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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 863Thermal Elastic Constitutive Equation of...

Thermal Elastic Constitutive Equation of Orthotropic Materials

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Abstract:

In the finite deformation range, the numbers of orthotropic 2n order elastic constants are studied on the basis of tensor function and of its representation theorem. On the basis of elastic constant research, the elastic orthotropic constitutive equation is derived by using the tensor method. Based on orthotropic elastic constitutive equations an in-depth study on the constitutive theory of orthotropic nonlinear thermal elasticity is carried out, and by considering the deformation produced by the coupling of temperature and load, nonlinear orthotropic thermoelastic constitutive equation is further derived with representation of the tensor invariant and scalar invariant. The constitutive equations could be used very convenient to the application in reality.

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Periodical:

Applied Mechanics and Materials (Volume 863)

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93-101

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.863.93

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Online since:

February 2017

Authors:

Chen Li*, Hai Ren Wang, Yan An Miao, Li Zhao

Keywords:

Constitutive Equations, Elastic Constants, Orthotropic, Thermal Elastic

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© 2017 Trans Tech Publications Ltd. All Rights Reserved

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[1] S. Tourchi, A. Hamidi, Thermo-mechanical constitutive modeling of unsaturated clays based on the critical state concepts, J. Rock Mech. Geotech. Eng. 7(2) (2015) 193-198.

DOI: 10.1016/j.jrmge.2015.02.004

[2] J. Mehdi, Z. N. Mohammad, G. Mehdi, Thermo-elastic analysis of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness undermechanical loading, Int. J. Eng. Sci. 96 (2015) 1-18.

DOI: 10.1016/j.ijengsci.2015.07.005

[3] S. Stefan, Z. Marco, C. A. Jan, S. Paul, Thermo-elastic deformations of the workpiece when dry turning aluminum alloys - A finite element model to predict thermal effects in the workpiece, CIRP J. Manuf. Sci. Technol. 7(3) (2014) 233-245.

DOI: 10.1016/j.cirpj.2014.04.006

[4] J. W. Kim, S. Y. Im, H. G. Kim, Numerical implementation of athermo-elastic–plastic constitutive equation in consideration of transformationplasticity in welding, Int. J. Plastic. 21(7) (2015) 1383-1408.

DOI: 10.1016/j.ijplas.2004.06.007

[5] A. R. Safari, M. R. Forouzan, M. Shamanian, Thermo-viscoplastic constitutive equation of austenitic stainless steel 310s, Comput. Mater. Sci. 68 (2013) 402-407.

DOI: 10.1016/j.commatsci.2012.10.039

[6] Z. George, Voyiadjisa, F. Danial, Microstructure to Macro-Scale Using Gradient Plasticity with Temperature and Rate Dependent Length Scale, Procedia IUTAM. 3 (2012) 205-227.

DOI: 10.1016/j.piutam.2012.03.014

[7] L. Anand, O. Aslan, S. A. Chester, A large-deformation gradient theory for elastic–plastic materials: Strain softening and regularization of shear bands, Int. J. Plastic. 30-31 (2012) 116-143.

DOI: 10.1016/j.ijplas.2011.10.002

[8] A. Goel, M. Sherafati, A. Negahban, Azizinamini, Y. Wang, A thermo-mechanical large deformation constitutive model for polymers based on material network description: Application to a semi-crystalline polyamide 66, Int. J. Plastic. 67 (2015).

DOI: 10.1016/j.ijplas.2014.10.004

[9] A. Maurel-Pantel, E. Baquet, J. Bikard, J. L. Bouvard, N. Billon, A thermo-mechanical large deformation constitutive model for polymers based on material network description: Application to a semi-crystalline polyamide 66, Int. J. Plastic. 67 (2015).

DOI: 10.1016/j.ijplas.2014.10.004

[10] J. L. Chaboche, G. Cailletaudb, Integration methods for complex plastic constitutive equations, Comput. Methods Appl. Mech. Eng. 133(1-2) (1996) 125-155.

DOI: 10.1016/0045-7825(95)00957-4

[11] X. Tian, Y. Zhang, Mathematical description for flow curves of some stable austenitic steels, Mater. Sci. Eng. A. 174(1) (1994) L1–L3.

DOI: 10.1016/0921-5093(94)91120-7

[12] C. Li, Hyperelastic Material Nonlinear Constitutive Theory, National Def. Ind. Pre, Beijing, (2012).

[13] C. Li, G. T. Yang, Z. Z. Huang, On Constitutive Equations of Isotropic Non-linear Elastic Medium, Eng. Mech. 27 (2010) 1-5.

[14] C. Li, G. T. Yang, Z. Z. Huang, Nonlinear Constitutive Equations and Potential Function of Transversely Isotropy Elastic Materials, Chin. Quarterly Mech. 30 (2009) 517-522.

[15] C. Li, G. T. Yang, Nonlinear Constitutive Equations and Potential Function of Orthogonal Aeolotropy Elastic Materials, Chin. Quarterly Mech. 30 (2009) 169-175.

[16] W. Yang, W. B. Lee, Mesoplasticity and Its Applications, Springer-Verlag, Berlin, (1993).

[17] Q. H. Tang, Z. P. Duan, Plastic meso mechanics, Science Press, Beijing, (1995).

