Theoretical model for analysis of elastic constants in orthotropic materials considering shear stress
DOI:
https://doi.org/10.31349/RevMexFis.70.061004Keywords:
elastic constants, Young modulus, Poisson's ratio, Shear modulusAbstract
Nowadays, a general theoretical model to describe the mechanical behavior of anisotropic or orthotropic materials is still an open challenge. In this study, we propose a new theoretical model to determine the elastic constants of these materials considering the shear components of the stress tensor.
To analyze the consistency of new approach in biaxial stress state on thin films, we used data reported in the literature, based in the $\sin^2 \psi$ technique. For the first time, the shear modulus value equal to $G_{xz} = 0.3 GPa$, for a polycrystalline Au thin film, was calculated, in addition to other elastic constants. Finally, we demonstrate that the new proposal theoretical model considering shear stress can be useful to determine elastic constants in orthotropic materials from experimentally measured data.
References
E. M. Santos et al., Model for Analysis of Biaxial and Triaxial Stresses by X-ray Diffraction Assuming Orthotropic, Jpn. J. Appl. Phys., 49 (2010) 056601, https://dx.doi.org/10.1143/JJAP.49.056601
J. Zaplotnik, J. Pisljar, M. Skarabot and M. Ravnik, Neural networks determination of material elastic constants and structures in nematic complex fluids, Sci Rep., 13 (2023) 6028, https://doi.org/10.1038/s41598-023-33134-x
H. Fukuda, A. Nagakubo and H. Ogi, Elastic constant of dielectric nano-thin films using three-layer resonance studied by picosecond ultrasonics, Jpn. J. Appl. Phys. 60 (2021) SDDA05, https://dx.doi.org/10.35848/1347-4065/abec5a
H. S. Cho, H. A. Kim, D. W. Seo and S. C. Jeoung, Poisson’s ratio measurement through engraving the grid pattern inside poly(dimethylsiloxane) by ultrafast laser Jpn. J. Appl. Phys. 60 (2021) 101004, https://dx.doi.org/10.35848/1347-4065/ac2424
I. Takahashi, N. Usami, K. Kutsukake, K. Morishita and K. Nakajima, Computational Investigation of Relationship between Shear Stress and Multicrystalline Structure in Silicon, Jpn. J. Appl. Phys. 49 (2010) 04DP01, https://dx.doi.org/10.1143/JJAP.49.04DP01
Y. Lou, L. Chen, T. Clausmeyer, A. E. Tekkaya and J. W. Yoon, Modeling of ductile fracture from shear to balanced biaxial tension for sheet metals, Int. J. Solids Struct. 112 (2017) 169-184, https://doi.org/10.1016/j.ijsolstr.2016.11.034
D. J. O’Shea, M. M. Attard and D. C. Kellermann, Int. J. Solids Struct. 129 (2019) 1-20, https://dx.doi.org/10.1016/j.ijsolstr.2018.07.013
H. Gang and H. G. Kwak, A strain rate dependent orthotropic concrete material model, Int. J. Impact Eng. 103 (2017) 211, https://dx.doi.org/10.1016/j.ijimpeng.2017.01.027
A. V. Melnik, X. Luo and R. W. Ogden, A parauniversal relation for orthotropic materials, Mech. Res. Commun. 97 (2019) 46, https://dx.doi.org/10.1016/j.mechrescom.2019.04.006
J. Zhou, J. Pan, L. Zhang, J. Zhao and Z. Li, Experimental study on mechanical behavior of high-strength high-performance concrete under biaxial loading, Constr. Build. Mater. 258 (2020) 119681, https://doi.org/10.1016/j.conbuildmat.2020.119681
N. Park, T. B. Stoughton and J. W. Yoon, A new approach for fracture prediction considering general anisotropy of metal sheets, Int. J. Plast. 124 (2020) 199-681, https://doi.org/10.1016/j.ijplas.2019.08.011
A. Mani, P. Aubert, F. Mercier, H. Khodja, C. Berthier and P. Houdy, Effects of residual stress on the mechanical and structural properties of TiC thin films grown by RF sputtering, Surf. Coat. Technol. 194 (2005) 190-195, https://doi.org/10.1016/j.surfcoat.2004.06.017
C. Minas and L. Salasoo, Three-dimensional thermal stresses in a superconducting coil assembly, IEEE Trans. Magn.27 (1991) 2381, https://doi.org/10.1109/20.133697
