Bounds of the effective elastic moduli of nanoparticle-reinforced composites based on composite sphere assemblage and interface stress model

Tang, Z.; Ye, W.

doi:10.24423/aom.4082

Powiadomienia systemowe

Sesja wygasła!
Sesja wygasła!

Artykuł - szczegóły

Tytuł artykułu

Bounds of the effective elastic moduli of nanoparticle-reinforced composites based on composite sphere assemblage and interface stress model

Autorzy

Tang Z. , Ye W.

Treść / Zawartość

Pełne teksty:

Pobierz

Identyfikatory

DOI

10.24423/aom.4082

Warianty tytułu

Języki publikacji

Abstrakty

Three different approaches are formulated to obtain the bounds of the effective elastic moduli of nanoparticle-reinforced composites based on the CSA and the interface stress model. It is found that the effective bulk modulus can be obtained by all three different approaches but the effective shear modulus can be obtained only by the energy approach. The bounds of the effective bulk modulus coincide and depend only on the interface bulk modulus, while those of the effective shear modulus are distinct and depend on two interface elastic constants. Furthermore, limit analysis discloses that the bounds of the effective bulk modulus of nanoparticles coincide but deviate from the bulk modulus of particle in the classical case, and the bounds of the effective shear modulus are distinct in contrast to the effective bulk modulus of nanoparticles or both effective moduli of conventional composites.

Słowa kluczowe

elastic moduli bulk modulus shear modulus composite sphere assemblage interface stress model

Wydawca

Instytut Podstawowych Problemów Techniki PAN

Czasopismo

Archives of Mechanics

Rocznik

2022

Tom

Vol. 74, nr 4

Strony

283--317

Opis fizyczny

Bibliogr. 52 poz., rys., wykr.

Twórcy

autor

Tang Z.

College of Aerospace Engineering, Chongqing University, Chongqing 400044, China
Chongqing Key Laboratory of Heterogeneous Material Mechanics, Chongqing University, Chongqing 400044, China

autor

Ye W.

