### Shape- Dependent Term Investigation of Khan- Liu Yield/ Fracture Criterion as a Function of Plastic Strain for Anisotropic Metals

Document Type: Research Paper

Authors

1 Marine Department, Malek-Ashtar University of Technology, Isfahan, Iran

2 Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran

3 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran

Abstract

The current paper primarily aims to suggest a mathematical model for the shape-dependent term of Khan- Liu (KL) Yield/ fracture criterion as a function of Plastic Strain for DP590 steel alloy. The shape-dependent term in the mention criterion can generalize the application of this criterion in order to predict the behavior of other materials. Plane stress case and the first quarter of the stress plane have been specifically studied. Uniaxial stresses in rolling and transverse directions of sheet and also the tensions caused by equal-biaxial tension have been experimentally used. Then, material constants of KL yield/ fracture criterion and Khan- Huang- Liang (KHL) constitutive equation are calculated using genetic algorithm (GA) optimization and the value of the shape-dependent factor in KL criterion is extracted. The same has been repeated for various plastic strains and finally a polynomial mathematical model based on the plastic strain for the KL shape-dependent factor is suggested. Hence, material constants of KL criterion could be calculated using at least tests namely experimental uniaxial stress test, experimental equal-biaxial stress, and one of the optimization models such as GA. Using the given mathematical model based on the plastic strain, correction term can be calculated and the generalized form of KL criterion can be used for various ductile metallic materials.

Keywords

[1] Khan A.S., Liu H., 2012, Strain rate and temperature dependent fracture criteria for isotropic and anisotropic metals, International Journal of Plasticity 37: 1-15.
[2] Khan A.S., Yu S., 2012, Deformation induced anisotropic responses of Ti–6Al–4V alloy. Part I: Experiments, International Journal of Plasticity 38: 1-13.
[3] Khan A.S., Yu S., Liu H., 2012, Deformation induced anisotropic responses of Ti–6Al–4V alloy Part II: A strain rate and temperature dependent anisotropic yield criterion, International Journal of Plasticity 38: 14-26.
[4] Boresi A., Schmidt R., Sidebottom O., 1993, Advanced Strength of Materials,Wiley, New York.
[5] Banabic D., 2010, Sheet Metal Forming Processes: Constitutive Modelling and Numerical Simulation, Springer Science & Business Media.
[6] Lin Y., Chen X. M., 2011, A critical review of experimental results and constitutive descriptions for metals and alloys in hot working, Materials & Design 32(4): 1733-1759.
[7] Boresi A., Schmidt R., Sidebottom O., 1993, Advanced Mechanics of Materials, NewYork, John Wiley & Sons.
[8] Jacob L., 1990, Plasticity Theory, New York, Macmillan Publishing Company.
[9] Banabic D., 2010, A review on recent developments of Marciniak-Kuczynski model, Computer Methods in Materials Science 10(4): 1-13.
[10] Barlat F., Banabic D., Cazacu O., 2002, Anisotropy in sheet metals, International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes, Jeju Island, Korea.
[11] Fields D., Backofen W., 1957, Determination of strain hardening characteristics by torsion testing, Proceeding of American Society for Testing and Materials 57: 1259-1272.
[12] Zhang X., 2003, Experimental and Numerical Study of Magnesium Alloy During Hot-Working Process, PhD Thesis, Shanghai Jiaotong University.
[13] Cheng Y.Q., 2008, Flow stress equation of AZ31 magnesium alloy sheet during warm tensile deformation, Journal of Materials Processing Technology 208(1): 29-34.
[14] Farhadzadeh F., Tajdari M., Salmani Tehrani M., 2017, Determination of material constants of Khan- Huang- Liang constitutive criterion by genetic and particle swarm algorithms for Ti-6Al-4V alloy, International Offshore Industries Conferences, Sharif-University of Technology: Tehran, Iran.
[15] Deng N., Kuwabara T., Korkolis Y., 2015, Cruciform specimen design and verification for constitutive identification of anisotropic sheets, Experimental Mechanics 55(6): 1005-1022.
[16] Khan A.S., Huang S., 1995, Continuum Theory of Plasticity, John Wiley & Sons.
[17] Barsoum I., 2008, The Effect of Stress State in Ductile Failure, PhD Thesis was carried out at the Department of Solid Mechanics at the Royal Institute of Technology (KTH) , Stockholm, Sweden.
[18] Altenbach H., Öchsner A., 2014, Plasticity of Pressure-Sensitive Materials, Springer.
[19] Liang R., Khan A.S., 1999, A critical review of experimental results and constitutive models for BCC and FCC metals over a wide range of strain rates and temperatures, International Journal of Plasticity 15(9): 963-980.
[20] Khan A.S., Suh Y.S., Kazmi R., 2004, Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys, International Journal of Plasticity 20(12): 2233-2248.
[21] Khan A.S., Kazmi R., Farrokh B., 2007, Multiaxial and non-proportional loading responses, anisotropy and modeling of Ti–6Al–4V titanium alloy over wide ranges of strain rates and temperatures, International Journal of Plasticity 23(6): 931-950.
[22] Khan A.S., Liang R., 1999, Behaviors of three BCC metal over a wide range of strain rates and temperatures: experiments and modeling, International Journal of Plasticity 15(10): 1089-1109.
[23] Farrokh B., Khan A.S., 2009, Grain size, strain rate, and temperature dependence of flow stress in ultra-fine grained and nanocrystalline Cu and Al: synthesis, experiment, and constitutive modeling, International Journal of Plasticity 25(5): 715-732.
[24] Holland J.H., Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, MIT Press Cambridge, USA.
[25] Goldberg D.E., 1989, Genetic Algorithm in Search, Optimization and Machine Learning, Addison-Wesley Longman Publishing , Boston, USA.
[26] Janikow C.Z., Michalewicz Z., 1991, An experimental comparison of binary and floating point representations in genetic algorithms, ICGA 1991: 31-36.
[27] Geiger M., Hußnätter W., Merklein M., 2005, Specimen for a novel concept of the biaxial tension test, Journal of Materials Processing Technology 167(2): 177-183.
[28] Hannon A., Tiernan P., 2008, A review of planar biaxial tensile test systems for sheet metal, Journal of Materials Processing Technology 198(1): 1-13.