Inverse method of eigenstrain determination of laser shock peening

The determination of eigenstrain from residual stress is a crucial aspect in process predicting and optimizing of laser peen forming. However, direct measurement of eigenstrain is not possible, and therefore an indirect method based on the Fredholm integral equation is proposed for determining eigenstrain from residual stress. The residual stress of full-coverage laser shock peening (LSP) is analyzed, and the governing equation of eigenstrain is derived from the elastic deformation of a linear elastic plate under full-coverage LSP. The governing equation is a second-kind Fredholm integral equation, which can be solved analytically using the weight function method. Since residual stress is difficult to measure accurately in LSP, an inverse method based on the integral governing equation is proposed for determining eigenstrain from an incomplete set of measurements. The validity of this method is demonstrated through simulation and experimental results, highlighting its high efficiency and engineering application value.