Shape and packing effects in particulate composites: micromechanical modelling and numerical verification

• Autorzy: Majewski Michał , Wichrowski Michał , Hołobut Paweł , Kowalczyk-Gajewska Katarzyna

Identyfikatory

DOI

10.1007/s43452-022-00405-9

• Języki publikacji: EN

Abstrakty

EN

The aim of this study is to analyse the joint effect of reinforcement shape and packing on the effective behaviour of particulate composites. The proposed semi-analytical modelling method combines the Replacement Mori-Tanaka scheme, by means of which the concentration tensors for non-ellipsoidal inhomogeneities are found numerically, and the analytical morphologically representative pattern approac to account for particle packing. Five shapes of inhomogeneities are selected for the analysis: a sphere, a prolate ellipsoid, a sphere with cavities, an oblate spheroid with a cavity as well as an in homogeneity created by three prolate spheroids crossing at right angles. Semi-analytical estimates are compared with the results of numerical simulations performed using the finite element method and with the outcomes of classical mean-field models based on the Eshelby solution, e.g. the Mori–Tanaka model or the self-consistent scheme.

Słowa kluczowe

EN

composite material; micromechanics; computational modelling; packing effect; shape effect

PL

materiały kompozytowe; mikromechanika; modelowanie obliczeniowe; efekt pakowania; efekt kształtu

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2022
• Tom: Vol. 22, no. 2
• Strony: art. no. e86, 1--22
• Opis fizyczny: Bibliogr. 46 poz., il., tab., wykr., wzory

Twórcy

autor

Majewski Michał

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

• https://orcid.org/0000-0001-9023-9194

autor

Wichrowski Michał

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland
• Interdisciplinary Center for Scientific Computing, Heidelberg University, Heidelberg, Germany

