Multiphysics model of thermomechanical and helium-induced damage of tungsten during plasma heat transients

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Abstract

A combination of transient heating and bombardment by helium and hydrogen atoms has been experimentally proven to lead to severe surface and sub-surface damage. We developed a computational model to determine the relationship between the thermomechanical loading conditions and the onset of damage and failure of tungsten surfaces. The model is based on a thermoelasticity fracture damage approach that was developed using the phase field method. The model simulates the distribution of helium bubbles inside the grains and on grain boundaries using space-dependent rate theory. In addition, the model is coupled with a transient heat conduction analysis for temperature distributions inside the material. The results show the effects of helium bubbles on reducing tungsten surface energy. Further, a temperature gradient in the material equals to 10 K/μm, resulted in deep cracks propagating from the tungsten surface.

Introduction

In nuclear fusion reactors, plasma-facing components (PFCs) (e.g. the divertor and the first wall), are subjected to high fluxes of energetic photons, neutrons, hydrogen, and helium ions. The impingement of these energetic atom fluxes leads to rapid and transient surface heating of the surface. Bombardment by helium isotopes leads to helium-induced damage accompanying micro-structural evolution (e.g. material swelling and the formation of blisters [1], [2], and dislocation loops and helium holes or bubbles [3], [4]). Several recent experiments (e.g., [5]) have shown that damage in the surface region and inside the material may degrade the thermophysical properties of tungsten. Other experiments have indicated that under helium and hydrogen ion bombardment conditions, some near-surface grains are ejected from the bulk to the surface region [6].

Divertors in fusion reactors are subjected to transient plasma events characterized by short durations of high thermal energy. One class of these events is the edge-localized mode (ELM), which is a highly nonlinear event accompanied by high thermal energy (3–10% of the core thermal energy). Typical values fall between 0.1 and 0.5 MJ/m2 for the Joint European Torus (JET) and between 1 and 5 MJ/m2 for the International Thermonuclear Experimental Reactor (ITER). The duration of these events is relatively short, usually between 0.1 and 1 ms.

Recently, tungsten has become a primary candidate material for PFCs because it possesses numerous favorable thermophysical properties [7]. Models that describe and study change and damage in the structure of tungsten are critical in determining the limits for tungsten’s operating conditions in extreme environments. The main objective of this paper is to develop a computational multiphysics model to investigate thermomechanical and helium-induced damage in tungsten under transient energetic ion bombardment conditions. The following sections present in Sections 2 Physical model description, 3 Finite element implementation, 4 Results and discussion, 5 Conclusions.

Section snippets

Thermal conduction

In fusion reactors, PFC materials are exposed to transient high heat fluxes that diffuse inside the material by heat conduction. This is expressed through the following heat equation, which, in the absence of a convective flow, takes the form:ρcpTt+·(-kT)=0where T is the temperature and k is the thermal conductivity. To simulate the transient conditions of the plasma, the tungsten surface is subjected to a heat flux from one side in the form:-n·q=qowhere n is the normal vector to the

Finite element implementation

The multiphysics model in Section 2 was developed and solved within the finite element analysis framework to study the synergistic effects of transient plasma events and the existence of helium bubbles concentrated along grain boundaries on the thermomechanical damage of tungsten. The modeled geometry was a two dimensional (700 μm × 600 μm) block, as shown in Fig. 3. The method of Voronoi diagrams was used to divide the geometry into a random number of grains with different sizes and orientations.

Results and discussion

During the applied transient heat flux, the temperature rises from its initial value and peaks at the end of the period of application. When the heat flux is turned off, the temperature starts to decrease and diffuses into the bulk of the material until it eventually reaches the temperature of the infinite element and becomes uniform throughout the material. This is illustrated in Fig. 4, Fig. 5 for the two tested heat loads. A comparison of the evolution of the tungsten surface temperature in

Conclusions

High heat fluxes and helium bombardment are characteristics of nuclear reactions in fusion reactors. We investigated the combined effect of severe transient plasma heat loads and helium irradiation on tungsten damage. A multiphysics model that combines thermoelasticity, crack damage, and thermal conduction was developed using the finite element framework. The model examined the relation between temperature magnitudes and distribution, pressure in helium bubbles, and the onset of damage manifest

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