Prediction of effective mechanical properties of composite materials using homogenization approach: Application to tungsten fiber reinforced bulk metallic glass matrix composite

Abstract

In this paper, the homogenization approach was presented to predict the effective mechanical properties of heterogeneous materials such as composite materials. Indeed, the main idea of this approach is to characterize the effective mechanical properties from a microstructural description of the heterogeneous materials and the knowledge of the local behavior of constituents using the homogenization process. It is a very efficient tool which is intensively developed in the field of numerical simulation of heterogeneous materials. Different scheme established from the solution of Eshelby’s inclusion problem are recalled such as Mori-Tanaka scheme, dilute scheme and Voigt and Reuss bounds. Homogenization approach was applied to estimate the effective mechanical properties of tungsten fiber reinforced bulk metallic glass matrix composite. Predicted values were confronted with those obtained by experimental approach from literature. These comparisons show good agreement between the predicted and experimental values. The maximum deviations remain lower than 10.5% using Voigt bound. A parametric study shows that the mechanical properties depend strongly on the shape of inclusions.

Keywords

• Composite materials,homogenization method,Eshelby’s inclusion problem

References

1. [1] Li, D.H., Guo, Q.R., Xu, D., and Yang, X. 2017. "Three-dimensional micromechanical analysis models of fiber reinforced composite plates with damage." Computers & Structures, 191 (Supplement C): 100-114.
2. [2] Perdahcıoğlu, E.S., and Geijselaers, H.J. 2011. "Constitutive modeling of two phase materials using the mean field method for homogenization." International journal of material forming, 4 (2): 93-102.
3. [3] Pierard, O., Friebel, C., and Doghri, I. 2004. "Mean-field homogenization of multi-phase thermo-elastic composites: a general framework and its validation." Composites Science and Technology, 64 (10): 1587-1603.
4. [4] Zaoui, A., Structural morphology and constitutive behaviour of microheterogeneous materials, in Continuum micromechanics, Springer. p. 291-347, 1997.
5. [5] Belhouideg, S., and Lagache, M. 2014. "Effects of the distribution and geometry of porosity on the macroscopic poro-elastic behavior: Compacted exfoliated vermiculite." International Journal of Mechanics, 8: 223-230.
6. [6] Eshelby, J.D. 1957. "The determination of the elastic field of an ellipsoidal inclusion, and related problems." In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences: The Royal Society, 376-396.
7. [7] Dormieux, L., Kondo, D., and Ulm, F.-J. 2006. "Microporomechanics". John Wiley & Sons.
8. [8] Guéry, A.A.-C., Cormery, F., Shao, J.-F., and Kondo, D. 2008. "A micromechanical model of elastoplastic and damage behavior of a cohesive geomaterial." Int. J. Solids Struct., 45 (5): 1406-1429.

9. [9] Hoxha, D., Giraud, A., Homand, F., and Auvray, C. 2007. "Saturated and unsaturated behaviour modelling of Meuse–Haute/Marne argillite." Int. J. Plast., 23 (5): 733-766.
10. [10] Zhang, Q., Jiang, W., Zhang, Y., Luo, Y., and Tu, S.-T. 2018. "Effective elastic constants of wire mesh material studied by theoretical and finite element methods." Composite Structures, 184 (Supplement C): 474-483.
11. [11] Burczyński, T., and Kuś, W. 2009. "Microstructure Optimization and identification in multi-scale modelling." In Eccomas multidisciplinary jubilee symposium: Springer, 169-181.
12. [12] Zhang, B., Chen, X., Wang, S., Lin, D., and Hui, X. 2013. "High strength tungsten wire reinforced Zr-based bulk metallic glass matrix composites prepared by continuous infiltration process." Materials Letters, 93: 210-214.
13. [13] Wang, G., Chen, D.M., Shen, J., Stachurski, Z.H., Qin, Q.H., Sun, J.F., and Zhou, B.D. 2006. "Deformation behaviors of a tungsten-wire/bulk metallic glass matrix composite in a wide strain rate range." Journal of Non-Crystalline Solids, 352 (36): 3872-3878.
14. [14] Inoue, A. 2000. "Stabilization of metallic supercooled liquid and bulk amorphous alloys." Acta materialia, 48 (1): 279-306.
15. [15] Greer, A., and Ma, E. 2007. "Bulk metallic glasses: at the cutting edge of metals research." MRS bulletin, 32 (8): 611-619.
16. [16] Hill, R. 1965. "A self-consistent mechanics of composite materials." J. Mech. Phys. Solids, 13 (4): 213-222.
17. [17] Withers, P. 1989. "The determination of the elastic field of an ellipsoidal inclusion in a transversely isotropic medium, and its relevance to composite materials." Philosophical Magazine A, 59 (4): 759-781.
18. [18] Sevostianov, I., Yilmaz, N., Kushch, V., and Levin, V. 2005. "Effective elastic properties of matrix composites with transversely-isotropic phases." International journal of solids and structures, 42 (2): 455-476.
19. [19] Kirilyuk, V., and Levchuk, O. 2005. "Stress state of a transversely isotropic medium with an arbitrarily oriented spheroidal inclusion." International Applied Mechanics, 41 (2): 137-143.
20. [20] Giraud, A., Huynh, Q.V., Hoxha, D., and Kondo, D. 2007. "Application of results on Eshelby tensor to the determination of effective poroelastic properties of anisotropic rocks-like composites." International journal of solids and structures, 44 (11): 3756-3772.
21. [21] Mori, T., and Tanaka, K. 1973. "Average stress in matrix and average elastic energy of materials with misfitting inclusions." Acta Metall., 21 (5): 571-574.
22. [22] Conner, R., Dandliker, R., and Johnson, W.L. 1998. "Mechanical properties of tungsten and steel fiber reinforced Zr 41.25 Ti 13.75 Cu 12.5 Ni 10 Be 22.5 metallic glass matrix composites." Acta Materialia, 46 (17): 6089-6102.
23. [23] Zhang, H., Zhang, Z., Wang, Z., Qiu, K., Zhang, H., Zang, Q., and Hu, Z. 2006. "Fatigue damage and fracture behavior of tungsten fiber reinforced Zr-based metallic glassy composite." Materials Science and Engineering: A, 418 (1): 146-154.
24. [24] Zhang, H., Zhang, Z., Wang, Z., and Zhang, H. 2008. "Deformation and damage evolution of tungsten fiber reinforced metallic glass matrix composite induced by compression." Materials Science and Engineering: A, 483: 164-167.