Effect of Stress Triaxiality on Yielding of Anisotropic Materials under Plane Stress Condition

Document Type: Research Paper


1 Department of Applied Mechanics, Maulana Azad National Institute of Technology

2 Scientist, Advanced Materials Processes Research Institute (CSIR)


The triaxiality of the stress state is known to greatly influence the amount of plastic strain which a material may undergo before ductile failure occurs. It is defined as the ratio of hydrostatic pressure, or mean stress, to the von Mises equivalent stress. This paper discusses the effects of stress triaxiality on yielding behavior of anisotropic materials. Hill-von Mises’s criteria for anisotropic material have been used with triaxiality factor (TF). Mathematical model that combines the yield stress and anisotropic ratio R (ratio of width strain to thickness strain) along with triaxiality have been formulated. This model is considered as an objective function subjected to inequality constraint. Constrained optimization is solved using genetic algorithm. The results obtained give the set of principal stresses along with corresponding critical triaxiality which is the maximum value at which the material can sustain without failure. If triaxiality extends further more the material will go to plastic deformation and may prone to failure. In this way, the critical triaxiality of materials can be determined to avoid fracture and failure of materials. This article is important from the industrial application point of view by considering triaxiality as a design parameter while designing the component.


[1] Hill R., 1948, A theory of yielding and plastic flow of anisotropic metals, International Journal of Mathematical, Physical and Engineering Sciences 193: 281-297.

[2] Chaudhary Sushil K., Kuwano Jiro, 1968, Anisotropic multiple yielding of dense toyoura sand in p'-constant shear plane, Soils and Foundations 43: 59-69.

[3] Yasushi Kurosaki, Matsumoto Masanobu, Kobayashi Masanori, 1988, Studies on anisotropic yield characteristics and press formability of metal sheets : investigation into pure stretch-forming, JSME International Journal, Series C, Mechanical Systems, Machine Elements and Manufacturing 31(4): 789-795.

[4] Harvey S.J., Adkin P., Jeans P.J., 2007, Anisotropic yield surfaces in cyclic plasticity, fatigue and fracture, Engineering Materials and Structures 6(1): 89-99.

[5] Banabicd Dorel, 2002, Recent anisotropic yield criteria for sheet metals, in: Proceedings of the Romanian Academy, Series A 3(3).

[6] Hu Weilong, 2002, Enhancement of yield criteria considering anisotropic behaviors of sheet metals, SAE International, 2002-01-0158.

[7] Sivakumar V., 2001, The effect of anisotropic elasticity on the yielding characteristics of over consolidated natural clay, Canadian Geotechnical Journal 38(1): 125-137(13).

[8] Padmanabhan R., 2009,Numerical study on the influence of initial anisotropy on optimal blank shape,Finite Elements in Analysis and Design 45(2): 71-80.

[9] Liao K.C., 2008, Applications of planar anisotropic yield criteria to porous sheet metal forming simulations, European Journal of Mechanics A/Solids 28(4): 806-810.

[10] Lee Daeyong, 1978, Anisotropic yielding behavior of a fiber-reinforced, directionally solidified eutectic alloy, Metallurgical and Materials Transactions A 9: 1477-1481.

[11] Masanobu Oda, 1989, Yield function for soil with anisotropic fabric, Journal of Engineering Mechanics 115(1): 89-104.

[12] Plunkett B., 2006, Anisotropic yield function of hexagonal materials taking into account texture development and anisotropic hardening, Acta Materialia 54: 4159-4169.

[13] Wakashima Kenji, Courtney T.H., 1980, Anisotropic yielding behaviour of directionally solidified, single-grained eutectics, Philosophical Magazine A 42(1): 47-62.

[14] Cazacu Oana, 2001,Generalization of drucker’s yield criterion to orthotropy, Mathematics and Mechanics of Solids 6(6): 613-630.

[15] Hosford William F., 1996, On the crystallographic basis of yield criteria, Textures and Microstructures 26–27: 479-493.

[16] Davis Richard W., Khaleel Mohammad A., 2002, Anisotropic yield locus evolution during cold pilgering of titanium alloy tubing, Engineering Material Technol 124(2): 125-135.