Voxel-Based Full-Field Eigenstrain Reconstruction of Residual Stresses

Abstract

Inverse eigenstrain (inherent strain) analysis methods are shown to be effective for the reconstruction of residual stresses in plane eigenstrain problems (continuously processed bodies) while conversely residual stress reconstruction in discontinuously processed bodies is extremely challenging and necessitates the use of complex regularizing assumptions. Herein, a new generic inverse eigenstrain method suitable for the reconstruction of residual stresses along with residual elastic strains and displacements in discontinuously processed bodies is introduced. The proposed method uses the superposition of eigenstrain radial basis functions together with a set of limited experimental data for model-free (unconstrained) determination of unknown eigenstrain fields. This approach eliminates the limitations introduced by global basis functions such as polynomials. The novel point of this method is the ability to account for all six components of strain in an isotropic body without using regularizing assumptions. By lifting complex guiding formulation, the fidelity of full-field eigenstrain reconstruction becomes directly related to the quality of experimental data and proper discretisation of the model domain. The FEniCS implementation has been validated using the experimental data of pointwise high-energy synchrotron X-ray diffraction measurements from a bent titanium alloy bar. A hybrid high throughput computing approach is also introduced for effective parallel computing.