  The onset of nonlinear effects in metals, such as plasticity and damage, is
strongly influenced by the heterogeneous stress distribution at the grain
level. This work is devoted to studying the local stress distribution of shear
stresses resolved in the slip systems as the critical driving force for plastic
deformations. Specific grain orientations with respect to load direction are
investigated in the linear elastic regime and at incipient plastic deformations
based on a large ensemble of microstructures. The elastic anisotropy of the
single crystal is found to have a crucial influence on the scatter of the
stress distribution, whereas the Young's modulus in the respective crystal
direction governs the mean stress in the grain. It is further demonstrated
that, for higher anisotropy, the shear stresses deviate from the normal
distribution and are better approximated by a log-normal fit. Comparing the
full-field simulations to the Maximum Entropy Method (MEM), reveals that the
MEM provides an excellent prediction up to the second statistical moment in the
linear elastic range. In a study on the spatial distribution of shear stresses,
the grain boundary is identified as a region of pronounced stress fluctuations
and as the starting point of yielding during the elastic-plastic transition.
