This study concerns with the evolution of morphological patterns that often arise on the interface of bi-material, so called metal-precipitate phase, due to the instability of the interfaces. The instability leads to growth or retraction of small perturbation, which may determine the formation of a variety of morphological patterns initially arising on surfaces of growing precipitates at small length scales. To better understand the cause of different patterns on the bi-material interfaces, an analytical study of the stability of the precipitate-matrix interface is performed. First, a wavy interface perturbation is used to examine the spontaneous variations that occur at the precipitate-matrix interface. Then, the analysis utilises Cerruti?s solution to compute the perturbed stress field surrounding the interface. It is shown that a virtually flat interface subjected to tension is in general unstable. The amplitude of sinusoidal perturbations decays for short wave lengths and grow for longer wave lengths. Both a critical wave length for which the perturbation amplitude is unaffected and a specific ditto which obtain maximum perturbation growth rate are derived

The stress driven growth of an expanding precipitate at a crack tip is studied. The material is assumed to be linearly elastic, and the expansion is considered to be isotropic or transversely isotropic. The extent of the precipitate is expected to be small as compared with the crack length and distance to boundaries. The problem has only a single length scale given by the squared ratio of the stress intensity factor and a critical hydrostatic stress that initiates the growth of the precipitate. Therefore, the growth occurs under self-similar conditions. The equations on non-dimensional form show that the free parameters are expansion strain, degree of anisotropy and Poisson’s ratio. It is found that the precipitate, once initiated, grows without remote load for expansion strains above a critical value. The anisotropy of the expansion strongly affects the shape of the precipitate but does not have a large effect on the crack tip shielding.

This pilot study uses a Landau-Lifshitz phase field model to study the growth of a precipitate originating from a crack tip. A boundary layer giving a remote square root singular elastic stress field is applied. The materials are assumed to be elastic-plastic with linear strain hardening. The precipitate is assumed to expand in a simplified anisotropic manner, meaning that the hydride is assumed to grow with an orientation giving maximum expansion perpendicular to the crack plane. The results show that the anisotropic expansion has a strong effect on the shape of the hydride. For anisotropic materials the hydride becomes wedge like. The resulting shapes for the anisotropic cases are in line with observations of internal crack tip hydrides in zirconium. The shapes resemble earlier results for Einstein-Smoluchowski stress driven diffusion using discrete models and simplified modelling of the growth process. The crack tip shielding caused by both precipitation and plastic yielding is examined using the J integral. It shows that the near tip value is a around a quarter of its remote value for elastic isotropic materials and around a half for anisotropic materials. © 2019 Elsevier Ltd

Aerodynamic resistance of a brush seal was mainly studied. The velocity distribution along three specified lines was presented. By considering the pressure differential, Reynolds number and Euler number (Eu) were modified. The effect of geometric arrangements and pressure differentials on Eu and leakage were analyzed. Two correlations were fitted based on the numerical results. The results reveal the velocity distribution is almost flat, asymmetric along the specified lines. The velocity increases and decreases almost linearly at centerlines. Eu decreases gradually less with the increase of pressure differential and trends towards a fixed value. A larger Eu indicates stronger resistance but not necessarily less leakage. Finally, two fitted correlations are developed and one is exponential to the row number fits better. © 2018 Elsevier Ltd

This work concerns spontaneous fracture of growing brittle precipitates in an elastic plastic matrix. The mass of the precipitate is increasing as more transformed matrix material is added to it. Under stress-free conditions, the new phase occupies a larger volume than the original matrix material. Just outside the expanding precipitate, the matrix undergoes stretching beyond the elastic limit. The influence of the elastic plastic material behaviour is studied. A phase field model that keeps track of the phase composition is used. Both cases with a crack and without a crack are included. The growth histories from microscopic to macroscopic precipitate sizes are followed. Growth of the precipitate is very slow and quasi-static mechanical equilibrium is assumed at all time. The result is compared with observations of hydride blisters that are formed on surfaces of zirconium alloys. The numerical model is qualified against a derived exact solution for a cylindrical precipitate without a crack. The numerical result predicts a position of the growing crack that is confirmed by the observations. Also, the predicted length of the crack is in fair agreement with the experimental observations. The depth of the blister is slightly larger than what is found at the experiments. Also, it is found that the incorporated transformed phase rejects the compression, which creates an increasing tensile stress in the inner part of the precipitate. © 2018 Wiley Publishing Ltd.

