Laser shock peening (LSP) fires a short, intense pulse through a transparent water layer at an opaque overlay on the metal surface. The overlay flash-vaporizes into a confined plasma; because the water tamps the expanding plasma instead of letting it vent freely, pressures reach several GPa instead of the sub-GPa achieved by open-air ablation.
Fabbro shock-pressure model (Fabbro et al., 1990):
P₀(GPa) = 0.01·√(α/(2α+3))·√Z·√I₀
α ≈ 0.2 (thermal-to-mechanical conversion, confined regime)
Z = 2 / (1/Z_water + 1/Z_target) [reduced acoustic impedance]
I₀ = laser intensity (GW/cm²)
The shock wave attenuates as it propagates into the metal. This engine models the depth profile as an exponential decay set by the material's longitudinal sound speed cL and the pulse duration τ (a longer pulse pushes the wavefront further before it decays):
P(z) = P₀ · exp(−z / λ), λ = k · c_L · τ
Plastic zone: every depth z where P(z) > HEL(material)
→ z_p = λ · ln(P₀ / HEL) (found by scanning the profile point-by-point)
Plastic deformation — and the compressive residual stress that gives LSP its fatigue benefit — only occurs where P(z) exceeds the material's Hugoniot Elastic Limit (HEL), its dynamic yield strength under shock loading.
Residual stress must self-equilibrate through the thickness:
∫ σ(z) dz ≈ 0 over the full cross-section
A compressive skin (−) is always balanced by a smaller-magnitude,
deeper tensile lobe (+). This engine solves the tensile lobe's
amplitude numerically so the two areas cancel exactly.
- Intensity / duration sliders — raise P₀ and λ, widening the plastic layer.
- Material — changes HEL, cL and yield strength, so the same P₀ gives a different depth and peak stress.
- Confinement toggle — shows the water-tamping effect that makes LSP practical.
Real-world use: LSP is applied to turbine blades, landing-gear components and welded joints to drive deep compressive residual stress into the surface, closing off the tensile stress that would otherwise drive fatigue-crack growth — extending service life several-fold without changing part geometry (Peyre & Fabbro, 1996).