| Summary: | High-energy synchrotron X-ray diffraction measurements of residual elastic strain were carried out in a thin slice parted off from a plate of titanium alloy that had been subjected to laser shock peening. The residual elastic strain varies with the distance from the laser shock peened surface, with high near-surface compressive strain changing to tensile strain in the middle of the sample, and then becoming compressive again on the opposite face. The measured residual elastic strain distribution was modelled using a distribution of laser shock induced eigenstrains near the surface, and the most likely eigenstrain profile was deduced using a variational matching procedure. The mathematical framework for this approach is presented and discussed, and the results of matching the predicted residual elastic strain distribution to the measurement are shown.
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