Abstract
It is widely accepted that failure due to plastic deformation in metals greatly depends on the stress triaxiality factor (TF). This article investigates the variation of stress triaxiality along the yield locus of ductile materials. Von Mises yield criteria and triaxiality factor have been used to determine the critical limits of stress triaxiality for the materials under plane strain condition. A generalized mathematical model for triaxiality factor has been formulated and a constrained optimization has been carried out using genetic algorithm. Finite element analysis of a two dimensional square plate has been carried out to verify the results obtained by the mathematical model. It is found that the set of values of the first and the second principal stresses on the yield locus, which results in maximum stress triaxiality, can be used to determine the location at which crack initiation may occur. Thus, the results indicate that while designing a certain component, such combination of stresses which leads the stress triaxiality to its critical value, should be avoided.
Similar content being viewed by others
References
Henry B. S., Luxmoore A. R., Engineering Fracture Mechanics, 57 (1997), 375.
Zhang Y., Chen Z., International Journal of Fracture, 143 (2007), 105.
Borona N., Gentile D., Pirondi A., Newas G., International Journal of Plasticity, 21 (2005), 981.
Imanaka M., Fujinami A., Suzuki Y., Journal of Materials Science, 35 (2000), 2481.
Trattnig G., Antretter T., Pippan R., Engineering Fracture Mechanics, 75 (2008), 223.
Mirone G., Engineering Fracture Mechanics, 72 (2005), 1049.
Nicolaou P.D., Semiatin S.L., Journal of Materials Science, 36 (2001), 5155.
Bao Y., Engineering Fracture Mechanics, 72 (2005), 502.
Bacha Daniel D., Journal of Materials Processing and Technology, 203 (2008), 480.
Mediavilla J., Peerlings R.H.J., Geers M.G.D., Computer Methods in Applied Mechanics and Engineering, 195 (2006) 4617.
Borvik T., Hopperstad O.S., Bersted T., European Journal of Mechanics A/Solids, 22 (2003), 15.
Kim J., Gao X., Srivatsan T.S., Engineering Fracture Mechanics, 71 (2004), 379.
Pardoen T., Computers and Structures, 84 (2006), 1641.
Deb K., Optimization for Engineering Design Algorithms and Examples, Prentice Hall, New Delhi, 1993
Kong X.M., Schluter N., Dahl W., Engineering Fracture Mechanics, 52 (1995), 379.
Bhadauria S.S., Hora M.S., Pathak K.K., Journal of Solid Mechanics, 1 (2009), 226.
Chawla K.K., Meyers M.A., Mechanical Behavior of Materials, Prentice Hall, 1998.
Kumar P., Elements of Fracture Mechanics, Wheeler Publishing Company, New Delhi, 1999.
Kreysgiz E., Advanced Engineering Mathematics, Wiley, 2008.
Meguid S.A., Engineering Fracture mechanics, Elsevier Applied Science, USA, 1983.
Srinath L.S., Advanced Mechanics of Solids, Tata Mc. Graw Hill, India, 2003
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Bhadauria, S.S., Pathak, K.K. & Hora, M.S. Determination of critical stress triaxiality along yield locus of isotropic ductile materials under plane strain condition. Mater Sci-Pol 30, 197–203 (2012). https://doi.org/10.2478/s13536-012-0029-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.2478/s13536-012-0029-9