# Coupled Modeling Approach for Laser Shock Peening of AA2198-T3: From Plasma and Shock Wave Simulation to Residual Stress Prediction

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Parameters

#### 2.2. Simulation Scheme

#### 2.2.1. Global LSP Model

#### 2.2.2. Finite Element Model

#### 2.3. Model Analysis

#### 2.3.1. Sensitivity Study

#### 2.3.2. Residual Stress Prediction

#### 2.3.3. Parameter Identification

## 3. Results and Discussion

#### 3.1. Pressure Profiles

#### 3.2. Residual Stresses

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

A | yield strength |

${A}_{\mathrm{p}}$ | coefficient of laser absorption by the plasma |

B | strengthening coefficient |

$\Gamma $ | mass flow |

C | rate dependency of the material |

D | shock wave velocity |

E | internal energy |

${E}_{\mathrm{Y}}$ | Young’s modulus |

${E}_{\Gamma}$ | energy exchange through mass flows |

${E}_{\mathrm{pk}}$ | kinetic plasma energy |

${E}_{\mathrm{pt}}$ | total plasma energy |

F | laser focus size |

I | laser intensity |

${I}_{\mathrm{max}}$ | peak of laser intensity |

L | plasma thickness |

P | pressure |

${P}_{\mathrm{max}}$ | maximum plasma pressure |

Q | specific phase change energy |

S | empiric parameters, which connect shock and particle velocities |

T | laser pulse FWHM |

${T}_{\mathrm{L}}$ | total pulse duration |

U | particles velocity |

${U}_{\mathrm{pm}}$ | expansion velocity of plasma in metal direction |

${U}_{\mathrm{pw}}$ | expansion velocity of plasma in water direction |

${U}_{\mathrm{s}}$ | velocity of sound |

${W}_{\mathrm{p}}$ | work done by plasma |

$\gamma $ | specific heat ratio |

${\epsilon}_{P}$ | plastic strain |

${\dot{\epsilon}}_{P}$ | plastic strain rate |

${\dot{\epsilon}}_{P,0}$ | reference plastic strain rate |

$\nu $ | Poisson’s ratio |

n | strain hardening exponent |

$\rho $ | mass density |

${\rho}_{\mathrm{pmax}}$ | maximum plasma density |

${\sigma}_{\mathrm{Y}}$ | yield stress |

${\sigma}_{xx}^{M}$ | measured residual stress in xx-direction |

${\sigma}_{yy}^{M}$ | measured residual stress in yy-direction |

${\sigma}_{xx}^{Sim}$ | calculated residual stress in xx-direction |

${\sigma}_{yy}^{Sim}$ | calculated residual stress in yy-direction |

t | time |

FE | finite element |

FWHM | full-width-at-half-maximum |

ICF | inertial confinement fusion |

LSP | laser shock peening |

RS | residual stress |

Subscript ’m’ | metal region |

Subscript ’0’ | unshocked region |

Subscript ’p’ | plasma region |

Subscript ’w’ | water region |

## References

- Vilhauer, B.; Bennett, C.R.; Matamoros, A.B.; Rolfe, S.T. Fatigue behavior of welded coverplates treated with Ultrasonic Impact Treatment and bolting. Eng. Struct.
**2012**, 34, 163–172. [Google Scholar] [CrossRef] - Hatamleh, O. A comprehensive investigation on the effects of laser and shot peening on fatigue crack growth in friction stir welded AA 2195 joints. Int. J. Fatigue
**2009**, 31, 974–988. [Google Scholar] [CrossRef] - Gujba, A.K.; Medraj, M. Laser Peening Process and Its Impact on Materials Properties in Comparison with Shot Peening and Ultrasonic Impact Peening. Materials
**2014**, 7, 7925–7974. [Google Scholar] [CrossRef] [PubMed][Green Version] - Zhu, J.; Jiao, X.; Zhou, C.; Gao, H. Applications of Underwater Laser Peening in Nuclear Power