Applications of the eigenstrain method in inclusion problems and micromechanics of coherent metal carbide precipitation in steel

In this thesis, the eigenstrain method, the equivalent inclusion method, and other micromechanical methods are applied to solve several inclusion problems. First, the elastic field caused by an inclusion embedded in an elastic half space is derived from the Green's functions for axisymmetric body forces in a semi-infinite elastic medium. With the assist of the equivalent inclusion method, the corresponding half-space inhomogeneous inclusion problem is solved. Next, the generalized self consistent method is applied to study the overall behavior of a particle-reinforced elastic-plastic material under hydrostatic loading. The effective bulk modulus is derived as a function of the hydrostatic loading, the yield stress of the matrix, the volume fraction, and the elastic moduli of both inclusion and matrix phases of the composite. The effect of misfitting inclusions is also considered.; Then, the eigenstrain method and the equivalent inclusion method are applied to estimate the energetics of coherent carbide precipitation in ultra-high strength steels. The linear elastic self energy estimation represents an upper bound to the true self energy. Calibration to the observed coherent precipitation behavior indicates that a correction factor of 0.4 should be applied. A simple bilinear approximation to the non-linearity is made to improve the estimation of the precipitate self energy. The magnitude of the correction factor is justified by the "non-linear" elastic self energy calculation which shows a self energy reduction of 40% for dilatation of 20 pct. Moreover, the dislocation-particle interaction energy and the particle-particle interaction energy are calculated to examine the energetics of heterogeneous nucleation. It is found that the dislocation-particle interaction can account for the heterogeneous nucleation at the start of precipitation, and the particle-particle interaction can account for the autocatalytic nucleation at the half-completion time. However, both analyses give smaller critical nucleus sizes than the ones observed experimentally. Finally, the problem of coherency loss due to the resolved shear stress on the carbide prism plane is addressed. The linear elastic calculation predicts that the resolved shear stresses in carbide prism plane is too high to allow coherency. But reduction of stresses by non-linearity to 35% would allow coherency with transition near observed size of 15A radius.