Modelo para análise de tensões principais biaxiais e triaxiais em materiais ortotrópicos através de medidas de difração de raios-x

Abstract

In this work it was developed expressions for the calculation of biaxial and triaxial principals stresses in polycrystalline anisotropic materials. Taken into account these mathematic expressions was possible to determine the elastic constants using the Theory of Elasticity Continuum for small deformations. The constitutive relation between strain and stress must be considered orthotropic, obeying the generalized Hooke's law. One technique that can be applied to obtain the stresses and elastic constants was the X-ray diffraction, because the experimental conditions are similar to the assumptions of the model, ie, measure small deformations compared the sample sizes and magnitude of stress is involved in the elastic range. Therefore, based on the equations obtained, here it is possible to use the technique of x-ray diffraction sin2 ? for materials with texture or anisotropic, determining, rst, a characterization of the texture through the pole gures in order to determine possible angles ?, which can be used in our equation. Next, it was determined the deformation for each diffraction peak with the angles ? obtained from the pole gures. As considering the elastic constants of the material knowledge, our can use equation to calculate the residual stress in a material. We presented a test of the consistency of our equations by comparing with the equations in the literature for isotropic materials, moreover we applied the model to biaxial principal stress, using experimental data from the work of D. Faurie et al, in order to be possible to compare the elastic constants obtained with the study reported.