Plant Maintenance. Energy Procedia
**2012**, 16, 153–158. [Google Scholar] [CrossRef][Green Version] - Colon, C.; de Andres-Garcia, M.I.; Moreno-Diaz, C.; Alonso-Medina, A.; Porro, J.A.; Angulo, I.; Ocana, J.L. Experimental Determination of Electronic Density and Temperature in Water-Confined Plasmas Generated by Laser Shock Processing. Metals
**2019**, 9, 808. [Google Scholar] [CrossRef][Green Version] - Radziejewska, J.; Strzelec, M.; Ostrowski, R.; Sarzyński, A. Experimental investigation of shock wave pressure induced by a ns laser pulse under varying confined regimes. Opt. Laser Eng.
**2020**, 126, 105913. [Google Scholar] [CrossRef] - Peyre, P.; Fabbro, R.; Berthe, L.; Dubouchet, C. Laser shock processing of materials, physical processes involved and examples of applications. J. Laser Appl.
**1996**, 8, 135. [Google Scholar] [CrossRef] - Askaryan, G.A.; Moroz, E.M. Pressure on evaporation of matter in a radiation beam. JETP Lett.
**1963**, 16, 1638. [Google Scholar] - White, R.M. Elastic Wave Generation by Electron Bombardment or Electromagnetic Wave Absorption. J. Appl. Phys.
**1963**, 34, 2123–2124. [Google Scholar] [CrossRef] - Lindl, J. Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain. Phys. Plasmas
**1995**, 2, 3933–4024. [Google Scholar] [CrossRef][Green Version] - Moscicki, T.; Hoffman, J.; Szymanski, Z. Modelling of plasma formation during nanosecond laser ablation. Arch. Mech.
**2011**, 63, 99–116. [Google Scholar] - Anderholm, N.C. Laser-generated stress waves. Appl. Phys. Lett.
**1970**, 16, 113–115. [Google Scholar] - O’Keefe, J.D.; Skeen, C.H.; York, C.M. Laser-induced deformation modes in thin metal targets. J. Appl. Phys.
**1973**, 44, 4622–4626. [Google Scholar] [CrossRef] - Fairand, B.P.; Clauer, A.H.; Jung, R.G.; Wilcox, B.A. Quantitative assessment of laser-induced stress waves generated at confined surfaces. Appl. Phys. Lett.
**1974**, 25, 431–433. [Google Scholar] [CrossRef] - Warren, A.W.; Guo, Y.B.; Chen, S.C. Massive parallel laser shock peening: Simulation, analysis, and validation. Int. J. Fatigue
**2008**, 30, 188–197. [Google Scholar] [CrossRef] - Hu, Y.; Yao, Z.; Hu, J. 3-D FEM simulation of laser shock processing. Surf. Coat. Technol.
**2006**, 201, 1426–1435. [Google Scholar] [CrossRef] - Golabi, S.; Vakil, M.R.; Amirsalari, B. Multi-Objective Optimization of Residual Stress and Cost in Laser Shock Peening Process Using Finite Element Analysis and PSO Algorithm. Lasers Manuf. Mater. Process.
**2019**, 6, 398–423. [Google Scholar] [CrossRef] - Braisted, W.; Brockman, R. Finite element simulation of laser shock peening. Int. J. Fatigue
**1999**, 21, 719–724. [Google Scholar] [CrossRef] - Zhai, P.; Dong, Z.; Miao, R.; Deng, X.; Chen, L. Investigation on the laser-induced shock pressure with condensed matter model. J. Appl. Phys.
**2015**, 54, 056203. [Google Scholar] [CrossRef] - Wei, X.L.; Ling, X. Numerical modeling of residual stress induced by laser shock processing. Appl. Surf. Sci.
**2014**, 301, 557–563. [Google Scholar] [CrossRef] - Kim, J.H.; Kim, Y.J.; Lee, J.W.; Yoo, S.H. Study on effect of time parameters of laser shock peening on residual stresses using FE simulation. J. Mech. Sci. Technol.
**2014**, 28, 1803–1810. [Google Scholar] [CrossRef] - Ding, K.; Ye, L. Simulation of multiple laser shock peening of a 35CD4 steel alloy. J. Mater. Process. Technol.
