ABSTRACT of the Doctoral Thesis
In continuum micromechanics, most of the modelling work on particulate composites has employed idealized particle shapes such as spheres, whereas actual composites are reinforced by highly irregularly shaped particles. The objective of the present study is to provide insight into the effects of polyhedral particle shapes on the effective macroscopic behaviour as well as on the microfields in the composites. For this purpose, three-dimensional multiparticle unit cell models containing spherical or convex polyhedral particles are generated and their thermomechanical and thermophysical responses are simulated.
The generation of the unit cell models is handled by a special-purpose code, based on the random sequential insertion algorithm and using the method of "separating axis" for overlap-checking of polyhedral particles. The particle arrangements generated are periodic, three-dimensional cube-shaped unit cells, the inhomogeneities taking the form of equiaxed, randomly positioned and, where applicable, randomly oriented spheres, regular octahedra, cubes or regular tetrahedra. Particle sizes considered are uniform and uniformly distributed with particle volume fractions of 20% and 30%, respectively. The macroscopic behavior of the volume elements approaches isotropy.
Generic constituent material parameters are used for thermoelastic and thermophysical analyses, with particle and matrix phases having an elastic contrast of 10:1, a ratio of Poisson numbers 1:3.3, a thermal expansion contrast of 0.1:1 and a thermal conductivity contrast of 10:1, respectively. For elasto-plastic analysis, a composite material consisting of elastic SiC particles embedded in an elasto-plastic Al6061 matrix with linear isotropic hardening and an initial yield stress of 69.5 MPa is modeled. The elastic contrast of particles and matrix for this case is approximately 6. For the thermo-elastic analysis 3 linearly independent uniaxial tensile and 3 shear load cases and 1 uniform temperature excursion are employed, whereas for the thermal conduction analysis 3 linearly independent heat flux load cases are applied to these phase arrangements. For the elasto-plastic analysis, the phase arrangements are subjected to 3 uniaxial tensile loads. Periodicity boundary conditions are employed and the Finite Element Method is used to evaluate effective macro- and microscopic responses of the phase arrangements.
The macroscopic responses are obtained in terms of the homogenized elasticity and thermal expansion tensors for the thermoelastic case, and homogenized resistivity tensors for the thermophysical case, respectively, from which the appropriate moduli are extracted. In the elasto-plastic regime, the stress-strain responses are considered. Ensemble averaging over a number of equivalent phase arrangements is used in all cases. The microscopic behaviour is described by the probability density distributions of the microfields in matrix and particles, as well as microfield averages and fluctuations within individual particles.
A clear and consistent dependence of the microscopic and effective macroscopic responses on the particle shapes is observed. The macroscopic moduli, namely, the Young's, bulk and shear moduli of composites reinforced by spheres are found to be smaller than those obtained for materials reinforced by the polyhedral particles. Among the polyhedra, tetrahedra, which have the sharpest vertices and smallest dihedral angle, give rise to the highest values of macroscopic moduli, followed by cubes and octahedra. The opposite trend is predicted for the coefficients of thermal expansion, as expected. Analogously, for thermophysical analyses, composites reinforced by polyhedral particles, in the sequence tetrahedra, cubes, octahedra, are found to be more conductive than sphere-reinforced ones. With an increase in particle volume fraction from 20% to 30%, there is a corresponding increase in the elastic moduli, decrease in the thermal expansion coefficient and increase in conductivity as expected due to increased contributions from the stiffer and more conductive particle phase.
The probability density distributions of the microfields, for the matrix and particles, also exhibit marked particle shape effects, typically becoming wider and much more skewed with tails at high values, as the particle shape varies in the order spheres, octahedra, cubes and tetrahedra. Particle averages of the microfields are also found to be much higher for the polyhedral, especially tetrahedral particles compared to the spheres. Similar trends are present for the macroscopic and microscopic responses in the elasto-plastic regime. Composites reinforced by tetrahedral particles show more pronounced strain hardening, followed by cubes, octahedra and spheres. The microfields depict a quantitatively similar, but much more pronounced particle shape dependence than in the elastic range.