Quantitative estimation of incompatibility stresses and elastic energy stored in ferritic steel

Abstract

Plastic incompatibility second-order stresses were determined for different orientations of a polycrystalline grain, using X-ray diffraction data and results of the self-consistent elasto-plastic model. The stresses in cold rolled ferritic steel were determined both in as-received and under tensile loaded conditions. It has been shown that the Reuss model and the self-consistent model applied to near surface volume provide the best approaches to determine diffraction elastic constants. For the first time, the elastic energy in an anisotropic material (arising from plastic incompatibilities between grains having various lattice orientations) has been determined. The second-order incompatibility stresses and stored elastic energy are presented in Euler space. research papers J. Appl. Cryst. (2008). 41, 854-867 A. Baczmanski et al. Stresses and elastic energy in ferritic steel 855

Application of multireflection grazing incidence method for stress measurements in polished Al–Mg alloy and CrN coating

“…In the case of a quasiisotropic sample and when the forces perpendicular to the surface are equal to zero, the interplanar spacing measured in the direction of scattering vector ( K in Fig. 1a) is given by the well known relation [3,11,12]:…”

“…(4)) corresponding to a given incidence angle˛(see Eq. (2)), a 0 is the strain free lattice parameter, while F ij (h k l, , ) are the stress factors calculated for different h k l reflections related to different and angles [3]. In this work, the free-surface self-consistent method [3] was used to calculate the F ij (h k l, , ) stress factors from single crystal elastic constants (given in Table 1) and experimentally determined crystallographic textures.…”

“…(2)), a 0 is the strain free lattice parameter, while F ij (h k l, , ) are the stress factors calculated for different h k l reflections related to different and angles [3]. In this work, the free-surface self-consistent method [3] was used to calculate the F ij (h k l, , ) stress factors from single crystal elastic constants (given in Table 1) and experimentally determined crystallographic textures. It should be underlined that F ij (h k l, , ) factors depend on the h k l reflection, especially for crystals having Table 1 Single crystal elastic constants of aluminium (used also for Al-Mg alloy AA5083) and CrN coating [18,19].…”

“…The standard method for stress determination (called sin 2 ) is based on the measurement of interplanar spacing for various directions of the scattering vector [1][2][3]. These directions are defined by and angles (Fig.…”

“…Diffraction methods are commonly used for determining lattice elastic deformation and distortion (i.e., of macrostrains and microstrains) from the displacement and broadening of the diffraction peak [1][2][3][4]. The stress present in the near surface volume can be measured using the standard X-ray sin 2 method.…”