Chu: Plane stress yield function for aluminium alloy sheets-part I: theory. Int. J. Plasticity 19 (2003), p.1297.

DOI: 10.1016/s0749-6419(02)00019-0

[9] F. Barlat, J.W. Yoon, O. Cazacu: On linear transformations of stress tensors for the description of plastic anisotropy. Int. J. Plasticity 23 (2007), p.876.

DOI: 10.1016/j.ijplas.2006.10.001

[10] D. Banabic, H. Aretz, D.S. Comsa, L. Paraianu: An improved analytical description of orthotropy in metallic sheets. International Journal of Plasticity 21 (2005), p.493.

DOI: 10.1016/j.ijplas.2004.04.003

[11] D. Banabic, T. Kuwabara, T. Balan, D.S. Comsa, D. Julean: -onquadratic yield criterion for orthotropic sheet metals under plane-stress conditions. International Journal of Mechanical Sciences 45 (2003), p.797.

DOI: 10.1016/s0020-7403(03)00139-5

[12] H. Vegter, Y.G. An, Y., H. Pijlman, J. Hue´tink: Advanced mechanical testing on aluminium alloys and low carbon steels for sheet forming. In: Gelin, J.C., Picart, P. (Eds. ), Proceedings NUMISHEET 99 (1999), p.3.

[13] H. Vegter, A.H. van den Boogaard: A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states. International Journal of Plasticity 22 (2006), p.557.

DOI: 10.1016/j.ijplas.2005.04.009

[14] G.I. Taylor: Plastic strain in metals. J. Inst. Metals 62 (1938), p.307.

[15] J.F. W. Bishop, , R. Hill: A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. Philos. Mag. 42 (1951), p.414.

[16] J.F. W. Bishop, R. Hill: A theoretical derivation of the plastic properties of a facecentred metal. Philos. Mag. 42 (1951), p.1298.

[17] P. Van Houtte: A comprehensive mathematical formulation of an extended Taylor- Bishop-Hill model featuring relaxed constraints, the Renouard-Wintenberger theory and a strain rate sensitivity model. Texture Microstruct. 8-9 (1988), p.313.

DOI: 10.1155/tsm.8-9.313

[18] P. Van Houtte, S. Li, M. Seefeldt, L. Delannay: Deformation texture prediction: from the Taylor model to the Advanced Lamel model. Int. J. Plasticity 21 (2005), p.589.

DOI: 10.1016/j.ijplas.2004.04.011

[19] H.J. Bunge: Some applications of the Taylor theory of polycrystal plasticity. Krist. Tech. 5 (1970), p.145.

[20] P. Van Houtte, K. Mols, A. Van Bael, E. Aernoudt: Application of yield loci calculated from texture data. Texture Microstruct. 11 (1989), p.23.

DOI: 10.1155/tsm.11.23

[21] P. Van Houtte, A. Van Bael, J. Winters: The incorporation of texture-based yield loci into elastoplastic finite element programs. Texture Microstruct. 24 (1995), p.255.

DOI: 10.1155/tsm.24.255

[22] P. Van Houtte, A. Van Bael: Convex plastic potentials of 4th and 6th rank for anisotropic materials. Int. J. Plasticity 20 (2004), p.1505.

DOI: 10.1016/j.ijplas.2003.11.005

[23] F. Grytten, B. Holmedal, O.S. Hopperstad and T. Borvik: Evaluation of identification methods for YLD2004-18p, Int. J. Plasticity 24 (2008), p.2248.

DOI: 10.1016/j.ijplas.2007.11.005

[24] P. Van Houtte, S. Jumar Yerra, A. Van Bael: The facet method; a hierarchic al multilevel modelling scheme for anisotropic convex plastic potentials, Int. J. Plasticity 25 (2009), p.332.

DOI: 10.1016/j.ijplas.2008.02.001

[25] O. Engler, Y.G. An: Correlation of texture and plastic anisotropy in the Al-Mg alloy, Solid State Phenomena Vol. 105 (2005) p.277.

DOI: 10.4028/www.scientific.net/ssp.105.277

[26] Y. G, An, E. Atzema, M. Workel, H. Vegter, L. Elliott, J. Moerman; A comparison of yield loci measured with mechanical tests and calculated from crystal plasticity for steel sheets, 1st International Conference on Super-high Strength Steels (2005).

[27] P. S. Bate, Y.G. An: Plastic anisotropy in AA5005 Al-1Mg: predictions using crystal plasticity finite element analysis, . Scritpa Materialia, 51 (2004), p.973.

DOI: 10.1016/j.scriptamat.2004.07.018

[28] P. Van Houtte: The 'MTM-FHM', software system Version 2, Katholieke Universiteit Leuven, Belgium, (1995).

[29] Y.G. An, H. Vegter: The difference in plastic behaviour between bulging test and through thickness compression test for sheet steels and aluminium alloys. IDDRG Working Group Meeting, 1998, Genval, Belgium.

[30] Y.G. An, H. Vegter: Analytical and experimental study of frictional behaviour in through-thickness compression test, Journal of Material Processing Technology, 160 (2005), p.148.

DOI: 10.1016/j.jmatprotec.2004.05.026

[31] Y.G. An, H. Vegter, L. Elliott: A novel and simple method for the measurement of plane strain work hardening, Journal of Materials Processing Technology, 155-156 (2004) p.1616.

DOI: 10.1016/j.jmatprotec.2004.04.344

[32] Y.G. An, H. Vegter, J. Heijne; Development of simple shear test for the measurement of work hardening, Journal of Materials Processing Technology, to be published.

DOI: 10.1016/j.jmatprotec.2008.11.007

[33] Y. Bergstrom; Dislocation model for the stress-strain behaviour of polycrystalline Fe with special emphasis on the variation of the densities of mobile and immobile dislocations. Materials Science and Engineering 5 (1969), p.193.

DOI: 10.1016/0025-5416(70)90081-9