**2006**, 178, 162–169. [Google Scholar] [CrossRef] - Yang, C.; Hodgson, P.D.; Liu, Q.; Ye, L. Geometrical effects on residual stresses in 7050-T7451 aluminum alloy rods subject to laser shock peening. J. Mater. Process. Technol.
**2008**, 201, 303–309. [Google Scholar] [CrossRef] - Wang, X.; Xia, W.; Wu, X.; Huang, C. Scaling Law in Laser-Induced Shock Effects of NiTi Shape Memory Alloy. Metals
**2018**, 8, 174. [Google Scholar] [CrossRef] - Kumar, G.R.; Rajyalakshmi, G. Modelling and multi objective optimization of laser peening process using Taguchi utility concept. IOP Conf. Ser. Mater. Sci. Eng.
**2017**, 263, 062055. [Google Scholar] [CrossRef] - Jiang, X.; Yu, X.; Deng, X.; Shao, Y.; Peng, P. Investigation on Laser-Induced Shock Pressure with Condensed Matter Model and Experimental Verification. Exp. Tech.
**2019**, 43, 161–167. [Google Scholar] [CrossRef] - Fabbro, R.; Fournier, J.; Ballard, P.; Devaux, D.; Virmont, J. Physical study of laser-produced plasma in confined geometry. J. Appl. Phys.
**1990**, 68, 775–784. [Google Scholar] [CrossRef] - Wu, B.; Shin, Y.C. A self-closed thermal model for laser shock peening under the water confinement regime configuration and comparisons to experiments. J. Appl. Phys.
**2005**, 97, 113517. [Google Scholar] [CrossRef] - Morales, M.; Porro, J.A.; Blasco, M.; Molpeceres, C.; Ocana, J.L. Numerical simulation of plasma dynamics in laser shock processing experiments. Appl. Surf. Sci.
**2009**, 255, 5181–5185. [Google Scholar] [CrossRef] - Zhang, W.; Yao, Y.L.; Noyan, I.C. Microscale Laser Shock Peening of Thin Films, Part 1: Experiment, Modeling and Simulation. J. Manuf. Sci. Eng.
**2004**, 126, 10–17. [Google Scholar] [CrossRef] - Pirri, A.N.; Root, R.G. Plasma Energy Transfer to Metal Surfaces Irradiated by Pulsed Lasers. AIAA J.
**1978**, 16, 1296–1304. [Google Scholar] [CrossRef] - Fortunato, A.; Orazi, L.; Cuccolini, G.; Ascari, A. Laser shock peening and warm laser shock peening: Process modeling and pulse shape influence. Proc. SPIE
**1978**, 8603, 86030G. [Google Scholar] - Sinha, S. Nanosecond laser ablation of graphite: A thermal model based simulation. J. Laser Appl.
**2018**, 30, 012008. [Google Scholar] [CrossRef] - MacFarlane, J.J.; Golovkin, I.E.; Woodruff, P.R. HELIOS-CR—A 1-D radiation-magnetohydrodynamics code with inline atomic kinetics modeling. J. Quant. Spectrosc. Radiat. Transf.
**2006**, 99, 381–397. [Google Scholar] [CrossRef][Green Version] - Lyon, S.P.; Johnson, J.D. SESAME: The Los Alamos National Laboratory Equation of State Database; Technical Report, LA-UR-92-3407; Los Alamos National Laboratory: Los Alamos, NM, USA, 1992.
- Bhamare, S.; Ramakrishnan, G.; Mannava, S.R.; Langer, K.; Vasudevan, V.K.; Qian, D. Simulation-based optimization of laser shock peening process for improved bending fatigue life of Ti–6Al–2Sn–4Zr–2Mo alloy. Surf. Coat. Technol.
