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Mixture model for thermo-chemo-mechanical processes in fluid-infused solids. (English) Zbl 07517075

Summary: This work presents a new thermodynamically consistent model for thermo-chemo-mechanical processes in open systems comprised of nonlinear elastic solids that are infused with reactive fluids and are undergoing large local strains. The interactions between different constituents of the material system are captured through locally homogenized mixture theory. The development of the formulation starts from constituent-wise balance equations for mass, momentum, and energy. The constitutive relations are derived to enforce non-negative entropy production and satisfy the second law of thermodynamics for the open system. The deformation due to thermal and chemical effects is carried out through a multiplicative split of the deformation gradient. Further assumptions on the fluid and solid material responses are introduced to specialize the model to a class of thermo-chemo-mechanical processes that arise in thermal oxidation of metallic and ceramic materials, lithiation of battery anodes, and other related problems. The model is implemented in the standard Galerkin finite element method using eight node hexahedral elements. A set of test cases involving fully coupled thermo-mechanical, chemo-mechanical, and thermo-chemical effects are analyzed. Numerical results obtained are in reasonable agreement with the experimental data for thermo-chemo-mechanical problems concerning the thermal oxidation of silicon carbide and FeCrAlY bond coat material in thermal barrier coatings.

MSC:

74-XX Mechanics of deformable solids
80-XX Classical thermodynamics, heat transfer
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[1] Al-Athel, K.; Loeffel, K.; Liu, H.; Anand, L., Modeling decohesion of a top-coat from a thermally-growing oxide in a thermal barrier coating, Surfing Coatings Technolology, 222, 68-78 (2013)
[2] Anguiano, M.; Masud, A., Reduced mixture model and elastic response of chemically swollen solids: application to Si oxidation and lithiation, Applied Engineering Science, 6, Article 100039 pp. (2021)
[3] Anguiano, M.; Gajendran, H.; Hall, R. B.; Masud, A., Coupled Anisothermal Chemomechanical Degradation Solutions in One Dimension, Challenges Mech. Time Depend. Mater. Vol. 2, 5-9 (2018), Springer International Publishing, Cham, A. Arzoumanidis, M. Silberstein, A. Amirkhizi (Eds.)
[4] Anguiano, M.; Gajendran, H.; Hall, R. B.; Rajagopal, K. R.; Masud, A., Chemo-mechanical coupling and material evolution in finitely deforming solids with advancing fronts of reactive fluids, Acta Mech, 231, 1933-1961 (2020) · Zbl 1440.74118
[5] Aronovici, M.; Bianchi, G.; Ferrari, L.; Barbato, M.; Gianella, S.; Scocchi, G.; Ortona, A., Heat and mass transfer in ceramic lattices during high-temperature oxidation, Journal of the American Ceramic Society, 98, 2625-2633 (2015)
[6] Atkin, R. J.; Craine, R. E., Continuum theories of mixtures: basic theory and historical development, Quarterly Journal of Mechanics and Applied Mathematics, 29, 209-244 (1976) · Zbl 0339.76003
[7] Atkin, R. J.; Craine, R. E., Continuum Theories of Mixtures: Applications, IMA Journal of Applied Mathematics, 17, 153-207 (1976) · Zbl 0355.76004
[8] Ayub, M.; Masud, A., A new stabilized formulation for convective-diffusive heat transfer, Numerical Heat Transfer Part B Fundamental, 44, 1-23 (2003)
[9] Bulíček, M.; Málek, J.; Průša, V., Thermodynamics and stability of non-equilibrium steady states in open systems, Entropy, 21 (2019)
[10] Bishop, S. R., Chemical expansion of solid oxide fuel cell materials: a brief overview, Acta Mechanica Sinica, 29, 312-317 (2013)
[11] Bowen, R. M., Incompressible porous media models by use of the theory of mixtures, International Journal of Engineering Science, 18, 1129-1148 (1980) · Zbl 0446.73005
[12] Bowen, R. M., Compressible porous media models by use of the theory of mixtures, International Journal of Engineering Science, 20, 697-735 (1982) · Zbl 0484.76102
[13] Chester, S. A.; Anand, L., A thermo-mechanically coupled theory for fluid permeation in elastomeric materials: Application to thermally responsive gels, Journal of Mechanics and Physics Solids., 59, 1978-2006 (2011) · Zbl 1270.74057
[14] Chester, S. A.; Di Leo, C. V.; Anand, L., A finite element implementation of a coupled diffusion-deformation theory for elastomeric gels, International Journal of Solids and Structures, 52, 1-18 (2015)
[15] Davis, A. W.; Evans, A. G., Some effects of imperfection geometry on the cyclic distortion of thermally grown oxides, Oxidation of Metals, 65, 1-14 (2006)
[16] Fasano, A.; Kannan, K.; Mancini, A.; Rajagopal, K. R., Modelling Ziegler-Natta Polymerization in High Pressure Reactors, Mater. Substruct. Complex Bodies, 206-237 (2007), Elsevier Science Ltd: Elsevier Science Ltd Oxford, in: G. Capriz, P.M. Mariano (Eds.)
