Numerical model of solid phase transformations governed by nucleation and growth. Microstructure development during isothermal crystallization

A simple numerical model which calculates the kinetics of crystallization involving randomly distributed nucleation and isotropic growth is presented. The model can be applied to different thermal histories and no restrictions are imposed on the time and the temperature dependencies of the nucleation and growth rates. We also develop an algorithm which evaluates the corresponding emerging grain size distribution. The algorithm is easy to implement and particularly flexible making it possible to simulate several experimental conditions. Its simplicity and minimal computer requirements allow high accuracy for two- and three-dimensional growth simulations. The algorithm is applied to explore the grain morphology development during isothermal treatments for several nucleation regimes. In particular, thermal nucleation, pre-existing nuclei and the combination of both nucleation mechanisms are analyzed. For the first two cases, the universal grain size distribution is obtained. The high accuracy of the model is stated from its comparison to analytical predictions. Finally, the validity of the Kolmogorov-Johnson-Mehl-Avrami model is verified for all the cases studied

Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

This paper presents a new proposition on how to derive mathematical formulas that describe an unknown Probability Density Function (PDF3) of the spherical radii (r3) of particles randomly placed in non-transparent materials. We have presented two attempts here, both of which are based on data collected from a random planar cross-section passed through space containing three-dimensional nodules. The first attempt uses a Probability Density Function (PDF2) the form of which is experimentally obtained on the basis of a set containing two-dimensional radii (r2). These radii are produced by an intersection of the space by a random plane. In turn, the second solution also uses an experimentally obtained Probability Density Function (PDF1). But the form of PDF1 has been created on the basis of a set containing chord lengths collected from a cross-section.The most important finding presented in this paper is the conclusion that if the PDF1 has proportional scopes, the PDF3 must have a constant value in these scopes. This fact allows stating that there are no nodules in the sample space that have particular radii belonging to the proportional ranges the PDF1

Cell size distribution in a random tessellation of space governed by the Kolmogorov-Johnson-Mehl-Avrami model: Grain size distribution in crystallization

The space subdivision in cells resulting from a process of random nucleation and growth is a subject of interest in many scientific fields. In this paper, we deduce the expected value and variance of these distributions while assuming that the space subdivision process is in accordance with the premises of the Kolmogorov-Johnson-Mehl-Avrami model. We have not imposed restrictions on the time dependency of nucleation and growth rates. We have also developed an approximate analytical cell size probability density function. Finally, we have applied our approach to the distributions resulting from solid phase crystallization under isochronal heating conditions

Stent-Graft Placement for Wide-Neck Aneurysm of the Vertebrobasilar Junction

We present a case in which a stent-graft was used to treat an aneurysm of the vertebrobasilar junction. According to our literature search, this is one of the first cases involving the intracranial placement of a stent-graft and the first case in which an aneurysm of the vertebrobasilar junction was treated in this manner. A stent-graft can be useful device for the neuroendovascular treatment of aneurysms in select patients

Mathematical and numerical model of directional solidification including initial and terminal transients of the process

Abstract The, developed in this study, simple model and numerical solution of diffusion growth of the solid phase under the conditions of directional solidification allow for the effect of constituent diffusion in both liquid and solid phase and assume the process run in which (like in reality) the preset parameter is the velocity of sample (pulling velocity) at a preset temperature gradient. The solid/liquid interface velocity is not the process parameter (like it is in numerous other solutions proposed so far) but a function of this process. The effect of convection outside the diffusion layer has been included in mass balance under the assumption that in the zone of convection the mixing is complete. The above assumptions enabled solving the kinetics of growth of the solid phase (along with the diffusion field in solid and liquid phase) under the conditions of diffusion well reflecting the process run starting with the initial transient state, going through the steady state period in central part of the casting, and ending in a terminal transient state. In the numerical solution obtained by the finite difference method with variable grid dimensions, the error of the mass control balance over the whole process range was 1 -2 %

New Computer Method of Derivative Thermal Express Analysis of Cast Iron for Operational Prediction of Quality of Melts and Castings

This method is based on the determination of similarity criterion Z as the average temperature difference between the reference and analyzed curves in the solidification region. The purpose of this work is to describe the thermal express-analysis (TDA) device created by us and the substantiation of the reliability and sensitivity of the results of the new method, including the definition of a two-sided confidence interval using Student's t-test. The error of the method was determined with the Student's criterion taken into account. The high sensitivity of the method to the metallurgical prehistory of the gray and white cast iron melts was confirmed. The method has been successfully tested under laboratory and experimental-industrial conditions on induction melting cast iron. The new method uses a disposable environmentally friendly submersible steel sampler with a heat-resistant coating inside and out. The method allows for the quick adaptation to the conditions of specific foundries (especially with the frequent changes of classes and types of cast iron) due to replenishing the database of the reference samples.The basic features of the new method are its universality, self-adaptability, speed, relative simplicity, and high sensitivity to the metallurgical prehistory of molten iron

Numerical modelling of grain refinement around highly reactive interfaces in processing of nanocrystallised multilayered metallic materials by duplex technique

Microstructure evolution around highly reactive interfaces in processing of nanocrystallised multilayered metallic materials have been investigated and discussed in the present work. Conditions leading to grain refinement during co-rolling stage of the duplex processing technique are analysed using the multi-level finite element based numerical model combined with three-dimensional frontal cellular automata. The model was capable to simulate development of grain boundaries and changes of the boundary disorientation angle within the metal structure taking into account crystal plasticity formulation. Appearance of a large number of structural elements, identified as dislocation cells, sub-grains and new grains, has been identified within the metal structure as a result of metal flow disturbance and consequently inhomogeneous deformation around oxide islets at the interfaces during the co-rolling stage. These areas corresponded to the locations of shear bands observed experimentally using SEM-EBSD analysis. The obtained results illustrate a significant potential of the proposed modelling approach for quantitative analysis and optimisation of the highly refined non-homogeneous microstructures formed around the oxidised interfaces during processing of such laminated materials

Modelling of Change in Density of Nodular Cast Iron During Solidification Using Cellular Automaton / Modelowanie Zmian Gęstości Żeliwa Sferoidalnego Podczas Krystalizacji Za Pomocą Automatu Komórkowego

Density change occurring in ductile iron castings is a phenomenon far more complicated than in other casting alloys. Initially, graphite nodules grow directly from liquid phase. That is the reason for decrease in alloy density and casting expansion. Decaying carbon concentration in liquid phase adjacent to graphite nodules favours growth of austenite, which covers them isolating from the liquid. In order for graphite to grow further diffusion of carbon through thickening solid solution layer is needed. At this time expansion fades and shrinkage begins. Industrial experience shows that whether or not shrinkage defects in ductile iron castings will occur depends on wall thickness