Investigation of the prediction capability of Yld89 yield criterion for highly anisotropic sheet materials

Year 2021, , 7 - 13, 15.06.2021

Bora Şener

https://doi.org/10.14744/ytu.jame.2021.00002

Abstract

In the present work, the prediction capability of Yld89 criterion from anisotropic yield func- tions was investigated in the view of the anisotropic behavior of the sheet metals. Investigation was conducted on two highly anisotropic sheet materials: an aluminum alloy (AA2090-T3) and an advanced high strength steel (TRIP 780). The in-plane variation of material anisotropy and normalized yield surface contours were considered in the evaluation of the prediction capability of the criterion. Firstly, the model coefficients were determined according to stress and strain based definitions. Then, the planar variations of the yield stress and plastic strain ratios and normalized yield surface contours of the materials were predicted according to both identification procedures. Finally, the computed results were compared with experiments to evaluate prediction capability of the model. It was observed from the comparisons that the pla- nar variations of the yield stress ratio could successfully predicted by stress based definition, while the variations of the plastic strain ratios in the sheet plane could accurately predicted by strain based definition. Besides, it was determined that elastic region predicted from strain based definition was larger than stress based definition for AA2090-T3, while the predicted elastic region from stress based definition was slightly larger in than that of strain based definition for TRIP 780 material.

Keywords

Plastic strain ratio, stress ratio, yield surface, Yld89 yield crite- rion

References

• [1] Hershey, A.V. (1954). The plasticity of an isotropic aggregate of anisotropic face centered cubic crystals, Journal of Applied Mechanics, 21, 241-249.
• [2] Hosford, W.F. (1972). A generalized isotropic yield criterion, Journal of Applied Mechanics, 39, 607-609.
• [3] Barlat, F., Richmond, O. (1987). Prediction of tricomponent plane stress yield surfaces and associated flow and failure behavior of strongly textured F.C.C polycrystalline sheets, Materials Science and Engineering, 95, 15-29.
• [4] Bassani, J.L. (1977). Yield characterization of metals with transversely isotropic plastic properties, International Journal of Mechanical Sciences, 19, 651-660.
• [5] Budiansky, B. (1984). Anisotropic plasticity of plane-isotropic sheets, Studies in Applied Mechanics, 6, 15-29.
• [6] 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(A), 281-297.
• [7] Woodthorpe, J., Pearce, R. (1970). The anomalous behavior of aluminum sheet under balanced biaxial tension, International Journal of Mechanical Sciences, 12, 341-347.
• [8] Hill, R. (1979). Theoretical plasticity of textured aggregates, Mathematical Proceedings of the Cambridge Philosophical Society, 85, 179-191.
• [9] Hill, R. (1990). Constitutive modeling of orthotropic plasticity in sheet metals, Journal of the Mechanics and Physics of Solids, 38, 405-417.
• [10] Hill, R. (1993). A user-friendly theory of orthotropic plasticity in sheet metals, International Journal of Mechanical Sciences, 35, 19-25.
• [11] Lin, S.B., Ding, J.L. (1996). A modified from of Hill’s orientationdashdependent yield criterion for orthotropic sheet metals, Journal of the Mechanics and Physics of Solids, 44, 1739-1764.
• [12] Barlat, F., Lian, J. (1989). Plastic behavior and stretchability of sheet metals. Part I: a yield function for orthotropic sheets under plane stress conditions, International Journal of Plasticity, 5, 51-66.
• [13] Barlat, F., Lege, D.J., Brem, J.C., Warren, C.J. (1991b). Constitutive behavior for anisotropic materials and application to a 2090-T3 Al-Li alloy, Modeling the Deformation of Crystalline Solids, Warrendale, pages 189-203.
• [14] Stoughton, T.B., Shi, M.F., Huang, G., Yoon, J.W. (2013). Material characterizations for benchmark 1 and benchmark 2, AIP Conference Proceedings, 1567(1), 9-14.
• [15] Nocedal, J., Wright, S.J. (2006). Numerical Optimization, Springer, 2nd Ed., pages 563-592, United States of America.