A New Method Based on Interation Algorithm to Extract Parameters of Constitutive Equations

Abstract:

These methods that extract parameters of constitutive equations can be divided into three groups: direct search-based strategies, gradient-based methods and evolutionary algorithms. By analyzing these strategies, a new method based on iteration algorithm was proposed. To obtain parameters of JC and ZA model for Ti-6Al-4V, the error between prediction data and SHPB experiment data was set as objective function, then initial value was calculated using iteration algorithm. The effect of convergence rate and precision at various steps and experiment data was invested. The main advantage of the method are as follows：fast calculation; compatible with SHPB data and orthogonal cutting data; compatible with the decoupling and coupling constitutive equations. Finally, it has shown that the algorithm is stable, and acceptable results can be obtained.

• Periodical: Applied Mechanics and Materials (Volume 281)
• Pages: 505-510
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.281.505
• Online since: January 2013
• Authors: Yong Zhi Hua, Li Wen Guan, Xin Jun Liu, Yu Hui Zhang
• Keywords: Constitutive Equation, Iteration Algorithm, Parameter Extraction

References

[1] GORDON R J , WILLIAM H C. A constitutive model and data for metals subjected to large strains high strain rates and high temperatures[J]. Proceedings of the Seventh Intional Symposium on Ballistics , The hague, The Netherlands , 1983, April 19-21: 541~547.

[2] SHI J, LIU C R. The influence of material models on finite element simulation of machining[J]. Journal of Manufacturing Science and Engineering. 2004, 126 : 849~857.

DOI: 10.1115/1.1813473

[3] LIANG R, KHAN A S. A critical review of experimental results and constitutive models for BCC and FCC metals over a wide range of strain rates and temperatures [J]. International Journal of Plasticity. 1999, 15: 963~980.

DOI: 10.1016/s0749-6419(99)00021-2

[4] HOPKINSON B. A method of measuring the pressure produced in the deformation of high explosives or by the impact of bullets [J]. Phil. Trans. Roy. Soc. 1914, A213: 437~452.

[5] KOLSKY H. An Investigation of the Mechanical Properties of Materials at very High Rates of Loading. Proc. Phys. Soc, 1949, B 62: 676.

DOI: 10.1088/0370-1301/62/11/302

[6] TOUNSIA N, VINCENTI J, OTHO A, et al. From the basic mechanics of orthogonal metal cutting toward the identification of the constitutive equation [J]. International Journal of Machine Tools & Manufacture. 2002, 42: 1373–1383.

DOI: 10.1016/s0890-6955(02)00046-9

[7] GUO Y B. An integral method to determine the mechanical behavior of materials in metal cutting [J]. Journal of Materials Processing Technology, 2007, 142: 72–81.

DOI: 10.1016/s0924-0136(03)00462-x

[8] PUJANA J, ARRAZOLA P J, SAOUBI R M, et al. Analysis of the inverse identification of constitutive equations applied in orthogonal cutting process [J]. International Journal of Machine Tools & Manufacture. 2007, 47: 2153–2161.

DOI: 10.1016/j.ijmachtools.2007.04.012

[9] LEE W S, LIN C F. High-temperature deformation behavior of Ti6Al4V alloy evaluated by high strain-rate compression tests [J]. Journal of Materials Processing Technology. 1998, 75: 127–136.

DOI: 10.1016/s0924-0136(97)00302-6

[10] HUBERT W. MEYER J R. DAVID S, et al. modeling the high strain rate behavior of titanium undergoing ballistic impact and penetration [J]. International Journal of Impact Engineering. 2001, 26: 509-521.

DOI: 10.1016/s0734-743x(01)00107-5

[11] CHAPARRO B M, THUILLIER S, MENEZES L F, et al. Material parameters identification: Gradient-based, genetic and hybrid optimization algorithms [J]. Comp. Mater. Sci. 2008, 44: 339–346.

DOI: 10.1016/j.commatsci.2008.03.028

[12] SASSO M, NEWAZ G, AMODIO D. Material characterization at high strain rate by Hopkinson bar tests and finite element optimization [J]. , Mater. Sci. Eng. 2008, A 487: 289–300.

DOI: 10.1016/j.msea.2007.10.042

[13] OZEL T, ZEREN E. Determination of work material flow stress and friction for FEA of machining using orthogonal cutting tests [J]. Journal of Materials Processing Technology. 2004, 153: 1019–1025.

DOI: 10.1016/j.jmatprotec.2004.04.162

[14] SHATLA M, KERK C, ALTAN T. Process modeling in machining. Part I: determination of flow stress data [J]. International Journal of Machine Tools & Manufacture. 2001, 41: 1511–1534.

DOI: 10.1016/s0890-6955(01)00016-5

[15] UMBRELLO D. Finite element simulation of conventional and high speed machining of Ti6Al4V alloy [J]. Journal of Materials Processing Technology. (2007).

DOI: 10.1016/j.jmatprotec.2007.05.007