Numerically efficient microstructure-based calculation of internal stresses in superalloys

According to the classical Eshelby inclusion problem, we introduce a new linear relation to calculate internal stresses in gamma/gamma' microstructures of superalloys via an effective stiffness method. To accomplish this, we identify regions with almost uniform deformation behavior within the microstructure. Assigning different eigenstrains to these regions results in a characteristic internal stress state. The linear relation between eigenstrains and internal stresses, as proposed by Eshelby for simpler geometries, is shown to be a valid approximation to the solution for complex microstructures. The fast Fourier transformation method is chosen as a very efficient numerical solver to determine the effective stiffness matrix. Numerical validation shows that this generalized method with the effective stiffness matrix is efficient to obtain appropriate internal stresses and that it can be used to consider the influence of internal stresses on plasticity and creep kinetics in superalloys.