**2013**, 232, 464–474. [Google Scholar] [CrossRef] - Peyre, P.; Fabbro, R.; Merrien, P.; Lieurade, H.P. Laser shock processing of aluminium alloys. Application to high cycle fatigue behaviour. Mater. Sci. Eng.
**1996**, 210, 102–113. [Google Scholar] [CrossRef] - Amarchinta, H.K.; Grandhi, R.V.; Clauer, A.H.; Langer, K.; Stargel, D.S. Simulation of residual stress induced by a laser peening process through inverse optimization of material models. J. Mater. Process. Technol.
**2010**, 210, 1997–2006. [Google Scholar] [CrossRef] - Johnson, G.; Cook, W. A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates, and High Temperatures. In Proceedings of the 7th International Symposium on Ballistics, The Hague, The Netherlands, 19–21 April 1983; pp. 541–547. [Google Scholar]
- Langer, K.; Olson, S.; Brockman, R.; Braisted, W.; Spradlin, T.; Fitzpatrick, M.E. High Strain-Rate Material Model Validation for Laser Peening Simulation. J. Eng.
**2015**, 2015, 150–157. [Google Scholar] [CrossRef] - Keller, S.; Chupakhin, S.; Staron, P.; Maawad, E.; Kashaev, N.; Klusemann, B. Experimental and numerical investigation of residual stresses in laser shock peened AA2198. J. Mater. Process. Technol.
**2018**, 255, 294–307. [Google Scholar] [CrossRef] - Schajer, G.S. Advances in hole-drilling residual stress measurements. Exp. Mech.
**2010**, 50, 159–168. [Google Scholar] [CrossRef] - Meyers, M. Shock Waves and High-Strain-Rate Phenomena in Metals; Springer: Boston, MA, USA, 1981; pp. 1033–1049. [Google Scholar]
- NIST Chemistry WebBook. Available online: https://webbook.nist.gov (accessed on 1 June 2019).
- Material Property Data. Available online: http://www.matweb.com (accessed on 1 June 2019).
- Liley, P.E. Thermophysical Properties of Fluids. In Mechanical Engineers Handbook: Energy and Power, 3rd ed.; Kutz, M., Ed.; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2005; Volume 4, pp. 1–45. [Google Scholar]
- Leitner, M.; Leitner, T.; Schmon, A.; Aziz, K.; Pottlacher, G. Thermophysical Properties of Liquid Aluminum. Metall. Mater. Trans. A
**2017**, 48, 3036–3045. [Google Scholar] [CrossRef][Green Version] - Simons, G.A. Momentum Transfer to a Surface When Irradiated by a High-Power Laser. AIAA J.
**1984**, 22, 1275–1280. [Google Scholar] [CrossRef] - Sticchi, M.; Staron, P.; Sano, Y.; Meixer, M.; Klaus, M.; Rebelo-Kornmeier, J.; Huber, N.; Kashaev, N. A parametric study of laser spot size and coverage on the laser shock peening induced residual stress in thin aluminium samples. J. Eng.
**2015**, 2015, 97–105. [Google Scholar] [CrossRef] - Ready, J.F. Effects of High-Power Laser Radiation; Academic: London, UK, 1971. [Google Scholar]
- Mahdavi, M.; Ghazizadeh, S.F. Linear absorption mechanisms in laser plasma interactions. J. Appl. Sci.
**2012**, 12, 12–21. [Google Scholar] [CrossRef] - Zhang, W.; Yao, Y.L. Modeling and Simulation Improvement in Laser Shock Processing. In Proceedings of the ICALEO 2001 Congress, Jacksonville, FL, USA, 15–18 October 2001; pp. 59–68. [Google Scholar]
- Rubio-Gonzalez, C.; Gomez-Rosas, G.; Ocana, J.; Molpeceres, C.; Banderas, A.; Porro, J.; Morales, M. Effect of an absorbent overlay on the residual stress field induced by laser shock processing on aluminum samples. Appl. Surf. Sci.
**2006**, 252, 6201–6205. [Google Scholar] [CrossRef] - Xu, Y.Y.; Ren, X.D.; Zhang, Y.K.; Zhou, J.Z.; Zhang, X.Q. Coating Influence on Residual Stress in Laser Shock Processing. Key Eng. Mater.
**2007**, 353–358, 1753–1756. [Google Scholar] [CrossRef] - Kallien, Z.; Keller, S.; Ventzke, V.; Kashaev, N.; Klusemann, B. Effect of laser peening process parameters and sequences on residual stress profiles. Metals
**2019**, 9, 655. [Google Scholar] [CrossRef][Green Version]

