EFFECTS OF DIFFERENT OPTIMIZATION METHODS ON THE PREDICTIONS OF YLD2000 YIELD CRITERION COEFFICIENTS
Abstract
The improved
yield criteria are generally used in the finite element simulations of plastic
deformation processes. Calculation accuracies of these criteria coefficients result
successful simulation outcomes. In this study, the coefficients of the YLD2000
yield criterion are calculated by three most widely used optimization methods
in literature, namely the least squares, nonlinear conditional optimization,
and genetic algorithm methods. Two different aluminum alloys, AA7003-T6 and
AA6063-T6 are selected to verify the prediction results. Results reveal that the
nonlinear conditional optimization and genetic algorithm methods are very
dependent on the initial values. Therefore, different result is determined for
each different case. For this reason, it has been concluded that the least
squares method should be preferred to calculate the coefficients of the yield
criterion by using optimizing method.
References
- [1] HILL R., "A theory of the yielding and plastic flow of anisotropic metals", Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 193, 281-297, 1948.
- [2] HILL R., "A user-friendly theory of orthotropic plasticity in sheet metals", Int J Mech Sci, 35, 19-25, 1993.
- [3] BARLAT F., BECKER R.C., HAYASHIDA Y., MAEDA Y., YANAGAWA M., CHUNG K., BREM J.C., LEGE D.J., MATSUI K., MURTHA S.J., HATTORI S., "Yielding description for solution strengthened aluminum alloys", Int J Plasticity, 13, 385-401, 1997.
- [4] BARLAT F., LEGE D.J., BREM J.C., "A six-component yield function for anisotropic materials", International Journal of Plasticity, 7, 693-712, 1991.
- [5] BARLAT F., MAEDA Y., CHUNG K., YANAGAWA M., BREM J.C., HAYASHIDA Y., LEGE D.J., MATSUI K., MURTHA S.J., HATTORI S., BECKER R.C., MAKOSEY S., "Yield function development for aluminum alloy sheets", Journal of the Mechanics and Physics of Solids, 45, 1727-1763, 1997.
- [6] BARLAT F., BREM J.C., YOON J.W., CHUNG K., DICK R.E., LEGE D.J., POURBOGHRAT F., CHOI S.H., CHU E., "Plane stress yield function for aluminum alloy sheets - Part 1: Theory", Int J Plasticity, 19, 23, 2003.
- [7] HOLGER A., "Applications of a new plane stress yield function to orthotropic steel and aluminium sheet metals", Modelling and Simulation in Materials Science and Engineering, 12, 491, 2004.
- [8] BARLAT F., ARETZ H., YOON J.W., KARABIN M.E., BREM J.C., DICK R.E., "Linear transfomation-based anisotropic yield functions", Int J Plasticity, 21, 1009-1039, 2005.
- [9] KILIÇ S., Farklı alüminyum alaşımlarında YLD2000 ve YLD2003 akma kriterlerinin performansının incelenmesi, in: II. International scientific and vocational studies congress (BILMES18), Nevşehir, 2018.
- [10] VAN DEN BOOGAARD T., HAVINGA J., BELIN A., BARLAT F., "Parameter reduction for the Yld2004-18p yield criterion", Int J Mater Form, 9, 175-178, 2016.
- [11] ACHANI D., HOPPERSTAD O.S., LADEMO O.G., "Behaviour of extruded aluminium alloys under proportional and non-proportional strain paths", Journal of Materials Processing Technology, 209, 4750-4764, 2009.
- [12] RADIOELEKTRONIKY K., Optimization Toolbox, lsqnonlin, in, 2018.
- [13] MathWorks Inc, MATLAB : the language of technical computing : computation, visualization, programming : installation guide for UNIX version 5, Natwick : Math Works Inc., 1996.
- [14] MathWorks Inc, Genetic Algorithm, in, 2018.
- [15] Wikipedia, Genetik algoritma, in, 2018.
- [16] BANABIC D., COMSA D.S., GAWAD J., Plastic Behaviour of Sheet Metals, in: Multiscale Modelling in Sheet Metal Forming, Springer, 2016.
Abstract
Plastik deformasyon proseslerinin sonlu
elemanlar simülasyonlarında genellikle gelişmiş akma kriterleri kullanılmaktadır.
