Abstract: This paper deals with numerical and analytical modelling of a diamond or silicon particle embedded in a metallic matrix. The numerical model of an elastic particle in a metallic matrix was created using the Abaqus software. Truncated octahedron-shaped and spherical-shaped diamond particles were considered. The numerical analysis involved determining the effect of temperature on the elastic and plastic parameters of the matrix material. The analytical model was developed for a spherical particle in a metallic matrix. The comparison of the numerical results with the analytical data indicates that the mechanical parameters responsible for the retention of diamond particles in a metal matrix are: the elastic energy of the particle, the elastic energy of the matrix and the radius of the plastic zone around the particle. An Al-based alloy containing 5% of Si and 2% of Cu was selected to study the mechanical behaviour of silicon precipitates embedded in the aluminium matrix. The model proposed to describe an elastic particle in a metallic matrix can be used to analyze other materials with inclusions or precipitates.
B I B L I O G R A F I A[1] Lachowski, J. & Borowiecka-Jamrozek, J. (2017). Modelling Thermomechanical Response of a Diamond Particle in a Metallic Matrix. Engineering Transactions. 65(1), 105-112.
[2] Borowiecka-Jamrozek, J. (2013). Engineering structure and properties of materials used as a matrix in diamond impregnated tools. Archives of Metallurgy and Materials. 58(1), 5-8. DOI: 10.2478/v10172-012-0142-0.
[3] Borowiecka-Jamrozek, J. & Lachowski, J. (2014). Analysis of Stresses in Al-5%Si Alloy under Loading Conditions. Journal of Achievements in Materials and Manufacturing Engineering. 65(1), 26-31.
[4] Akyuz, D.A. (1999). Interface and microstructure in cobalt-based diamond tools containing chromium. PhD thesis, Ecole Polytechnique Federale de Lausanne, Lausanne, 105-108.
[5] SIMULIA Dassault System, Abaqus analysis user’s guide, ver. 6.14 (2014). Computer Cluster at Kielce University of Technology.
[6] Landau, L.D. & Lifszitz, E.M. (1975). Theory of Elasticity. 2nd ed. , Pergamon Press Ltd., Oxford, 20-21.
[7] Hill, R. (1950, reprinted 2009). The Mathematical Theory of Plasticity. Clarendon Press. Oxford. 97-101.
[8] Hampel, C.A. ed., (1961). Rare Metals Handbook, Reinhold Publishing Corporation, London, 124-126.
[9] Rosler, J., Harders, H., Baker, M. (2007). Mechanical Behaviour of Engineering Materials. Springer-Verlag, Berlin. 60-62.
[10] SIMULIA Dassault System, Abaqus Analysis User’s Guide, Output Variable and Element Indexes, ver. 6.14 (2014).
[11] Gurson, A.L. (1977). Continuum theory of ductile rupture by void nucleation and growth. Journal of Engineering Materials Technology. 99, 2-15.
[12] Kossakowski, P.G. (2012). The prediction of ductile fracture to S235JR steel using the stress modified critical strain and Gurson-Tvergaard-Needleman models. Journal of Materials in Civil Engineering. 24, 1492-1500.
[13] Neimitz, A. & Grzegorczyk, A. (2014). Numerical analysis of the failure processes of plates made of S 960 QC steel. Key Engineering Materials. 598, 184-189.
[14] Huber, G., Brechet, Y. & Pardoen, T. (2005). Predictive model for void nucleation and void growth controlled ductility in quasi-eutectic cast aluminium alloys. Acta Materialia. 53, 2739-2749.
[15] Koplik, J. & Needleman, A. (1988).Void coalescence in porous plastic solids. International Journal of Solids Structures. 24(8), 835-85 
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