Unified description for the geometry of X-ray stress analysis: proposal for a consistent approach

Many X-ray stress acquisition strategies are proposed in the literature. They have appeared because of the variety of rotation controls that are allowed on modern goniometers and the development of two-dimensional detectors. In the present paper, a consistent set of axes, rotations and angles is proposed to describe all possible geometries. It is based on the splitting of the useful angles into three groups: the sampling angles, the goniometric angles and the diffractometric angles. The first two groups are used to orientate the goniometer and the specimen relative to one another, while the third describes the diffraction for a zero-, one- or two-dimensional detector. The mathematical relations between these angles are given, along with the expression of the penetration depth. Various acquisition strategies are described in the proposed scheme and conveniently represented on stereographic projections.