wye@cqu.edu.cn

College of Aerospace Engineering, Chongqing University, Chongqing 400044, China

Bibliografia

1. J.D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proceedings of the Royal Society of London Series A – Mathematical and Physical Sciences, 241, 376–396, 1957.
2. R. Hill, A self-consistent mechanics of composite materials, Journal of the Mechanics and Physics of Solids, 13, 213–222, 1965.
3. T. Mori, K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica, 21, 571–574, 1973.
4. M. Hori, S. Nemat-Nasser, Double-inclusion model and overall moduli of multi-phase composites, Mechanics of Materials, 14, 189–206, 1993.
5. Z. Hashin, The Elastic Moduli of Heterogeneous Materials, Journal of Applied Mechanics, 29, 143–150, 1962.
6. Z. Hashin, B.W. Rosen, The elastic moduli of fiber-reinforced materials, Journal of Applied Mechanics, 31, 223–232, 1964.
7. Z. Hashin, S. Shtrikman, A variational approach to the theory of the elastic behaviour of multiphase materials, Journal of the Mechanics and Physics of Solids, 11, 127–140, 1963.
8. Z. Hashin, Analysis of composite materials - A survey, Journal of Applied Mechanics, 50, 481–505, 1983.
9. K.E. Aifantis, H. Askes, Gradient elasticity with interfaces as surfaces of discontinuity for the strain gradient, Journal of the Mechanical Behavior of Materials, 18, 283–306, 2007.
10. Y. Ban, C. Mi, On spherical nanoinhomogeneity embedded in a half-space analyzed with Steigmann–Ogden surface and interface models, International Journal of Solids and Structures, 216, 123–135, 2021.
11. Q.H. Fang, Y.W. Liu, B. Jin, P.H. Wen, Interaction between a dislocation and a coreshell nanowire with interface effects, International Journal of Solids and Structures, 46, 1539–1546, 2009.
12. H.M. Shodja, H. Ahmadzadeh-Bakhshayesh, M.Y. Gutkin, Size-dependent interaction of an edge dislocation with an elliptical nano-inhomogeneity incorporating interface effects, International Journal of Solids and Structures, 49, 759–770, 2012.
13. M. Wang, W. Ye, Size-dependent elastic field of nano-inhomogeneity: from interface effect to interphase effect, Archive of Applied Mechanics, 90, 2319–2333, 2020.
14. G. Chatzigeorgiou, F. Meraghni, A. Javili, Generalized interfacial energy and size effects in composites, Journal of the Mechanics and Physics of Solids, 106, 257–282, 2017. Bounds of the effective elastic moduli. . . 315
15. Z. Hashin, The spherical inclusion with imperfect interface, Journal of Applied Mechanics, 58, 444–449, 1991.
16. S. Firooz, G. Chatzigeorgiou, F. Meraghni, A. Javili, Homogenization accounting for size effects in particulate composites due to general interfaces, Mechanics of Materials, 139, 103204, 2019.
17. S. Firooz, G. Chatzigeorgiou, F. Meraghni, A. Javili, Bounds on size effects In composites via homogenization accounting for general interfaces, Continuum Mechanics and Thermodynamics, 32, 173–206, 2020.
18. R. Shuttleworth, The surface tension of solids, Proceedings of the Physical Society. Section A, 63, 444, 1950.
19. M.E. Gurtin, A.I. Murdoch, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis, 57, 291–323, 1975.
20. R.E. Miller, V.B. Shenoy, Size-dependent elastic properties of nanosized structural elements, Nanotechnology, 11, 139, 2000.
21. R. Dingreville, J. Qu, Interfacial excess energy, excess stress and excess strain In elastic solids: planar interfaces, Journal of the Mechanics and Physics of Solids, 56, 1944–1954, 2008.
22. R. Dingreville, J.M. Qu, M. Cherkaoui, Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films, Journal of the Mechanics and Physics of Solids, 53, 1827–1854, 2005.
23. S. Li, W. Yiming, H. Zhuping, W. Jianxiang, Interface effect on the effective bulk modulus of a particle-reinforced composite, Acta Mechanica Sinica, 20, 676–679, 2004.
24. T. Chen, G.J. Dvorak, C.C. Yu, Solids containing spherical nano-inclusions with interface stresses: effective properties and thermal–mechanical connections, International Journal of Solids and Structures, 44, 941–955, 2007.
25. G.W. Milton, S.K. Serkov, Neutral coated inclusions in conductivity and anti–plane elasticity, Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, 457, 1973–1997, 2001.
26. R.M. Christensen, K.H. Lo, Solutions for effective shear properties in three chase sphere and cylinder models, Journal of the Mechanics and Physics of Solids, 27, 315–330, 1979.
27. H.L. Duan, J. Wang, Z.P. Huang, B.L. Karihaloo, Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress, Journal of the Mechanics and Physics of Solids, 53, 1574–1596, 2005.
