Mechanical properties in the initial stage of sintering

Silicon nitride-based ceramics with different compositions were sintered in the 60%–90% range of theoretical density. Linear correlations between the apparent density and the modulus of elasticity, the three- and four-point bend strengths or the Vickers hardness, were observed. The slopes of the straight lines were nearly the same for all compositions. Furthermore, the modulus of elasticity, hardness, fracture toughness and strength were calculated as functions of density by modelling the structure as a random arrangement of spheres as suggested by Fischmeister and Arzt. The relationships obtained have been compared with the measured ones.Nomenclature a average contact area - a_c increase of the area of a crack - A area of the reference plane - b size of the critical defect - c constant in Equation 4 - D density - D₀ density before shrinkage - D_T theoretical density - e direction of macroscopic strain - E modulus of elasticity - E₀ modulus of elasticity of the dense material - f force loading a contact - f() projection of force f to e - F force loading the reference plane - g geometry parameter in the Griffiths relationship - H hardness - K_IC fracture toughness - N number of particles in unit volume - N() the fraction of N in a given spherical angle - n() number of particles in the volume around the reference plane - P porosity - R initial particle radius - R particle radius after fictitious growth - R particle radius after redistribution of material - R_SQ shared correlation coefficient - S surface energy of the defect - vector connecting the centres of neighbouring particles - W work necessary for increase the area of a crack - Z average coordination number - Z₀ initial coordination number - strain - _T strain at theoretical strength - strength - _T theoretical strength (limit of elasticity) - angle between v and e