Non-linear sin
2ψ relations are sometimes observed when the X-ray stress analysis was performed on the materials having preferred orientations. Therefore, the stress determination by the Sin
2ψ method is impossible for such case. There are three main factors influencing the oscillation of lattice strain with Sin
2ψ as follows: 1) Elastic anisotropy, 2) Plastic anisotropy and 3) Instrumental effect caused by the X-ray optics.
This paper deals with the possibility of residual stress measurement for cold-rolled steels having a typical preferred orientation.
The results obtained are summarized as follows:
1) The distribution of X-ray elastic constants with respect to Sin
2ψ for the (211) diffraction was precisely calculated based on the modified Dölle model and it agreed with the experimental result.
2) The experimental values of X-ray elastic constants also agreed with the analytical values for the isotropic steel by the Reuss model at Sin
2ψ=0 and 0.75. Since the X-ray elastic strains at such positions are linear with Sin
2ψ, we can determine the elastic stresses in textured steels by using the isotropic X-ray elastic constant by the Reuss model.
3) A remarkable oscillation in the Sin
2ψ diagram was observed by the fixed ψ
0 method. This oscillation originated from the X-ray optics was analyzed by the numerical simulation. The result indicates that both the X-ray strains at Sin
2ψ=0 and 0.75 on the (211) diffraction agree with those by the fixed ψ method. Thus, we proved that the residual stresses in textured steels can be measured by using both X-ray strains at such values of Sin
2ψ.
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