The Influence of Cylindrical Geometry on X-ray Stress Tensor Analysis. I. General Formulation

Abstract

Stress analysis by X-ray diffraction, usually performed on a specimen with plane geometry, becomes very difficult on more complex surfaces. A model is proposed to calculate the six independent components of the stress tensor for cylindrical symmetry. The mathematical approach described highlights two distinct effects that modify values of measured strain by X-ray diffraction, a rotation effect and a translation effect. The X-ray absorption by the material is taken into consideration and two models are proposed to undertake the mathematical processing on thick materials and thin layers. It is equally possible to take into account, for example, crystallographic texture and experimental features as q~ oscillations., Examples and applications will be given in paper II [Dionnet, Franqois, Sprauel & Nardou (1995). In preparation].

Residual Stresses in Friction-Stir-Welded 2195 and 7075 Aluminum Alloys

“…For example, samples' surface characteristics such as extreme preferred orientation, technique of sample preparation, excessive surface roughness, curvature, and grain size can adversely affect the accuracy of the measurements, [9] because the MET for determining RSs by means of XRD assumes that samples are both flat and macroscopically isotropic. [21] In addition, precise knowledge of the proper elastic constant is required to convert the X-ray intensity into measured strain, because use of an incorrect elastic constant can cause the overall accuracy of the measurements to decrease. [9] If samples are flat and the proper elastic constant is used, the larger scatter in RS measurements derived from XRD arises from measuring materials with large grain size.…”

Determination of the accuracy of phase analysis measurements on spherical surfaces through X-ray diffraction

“…Several past investigations have presented analyses and derived correction models for XRD measurements of stresses in cylindrical surfaces [8][9][10][11]17] and surfaces exhibiting texture [13,18]. But these studies were limited to the analysis of convex and concave surfaces [17], and so far only the research by Oguri et al [12] has considered stresses in spherical surfaces.…”

“…Instrumental errors are those associated with diffractometer misalignments, but even these are created partly by a sample's surface curvature. In fact, a sample's surface characteristics greatly influence residual stress measurement since the sin 2 c technique for determining residual stresses by means of XRD assumes that samples are both flat and macroscopically isotropic [9]. Therefore, in situations where the surfaces to be inspected are cylindrical or spherical, the effect of surface geometry on stress measurements will not necessarily be negligible; on the contrary, mathematical corrections must be considered [9].…”

“…However, to evaluate the surface characteristics of such parts accurately through XRD techniques-in the absence of fine grain size structure and smooth and flat surfaces [12,16]-it is imperative to create a mathematical correction where surface characteristics like residual stresses and phase analysis can be quantified accurately by correcting the errors induced by geometry [12,16]. According to Fracois et al [9] the magnitude error introduced by geometrical errors is not trivial. The practical relevance of developing a mathematical correction model is thus apparent and could even allow XRD to be used to make more representative estimates of such characteristics as fatigue life can be made.…”

“…In fact, a sample's surface characteristics greatly influence residual stress measurement since the sin 2 c technique for determining residual stresses by means of XRD assumes that samples are both flat and macroscopically isotropic [9]. Therefore, in situations where the surfaces to be inspected are cylindrical or spherical, the effect of surface geometry on stress measurements will not necessarily be negligible; on the contrary, mathematical corrections must be considered [9]. In fact, some of the intricacies of geometrical effects on the accuracy of XRD residual stress measurements have been exposed by past studies, which have revealed that measurement of hoop stresses (s 22 ) are impacted more by geometrical factors, such as surface curvature, than those of axial stresses [10].…”