Determination of in-plane residual stress and eigenstrain in laser peened thin sheet using unit pulse function and equilibrium constraint

•Spatial distribution of residual stress in thin sheet with large deflection was experimentally investigated.•The unit pulse function and Tikhonov regularization were adopted in the slitting method for measurement of in-plane residual stress.•A backward solution for the LSP-induced residual stress and eigenstrain was proposed and verified. The residual stress field is a critical physical quantity for the predicting fatigue life and adjusting forming shape in the peening industry. It is an important engineering requirement to accurately obtain the reliable residual stress of treated coupons and components. To improve the spatial resolution and accuracy of stress measurements in laser peened targets, the slitting method via unit pulse function was carried out in the present study. A 4 mm thick rectangular sheet subjected to uniform laser peening was studied thoroughly via theoretical analysis and experimental tests. First, the physical interpretation and basic implementation of the unit pulse function were described. The relevant regularization, error reduction, and analysis methods were expounded. Then, a safe distance of multiple slitting measurements was proposed and further investigated through numerical simulation. The effect of stress relaxation and the positions of the strain gauges employed were also verified. Experimentally, a biaxial through-thickness distribution of residual stress was calculated using the unit pulse approach. Then, a cross-method validation procedure was performed through an incremental X-ray diffraction (XRD). Finally, the distribution patterns of the bending and elongating stress components were analyzed. The unbalanced laser peening-induced stress was obtained through a backward calculation using the equilibrium constraint. The results indicated that general stress field was in a biaxial state, which possessed a roughly equivalent amplitude and uniform distribution. Along the depth direction, both the peened and unpeened faces were under compression, while the sheet center was in tension for global compensation. Further research revealed that the residual stress introduced by laser peening was fundamental to the process, which can provide a test-oriented solution for eigenstrain and reliable data support for deformation prediction.