# Impacts of mechanical fields on hydrogen transport in ITER divertor monoblocks

Shihao Bian, Jonathan Mougenot, Yann Charles, Xavier Bonnin, Tom Wauters, Richard Pitts

► To cite this version:

Shihao Bian, Jonathan Mougenot, Yann Charles, Xavier Bonnin, Tom Wauters, et al. Impacts of mechanical fields on hydrogen transport in ITER divertor monoblocks. 4th International Conference on Metals and Hydrogen, Oct 2022, Ghent, Belgium. . [hal-03886786](https://hal.science/hal-03886786)

HAL Id: hal-03886786

https://hal.science/hal-03886786

Submitted on 6 Dec 2022

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Distributed under a Creative Commons Attribution 4.0 International License
## In a few words

### Objective

Get the role of the thermo-mechanical fields on hydrogen diffusion and retention in ITER divertor monoblocks

<figure><img src="image_2.png" /></figure>

### Method

3D finite element simulations
→ Abaqus software + User subroutines

<figure><img src="image_3.png" /></figure>

Pitts et al. (2017). *Nuclear Materials and Energy*, 12, 60-74.

### Main results

* Estimation of H retention in divertor monoblocks (10 mg)

* Estimation of the H permeated to the cooling pipes

* Estimation of the impact of the operation cycles

## Modelling

<figure><img src="image_4.png" /></figure>

19266 linear full integration elements (C3D8T)

### Loading scenario

<figure><img src="image_5.png" /></figure>

Elasticity: $E(T)$ & $v(T)$

Plasticity (Isotropic Hardening): $\sigma_y = \sigma_0(T) + K(T)(1 - e^{-C(T)\epsilon_p})$

Thermal expansion: $\epsilon_{th} = (\alpha(T) \Delta T)I$

H transport equation: $\frac{\partial C_L}{\partial t} + \frac{\partial C_T}{\partial t} = \nabla(D_L(T)\nabla C_L + \frac{D_L(T)V_H}{RT}C_L\nabla P_H)$

Heat transfer: $\rho(T)C_p(T)\frac{\partial T}{\partial t} = \nabla(\lambda(T)\nabla T)$
Material interfaces: $C_L/S(T)$ continuity

H trapping equation: $\frac{\partial C_T}{\partial t} = \frac{k}{N_L}C_L(N_T(\epsilon_p) - C_T) - pC_T$

E(T) & v(T): Young's modulus & Poisson ratio / $\sigma_y$: yield stress / $\sigma_0(T)$: elastic limit / K(T) & C(T): material parameters / $\epsilon_p$: plastic strain / $\alpha(T)$: CTE
C_L & C_T: diffusing & trapping concentration of H / D_L: diffusion coefficient of H / V_H: molar volume of H / P_H: hydrostatic stress
k & p: trapping & detrapping parameters / N_L & N_T: density of lattice sites & trapping sites / S(T): solubility of H

## Results

### Phase 1

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* H stored in W, near the W/Cu interface

* Estimation of total H for all divertor monoblocks (assuming same exposure conditions): 10 mg

<figure><img src="image_7.png" /></figure>

* $\epsilon_{th}$ mismatches at bi-material interfaces → plastic strain

* T gradient & plastic strain → stress field ($P_H$)

### Phase 2

<figure><img src="image_8.png" /></figure>

* 0.3% of H remained mainly in the half upper part of W

* 47% of H passed towards cooling pipe

### Phase 3

<figure><img src="image_9.png" /></figure>

* No impact of the maintenance phase on remaining amount of H

## Model and data

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Terentyev D et al. (2015). Journal of Applied Physics, 117(8): 083302

Reproduction of H desorption in deformed W to determine the trap density (in traps/m³ instead of traps/m²)

W → 2 traps

* (intrinsic): 0.87/1 eV ; 6.95 10¹⁶/3.16 10¹⁶mm⁻³

* (created by plastic strain): 0.87 eV

Cu → 1 trap

0.5 eV ; 4.25 10¹⁵ mm⁻³

CuCrZr → 1 trap

0.85 eV ; 1.30 10¹⁵ mm⁻³

<figure><img src="image_11.png" /></figure>

Traps created by plastic strain

$$N_T^{\text{created}}(\epsilon_p) = 1.85 \times 10^{15} (1 - e^{-57.6\epsilon_p})$$