• https://orcid.org/0000-0002-3644-3917

autor

Hołobut Paweł

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

• https://orcid.org/0000-0001-9820-4340

autor

Kowalczyk-Gajewska Katarzyna

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

• https://orcid.org/0000-0002-7154-2507

Bibliografia

• 1. Olson G. Computational design of hierarchically structured materials. Science. 1997;277:1237-42. https://doi.org/10.1126/ science.277.5330.1237.
• 2. Matouš K, Geers MGD, Kouznetsova VG, Gillman A. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials. J Comput Phys. 2017;330:192-220.
• 3. Clyne TW, Hull D. An introduction to composite materials. 3rd ed. Cambridge: Cambridge University Press; 2019.
• 4. Rajak DK, Pagar DD, Kumar R, Pruncu CI. Recent progress of reinforcement materials: a comprehensive overview of composite materials. J Mater Res Technol. 2019;8:6354-74. https://doi.org/10.1016/j.jmrt.2019.09.068.
• 5. Christensen RM. A critical evaluation for a class of micromechanics models. J Mech Phys Solids. 1990;38:379-404.
• 6. Eshelby JD. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc A-Math Phy.1957;241:376-96. https://doi.org/10.1098/rspa.1957.0133.
• 7. Kanaun SK, Levin VM. Self-consistent methods for composites, vol 1: static problems. Dordrecht: Springer; 2008. p. 172-186.
• 8. Castaneda PP, Willis JR. The effect of spatial distribution on the effective behavior of composite materials and cracked media. J Mech Phys Solids. 1995;43:1919-1951. https://doi.org/10.1016/0022- 5096(95) 00058-Q.
• 9. Torquato S. Effective stiffness tensor of composite media: II. Applications to isotropic dispersions. J Mech Phys Solids. 1998;46:1411-40.
• 10. Marcadon V, Herve E, Zaoui A. Micromechanical modeling of packing and size effects in particulate composites. Int J Solids Struct. 2007;44:8213-28.
• 11. Majewski M, Kursa M, Holobut P, Kowalczyk-Gajewska K. Micromechanical and numerical analysis of packing and size effects in elastic particulate composites. Compos B Eng. 2017;124:158-174. https://doi.org/10.1016/j.compositesb.2017.05.004.
• 12. Diani J, Gilormini P, Merckel Y, Vion-Loisel F. Micromechanical modeling of the linear viscoelasticity of carbon-black filled styrene butadiene rubbers: the role of the filler-rubber interphase. Mech Mater. 2013;59:65-72.
• 13. Majewski M, Holobut P, Kursa M, Kowalczyk-Gajewska K. Packing and size effects in elastic-plastic particulate composites: micromechanical modelling and numerical verification. Int J Eng Sci. 2020;151:103271.
• 14. Chaboche JL, Kanouté P, Roos A. On the capabilities of mean field approaches for the description of plasticity in metal matrix composites. Int J Plast. 2005;21:1409-1434.
• 15. Sevostianov I, Mogilevskaya SG, Kushch VI. Maxwell’s methodology of estimating effective properties: alive and well. Int J Eng Sci. 2019;140:35-88. https:// doi.org/10.1016/j.ijeng sci.2019. 05.001.
• 16. Kowalczyk-Gajewska K, Majewski M, Mercier S, Molinari A. Mean field interaction model accounting for the spatial distribution of inclusions in elastic viscoplastic composites. Int J Solids Struct. 2021;224:111040.
• 17. Segurado J, Llorca J. Computational micromechanics of composites: the effect of particle spatial distribution. Mech Mater. 2006;38:873-883. https://doi.org/10. 016/j. mechmat.2005.06.026.
• 18. Dastgerdi JN, Anbarlooie B, Miettinen A, Hosseini-Toudeshky H, Remes H. Effects of particle clustering on the plastic deformation and damage initiation of particulate reinforced composite utilizing X-ray CT data and finite element modeling. Compos B Eng. 2018;153:57-69.
• 19. Escoda J, Willot F, Jeulin D, Sanahuja J, Toulemonde C. Influence of the multiscale distribution of particles on elastic properties of concrete. Int J Eng Sci. 2016;98:60-71.
• 20. de Francqueville F, Gilormini P, Diani J, Vandenbroucke A. Comparison of the finite strain macroscopic behavior and local damage of a soft matrix highly reinforced by spherical or polyhedral particles. Eur J Mech A Solids. 2020;84:104070.
• 21. Liu LP. Solutions to the Eshelby conjectures. Proc R Soc A-Math Phys. 2008;464:573-594. https://doi.org/10.1098/rspa. 2007.0219.
• 22. Klusemann B, Böhm HJ, Svendsen B. Homogenization methods for multi-phase elastic composites with non-elliptical reinforcements: comparisons and benchmarks. Eur J Mech A Solids. 2012;34:21-37.
• 23. Zheng QS, Du DX. An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution. J Mech Phys Solids. 2001;49:2765-2788.
• 24. Du DX, Zheng QS. A further exploration of the interaction direct derivative (IDD) estimate for the effective properties of multiphase composites taking into account inclusion distribution. Acta Mech. 2002;157:61-80.
• 25. Nogales S, Böhm HJ. Modeling of the thermal conductivity and thermomechanical behavior of diamond reinforced composites. Int J Eng Sci. 2008;46:606-19. https://doi.org/10.1016/j.ijeng sci.2008.01.011.
• 26. Kachanov M, Tsukrov I, Shafiro B. Effective moduli of solids with cavities of various shapes. Appl Mech Rev. 1994;47:151-174. https://doi org 10 1115/1 3122810.
• 27. Segurado J, Llorca J. A numerical approximation to the elastic properties of sphere-reinforced composites. J Mech Phys Solids. 2002;50:2107-21.
• 28. Hassani B, Hinton E. A review of homogenization and topology optimization I - homogenization theory for media with periodic structure. Comput Struct. 1998;69:707-717.
• 29. Ranganathan SI, Ostoja-Starzewski M. Scaling function, anisotropy and the size of RVE in elastic random polycrystals. J Mech Phys Solids. 2008;56:2773-91.
• 30. Hashin Z. The elastic moduli of heterogeneous materials. J Appl Mech. 1962;29:143-150. https://doi.org/10.1115/1.3636446.
• 31. Herve E, Zaoui A. n-Layered inclusion-based micromechanical modelling. Int J Eng Sci. 1993;31:1-10.
• 32. Hori M, Nemat-Nasser S. Double-inclusion model and overall moduli of multi-phase composites. Mech Mater. 1993;14:189-206.
• 33. Suquet P. Effective properties of nonlinear composites. In: Suquet P, editor. Continuum micromechanics. Vienna: Springer; 1997. p. 197-264
• 34. Mori T, Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 1973;21:571-574.
• 35. Schöberl J. NETGEN - an advancing front 2D/3D-mesh generator based on abstract rules. Comput Vis Sci. 1997;1:41-52.
• 36. Korelc J. Multi-language and multi-environment generation of nonlinear finite element codes. Eng Comput. 2002;18:312-27. https://doi.org/10.1007/s0036 60200 028.
• 37. Markov A, Trofimov A, Sevostianov I. A unified methodology for calculation of compliance and stiffness contribution tensors of in homogeneities of arbitrary 2D and 3D shapes embedded in isotropic matrix - open access software. J Mech Phys Solids. 2020;157:103390.
• 38. Kowalczyk-Gajewska K, Ostrowska-Maciejewska J. Review on spectral decomposition of Hooke’s tensor for all symmetry groups of linear elastic material. Eng Trans. 2009; 57:145-183.
• 39. Šmilauer V et al. Yade Documentation. 3rd ed. The Yade Project. Zenodo; 2021. https:/doi.org/10.5281/zenodo.5705394.
• 40. Mazzucco G, Pomaro B, Salomoni VA, Majorana CE. Numerical modelling of ellipsoidal inclusions. Constr Build Mater. 2018;167:317-324.
• 41. Kursa M, Kowalczyk-Gajewska K, Petryk H. Multi-objective optimization of thermo-mechanical properties of metal-ceramic composites. Compos B Eng. 2014;60:586-596.
• 42. Hill R. Continuum micro-mechanics of elastoplastic polycrystals. J Mech Phys Solids. 1965;13:89-101.
• 43. Kowalczyk-Gajewska K, Maździarz M. Elastic properties of nanocrystalline materials of hexagonal symmetry: the core-shell model and atomistic estimates. Int J Eng Sci. 2020;157:103393.
• 44. Celentano DJ, Chaboche JL. Experimental and numerical characterization of damage evolution in steels. Int J Plast. 2007;23:1739-62.
• 45. Steinmann P. Formulation and computation of geometrically nonlinear gradient damage. Int J Numer Methods Eng. 1999;46:757-779.
• 46. Rutecka A, Kursa M, Pietrzak K, Kowalczyk-Gajewska K, Makowska K, Wyszkowski M. Damage evolution in AA2124/SiC metal matrix composites under tension with consecutive un loadings. Arch Civ Mech. 2020;20:135. https://doi.org/10.1007/s43452- 020- 00134-x.

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)