YLD 2000 akma fonksiyonu parametrelerinin belirlenmesinde ardışık kuadratik programlama ve aktif set metotlarının performanslarının incelenmesi

Öz

Bu çalışmada, Yld2000 akma fonksiyonunun katsayılarının belirlenmesinde nümerik optimizasyon tekniklerinden ardışık kuadratik programlama ve aktif-set metotlarının performansları değerlendirilmiştir. Çalışmada iki alüminyum alaşımı (AA6111-T4, AA6181-T4) ve bir yüksek mukavemetli sac malzeme (DP980) seçilmiştir. Yöntemler, hata fonksiyonunu yakınsama hızlarına ve minimizasyon sırasında inceledikleri fonksiyon sayısına göre değerlendirilmiş olup, üç malzeme için de aktif-set metodunun ardışık kuadratik programlamaya göre daha başarılı olduğu belirlenmiştir. Metodu doğrulamak için, belirlenmiş katsayılara göre malzemelerin akma gerilmesi oranları, Lankford katsayılarının sac düzlemi içerisindeki değişimleri ve akma yüzeylerinin pozitif bölgeleri tahmin edilmiş ve teorik sonuçlar deneysel sonuçlarla karşılaştırılmıştır. Yapılan karşılaştırmalardan malzemelerin düzlemsel anizotropilerinin ve pozitif bölgede akma yüzeylerinin başarılı bir şekilde tahmin edilebildiği görülmüştür.

Anahtar Kelimeler

• Yld2000
• Ardışık kuadratik programlama
• Aktif-set metot
• Düzlemsel anizotropi
• Akma yüzeyleri

Investigation of performances of sequential quadratic programming and active-set methods in the determination of YLD2000 yield function parameters

Abstract

In this study, performances of sequential quadratic programming and active-set methods from numerical optimization techniques were investigated in the determination of Yld2000 yield function coefficients. Two aluminum alloys (AA6111-T4, AA6181-T4) and a high strength steel sheet material (DP980) were selected in the study. Methods were examined according to their convergence rate and the number of function evaluations that occurred during the minimization and it was determined that active-set method was more successful than sequential quadratic programming for three materials. The variations of the yield stress ratios and Lankford coefficients in the sheet plane and positive regions of yield surfaces of the materials were predicted and theoretical results were compared with experimental results to validate the method. It is seen from the comparisons that planar anisotropy and yield surfaces of the materials in the positive regions could be successfully predicted.

Keywords

• Yld2000
• Sequential quadratic programming
• Active-set method
• Planar anisotropy
• Yield surfaces

Kaynakça

1. G. E. Dieter, Mechanical Metallurgy. McGraw-Hill Book Company, 1988.
2. R. Hill, 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 (A), 281–297, 1948. https://doi.org/10.1098/rspa. 1948.0045.
3. D. Banabic, Sheet Metal Forming Processes Constitutive Modelling and Numerical Simulation. Springer, 2010.
4. K. Mattiasson and M. Sigvant, An evaluation of some recent yield criteria for industrial simulations of sheet forming processes. International Journal of Mechanical Sciences, 50, 774-787, 2008. https://doi.org/10.1016/ j.ijmecsci.2007.11.002.
5. F. Barlat, J. C. Brem, J. W. Yoon, K. Chung, R. E. Dick, D. J. Lege, F. Pourboghrat, S. H. Choi, and E. Chu, Plane stress yield function for aluminum alloy sheets-part 1: theory. International Journal of Plasticity, 19, 1297-1319, 2003. https://doi.org/10.1016/S0749-6419(02)00019-0.
6. O. Cazacu and F. Barlat, Application of the theory of representation to describe yielding of anisotropic aluminum alloys. International Journal of Engineering Science, 41, 1367-1385,2003. https://doi.org/10.1016/ S0020- 7225(03)00037-5.
7. H. Aretz, O. S. Hopperstad, O-G. Lademo, Yield function calibration for orthotropic sheet metals based on uniaxial and plane strain tensile tests. Journal of Materials Processing Technology,186, 221-235, 2007. https://doi.org/10.1016/j.jmatprotec.2006.12.037.
8. J. S. Arora, Introduction to Optimum Design. Elsevier, 2004.

9. D. Banabic, T. Balan, D. S. Comsa, A new yield criterion for orthotropic sheet metals under plane-stress conditions. Proceedings of the 7th Conference, sayfa 217-224, Cluj Napoca, Romania, 11-12 May 2000.
10. H. Aretz, A non-quadratic plane stress yield function for orthotropic sheet metals. Journal of Materials Processing Technology,168,1-9,2005. https://doi.org/ 10.1016/j. jmatprotec.2004.10.008.
11. D. S. Comsa and D. Banabic, Plane-stress yield criterion for highly-anisotropic sheet metals, Proceedings of the 7th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, sayfa 43-48, Interlaken, Switzerland, 1-5 September 2008.
12. C. P. Kohar, A. Brahme, J. Imbert, R. K. Mishra, and K. Inal, Effects of coupling anisotropic yield functions with the optimization process of extruded aluminum front rail geometries in crashworthiness. International Journal of Solids and Structures, 128, 174-198, 2017. https://doi.org/10.1016/j.ijsolstr.2017.08.026.
13. A. Abedini, C. Butcher, T. Rahmaan, and M. J. Worswick, Evaluation and calibration of anisotropic yield criteria in shear loading: constraints to eliminate numerical artefacts. International Journal of Solids and Structures, 151, 118-134, 2018. https://doi.org/ 10.1016/j. ijsolstr.2017.06.029.
14. S. Kılıç, İ. Kaçar, F. Öztürk, and S. Toros, Effects of different optimization methods on the predictions of Yld2000 yield criterion coefficients. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 8, 447-463, 2019. https://doi.org/10.28948/ngumuh. 517160.
15. L. La ̆za ̆rescu, I. Nicodim, I. Ciobanu, D. S. Comşa, and D. Banabic, Determination of material parameters of sheet metals using the hydraulic bulge test. Acta Metallurgica Slovaca, 19, 4-12, 2013. https://dx.doi.org/10. 12776/ams.v19i1.81.
16. Matlab Optimization Toolbox User’ Guide. The MathWorks, Inc. 2016.
17. J. C. Brem and F. Barlat, Characterization of aluminum alloy (6111-T4). 5th International Conference and Numerical Simulation of 3D Sheet Metal Forming Processes, Jeju Island, Korea, 21-25 October 2002.
18. D. Banabic, H. Aretz, D. S. Comsa, and L. Paraianu, An improved analytical description of orthotropy in metallic sheets. International Journal of Plasticity, 21, 493-512, 2005. https://doi.org/10.1016/j.ijplas.2004.04.003.
19. T. Kuwabara, Hole expansion of high strength steel sheet. 11th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, Tokyo, Japan, 30 July-3 August 2018