Using genetic programming and the stress equilibrium method to obtain the un-stressed lattice parameter for calculating residual stresses

While it is known that the crucial requirement for investigating residual stresses using diffraction is the use of a reliable unstressed lattice parameter, the robustness of genetic programming to accomplish this task will be shown here. The parameter obtained from genetic programming in the context of the stress equilibrium method is compared with values resulting from other approaches of this method. This gives support and strength to the use of genetic programming to investigate microscopic residual stresses from real, experimental information. This is, so far, absent in theoretical models recently proposed. Whereas residual stress fields determination by diffraction methods at a macroscopic scale (scale of the sample size) offers no serious difficulties, the stress determination at the microscopic scale (i.e., stresses varying among neighboring grains) is still a pending task. Understanding these microscopic stresses is, however, of a great technological importance, as they may be the cause of fatigue damage and/or stress corrosion cracking in many structural components. Despite that theoretical but solid alternatives, for example those based on phase field models, are being used to unveil the stresses developed at the grain scale after known thermo-mechanical treatments, the results obtained still need to be assessed by experimental results linked to real microstructures. On the contrary, recent works propose the use of genetic programming approaches to investigate these microscopic stresses on the basis of data recorded from real stressed samples; specifically, from neutron diffraction and detailed knowledge of the microstructure and its characteristics; e.g., the texture gradient developed.