Hill48 akma kriteri kullanarak alüminyum alaşımlarının anizotropik davranışlarının modellenmesi ve optimizasyonu

Year 2024, Volume: 6 Issue: 1, 16 - 21, 20.08.2024

Süleyman Kılıç

Abstract

Bu çalışmada, Hill48 akma kriteri kullanılarak alüminyum alaşımı Al7075’in anizotropik davranışı modellenmiştir. Hill48 akma kriteri, malzemelerin plastik deformasyon başlangıcını tahmin etmek için geliştirilmiş bir matematiksel modeldir. Anizotropik malzemelerin sonlu elemanlar analizlerinde parametre sayısının az olması nedeniyle günümüzde de yaygın olarak kullanılmaktadır. Al7075 alaşımının deneysel verilerinden elde edilen mekanik özellikler (anizotropi katsayıları ve akma gerilmesi değerleri) kullanılarak model katsayıları hesaplanmıştır. Model parametreleri olan F, G, H ve N katsayıları, anizotropi ve gerilme oranlarına bağlı olarak iki farklı şekilde belirlenmiştir. Ayrıca, optimizasyon tekniği ile bu katsayıların daha hassas belirlenmesi sağlanmış ve hata miktarı %2 olarak tespit edilmiştir. Bu çalışma, Hill48 kriterinin mühendislik uygulamalarındaki etkinliğini vurgulamakta ve optimizasyonun parametre belirlemedeki önemini ortaya koymaktadır. Sonuç olarak, optimizasyon tekniğinin model parametrelerinin belirlenmesinde daha başarılı sonuçlar verdiği gösterilmiştir.

Keywords

Hill48 akma kriteri, model parametreleri, optimizasyon teknikleri

Modeling and optimization of the anisotropic behavior of aluminum alloys by using the Hill48 yield criterion

Abstract

In this study, the anisotropic behavior of aluminum alloy AA7075 was modeled using the Hill48 yield criterion. The Hill48 yield criterion is a mathematical model developed to predict the onset of plastic deformation of materials. It is still widely used today in finite element analyzes of anisotropic materials due to the small number of parameters. Model coefficients were calculated using the mechanical properties (anisotropy coefficients and yield stress values) obtained from the experimental data of AA7075 alloy. Model parameters F, G, H and N coefficients were determined in two different ways depending on anisotropy and stress rates. In addition, with the optimization technique, these coefficients were determined more precisely and the error amount was determined as 2%. This study emphasizes the effectiveness of the Hill48 criterion in engineering applications and reveals the importance of optimization in parameter determination. As a result, it has been shown that the optimization technique gives more successful results in determining the model parameters.

