# FE Analysis of Laser Shock Peening on STS304 and the Effect of Static Damping on the Solution

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## Abstract

**:**

## 1. Introduction

## 2. LSP Process Modeling

#### 2.1. Conservation Equations for Explicit Analysis

#### 2.2. Static Damping

#### 2.3. Stress–Strain Model

#### 2.4. Pressure Load Model

#### 2.5. Overlapped Multiple LSP

## 3. Experiment and FE Analysis Condition

#### 3.1. LSP Experiment Setup

#### 3.2. LSP FE Simulation Setup

## 4. Results and Discussion

#### 4.1. Single LSP FE Analysis

#### 4.1.1. Energy Summary

#### 4.1.2. Transient Analysis

#### 4.1.3. Deformation Distribution

#### 4.1.4. Minimum Principal Stress Distribution

#### 4.1.5. Discussion on Single LSP FE Analysis

#### 4.2. Multiple LSP FE Analysis

#### 4.2.1. Deformation Distribution

#### 4.2.2. Minimum Principal Stress Distribution

#### 4.3. Residual Stress Distribution of LSP Material

## 5. Conclusions

- The single and multi-shot explicit dynamic LSP FE analysis was conducted with the proposed static damping model by ANSYS Autodyn.
- An implicit analysis that involved stabilizing the geometry can be skipped by adding the static damping value.
- The static damping quickly settles the model after shock loading, but with large damping, residual stress is formed near the surface of the geometry, albeit not deeply, and relatively small plastic deformation can be obtained.
- A comparison of residual stress measurement results on the LSP specimen with compressed residual stress obtained from the simulation showed a similar tendency.
- The residual stress of the FE simulation and that measured by hole drilling showed a small anisotropic relationship due to the LSP process parameters.
- By using the proper static damping value in LSP FE simulation, the calculation time can be reduced and there is no significant effect on the simulation result.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

FEM | Finite Element Method |

LSP | Laser Shock Peening |

PDE | Partial Differential Equations |

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**Figure 1.**Analysis flow chart: (

**a**) Typical explicit and implicit method; (

**b**) SEATD explicit method; (

**c**) Proposed static damping explicit method.

**Figure 5.**FE model setup; (

**a**) Pressure load and boundary condition faces; (

**b**) Edge sizing for fine mesh generation.

**Figure 6.**Example of the overlapped multiple LSP pattern; (

**a**) Pressure load timing on face No. 16; (

**b**) Pressure loading sequence. The gray-colored dotted line indicates the laser pulse path.

**Figure 7.**Energy summary of solution. The differential of internal energy ($\Delta {E}_{Internal}/\Delta t$) is plotted to evaluate the stabilizing time for each damping value.

**Figure 9.**Z-directional deformation of single LSP FE solution. Top (x–y plane) and cross-section (x–z plane) view: (

**a**) ${R}_{d}$ = 0; (

**b**) ${R}_{d}=4.6\times {10}^{-5}$; (

**c**) ${R}_{d}=50\times {10}^{-5}$; (

**d**) ${R}_{d}=500\times {10}^{-5}$.

**Figure 11.**Minimum principal stress of single LSP FE solution. Top (x–y plane) and cross-section (x–z plane) view: (

**a**) ${R}_{d}$ = 0; (

**b**) ${R}_{d}=4.6\times {10}^{-5}$; (

**c**) ${R}_{d}=50\times {10}^{-5}$; (

**d**) ${R}_{d}=500\times {10}^{-5}$.

**Figure 12.**Minimum principal stress of single LSP FE solution in the depth (z-) direction at the center of the pressure load applied.

**Figure 14.**Z-directional deformation of multiple LSP FE solution. Top (x–y plane) and cross-section (x–z plane) view: (

**a**) ${R}_{d}$ = 0; (

**b**) ${R}_{d}=4.6\times {10}^{-5}$; (

**c**) ${R}_{d}=50\times {10}^{-5}$; (

**d**) ${R}_{d}=500\times {10}^{-5}$.

**Figure 16.**Minimum principal stress of multiple LSP FE solution. Top (x–y plane) and cross-section (x–z plane) view: (

**a**) ${R}_{d}$ = 0; (

**b**) ${R}_{d}=4.6\times {10}^{-5}$; (

**c**) ${R}_{d}=50\times {10}^{-5}$; (

**d**) ${R}_{d}=500\times {10}^{-5}$.

**Figure 17.**Minimum principal stress of multiple LSP FE solution in the depth (z-) direction at face No. 16 in Figure 6.

**Figure 19.**Residual stress of the geometry surface (${R}_{d}=0$): (

**a**) normal stress ${\sigma}_{x}$ and (

**b**) normal stress ${\sigma}_{y}$.

**Figure 20.**Residual stress comparison of the experiment and simulation result in the depth (z-) direction.

Laser Pulse Energy | Laser Pulse Width | Beam Diameter | Overlap | Repetition Rate | Laser Type & Wavelength | Beam Shape | Overlay |
---|---|---|---|---|---|---|---|

(J) | (ns) | (mm) | (%) | (Hz) | (nm) | ||

4.2 | 10 | 3 | 50 | 1 | Nd:YAG, 1064 | Flat-top | Water |

Material | Density | Poisson’s Ratio | Young’s Modulus | A | B | C | n | $\dot{{\mathit{\epsilon}}_{0}}$ |
---|---|---|---|---|---|---|---|---|

(Kg/m${}^{3}$) | (GPa) | (MPa) | (MPa) | (MPa) | (${\mathit{s}}^{-1}$) | |||

STS304 | 7750 | 0.31 | 207 | 310 | 100 | 0.07 | 0.65 | 1 |

Static Damping Value ($\times {10}^{-5}$) | Time for Stabilization | Maximum Depth of Minimum Principal Stress | Maximum Deformation on the Surface |
---|---|---|---|

0 | 1.00 | 1.00 | 1.00 |

1 | 0.90 | 0.95 | 0.97 |

4.6 | 0.61 | 0.90 | 0.94 |

10 | 0.50 | 0.87 | 0.86 |

50 | 0.20 | 0.57 | 0.58 |

250 | 0.10 | 0.24 | 0.21 |

500 | 0.06 | 0.22 | 0.10 |

Material | Analysis Method | Hole Step | Step Method | Hole Depth (mm) | Analysis Step | Analysis Step Method | Analysis Depth (mm) | Drill dia. (mm) |
---|---|---|---|---|---|---|---|---|

STS304 | ASTM E837-13 | 24 | Linear | 1.2 | 20 | Linear | 1 | 1.6 |

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**MDPI and ACS Style**

Kim, R.; Suh, J.; Shin, D.; Lee, K.-H.; Bae, S.-H.; Cho, D.-W.; Yi, W.-G. FE Analysis of Laser Shock Peening on STS304 and the Effect of Static Damping on the Solution. *Metals* **2021**, *11*, 1516.
https://doi.org/10.3390/met11101516

**AMA Style**

Kim R, Suh J, Shin D, Lee K-H, Bae S-H, Cho D-W, Yi W-G. FE Analysis of Laser Shock Peening on STS304 and the Effect of Static Damping on the Solution. *Metals*. 2021; 11(10):1516.
https://doi.org/10.3390/met11101516

**Chicago/Turabian Style**

Kim, Ryoonhan, Jeong Suh, Dongsig Shin, Kwang-Hyeon Lee, Seung-Hoon Bae, Dae-Won Cho, and Won-Geun Yi. 2021. "FE Analysis of Laser Shock Peening on STS304 and the Effect of Static Damping on the Solution" *Metals* 11, no. 10: 1516.
https://doi.org/10.3390/met11101516