[18] S. H. Chen, Q. H. Tang, Micro-scale Plasticity Mechanics, University of Science & Technology China press, Hefei, (2009).

[19] G. I. Taylor, Plastic strain in metals, J. Inst. Met. 62 (1938) 307-324.

[20] R. Hill, Continuum micro-mechanics of elastoplastic polycrystals, J. Mech. Phys. Solids. 13(2) (1965) 89-101.

DOI: 10.1016/0022-5096(65)90023-2

[21] F. Roters, P. Eisenlohr, L. Hantcherli, et al, Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia. 58(4) (2010).

DOI: 10.1016/j.actamat.2009.10.058

[22] Q. W. Wang, X. G. Yang, H. Y. QI, D. Q. Shi, Crystal lographic Constitutive Models for Single Crystal Nickel Base Superalloys, Failire Anal. Prevent. 3 (2008) 28-34.

[23] L. Anand, O. Aslan, S. A. Chester, A large-deformation gradient theory for elastic–plastic materials: Strain softening and regularization of shear bands, Int. J. Plastic. 30-31 (2012) 116-143.

DOI: 10.1016/j.ijplas.2011.10.002

[24] Z. George, Voyiadjisa, F. Danial, Microstructure to Macro-Scale Using Gradient Plasticity with Temperature and Rate Dependent Length Scale, Procedia IUTAM. 3 (2012) 205-227.

DOI: 10.1016/j.piutam.2012.03.014

[25] C. Chen, Q. H. Tang, T. C. Wang, A new thermo-elasto-plasticity constitutive theory for polycrystalline metals, Acta Mechanica Sinica. 31(3) (2015) 338-348.

DOI: 10.1007/s10409-015-0462-1

[26] A. Goel, M. Sherafati, A. Negahban, A. Azizinamini, Y. N. Wang, A thermo-mechanical large deformation constitutive model for polymers based on material network description: Application to a semi-crystalline polyamide 66, Int. J. Plastic. 67 (2015).

DOI: 10.1016/j.ijplas.2014.10.004

[27] Z. Li, L. Chen, Thermal Stress Constitutive Equations of Non-Linear Isotropic Elastic Material, Appl. Math. Mech. 34 (2013) 183-189.

[28] Z. X. Wang, X. F. Liu, J. X Xie, Constitutive Relationship of Hot Deformation of AZ91 Magnesium Alloy, Acta Metallurgica Sinica. 44(11) (2008) 1378-1383.

[29] Y. Liu, Y. Tao, J. Jia, Characteristics of Flow Curves and Constitutive Equation of Nickel-Based P /M Superalloy FGH98, J. Aeronautic. Mater. 31(6) (2011) 12-18.

[30] W. G. Zhao, X. Li, S. Q. Lu, etc, Study on constitutive relationship of TC11 titanium alloy during high temperature deformation, J. Plastic. Eng. 15 (2008) 123-127.

[31] M. O. Alniak, F. Bedir, Change in graid size and flow strength in P/M Rene 95 under isothermal forging conditions, Mater. Sci. Eng. (B). 130(1-3) (2006) 254-263.

DOI: 10.1016/j.mseb.2006.03.011

[32] A. Thomasa, M. El-Wahabi, J. M. Cabrera, J. M. Prado, High temperature deformation of Inconel 718, J. Mater. Process. Technol. 177(1-3) (2006) 469-472.

DOI: 10.1016/j.jmatprotec.2006.04.072

[33] J. Lubliner, F. Auricchio, Generalized plasticity and shape-memory alloys, Int. J. Solids Struct. 33(7) (1996) 991-1003.

DOI: 10.1016/0020-7683(95)00082-8

[34] G. T. Houlsby, A. M. Puzrin, A thermomechanical frame work for constitutive models for rate-independent dissipative materials, Int. J. Plastic. 16(9) (2000) 1017-1047.

DOI: 10.1016/s0749-6419(99)00073-x

[35] X. X. Zhang, B. Z. Zhou, Elastic constitutive relation analysis of orthotropic materials, Aeroengine. 1 (1997) 20-25.

[36] C. Li, G. T. Yang, Nonlinear constitutive equation and potential function of orthogonal aeolotropy elastic materials, Chin. Quarterly Mech. 30 (2009) 169-175.

[37] Y. X. Han, 3-D elasto-plastic analysis of orthogonal anisotropic materials, ACTA Aeronautica ET Astronautica Sinica. 7(3) (1986) 225-233.

[38] C. C. Wang, A new representation theorem for isotropic functions, Part I and II, Archive for Rational Mech. Anal. 36 (1970) 166-223.

DOI: 10.1007/bf00272241

[39] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(4) (2010).

DOI: 10.1016/j.actamat.2009.10.058

[40] Q. S. Zheng, Theory of representations for tensor functions: a unified invariant approach to constitutive equations, Appl. Mech. Rev. 26 (1996) 114-137.

[41] Z. H. Guo, Tensor (Theroy and Application), Science Press, Beijing, (1988).

[42] D. J. Macon, R. J. Farris, A New Analytical and Experimental Approach To Rubber Thermodynamics, Macromolecules. 32(15) (1999) 5004-5016.

DOI: 10.1021/ma9806763