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The usual formulation used for determining stresses by X‐ray diffraction with a flat specimen is not valid when the sample has a curved surface. In the first paper of this series [François et al. (1995). J. Appl. Cryst.28, 761–767], a general formulation was presented, showing that two effects arise simultaneously: a translation and a rotation effect. In the present paper, analytical formulae, derived from the general expression and valid under certain assumptions, are given. They exhibit a linear relation between the measured strain and sin2ψ and they can be used in many practical cases. Experimental and numerical examples of the use of the simplified and the general formulation on thick and thin wires, thin layers on wires, convex and concave specimens, and isotropic and textured samples are given. The range in which the classical and the present formulation are valid is also studied.

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].

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