A model is established that describes stress driven diffusion, resulting in formation and growth of an expanded precipitate at the tip of a crack. The new phase is transversely isotropic. A finite element method is used and the results are compared with a simplified analytical theory. A stress criterium for formation of the precipitate is derived by direct integration of the Einstein-Smoluchowski law for stress driven diffusion. Thus, the conventional critical concentration criterium for precipitate growth can be replaced with a critical hydrostatic stress. The problem has only one length scale and as a consequence the precipitate grows under self-similar conditions. The length scale is given by the stress intensity factor, the diffusion coefficient and critical stress versus remote ambient concentrations. The free parameters involved are the expansion strain, the degree of anisotropy and Poisson's ratio. Solutions are obtained for a variation of the first two. The key result is that there is a critical phase expansion strain below which the growth of the new phase is stable and controlled by the stress intensity factor. For supercritical expansion strains, the precipitate grows even without remote load. The anisotropy of the expansion strongly affects the shape of the precipitate, but does not have a large effect on the crack tip shielding. (C) 2018 The Authors. Published by Elsevier B.V.

It is a common belief that embedded expanding inclusions are subjected to an internal homogeneous compressive hydrostatic stress. Still, cracks that appear in precipitates that occupy a larger volume than the original material, are frequently observed. The appearance of cracks has since long been regarded as a paradox. In the present study it is shown that matrix materials that increases its volume even several percent during the precipitation process develop a tensile hydrostatic stress in the centre of the precipitate. This is the result of a complicated mechanical-chemical phase transformation process. The process is here studied using a Landau phase feld model. Before the material is transformed and incorporated in a precipitate it undergoes stretching beyond the elastic strain limit because of the presence of already expanded material. During the phase transformation, the accompanying volumetric expansion cannot be fully accommodated which instead creates an internal compressive stress and adds tension in the surrounding material. As the growth of the precipitate proceeds, a region with increasing tensile stress develops in the interior of the precipitate. This is suggested to be the most probable cause of the observed cracks. First the mechanics that lead to the tension is computed. The infuence of elastic-plastic properties is studied both for cases both with and without cracks. The growth history from microscopic to macroscopic precipitates is followed and the result is compared with observations of so called hydride blisters that are formed on surfaces of zirconium alloys in the presence of hydrogen. A common practical situation is when the zirconium is in contact with an object of lower temperature. Then the cooled spot attracts hydrogen that make the zirconium transform to a metal hydride with the shape of a blister. The simulations predicts a final size and position of the growing crack that compares well with the experimental observations.

Formation of metal hydrides is a serious complication that occur when hydride forming metals such as zirconium, niobium, vanadium and magnesium are exposed to long term hydrogen environment. The main concern is that the hydride, as being a brittle material, has very poor fracture mechanical properties. Formation of hydride is associated with transportation of hydrogen along the gradients of increasing hydrostatic stress, which leads to crack tips and other stress concentrators, where it forms the hydride. In the present study the thermodynamics of the evolving hydrides is studied. The process is driven by the release of free strain, chemical, and gradient energies. A phase field model is used to capture the driving forces that the release of the free energy causes. The study gives the conditions that lead to hydride advancement versus retreat and under which conditions the metal-hydride interface becomes unstable and develops a waviness. The spatial frequency spectrum leading to instability is found to depend on the ratio of the elastic strain energy density and parameters related to the interface energy.

Measuring the diffusivity of various substances in cortical bone is in general difficult. For instance, making use of micro computed tomography requires agents that can be separated from bone, blood and other substances that exist in cortical bone. Here a more easily accessible method is presented. A series of cortical bovine bone samples were put in a saturated solution of potassium chloride for a time period that was long enough for the samples to be regarded as saturated. The samples were removed from the solution and moulded in polyester leaving only the radial directions open. In the next step, the bone samples were put in distilled water and the conductivity of the water was registered over time. An analytical model fulfilling Ficks law was introduced and by means of Kalman filtering an estimation for the diffusion coefficient of potassium chloride in bovine bone is presented.