Further insights on the stress equilibrium method to investigate macroscopic residual stress fields: Case of aluminum alloys cylinders

•Macro residual stresses after fast and slow cooling Al alloys are studied from neutron and synchrotron radiation diffraction.•The stress equilibrium method and the “composite model” or the Rietveld method are used in the calculations of the M-RS.•Texture gradient is not a relevant factor affecting the M-RS profile developed with quenching.•The different M-RS from the individual peak and Rietveld analysis of the slow cooled sample are associated with a m-RS.•A comprehensive understanding of the RS state in polycrystalline materials requires a multi-scale analysis of the M- and m-RS.