How to model accurately the residual stresses build up in a billet?

Dear iMechanica community,I have the following question: in Al7050 (T7651) billet manufacturing, when the billet undergoes rolling and subsequent quenching, tempering and stretching, the residual stresses through the thickness are no-longer represented by a bell shaped curve but show some typical ears towards the edges of the billet. Do you know what is the origin of that occurrence. Similar but smaller pronounced effect can be seen in the centre of the billet (you may see the figure below). From my understanding most of the stresses upon the heat treatment are removed, yet it should be expected that close to the edges you have a texture component defined by the high shear stresses acting by the roller, while towards the centre someone should expect typical rolled textures given by plane strain compression.Would you be able to point out to some relevant published work how they model the stresses close to the edges?Also do you have any sources where I could find material properties (thermal expansion coef, stress-strain curves) at high temperature and high strain rates as well for 7050 alloy?Kind regards,Panos