  In the presented research, the intergranular elastic interaction and the
second-order plastic incompatibility stress in textured ferritic and austenitic
steels were investigated by means of diffraction. The lattice strains were
measured inside the samples by the multiple reflection method using high energy
X-rays diffraction during uniaxial in situ tensile tests. Comparing experiment
with various models of intergranular interaction, it was found that the
Eshelby-Kr\"oner model correctly approximates the X-ray stress factors (XSFs)
for different reflections hkl and scattering vector orientations. The verified
XSFs were used to investigate the evolution of the first and second-order
stresses in both austenitic and ferritic steels. It was shown that considering
only the elastic anisotropy, the non-linearity of $\sin^2{\psi}$ plots cannot
be explained by crystallographic texture. Therefore, a more advanced method
based on elastic-plastic self-consistent modeling (EPSC) is required for the
analysis. Using such methodology the non-linearities of $\cos^2{\phi}$ plots
were explained, and the evolutions of the first and second-order stresses were
determined. It was found that plastic deformation of about 1- 2% can completely
exchange the state of second-order plastic incompatibility stresses.
