Effects of disoriented grains on the elastic constants of directionally solidified superalloys

Two models, namely, coaxial and non-coaxial, are proposed to estimate the elastic constants of directionally solidified superalloys, which behave like transversely isotropic materials and require five independent elastic constants. Coaxial model considers each grain as an individual and obtains the averaged values. Because of the longitudinal grain structure, three independent constants are carried over from original cubic single crystal and the other two are obtainable through the averaging process. For each disoriented direction in the non-coaxial model, a lumped grain, which behaves like a transverse isotropy is proposed. By assuming the disoriented angle follows Weibull distribution, non-coaxial model obtains the expectations of compliances from probability consideration. Disoriented effect could be simulated through the parameters of Weibull distribution. Experimental off-axis Youngʹs modulus data are compared with numerical predictions by both models. Excellent agreement is observed between coaxial model and 90° off-axis experimental data. However, the coaxial model over predicts the 45° off-axis Youngʹs modulus, because anisotropic coupling effect is very strong in the real off-axis specimens. As non-coaxial model considers the disoriented effect, excellent agreement is observed between non-coaxial model and 45° off-axis experiment data. Disoriented grain consideration reduces the anisotropic coupling effect and predicts better to the real off-axis specimens.