28. J. Wang, H.L. Duan, Z. Zhang, Z.P. Huang, An anti-interpenetration model and connections between interphase and interface models in particle-reinforced composites, International Journal of Mechanical Sciences, 47, 701–718, 2005.
29. H.L. Duan, J. Wang, Z.P. Huang, Z.Y. Luo, Stress concentration tensors of inhomogeneities with interface effects, Mechanics of Materials, 37, 723–736, 2005.
30. H. Duan, B. Karihaloo, Thermo-elastic properties of heterogeneous materials with imperfect interfaces: Generalized Levin’s formula and Hill’s connections, Journal of the Mechanics and Physics of Solids, 55, 1036–1052, 2007.
31. L.J. Walpole, A coated inclusion in an elastic medium, Mathematical Proceedings of the Cambridge Philosophical Society, 83, 495–506, 1978.
32. E. Herve, A. Zaoui, n-Layered inclusion-based micromechanical modelling, International Journal of Engineering Science, 31, 1–10, 1993.
33. E. Hervé-Luanco, Elastic behaviour of multiply coated fibre-reinforced composites: simplification of the (n+1)-phase model and extension to imperfect interfaces, International Journal of Solids and Structures, 196-197, 10–25, 2020.
34. E. Hervé-Luanco, Elastic behavior of composites containing multi-layer coated particles with imperfect interface bonding conditions and application to size effects and mismatch in these composites, International Journal of Solids and Structures, 51, 2865–2877, 2014.
35. D.-C. Pham, T.-K. Nguyen, B.-V. Tran, Macroscopic elastic moduli of sphericallysymmetric-inclusion composites and the microscopic stress-strain fields, International Journal of Solids and Structures, 169, 141–165, 2019.
36. D.C. Pham, T.K. Nguyen, The microscopic conduction fields in the multi-coated sphere composites under the imposed macroscopic gradient and flux fields, Zeitschrift für angewandte Mathematik und Physik, 70, 24, 2019.
37. D.C. Pham, Solutions for the conductivity of multi-coated spheres and spherically symmetric inclusion problems, Zeitschrift für angewandte Mathematik und Physik, 69, 13, 2018.
38. D.C. Pham, N. Phan-Thien, Bounds and extremal elastic moduli of isotropic quasisymmetric multicomponent materials, International Journal of Engineering Science, 36, 273–281, 1998.
39. D.-C. Pham, Bounds on the effective conductivity of statistically isotropic multicomponent materials and random cell polycrystals, Journal of the Mechanics and Physics of Solids, 59, 497–510, 2011.
40. D.C. Pham, L.D. Vu, V.L. Nguyen, Bounds on the ranges of the conductive and elastic properties of randomly inhomogeneous materials, Philosophical Magazine, 93, 2229–2249, 2013.
41. S. Firooz, P. Steinmann, A. Javili, Homogenization of composites with extended general interfaces: comprehensive review and unified modeling, Applied Mechanics Reviews, 73, 2021.
42. J.D. Eshelby, The Continuum Theory of Lattice Defects, in: F. Seitz, D. Turnbull (Eds.) Solid State Physics, Academic Press, pp. 79–144, 1956.
43. Y. Benveniste, T. Miloh, Imperfect soft and stiff interfaces in two-dimensional elasticity, Mechanics of Materials, 33, 309–323, 2001.
44. S. Biwa, N. Ito, N. Ohno, Elastic properties of rubber particles in toughened PMMA: ultrasonic and micromechanical evaluation, Mechanics of Materials, 33, 717–728, 2001.
45. Q. Xu, K.E. Jensen, R. Boltyanskiy, R. Sarfati, R.W. Style, E.R. Dufresne, Direct measurement of strain-dependent solid surface stress, Nature Communications, 8, 555, 2017.
46. Q. Xu, R.W. Style, E.R. Dufresne, Surface elastic constants of a soft solid, Soft Matter, 14, 916–920, 2018.
47. R. Dingreville, J. Qu, A semi-analytical method to compute surface elastic properties, Acta Materialia, 55, 141–147, 2007.
48. R. Dingreville, J. Qu, A semi-analytical method to estimate interface elastic properties, Computational Materials Science, 46, 83–91, 2009.
49. C. Mi, S. Jun, D.A. Kouris, S.Y. Kim, Atomistic calculations of interface elastic properties in noncoherent metallic bilayers, Physical Review B, 77, 075425, 2008.
50. V.B. Shenoy, Atomistic calculations of elastic properties of metallic fcc crystal surfaces, Physical Review B, 71, 094104–094111, 2005.
51. Z. Tang, Y. Chen, W. Ye, Calculation of surface properties of cubic and hexagonal crystals through molecular statics simulations, Crystals, 10, 2020.
52. W. Ye, B. Chen, Investigation of the surface elasticity of GaN by atomistic simulations and its application to the elastic relaxation of GaN nanoisland, Materials Letters, 141, 245–247, 2015.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-9aabf381-71b5-494d-b5f6-158c1d6dc167