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.
Cet article vise à fournir des expressions exactes pour les champs mécaniques induits par le grenaillage laser et à les comparer à leurs estimations numériques. Nous utilisons une hypothèse de champ de déformation uniaxial avec un comportement élastique parfaitement plastique pour obtenir l’équation de l’onde de contrainte. Une solution exacte de cette équation est donnée en utilisant la méthode des caractéristiques pour un profil temporel de la charge de pression, et numériquement en utilisant des schémas de différences finies adaptés à cette équation hyperbolique. Une modélisation supplémentaire des contraintes résiduelles est utilisée, fournissant la distribution des contraintes résiduelles en supposant une plaque infinie plane avec une épaisseur finie. Les résultats sont présentés pour trois pressions de chargement, chacune correspondant à une structure différente dans la solution exacte. Les résultats exacts et numériques présentent une bonne concordance, ce qui permet soit d’utiliser la solution exacte pour une estimation initiale des champs mécaniques, soit de tester la précision d’autres méthodes numériques.
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Mot clés : Grenaillage laser, Propagation d’ondes élasto-plastiques, Simulation numérique, Solution analytique, Déformations plastiques, Contraintes résiduelles
Lucas Lapostolle 1; Léo Morin 2; Katell Derrien 1; Laurent Berthe 1; Olivier Castelnau 1
CC-BY 4.0
@article{CRMECA_2023__351_G2_459_0,
author = {Lucas Lapostolle and L\'eo Morin and Katell Derrien and Laurent Berthe and Olivier Castelnau},
title = {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},
journal = {Comptes Rendus. M\'ecanique},
pages = {459--484},
publisher = {Acad\'emie des sciences, Paris},
volume = {351},
year = {2023},
doi = {10.5802/crmeca.227},
language = {en},
}
TY - JOUR AU - Lucas Lapostolle AU - Léo Morin AU - Katell Derrien AU - Laurent Berthe AU - Olivier Castelnau TI - 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 JO - Comptes Rendus. Mécanique PY - 2023 SP - 459 EP - 484 VL - 351 PB - Académie des sciences, Paris DO - 10.5802/crmeca.227 LA - en ID - CRMECA_2023__351_G2_459_0 ER -
%0 Journal Article %A Lucas Lapostolle %A Léo Morin %A Katell Derrien %A Laurent Berthe %A Olivier Castelnau %T 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 %J Comptes Rendus. Mécanique %D 2023 %P 459-484 %V 351 %I Académie des sciences, Paris %R 10.5802/crmeca.227 %G en %F CRMECA_2023__351_G2_459_0
Lucas Lapostolle; Léo Morin; Katell Derrien; Laurent Berthe; Olivier Castelnau. 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. Comptes Rendus. Mécanique, Volume 351 (2023), pp. 459-484. doi : 10.5802/crmeca.227. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.227/
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