A numerical model for hydride embrittlement in Zirconium alloy (Zr-2.5Nb) is developed utilizing the extended finite element method (XFEM). Hydride embrittlement reduces the ductility and failure time of a metal/alloy. During hydride embrittlement, stress-directed hydrogen diffusion, metal-hydride phase transformation, mechanical deformation, and hydride precipitation occur simultaneously. The present model incorporates all these processes and is able to predict the hydrogen concentration and the hydride fraction distribution under any externally applied stress field. In this work, both the steady and transient hydrogen diffusion cases are evaluated. Further, the XFEM is utilized to develop a model of hydride embrittlement in the presence of a crack. The first step of the hydride embrittlement process is the diffusion of hydrogen. According to Fick’s law of diffusion, hydrogen diffusion is directly dependent on hydrostatic stresses and hydrogen concentration gradient under external stresses. The next step is the hydride precipitation in hydride embrittlement, where the expansion of material takes place that changes the hydrostatic stress field. Thus, studying the effect of precipitation of hydride on hydrostatic stresses is essential. Moreover, the process of hydride embrittlement is highly influenced by residual stresses in the structure. Hence, the effect of residual stress present in the zirconium alloy pressure tube (PT) is also evaluated. The results indicate that the residual tensile stresses contribute to the growth of hydride, which will reduce the material failure time.

• Book : 25(2)
• Pub. Date : 2025
• Page : pp.2440002
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Abstract

The neoclassical ambipolarity condition governing the radial electric field in stellarators can have several solutions, and sudden transitions (in radius) between these can then take place. The radial position and structure of such a transition cannot be determined from local transport theory, and instead a non-rigorous model based on a diffusion equation for the electric field is usually employed for this purpose (Turkin et al 2011 Phys. Plasmas18 022505). We compare global (full plasma volume) drift-kinetic simulations of neoclassical transport in the Wendelstein 7-X stellarator with this model and find significant discrepancies. The position r0 of the transition is not predicted correctly by the diffusion model, but the radial structure of the transition layer is in reasonable agreement if the diffusion coefficient is chosen appropriately. In particular, it should depend on the plasma temperature in the same way as the plateau-regime coefficient of neoclassical transport theory or the gyro-Bohm diffusion coefficient. In the small-gyroradius limit, the prediction of r0 by the diffusion model simplifies to the so-called Maxwell construction (Shaing 1984 Phys. Fluids27 1567-9; Shaing 1984 Phys. Fluids27 1924-6). However, this property also emerges from a wide range of other mathematical models in the appropriate limit. The basic assumption underlying these models is that the diffusion, or generalisations thereof, is independent of the radial electric field, which is however unlikely to be the case in practice. Presumably this fact explains the discrepancy between the diffusion model and the drift-kinetic simulations. Finally, it is found that global simulations replicate the phenomenon of spontaneous root transitions driven by variations in the electron-to-ion temperature ratio, as predicted by local theory in the small-gyroradius limit.

• Book : 65(1)
• Pub. Date : 2025
• Page : pp.016019
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• Book : 604()
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• Book : 123()
• Pub. Date : 2025
• Page : pp.1052-1060
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