Keywords

Hill48 yield criterion, model parameters, optimization techniques

References

• Abspoel, M., Scholting, M. E., Lansbergen, M., An, Y., & Vegter, H. (2017). A new method for predicting advanced yield criteria input parameters from mechanical properties. Journal of Materials Processing Technology, 248, 161-177.
• Akşen, T. A., Özsoy, M., & Fırat, M. (2024). Earing prediction performance of homogeneous polynomial-based yield function coupled with the combined hardening model for anisotropic metallic materials. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 30(1), 1-9.
• An, Y., Vegter, H., Carless, L., & Lambriks, M. (2011). A novel yield locus description by combining the Taylor and the relaxed Taylor theory for sheet steels. International Journal of Plasticity, 27(11), 1758-1780.
• Banabic, D. (1997). Sheet metal formability predicted by using the new (1993) Hill’s yield criterion. In M. Predeleanu & P. Gilormini (Eds.), Studies in Applied Mechanics. Elsevier.
• Banabic, D. (2010). Sheet metal forming processes: Constitutive modelling and numerical simulation. Springer Science & Business Media.
• Byrd, R. H., Gilbert, J. C., & Nocedal, J. (2000). A trust region method based on interior point techniques for nonlinear programming. Mathematical Programming, 89, 149-185.
• Hakoyama, T., Hakoyama, C., & Furusato, D. (2022). Measurement of shear deformation behavior in thickness direction for a mild steel sheet. Materials Research Proceedings, 41.
• Hariharan, K., Prakash, R. V., & Sathya Prasad, M. (2010). Influence of yield criteria in the prediction of strain distribution and residual stress distribution in sheet metal formability analysis for a commercial steel. Materials and Manufacturing Processes, 25(8), 828-836.
• Hill, R. (1948). 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(1033), 281-297.
• Hosford, W. F. (1985). Comments on anisotropic yield criteria. International Journal of Mechanical Sciences, 27(7-8), 423-427.
• Jeong, K., Lee, K., Kwon, D., Lee, M.-G., & Han, H. N. (2024). Parameter determination of anisotropic yield function using neural network-based indentation plastometry. International Journal of Mechanical Sciences, 263, 108776.
• Khalfallah, A., Alves, J. L., Oliveira, M. C., & Menezes, L. F. (2015). Influence of the characteristics of the experimental data set used to identify anisotropy parameters. Simulation Modelling Practice and Theory, 53, 15-44.
• Kilic, S. (2019). Experimental and numerical investigation of the effect of different temperature and deformation speeds on mechanical properties and springback behaviour in Al-Zn-Mg-Cu alloy. Mechanika, 25(5), 406-412.
• Lian, J., Shen, F., Jia, X., Ahn, D.-C., Chae, D.-C., Münstermann, S., & Bleck, W. (2018). An evolving non-associated Hill48 plasticity model accounting for anisotropic hardening and r-value evolution and its application to forming limit prediction. International Journal of Solids and Structures, 151, 20-44.
• Mu, Z., Zhao, J., Meng, Q., Huang, X., & Yu, G. (2022). Applicability of Hill48 yield model and effect of anisotropic parameter determination methods on anisotropic prediction. Journal of Materials Engineering and Performance, 31(3), 2023-2042.
• Ozturk, F., Toros, S., & Kilic, S. (2014). Effects of anisotropic yield functions on prediction of forming limit diagrams of DP600 advanced high strength steel. Procedia Engineering, 81, 760-765.
• Park, N., Huh, H., Lim, S. J., Lou, Y., Kang, Y. S., & Seo, M. H. (2017). Fracture-based forming limit criteria for anisotropic materials in sheet metal forming. International Journal of Plasticity, 96, 1-35.
• Pijlman, H. H. (2001). Sheet material characterisation by multi-axial experiments.
• Shahid, S., & Gukhool, W. (2020). Experimental testing and material modeling of anisotropy in injection moulded polymer materials [Master’s thesis, Blekinge Institute of Technology].
• Tang, B., & Lou, Y. (2019). Effect of anisotropic yield functions on the accuracy of material flow and its experimental verification. Acta Mechanica Solida Sinica, 32(1), 50-68.
• Wang, H., Wan, M., Yan, Y., & Wu, X. (2013). Effect of the solving method of parameters on the description ability of the yield criterion about the anisotropic behavior. Journal of Mechanical Engineering, 49(24), 45-53.
• Yan, Y., Wang, H., & Li, Q. (2015). The inverse parameter identification of Hill 48 yield criterion and its verification in press bending and roll forming process simulations. Journal of Manufacturing Processes, 20, 46-53.
• Yu, Y., Jie, B., Xu, X., & Haibo, W. (2021). In-depth analysis of convexity of Hill’48 anisotropic yield criterion. Journal of Plasticity Engineering, 28(12), 184-191.
• Zhang, H.-X., Li, F.-F., & Fang, G. (2024). Predicting plastic behavior of magnesium alloy tube bending with comprehensive constitutive models. Mechanics of Materials, 195, 105030.
• Zhang, H., & Liu, Y. (2017). The inverse parameter identification of Hill’48 yield function for small-sized tube combining response surface methodology and three-point bending. Journal of Materials Research, 32(12), 2343-2351.
• Zhang, S. Y., Leotoing, L., Guines, D., & Thuillier, S. (2013). Calibration of material parameters of anisotropic yield criterion with conventional tests and biaxial test. Key Engineering Materials, 554, 2111-2117.
• Zhang, Y., Duan, Y., Mu, Z., Fu, P., & Zhao, J. (2024). Non-associated flow rule constitutive modeling considering anisotropic hardening for the forming analysis of orthotropic sheet metal. Experimental Mechanics, 64(3), 305-323.