[17] Faghihi, D.; Feng, X.; Lima, E. A.B. F.; Oden, J. T.; Yankeelov, T. E., A coupled mass transport and deformation theory of multi-constituent tumor growth, Journal of Mechanics and Physics Solids., 139, Article 103936 pp. (2020) · Zbl 1477.74032
[18] Freidin, A. B.; Vilchevskaya, E. N.; Korolev, I. K., Stress-assist chemical reactions front propagation in deformable solids, International Journal of Engineering Science, 83, 57-75 (2014) · Zbl 1423.74328
[19] Gajendran, H.; Hall, R. B.; Masud, A., Edge stabilization and consistent tying of constituents at Neumann boundaries in multi-constituent mixture models, International Journal for Numerical Methods in Engineering, 110, 1142-1172 (2017)
[20] Gajendran, H.; Hall, R. B.; Masud, A.; Rajagopal, K. R., Chemo-mechanical coupling in curing and material-interphase evolution in multi-constituent materials, Acta Mechanics, 229, 3393-3414 (2018) · Zbl 1396.74053
[21] Gonzalez, J.; Sun, K.; Huang, M.; Lambros, J.; Dillon, S.; Chasiotis, I., Three dimensional studies of particle failure in silicon based composite electrodes for lithium ion batteries, Jounal of Power Sources., 269, 334-343 (2014)
[22] Goto, D.; Hijikata, Y., Unified theory of silicon carbide oxidation based on the Si and C emission model, Journal of Physics D. Applied Physics, 49, Article 225103 pp. (2016)
[23] Goto, D.; Hijikata, Y.; Yagi, S.; Yaguchi, H., Differences in SiC thermal oxidation process between crystalline surface orientations observed by in-situ spectroscopic ellipsometry, Journal of Applied Physics, 117, 0-6 (2015)
[24] Haberman, B. A.; Young, J. B., Three-dimensional simulation of chemically reacting gas flows in the porous support structure of an integrated-planar solid oxide fuel cell, International Journal of Heat Mass Transfer, 47, 3617-3629 (2004) · Zbl 1079.76678
[25] Hall, R.; Gajendran, H.; Masud, A., Diffusion of chemically reacting fluids through nonlinear elastic solids: mixture model and stabilized methods, Mathematics Mechanics Solids., 20, 204-227 (2015) · Zbl 07278987
[26] Hall, R.; Rajagopal, K., Diffusion of a fluid through an anisotropically chemically reacting thermoelastic body within the context of mixture theory, Mathematics and Mechanics Solids., 17, 131-164 (2012) · Zbl 1291.76305
[27] Hall, R. B., A mixture-compatible theory of chemothermal deposition and expansion in n -constituent finitely deforming composite materials with initially circularly cylindrical microstructures, Mathematics and Mechanics Solids., 20, 228-248 (2015) · Zbl 07278988
[28] Hay, R. S., Growth stress in SiO 2 during oxidation of SiC fibers, Journal of Applied Physics, 111, Article 063527 pp. (2012)
[29] Humphrey, J. D.; Rajagopal, K. R., A constrained mixture model for growth and remodeling of soft tissues, Mathematics Modeling Methods Applied Science, 12, 407-430 (2002) · Zbl 1021.74026
[30] Hughes, T. J.R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (2000), Dover Publications: Dover Publications Mineola, NY · Zbl 1191.74002
[31] Jiang, T.; Rudraraju, S.; Roy, A.; Van Der Ven, A.; Garikipati, K.; Falk, M. L., Multiphysics Simulations of Lithiation-Induced Stress in Li1+xTi2O4Electrode Particles, Journal of Physics and Chemistry C., 120, 27871-27881 (2016)
[32] Kannan, K.; Rajagopal, K. R., A thermodynamical framework for chemically reacting systems, Zeitschrift Für Angew. Mathematics Under Physics, 62, 331-363 (2011) · Zbl 1273.74098
