A new development in the determination of residual stresses in thin surface layers and coatings is presented. The procedure, based on the grazing‐incidence X‐ray diffraction geometry (referred to here as the `g‐sin2 ψ' geometry), enables non‐destructive measurement at a chosen depth below the sample surface. The penetration depth of the X‐ray radiation is well defined and does not change during the experiment. The method is particularly useful for the analysis of non‐uniform stresses in near‐surface layers. The g‐sin2 ψ geometry was applied for measurements of the residual stresses in TiN coatings. Anisotropic diffraction elastic constants of textured material were used to determine the stress value from the measured lattice strains. A new method of data treatment enables reference‐free measurements of residual stresses.

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

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Owing to its selectivity, diffraction is a powerful tool for analysing the mechanical behaviour of polycrystalline materials at the mesoscale (phase and/ or grain scale). In situ neutron diffraction during tensile tests and elastoplastic self-consistent modelling were used to study slip phenomena occurring on crystallographic planes at small and large deformation. The critical resolved shear stresses in both phases of duplex stainless steel were found for samples subjected to different thermal treatments. The evolution of grain loading was also determined by showing the large differences between stress concentration for grains in ferritic and austenitic phases. It was found that, for small loads applied to the sample, linear elastic deformation occurs in both phases. When the load increases, austenite starts to deform plastically, while ferrite remains in the elastic range. Finally, both phases undergo plastic deformation until sample fracture. By using an original calibration of diffraction data, the range of the study was extended to large sample deformation. As a result, mechanical effects that can be attributed to damage processes initiated in ferrite were observed. research papers J. Appl. Cryst. (2011). 44, 966-982 A. Baczmanski et al. Aged duplex stainless steel under deformation 967 research papers J. Appl. Cryst. (2011). 44, 966-982 A. Baczmanski et al. Aged duplex stainless steel under deformation 977 Figure 11Elastic lattice strains (h" TD i fhklg ) perpendicular to the loading direction (RD) versus the applied true stress AE RD for aged UR45N samples deformed in the tensile test. research papers J. Appl. Cryst. (2011). 44, 966-982 A. Baczmanski et al. Aged duplex stainless steel under deformation 981

In situ time of flight neutron diffraction and X-ray synchrotron diffraction methods were applied to measure lattice strains in duplex steels during a tensile test. The experimental results were used to study slips on crystallographic planes and the mechanical effects of damage occurring during plastic deformation. For this purpose the prediction of an elastoplastic self-consistent model was compared with the experimental data. The used methodology allowed to determine the elastic limits and parameters describing work hardening in both phases of studied polycrystalline materials. In the second part of this work the developed elastoplastic model was applied to study damage occurring in the ferritic phase. The theoretical results showed a significant reduction of stresses localized in the damaged phase (ferrite) and confirmed the evolution of the lattice strains measured in the ferritic and austenitic phases.

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