X. Zhang, A. Misra, H. Wang, A. L. Lima, M. F. Hundley and R. G. Hoagland, Effects of deposition parameters on residual stresses, hardness and electrical resistivity of nanoscale twinned 330 stainless steel thin films, J. Appl. Phys. 97 94302, https://doi.org/10.1063/1.1883724
P. S. Prevey and J. T. Cammett, The influence of surface enhancement by low plasticity burnishing on the corrosion fatigue performance of AA7075-T6 Int. J. Fatigue. 26 (2004) 975-982, https://doi.org/10.1016/j.ijfatigue.2004.01.010
E. C. Oliver, T. Mori, M. R. Daymond and P. J. Withers, Orientation dependence of martensite variants during loading of Fe-Pd shape memory alloy, Scripta Mater. 53 (2005) 609-612, https://doi.org/10.1016/j.scriptamat.2005.04.021
P. S. Prevey, M. J. Shepard and P. R. Smith, The Effect of Low Plasticity Burnishing (LPB) on the HCF Performance and FOD Resistance of Ti-6Al-4V, Proc. 6th National Turbine Engine HCF Conference (2011) March 5-8, Jacksonville, FL
Y. D. Wang, R. L. Peng, X. L. Wang and R. L. McGreevy, High anisotropy of orientation dependent residual stress in austenite of cold rolled stainless steel, Acta Mater. 41 (1999) 995-1000, https://doi.org/10.1016/S1359-6462(99)00248-1
M. E. Fitzpatrick and A. Lodini, Analysis of Residual Stress by Diffraction Using Neutron and Synchrotron Radiation, (Taylor & Francis, London) (1st ed.). CRC Press.(2003) p.78, https://doi.org/10.1201/9780203608999
H. R. Wenk and P. V. Houtte, Texture and anisotropy, Rep. Prog. Phys. 67 (2004) 1367-1428, https://doi.org/10.1088/0034-4885/67/8/r02
T. Roland, D. Retraint, K. Lu and J. Lu, Fatigue life improvement through surface nanostructuring of stainless steel by means of surface mechanical attrition treatment, Scrip. Mater. 54 (2006) 1949-1954, https://doi.org/10.1016/j.scriptamat.2006.01.049
B. M. Lempriere, Poisson’s ratio in orthotropic materials, AIAA J. 6 (1968) 2226-2227, https://doi.org/10.2514/3.4974
B. R. Lake, F. J. Appl and C. W. Bert 1970 An investigation of the hole-drilling technique for measuring planar residual stress in rectangularly orthotropic materials Exp. Mech. 10 (1970) 233-239, https://doi.org/10.1007/BF02324095
G. S. Schajer, Advances in Hole-Drilling Residual Stress Measurements, Exp. Mech. 50 (2010) 159-168, https://doi.org/10.1007/s11340-009-9228-7
B. M. Clemens and J. A. Bain, Stress Determination in Textured Thin Films Using X-Ray Diffraction MRS Bull. 17 (1992) 46-51, https://doi.org/10.1557/S0883769400041658
D. Faurie, D. O. Renault, E. L. Bourhis, P. Villain, Ph. Goudeau and F. Badawi, Measurement of thin film elastic constants by X-ray diffraction, Thin Solid Films 469-470 (2004) 201, https://doi.org/10.1016/j.tsf.2004.08.097
D. Faurie, D. O. Renault, E. L. Bourhis and Ph. Goudeau, Determination of elastic constants of a fiber-textured gold film by combining synchrotron x-ray diffraction and in situ tensile testing, J. Appl. Phys. 98 (2005) 093511, https://doi.org/10.1063/1.2126154
N. T. Mascia, Concerning the elastic orthotropic model applied to wood elastic properties Maderas: Cienc. Technol. 5 (2003) 3-11, https://doi.org/10.4067/S0718-221X2003000100001
D. Faurie and P. Djemia and E. Le Bourhis and P.- O. Renault and Y. Roussign and S.M. Chcrif and R. Brenner and O. Castelnau and G. Patriarche and Ph. Goudeau, Elastic anisotropy of polycrystalline Au films: Modeling and respective contributions of X-ray diffraction, nanoindentation and Brillouin light scattering, Acta Mater. 58 (2010) 4998-5008, https://doi.org/10.1016/j.actamat.2010.05.034
B. D. Annin and N. I.Ostrosablin, Anisotropy of elastic properties of materials, J. Appl. Mech. Tech. Phys. 49 (2008) 998-1914, https://doi.org/110.1007/s10808-008-0124-1
L. Bos et al., Classes of Anisotropic Media: A Tutorial, Stud. Geophys. Geod. 48 (2004) 265-287, https://doi.org/10.1023/B:SGEG.0000015596.68104.31
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Á. S. Alves, M. S. R. Miltão, E. S. Ferreira, J. A. Leyva Cruz
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