**Figure 2.**Schematic of the applied LSP simulation scheme, including the comparison of predicted and experimentally determined RS. The global LSP model yields the plasma pressure. This pressure is used in FE simulations to determine the RS numerically. The predicted RS are compared with measurements to determine unknown plasma parameters for the case of a 5 J energy pulse without coating. Based on this, the global model is adjusted to allow for predictions of RS state at different laser intensities and coating materials.

**Figure 3.**Non-symmetric temporal profile of the laser pulse used in the current research with FWHM $T=20\phantom{\rule{3.33333pt}{0ex}}\mathrm{ns}$ and the total duration ${T}_{\mathrm{L}}=80\phantom{\rule{3.33333pt}{0ex}}\mathrm{ns}$.

**Figure 4.**Schematic of the global LSP model with water curtain. The region of water–metal–plasma interaction is separated into five parts: unshocked and shocked water, unshocked metal, shocked metal coupled with a coating material and a plasma of thickness L. Expansion velocities of plasma in water ${U}_{\mathrm{pw}}$ and metal ${U}_{\mathrm{pm}}$ directions are depicted.

**Figure 5.**FE model of the LSP process for square laser focus. The borders in x- and y-direction were fixed in all degrees of freedom, where the bottom surface was modeled as a free surface. The laser pulses were modeled as pressure loading, obtained from the global model, in the shown order, corresponding to the applied laser pulse sequence.

**Figure 6.**Sensitivity analysis of the maximum plasma pressure dependent on initial plasma density ${\rho}_{\mathrm{p}0}$ for different absorption coefficients ${A}_{\mathrm{p}}$. LSP of aluminum with a laser pulse energy of 5 J without coating is simulated. The points P1, P2, P3 and P4 correspond to the borders of the parameter space and represent pairs of values ${\rho}_{\mathrm{p}0}$ and ${A}_{\mathrm{p}}$, which were used within the sensitivity study. The star corresponds to identified simulation parameters based on the comparison to experimental RS results; see Section 2.3.3.

**Figure 7.**Temporal distributions of particle velocities in water (

**a**) and metal (

**c**); the expansion speed of plasma in water (

**b**) and metal (

**d**) directions for the four points P1–P4; see Figure 6. The particle velocity of water is approximately five times larger than the velocity of metal particles. The expansion speed of plasma in the direction of water is one order higher than the expansion speed in the direction of metal.

**Figure 8.**Time-dependent mass flows from water region (

**a**) and metal region (

**b**) to plasma for the four border points P1–P4; see Figure 6. The major mass flow from water indicates that the plasma mostly consists of water particles.

**Figure 9.**Plasma pressure distributions for the four border points P1–P4 defined in Figure 6 without relaxation (

**a**) and with relaxation (

**b**), which happens after laser pulse terminates and results in a pressure drop.

**Figure 10.**(

**a**) Resulting RS distribution after the application of the four pressure pulses (P1–P4) shown in Figure 9b, which were defined for the four border points P1–P4; see Figure 6. (

**b**) Sensitivity study of the maximum plasma pressure regarding the calculated maximum plasma density ${\rho}_{\mathrm{pmax}}$ at different absorption coefficients ${A}_{\mathrm{P}}$. The star corresponds to identified simulation parameters based on the comparison to experimental RS; see Section 2.3.3.