[33] Kageshima, H.; Uematsu, M.; Shiraishi, K., Theory of thermal Si oxide growth rate taking into account interfacial Si emission effects, Microelectronic Engineering, 59, 301-309 (2001)
[34] Kao, Dah-Bin; McVittie, J. P.; Nix, W. D.; Saraswat, K. C., Two-dimensional silicon oxidation experiments and theory, 1985 International Electronic Devices Meetings, IRE, 388-391 (1985)
[35] Kajihara, K.; Kamioka, H.; Hirano, M.; Miura, T.; Skuja, L.; Hosono, H., Interstitial oxygen molecules in amorphous SiO 2. III. Measurements of dissolution kinetics, diffusion coefficient, and solubility by infrared photoluminescence, Journal of Applied Physics, 98, Article 013529 pp. (2005)
[36] Kouda, K.; Hijikata, Y.; Yagi, S.; Yaguchi, H.; Yoshida, S., Oxygen partial pressure dependence of the SiC oxidation process studied by in-situ spectroscopic ellipsometry, Journal of Applied Physics, 112 (2012)
[37] Konica, S.; Sain, T., A thermodynamically consistent chemo-mechanically coupled large deformation model for polymer oxidation, Journal of Mechanics and Physics Solids., 137, Article 103858 pp. (2020)
[38] Lofaj, F.; Kaganovskii, Y. S., Kinetics of WC-Co oxidation accompanied by swelling, Journal of Materials Science, 30, 1811-1817 (1995)
[39] Jacobson, N. S., Corrosion of Silicon-based ceramics in combustion environments, Journal of the American Ceramic Society, 76, 3-28 (1993)
[40] Loeffel, K.; Anand, L.; Gasem, Z. M., On modeling the oxidation of high-temperature alloys, Acta Materialia, 61, 399-424 (2013)
[41] Loeffel, K.; Anand, L., A chemo-thermo-mechanically coupled theory for elastic-viscoplastic deformation, diffusion, and volumetric swelling due to a chemical reaction, International Journal of Plasticity, 27, 1409-1431 (2011) · Zbl 1426.74137
[42] Masud, A.; Truster, T. J., A framework for residual-based stabilization of incompressible finite elasticity: Stabilized formulations and F bar methods for linear triangles and tetrahedra, Computing Methods Applied Mechanics Engineering, 267, 359-399 (2013) · Zbl 1286.74018
[43] Merzouki, T.; Blond, E.; Schmitt, N.; Bouchetou, M.-L.; Cutard, T.; Gasser, A., Modelling of the swelling induced by oxidation in SiC-based refractory castables, Mechanics of Materials, 68, 253-266 (2014)
[44] Mohankumar, K. V.; Průša, V.; Kannan, K.; Wineman, A. S., Remarks on continuum theory of mixtures: editorial to special issue on mixture theory, International Journal of Advanced Engineering Science Applied Mathematics, 9, 120-134 (2017) · Zbl 1381.74065
[45] Padture, N. P., Advanced structural ceramics in aerospace propulsion, Nature Materials, 15, 804-809 (2016)
[46] Prasad, S. C.; Rajagopal, K. R., On the diffusion of fluids through solids undergoing large deformations, Mathematics Mechanics Solids., 11, 291-305 (2006) · Zbl 1143.74026
[47] Rajagopal, K. R.; Tao, L., Mechanics of Mixtures, Series on Advances in Mathematics for Applied Sciences, World Scientific, 35 (1995) · Zbl 0941.74500
[48] Rajagopal, K. R.; Srinivasa, A. R., On the thermomechanics of materials that have multiple natural configurations Part I: viscoelasticity and classical plasticity, Zeitschrift Für Angew. Math. Und Phys. ZAMP., 55, 861-893 (2004) · Zbl 1180.74006
