Pre-print: 10.2139/ssrn.4789333 Published article: 10.1016/j.matchar.2025.115952 This data set contains data for publication on methodology of EBSD with emphasis on the characterization of materials deformation states. The set contains raw data - the EBSD maps of 4 deformations states of 316L stainelss steel after Low Cycle Fatigue testing at different aplitudes of total deformation. The data are further processed using MATLAB 2022a and the MTex toobox v 5.7.0. There are 2 critical reason for using the MTex, rather than the official software of the Oxford Instruments comapany. First, the MTex includes the Half Quadratic Filter. Second, the calculation of the Geometrically Necessary Dislocations in MTex is based on the 'Pantleons method'. The processing scripts are in separated .zip files.