Model for analysis of biaxial and traxial stresses by X-ray diffraction assuming orthotropic materials

Abstract

In this work we aim to develop expressions for the calculation of biaxial and triaxial stresses in polycrystalline anisotropic materials, and to determine their elastic constants using the theory of elasticity for continuum isochoric deformations; thus, we also derive a model to determine residual stress. The constitutive relation between strain and stress in these models must be assumed to be orthotropic, obeying the generalized Hooke’s law. One technique that can be applied with our models is that of X-ray diffraction, because the experimental conditions are similar to the assumptions in the models, that is, it measures small deformations compared with the sample sizes and the magnitude of the tensions involved, and is insufficient to change the volume (isochoric deformation). Therefore, from the equations obtained, it is possible to use the sin2 ψ technique for materials with texture or anisotropy by first characterizing the texture through the pole figures to determine possible angles ψ that can be used in the equation, and then determining the deformation for each diffraction peak with the angles ψ obtained from the pole figures. we give a proof of the consistency of these equations by comparing them with previously reported models for isotropic materials, and then we apply our model for biaxial stress using the experimental data obtained by Faurie et al. As a result, we can observe the magnitude of the elastic constants determined by our model.