  Rapid solidification in Additively Manufactured (AM) metallic materials
results in the development of significant microscale internal stresses, which
are attributed to the printing induced dislocation substructures. The resulting
backstress due to the Geometrically Necessary Dislocations (GNDs) is
responsible for the observed Tension-Compression (TC) asymmetry. We propose a
combined Phase Field (PF)-Strain Gradient $J_2$ Plasticity (SGP) framework to
investigate the TC asymmetry in such microstructures. The proposed PF model is
an extension of Kobayashi's dendritic growth framework, modified to account for
the orientation-based anisotropy and multi-grain interaction effects. The SGP
model has consideration for anisotropic temperature-dependent elasticity,
dislocation strengthening, solid solution strengthening, along with GND-induced
directional backstress. This model is employed to predict the solute
segregation, dislocation substructure and backstress development during
solidification and the post-solidification anisotropic mechanical properties in
terms of the TC asymmetry of rapidly solidified Fe-Cr alloys. It is observed
that higher thermal gradients (and hence, cooling rates) lead to higher
magnitudes of solute segregation, GND density, and backstress. This also
correlates with a corresponding increase in the predicted TC asymmetry. The
results presented in this study point to the microstructural factors, such as
dislocation substructure and solute segregation, and mechanistic factors, such
as backstress, which may contribute to the development of TC asymmetry in
rapidly solidified microstructures.