Bu kriterlerin katsayılarının doğru hesaplanması simülasyonun sonuçlarının
başarısına etki etmektedir. Bu çalışmada literatürde en çok kullanılan üç
optimizasyon yöntemlerinden en küçük kareler, nonlineer şartlı optimizasyon ve
genetik algoritma kullanılarak, YLD2000 akma kriterinin katsayıları hesaplanmıştır.
Tahmin edilen sonuçları doğrulamak için iki farklı alüminyum alaşımı
seçilmiştir. Elde edilen sonuçlara göre nonlineer şartlı optimizasyon ve
genetik algoritma yöntemlerinin girilen başlangıç değerlerine çok bağlı olduğu
ve her farklı durum için farklı sonuçlar verdiği tespit edilmiştir. Bu nedenle
akma kriterlerinin katsayılarının optimizasyon medodu ile hesaplanması
işlemlerinde en küçük kareler yönteminin tercih edilmesi gerektiği sonucuna varılmıştır.
References
- [1] HILL R., "A theory of the yielding and plastic flow of anisotropic metals", Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 193, 281-297, 1948.
- [2] HILL R., "A user-friendly theory of orthotropic plasticity in sheet metals", Int J Mech Sci, 35, 19-25, 1993.
- [3] BARLAT F., BECKER R.C., HAYASHIDA Y., MAEDA Y., YANAGAWA M., CHUNG K., BREM J.C., LEGE D.J., MATSUI K., MURTHA S.J., HATTORI S., "Yielding description for solution strengthened aluminum alloys", Int J Plasticity, 13, 385-401, 1997.
- [4] BARLAT F., LEGE D.J., BREM J.C., "A six-component yield function for anisotropic materials", International Journal of Plasticity, 7, 693-712, 1991.
- [5] BARLAT F., MAEDA Y., CHUNG K., YANAGAWA M., BREM J.C., HAYASHIDA Y., LEGE D.J., MATSUI K., MURTHA S.J., HATTORI S., BECKER R.C., MAKOSEY S., "Yield function development for aluminum alloy sheets", Journal of the Mechanics and Physics of Solids, 45, 1727-1763, 1997.
- [6] BARLAT F., BREM J.C., YOON J.W., CHUNG K., DICK R.E., LEGE D.J., POURBOGHRAT F., CHOI S.H., CHU E., "Plane stress yield function for aluminum alloy sheets - Part 1: Theory", Int J Plasticity, 19, 23, 2003.
- [7] HOLGER A., "Applications of a new plane stress yield function to orthotropic steel and aluminium sheet metals", Modelling and Simulation in Materials Science and Engineering, 12, 491, 2004.
- [8] BARLAT F., ARETZ H., YOON J.W., KARABIN M.E., BREM J.C., DICK R.E., "Linear transfomation-based anisotropic yield functions", Int J Plasticity, 21, 1009-1039, 2005.
- [9] KILIÇ S., Farklı alüminyum alaşımlarında YLD2000 ve YLD2003 akma kriterlerinin performansının incelenmesi, in: II. International scientific and vocational studies congress (BILMES18), Nevşehir, 2018.
- [10] VAN DEN BOOGAARD T., HAVINGA J., BELIN A., BARLAT F., "Parameter reduction for the Yld2004-18p yield criterion", Int J Mater Form, 9, 175-178, 2016.
- [11] ACHANI D., HOPPERSTAD O.S., LADEMO O.G., "Behaviour of extruded aluminium alloys under proportional and non-proportional strain paths", Journal of Materials Processing Technology, 209, 4750-4764, 2009.
- [12] RADIOELEKTRONIKY K., Optimization Toolbox, lsqnonlin, in, 2018.
- [13] MathWorks Inc, MATLAB : the language of technical computing : computation, visualization, programming : installation guide for UNIX version 5, Natwick : Math Works Inc., 1996.
- [14] MathWorks Inc, Genetic Algorithm, in, 2018.
- [15] Wikipedia, Genetik algoritma, in, 2018.
- [16] BANABIC D., COMSA D.S., GAWAD J., Plastic Behaviour of Sheet Metals, in: Multiscale Modelling in Sheet Metal Forming, Springer, 2016.
Details
| Primary Language | English |
|---|---|
| Subjects | Mechanical Engineering |
| Journal Section | Mechanical Engineering |
| Authors | |
| Publication Date | January 28, 2019 |
| Submission Date | July 3, 2018 |
| Acceptance Date | September 13, 2018 |
| Published in Issue | Year 2019 Volume: 8 Issue: 1 |
