# Influence of Trapped Gas on Pore Healing under Hot Isostatic Pressing in Nickel-Base Superalloys

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## Abstract

**:**

## 1. Introduction

## 2. Micromechanical Modeling

#### 2.1. Crystal Plasticity Model

#### 2.2. Model Calibration

#### 2.3. Modeling Gas inside Pores

## 3. Numerical Study and Results

#### 3.1. Influence of HIP Processing Conditions

#### 3.2. Influence of Pore Shape

#### 3.3. Influence of Pore Size

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

HIP | Hot isostatic pressing |

AM | Additive manufacturing |

CP | Crystal plasticity |

## References

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**Figure 3.**Comparison of void volume fraction evolution curves between experimental and simulation results. The experimental curve is obtained from Epishin et al. [21]. The figure inset indicates the two stages of HIP loading.

**Figure 4.**Planar view of a gas-filled spherical pore subjected to external applied load ${P}_{HIP}$. The pressure exerted by the trapped gas on the pore surface is represented as ${P}_{GAS}$.

**Figure 5.**Void volume reduction in Stage 1 and Stage 2 HIP loading for spherical void of radius 1 μm under different magnitudes of the isostatic pressure and different holding times at 1561 K.

**Figure 6.**Pore volume reduction and gas pressure evolution in Stage 1 and Stage 2 HIP loading for spherical pore of radius 1 μm under different magnitudes of the isostatic pressure and different holding times at 1561 K.

**Figure 7.**1/8th spherical (

**left**) and 1/8th ellipsoidal (

**right**) model mesh configurations used in HIP simulations.

**Figure 8.**Von Mises stress (

**a**) and plastic strain (

**b**) evolution around a spherical void (zoomed area) with increasing simulation time under 100 MPa isostatic pressure at 1561 K.

**Figure 9.**Von Mises stress (

**a**) and plastic strain (

**b**) evolution around an ellipsoidal void (zoomed area) with increasing simulation time under 100 MPa isostatic pressure at 1561 K.

**Figure 10.**Void volume reduction in Stage 1 and Stage 2 HIP loading for spherical and ellipsoidal voids of identical volume under 100 MPa isostatic pressure at 1561 K.

**Figure 11.**Pore volume reduction in Stage 1 and Stage 2 HIP loading for spherical and ellipsoidal pores of identical volume under 100 MPa isostatic pressure at 1561 K.

**Figure 12.**Quasi-2D representative CPFE model with finite element mesh and boundary conditions for the irregular shaped void. ‘P’ represents the isostatic pressure applied on the outer boundaries.

**Figure 13.**Von Mises stress (

**a**) and plastic strain (

**b**) evolution around irregular-shaped void (Quasi-2D) with increasing simulation time under 100 MPa isostatic pressure at 1561 K.

**Figure 14.**Void volume reduction ratio in Stage 1 and Stage 2 HIP loading for spherical voids of various radii under 100 MPa isostatic pressure at 1561 K.

**Figure 15.**(

**Top**) Final pore volume and final gas pressure under HIP loading as a function of initial pore volume. (

**Bottom**) Snapshots of hydrostatic stress distribution around pores (zoomed area) taken at the end of simulations. Simulations are done with spherical pores of various radii under 100 MPa isostatic pressure at 1561 K.

**Table 1.**Fitted material parameters for CMSX-4 superalloy. ${\widehat{\tau}}_{0}^{\mathrm{slip}}$ is the initial slip resistance produced by dislocation interaction.

Parameter | Value | Unit |
---|---|---|

G | 69.4 | GPa |

b | 0.254 | nm |

${D}_{0}$ | 3.36 × 10${}^{-4}$ [26] | ${\mathrm{m}}^{2}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{s}}^{-1}$ |

${Q}_{sd}$ | 292 [26] | $\mathrm{kJ}\phantom{\rule{4.pt}{0ex}}{\mathrm{mol}}^{-1}$ |

A | 1.2 × 10${}^{-10}$ | - |

${p}_{1}$ | 3.0 | - |

${p}_{2}$ | 0.05 | - |

${\widehat{\tau}}_{0}^{\mathrm{slip}}$ | 40 | MPa |

${\widehat{\tau}}^{\mathrm{sat}}$ | 600 | MPa |

${h}_{0}$ | 60 | MPa |

${v}_{1}$ | 60 | MPa |

${v}_{2}$ | 2.0 | - |

**Table 2.**Parameters used for modeling gas inside pores. The gas considered for simulations is argon.

${\mathit{M}}_{\mathit{w}}$ (kg mol${}^{-1}$) | R (JK${}^{-1}$mol${}^{-1}$) | ${\mathit{P}}_{\mathbf{ref}}$ (MPa) | ${\mathit{P}}_{\mathbf{amb}}$ (MPa) | ${\mathit{T}}_{\mathbf{ref}}$ (K) |
---|---|---|---|---|

0.039948 | 8.314 | 0 | 0.101 | 1728.15 |

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**MDPI and ACS Style**

Prasad, M.R.G.; Gao, S.; Vajragupta, N.; Hartmaier, A.
Influence of Trapped Gas on Pore Healing under Hot Isostatic Pressing in Nickel-Base Superalloys. *Crystals* **2020**, *10*, 1147.
https://doi.org/10.3390/cryst10121147

**AMA Style**

Prasad MRG, Gao S, Vajragupta N, Hartmaier A.
Influence of Trapped Gas on Pore Healing under Hot Isostatic Pressing in Nickel-Base Superalloys. *Crystals*. 2020; 10(12):1147.
https://doi.org/10.3390/cryst10121147

**Chicago/Turabian Style**

Prasad, Mahesh R. G., Siwen Gao, Napat Vajragupta, and Alexander Hartmaier.
2020. "Influence of Trapped Gas on Pore Healing under Hot Isostatic Pressing in Nickel-Base Superalloys" *Crystals* 10, no. 12: 1147.
https://doi.org/10.3390/cryst10121147