**Figure 11.**Temporal pressure distributions for the cases with aluminum ablative surface (solid black line) and with steel foil as a coating material (dashed-dotted red line) in comparison with laser intensity profiles (dashed blue line) for laser pulse energy of 3 J (

**a**) and 5 J (

**b**).

**Figure 12.**Temporal distribution of the expansion speed of plasma in water direction for the cases with aluminum ablative surface (solid black line) and with steel foil as a coating material (red line) for laser pulse energy of 3 (

**a**) and 5 J (

**b**).

**Figure 13.**Time-dependent mass flows from metal to plasma for the cases with aluminum ablative surface (solid black line) and with steel foil as a coating material (red line) for laser pulse energy of 3 (

**a**) and 5 J (

**b**).

**Figure 14.**Comparison between calculated (${\sigma}_{xx}^{Sim}={\sigma}_{yy}^{Sim}$) and experimentally determined (${\sigma}_{xx}^{M}$, ${\sigma}_{yy}^{M}$) RS in AA2198-T3 after LSP treatment for different laser pulse energies and coating materials. (

**a**) 3 J pulse energy, no coating. (

**b**) 5 J pulse energy, no coating. (

**c**) 3 J pulse energy, aluminum foil. (

**d**) 5 J pulse energy, aluminum foil. (

**e**) 3 J pulse energy, steel foil. (

**f**) 5 J pulse energy, steel foil.

**Table 1.**Material parameters employed, assuming pressure of unshocked regions ${P}_{0}$ of ${10}^{5}$ Pa for all materials.

Parameter | Water | Aluminum | Steel |
---|---|---|---|

Density ${\rho}_{0}$, $\phantom{\rule{0.166667em}{0ex}}{\mathrm{kg}/\mathrm{m}}^{3}$ | 1000 | 2800 | 7900 |

Sound velocity ${U}_{s}$ [43], m/s | 2393 | 5328 | - |

Coefficient S [43] | 1.333 | 1.338 | - |

Specific phase change energy Q [44,45,46,47], $\phantom{\rule{0.166667em}{0ex}}\mathrm{MJ}/\mathrm{kg}$ | ≈3 | ≈15 | ≈9 |

Parameter | AA2198-T3 |
---|---|

Young’s modulus ${E}_{\mathrm{Y}}$, GPa | 78 |

Poisson’s ratio $\nu $ | 0.33 |

Quasi-static yield strength A, MPa | 310 |

Strengthening coefficient B, MPa | 1177 |

Strain hardening exponent n | 0.894 |

Reference plastic strain rate ${\dot{\epsilon}}_{P,0}$, s${}^{-1}$ | 1.8 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{-4}$ |

Dynamic strain hardening coefficient C | 0.01 |

Parameter | Initial Value |
---|---|

Expansion velocities ${U}_{\mathrm{pw}}$ and ${U}_{\mathrm{pm}}$, m/s | 0 |

Plasma density ${\rho}_{\mathrm{p}0}$, kg/m${}^{3}$ | 0.1–10 |

Plasma pressure ${P}_{\mathrm{p}0}$, Pa | ${10}^{5}$ |

Absorption coefficient ${A}_{\mathrm{p}},\%$ | 10–50 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pozdnyakov, V.; Keller, S.; Kashaev, N.; Klusemann, B.; Oberrath, J.
Coupled Modeling Approach for Laser Shock Peening of AA2198-T3: From Plasma and Shock Wave Simulation to Residual Stress Prediction. *Metals* **2022**, *12*, 107.
https://doi.org/10.3390/met12010107

**AMA Style**

Pozdnyakov V, Keller S, Kashaev N, Klusemann B, Oberrath J.
Coupled Modeling Approach for Laser Shock Peening of AA2198-T3: From Plasma and Shock Wave Simulation to Residual Stress Prediction. *Metals*. 2022; 12(1):107.
https://doi.org/10.3390/met12010107

**Chicago/Turabian Style**

Pozdnyakov, Vasily, Sören Keller, Nikolai Kashaev, Benjamin Klusemann, and Jens Oberrath.
2022. "Coupled Modeling Approach for Laser Shock Peening of AA2198-T3: From Plasma and Shock Wave Simulation to Residual Stress Prediction" *Metals* 12, no. 1: 107.
https://doi.org/10.3390/met12010107