Computer simulation of morphological evolution of hydride in zirconium under applied stress

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Computer simulation of morphological evolution of hydride in zirconium under applied stress


Author: Ma, Xingqiao
Title: Computer simulation of morphological evolution of hydride in zirconium under applied stress
Degree: Ph.D.
Year: 2003
Subject: Hong Kong Polytechnic University -- Dissertations.
Hydrides -- Morphology.
Morphology -- Computer simulation.
Department: Dept. of Mechanical Engineering
Pages: xvi, 177 leaves : ill. ; 30 cm.
Language: English
InnoPac Record:
Abstract: For hydride forming metals and alloys such as titanium, zirconium, niobium and vanadium, an important mechanism for hydrogen related fracture is due to the stress-induced formation and subsequent fracture of hydrides at stress concentrators such as flaws. It is believed that critical conditions for the fracture initiation at hydrides are controlled by the morphology and microstructure of hydride precipitates at flaw tips. Experimental investigation on three-dimensional (3-D) morphological evolution of hydride precipitates at flaw tips is very difficult. This work will make the best use of the fast evolving computing technology, to develop the capability of predicting realistic morphological evolution of hydride precipitates in metals such as zirconium. A conserved parameter c(r,t), is used to describe hydrogen concentration and non-conserved parameters n(r,t), the long-range order parameter, are used to describe the structure change during the phase transformation. The governing equations for these parameters are Cahn-Hilliard equation and time-depended Ginzberg-Landau (TDLG) equation. The energy terms, including bulk chemical free energy, surface energy, elastic energy, grain boundary energy etc., are considered in the study here. Simulations on the precipitation of y-hydride under uniformly applied stress have been done. The result shows that when no stress applied to the sample, the hydride precipitate along three <1120> direction. But when a tensile stress perpendicular to the [1120] direction was applied, the hydrides along the [1120] direction developed and the hydrides along the other two directions disappeared. This is in well accordance with the experiments. The results here also shown that the stress applied in the nucieation stage influenced more strongly on the orientation of the precipitate than in the growth stage. A bi-crystal is the simplest form of poIycrystalline. In a polycrystal, the crystalline orientation of each grain is different and grain boundary energy need to be considered. In this part, we have constructed a model that can reflect these features. We have extended the theoretical concept from Shotkey, and proposed a description of grain boundary energy due to hydride formation. By adopting a total of six long-range order (LRO) parameter with three LRO in each grain, the hydride precipitation process in a bi-crystal system has been simulated. The hydride morphologies obtained from the simulation are similar to those obtained from the TEM observations. The simulation results show: The nucieation density of the hydride at the grain boundary is higher than that in the bulk; Hydrides will precipitate and grow in those habit planes that are near the perpendicular direction of the applied tensile load; The effect of an external load on the precipitation can be stronger than that of grain boundaries. Most engineering materials are polycrystalline materials. When the dimension of a grain is smaller than that of a hydride, The material could be treated as a continuum media. Models for the diffusion and precipitation of hydrides under non-uniform applied stress in the continuum model have been built up in this work respectively. In this work, we discussed the hydrogen diffusion under the stress field in a loaded sample with a blunt notch. The stress field caused by the loading was calculated by finite element method. Khachaturyan's elastic theory was adopted to calculate the elastic energy. The phase field evolution equation was solved by explicit finite difference method. The result shows that hydrogen atoms diffuse to the high tensile hydrostatic region near the notch tip. The concentration of hydrogen near the notch tip increased by 13% at 250 oC. The diffusion process was faster in the first 10 hours, during which the peak hydrogen concentration reached 98% of its equilibrium value; The stress distribution around the notch was modified by hydrogen interstitials by only 0.7%. This indicates that redistribution of stress due to H atoms can be neglected. The hydride precipitation under a non-uniformly distributed applied stress is the general case found in engineering practice. To study the hydride morphology under this condition, we built a multi-variant model. The hydrides may vary their direction of precipitation nearly continually. When a uniform tensile stress is applied, the hydride always precipitates perpendicular to the tensile loading direction. We also studied the case of non-uniformly loaded sample with a notch. The result shows that the density of hydrides in front of the notch tip is higher than in other areas. The hydride at the notch tip likely takes the direction that is perpendicular to the surface of the notch tip. This is very harmful to the material, because fracture is easy to develop along these hydrides under applied stress. The hydrides away from the tip precipitate along the curcumfencial direction. This is due to the stress field around the notch.

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