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MATS15501 Computing and Communication

Computational Materials Science - Final Assignment

Introduction

A fire-proof steel structure collapsed unexpectedly during a fire, which had lasted several hours. There are two reasons for why this collapse could have happened: either the structure became too hot because not enough water was used to cool    the fire, or the steel failed at a temperature at which it should not have failed. In order to determine the cause, we need to   determine the temperature of the fire.

The task

You task is to determine the temperature of fire by analysing the microstructure of the steel and making predictions using simple model for grain growth, calibrated from data obtained from controlled tests. First think about the task you have been asked to perform and consider the information that you have been given. You have an image of the microstructure of the steel from the fire that you need to analyse. You also have some experimental data and some analytical models of grain size as a function of time and temperature.

The first equation is for the evolution of grain size with time at a particular temperature. The values of the parameters K and n need to be determined from the data that you have been given. This is one sub-task.

You will be able to determine a value of K for each temperature for which you have experimental data. These values will then allow you to determine the values of the parameters in the second equation. This is another sub-task.

You should now have a set of equations, including values of the parameters, for how the grain size should change over  time at a given temperature. Your final subtask, before drawing your conclusions, is to extract the relevant data from the image of the microstructure from the fire and apply the equations.

Laboratory tests

A series of laboratory tests were carried on samples from a region of the building not affected by the fire. These samples   were heated up in furnace to 3 different temperatures: 600, 750 and 800∘ C, and for different durations: 5, 10, 15, 60, 120 and 200 seconds. The grain size was then measured using the standard mean linear intercept method. The results are in  the table below. Grain sizes are given in µm.

Grain growth model

At high temperatures, the grains in polycrystalline materials have a tendency to grow. This is because as the grains grow, the grain boundary area decreases. Since grain boundaries are regions of high energy, decreasing the grain boundary energy decreases the overall energy of the material.

In order for grains to grow, atoms and defects must diffuse through the crystals. Because diffusion is thermally activated, i.e. it becomes easier with increasing temperature, grain growth is also thermally activated.

Studies of grain growth have shown that, at a given temperature, grain size changes with time according to the following equation:

where D0 is the starting grain size, t is time, and K and n are material parameters.

The value of K changes with temperature according to the following equation:

where Ea  is the activation energy, R is the gas constant and T is the temperature. The parameter n can be assumed to be independent of temperature.

Incident sample

A sample from the steel extracted form the collapsed structure was also examined at the same magnification as the  laboratory tests. A number of images of the microstructure were acquired and can be found in the   results  folder.

Calculations and results

Use a Jupyter python notebook to analyse the data and present your results. Submit your notebook via Bb9 in the usual way. Submit only your notebook (the .ipynb file). Do not submit the images or any other supporting files.

You should work in pairs to complete this assignment. At the top of the notebook you must include your name and that of   your partner. This is very important since we will expect very similar notebooks from partners, but different notebooks from different teams.

There will be zero tolerance to academic malpractice. If we identify identical code or text in notebooks that do not belong to the same team, we will penalise both submissions. This is because it is not usually possible to determine who copied  from whom. This does not mean you should not discuss the assignement with people that are not your partners: you should do this as much as possible! However, you must refrain from copying work from each other, as it is against the rules.