# Numerical Simulations of Laser-Induced Shock Experiments on Graphite

^{*}

## Abstract

**:**

## 1. Introduction

^{2}with nanosecond pulses, thus heating the impacted surface until it reaches plasma conditions. From the successive plasma expansion, a shockwave is generated into the target, producing spallation conditions when it is reflected by the back surface.

## 2. Laser-Induced Shockwaves in Solids

## 3. Numerical Simulation Case Study

## 4. Numerical Approach

#### 4.1. Helios

#### 4.2. LS-Dyna

#### Material Model

^{3}[57,58]. This material is essentially brittle, but the porosity significantly increases the difficulty of describing its behaviour.

## 5. Results

#### 5.1. South Beam Shots

#### 5.2. North Beam Shots

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Graphical representation of: (

**a**) the shockwave formation; (

**b**) the propagation and attenuation of the shockwave, where S is the shock front and R is the release part of the shock, U

_{S}is the shock front velocity, U

_{P}is the particle velocity and C is the sound velocity at a particular pressure.

**Figure 2.**Helios hydrodynamic simulation of the evolution of a laser-induced shockwave inside the target for the shot S7 of the experimental case study explained below.

**Figure 3.**(

**a**) Representation of the free surface velocity history. (

**b**) Distance–time diagram of the compressive (green) and tensile (red) waves trajectories.

**Figure 4.**Schematic comparison between the actual phenomenon (

**left side**) and the LS-Dyna model (

**right side**).

**Figure 5.**Pressure temporal profile (

**a**) and velocity temporal profile (

**b**) coming from Helios and applied as boundary condition in LS-Dyna. Notice that the applied pressure is still roughly 250 MPa at 140 ns.

**Figure 6.**Representation of the pressure plots of the shot S7 used to find the shockwave front at the end deposition time. The figure on the right is the magnification of the left one.

**Figure 7.**Comparison between numerical simulation and shadowgraphies of the shot S7 (reprinted from [28]).

**Figure 8.**Axial velocity of the node at radius = 0 mm on the rear surface. The figure on the

**right**is a portion of the

**left**one.

**Figure 10.**Representative shadowgraphies of shots S7, S15 and S17 (reprinted from [28]) and the respective numerical simulations.

**Figure 12.**Numerical simulations of shots N13, N11, N9 and N8 and the respective shadowgraphies (reprinted from [28]).

Laser Beam | Shot | $\mathbf{t}\text{}\left(\mathbf{m}\mathbf{m}\right)$ | $\mathbf{E}\text{}\left(\mathbf{J}\right)$ | ${\mathit{I}}_{\mathit{m}}$ $(\mathbf{T}\mathbf{W}/\mathbf{c}{\mathbf{m}}^{2})$ | ${\mathit{P}}_{\mathit{a}\mathit{b}}$ $\left(\mathbf{G}\mathbf{P}\mathbf{a}\right)$ | Damage Regime |
---|---|---|---|---|---|---|

SOUTH BEAM | S10 | 1 | 235 | 1.72 | 46.7 | D1–D2 |

S7 | 0.75 | 121 | 0.89 | 27.4 | D2 | |

S15 | 0.75 | 259 | 1.89 | 50.4 | D3 | |

S17 | 0.75 | 547 | 4 | 91.7 | D4 | |

NORTH BEAM | N13 | 2 | 564 | 3.11 | 74.9 | D1 |

N16 | 0.75 | 167 | 0.92 | 28.3 | D1–D2 | |

N9 | 1 | 636 | 3.50 | 82.5 | D2 | |

N8 | 0.75 | 652 | 3.59 | 84.2 | D3 | |

N11 | 1.5 | 608 | 3.35 | 79.6 | D4 |

$\mathbf{Density}\text{}\left[\mathbf{kg}\u2044{\mathbf{m}}^{3}\right]$ | $1.768$ |
---|---|

$\mathrm{Young}\text{}\mathrm{Modulus}\text{}\mathrm{E}\text{}\left[\mathrm{MPa}\right]$ | $11,500$ |

$\mathrm{Yield}\text{}\mathrm{stress}\text{}\left[\mathrm{MPa}\right]$ | $102.5$ |

$\mathrm{Spall}\text{}\mathrm{tension}\text{}\left[\mathrm{MPa}\right]$ | $140$ |

$\mathrm{Bulk}\text{}\mathrm{sound}\text{}\mathrm{speed}\text{}\left[\mathrm{m}/\mathrm{s}\right]$ | $2200$ |

${\mathrm{S}}_{1}\text{}\mathrm{Gruneisen}\text{}\mathrm{parameter}$ | $1.55$ |

**Table 3.**Helios shot results concerning the shockwave depth reached at the end deposition time and the resulting target specimen after the deduction of the removed thickness.

Shot | $\mathbf{Shockwave}\text{}\mathbf{Depth}\text{}\left[\mathsf{\mu}\mathbf{m}\right]$ | $\mathbf{FEM}\text{}\mathbf{Model}\text{}\mathbf{Thickness}\text{}\left[\mathsf{\mu}\mathbf{m}\right]$ |
---|---|---|

S7 | 35 | 715 |

S10 | 50 | 950 |

S15 | 50 | 700 |

S17 | 70 | 680 |

N13 | 62 | 1938 |

N11 | 63 | 1437 |

N16 | 35 | 715 |

N9 | 68 | 932 |

N8 | 68 | 682 |

**Table 4.**Comparison between the speed data of the PDV and VISAR measurements from (adapted from [28]) and of the numerical simulations.

Shot | Peak Velocity [m/s] | Average Debris Velocity [m/s] | |||
---|---|---|---|---|---|

Exp. (PDV) | Exp. (VISAR) | Simulation | Exp. (PDV) | Simulation | |

Shot S7 | 150 | 169 | 145 | 75 | 70 |

Shot S15 | 250 | 272 | 324 | 85 | 250 |

Shot S17 | 400 | 564 | 558 | 100 | 517 |

**Table 5.**Comparison between the speed data of the PDV and VISAR measurements (adapted from [28]) and of the numerical simulations.

Shot | Peak Velocity [m/s] | Average Debris Velocity [m/s] | |||
---|---|---|---|---|---|

Exp. (PDV) | Exp. (VISAR) | Simulation | Exp. (PDV) | Simulation | |

Shot N13 | 75 | 100 | 94 | 15 | 60 |

Shot N11 | 140 | 163 | 169 | 80 | 123 |

Shot N9 | 250 | 332 | 355 | 100 | 225 |

Shot N8 | 360 | 511 | 486 | 100 | 391 |

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Morena, A.; Peroni, L.
Numerical Simulations of Laser-Induced Shock Experiments on Graphite. *Materials* **2021**, *14*, 7079.
https://doi.org/10.3390/ma14227079

**AMA Style**

Morena A, Peroni L.
Numerical Simulations of Laser-Induced Shock Experiments on Graphite. *Materials*. 2021; 14(22):7079.
https://doi.org/10.3390/ma14227079

**Chicago/Turabian Style**

Morena, Alberto, and Lorenzo Peroni.
2021. "Numerical Simulations of Laser-Induced Shock Experiments on Graphite" *Materials* 14, no. 22: 7079.
https://doi.org/10.3390/ma14227079