[49] Rajagopal, K. R.; Srinivasa, A. R., A Gibbs-potential-based formulation for obtaining the response functions for a class of viscoelastic materials, Proceedings of Royal Society A Mathematics Physics Engineering Science, 467, 39-58 (2011) · Zbl 1219.74004
[50] Snead, L. L.; Nozawa, T.; Katoh, Y.; Byun, T. S.; Kondo, S.; Petti, D. A., Handbook of SiC properties for fuel performance modeling, Journal of Nuclear Materials, 371, 329-377 (2007)
[51] Smialek, J.; Jacobson, N. S., Oxidation of high-temperature aerospace materials, high temp, Matererial of Mechanics, 95-162 (2014)
[52] Souček, O.; Heida, M.; Málek, J., On a thermodynamic framework for developing boundary conditions for Korteweg-type fluids, International Journal of Engineering Science, 154, Article 103316 pp. (2020) · Zbl 07228661
[53] She, X.; Huang, A. Q.; Lucía, Ó.; Ozpineci, B., Review of Silicon Carbide power devices and their applications, Ieee Transactions on Industrial Electronics, 64, 8193-8205 (2017)
[54] Song, Y.; Dhar, S.; Feldman, L. C.; Chung, G.; Williams, J. R., Modified Deal Grove model for the thermal oxidation of silicon carbide, Journal of Applied Physics, 95, 4953-4957 (2004)
[55] Shoaib, T.; Carmichael, A.; Corman, R. E.; Shen, Y.; Nguyen, T. H.; Ewoldt, R. H.; Espinosa-Marzal, R. M., Self-adaptive hydrogels to mineralization, Soft Matter, 13, 5469-5480 (2017)
[56] Souček, O.; Orava, V.; Málek, J.; Bothe, D., A continuum model of heterogeneous catalysis: thermodynamic framework for multicomponent bulk and surface phenomena coupled by sorption, International Journal of Engineering Science, 138, 82-117 (2019) · Zbl 1425.74186
[57] Tandon, G. P.; Pochiraju, K. V.; Schoeppner, G. A., Modeling of oxidative development in PMR-15 resin, Polymer Degradation and Stability, 91, 1861-1869 (2006)
[58] Truesdell, C., Rational Thermodynamics, Second (1984), Springer New York, New York, NY · Zbl 0598.73002
[59] Truesdell, C.; Noll, W., The Non-Linear Field Theories of Mechanics, Third (2004), Springer Berlin Heidelberg, Berlin, Heidelberg · Zbl 0779.73004
[60] Truster, T. J.; Masud, A., A unified mixture formulation for density and volumetric growth of multi-constituent solids in tissue engineering, Computing Methods Applied Mechanics Engineering, 314, 222-268 (2017) · Zbl 1439.74094
[61] Tao, L.; Rajagopal, K. R.; Wineman, A. S., Unsteady diffusion of fluids through solids undergoing large deformations, Mathematics Modeling Methods Applied Science, 01, 311-346 (1991) · Zbl 0738.76069
[62] Wilson, M.; Opila, E., A review of SiC fiber oxidation with a new study of Hi-Nicalon SiC fiber oxidation, Advanced Engineering Materials, 18, 1698-1709 (2016)
[63] Yang, H.; Fan, F.; Liang, W.; Guo, X.; Zhu, T.; Zhang, S., A chemo-mechanical model of lithiation in silicon, Journal of Mechanics and Physics Solids., 70, 349-361 (2014)
[64] Yuan, P.; McCracken, J. M.; Gross, D. E.; Braun, P. V.; Moore, J. S.; Nuzzo, R. G., A programmable soft chemo-mechanical actuator exploiting a catalyzed photochemical water-oxidation reaction, Soft Matter, 13, 7312-7317 (2017)
[65] Zhang, S., Chemomechanical modeling of lithiation-induced failure in high-volume-change electrode materials for lithium ion batteries, NPJ Computing Materials, 3, 1-10 (2017)
[66] Zhang, X.; Zhong, Z., A coupled theory for chemically active and deformable solids with mass diffusion and heat conduction, Journal of Mechanics and Physics Solids., 107, 49-75 (2017)
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