Exact expressions of the uniaxial perfectly elasto-plastic stress wave and induced mechanical fields in the case of a finite impact: application to laser shock peening

Abstract

This paper aims at providing exact expressions for the mechanical fields induced by Laser Shock Peening and comparing them to their numerical estimations. We use a uniaxial strain field hypothesis with an elastic perfectly plastic behavior to derive the stress wave equation. An exact solution to this equation is given using the method of characteristics for a step time profile for the pressure loading, and numerically using finite differences schemes adapted for this hyperbolic equation. An additional residual stress modeling is used, providing the residual stress distribution assuming a planar infinite plate with a finite thickness. Results are presented for three loading pressures, each one corresponding to a different structure in the exact solution. The exact and numerical results present a good match, allowing either the use of the exact solution for an initial estimation of the mechanical fields, or to test the accuracy of other numerical methods. © 2023 Elsevier Masson SAS. All rights reserved