diff --git a/Chapters/Cavitation.tex b/Chapters/Cavitation.tex new file mode 100644 index 0000000..35f2cf2 --- /dev/null +++ b/Chapters/Cavitation.tex @@ -0,0 +1,144 @@ +\documentclass[../Thesis]{subfiles} + +\begin{document} + + + + +\chapter{Introduction} +\section{General Background} + + +%Analysis: The paragraph effectively introduces the challenge of cavitation erosion in fluid-handling systems and discusses the need for materials with improved resistance or proposes potential mitigation strategies. + +%Problem Statement: It starts by clearly stating the prevalence and detrimental effects of cavitation (e.g., material erosion, reduced efficiency, noise, vibration, component failure) in key applications (e.g., pumps, propellers, turbines, valves), establishing the necessity for effective solutions. + +%Focus Area / Proposed Solution: It highlights the goal of developing or utilizing materials/coatings/treatments with enhanced cavitation resistance, or introduces specific approaches intended to combat the damage. + +%Mechanism: It explains the fundamental mechanism of cavitation damage (e.g., vapor bubble formation and violent collapse, generation of shockwaves and micro-jets) leading to material erosion, and potentially discusses how a proposed solution resists this mechanism. + +%Context/Validation: It grounds the issue by referencing specific industries or critical components where cavitation erosion is a significant operational problem (e.g., marine propulsion, hydropower generation, hydraulic machinery, chemical processing) and underscores the importance of resistant materials in these contexts. + +%Relevant Properties: It lists specific material characteristics or properties deemed crucial for resisting cavitation erosion (e.g., toughness, hardness, fatigue strength, work-hardening capacity, corrosion resistance, grain structure, phase stability). + +%Knowledge Gap: Critically, it may point out limitations in current materials, testing standards, predictive models, or fundamental understanding, such as predicting erosion rates accurately, performance under combined erosion-corrosion conditions, or the behavior of novel materials. + +%Call for Research/Development: Consequently, it emphasizes the need for further research, development of new materials/coatings, improved testing protocols, or advanced modeling techniques to better predict and mitigate cavitation erosion. + +%Potential Applications: It suggests specific components (e.g., impellers, propellers, valve seats, cylinder liners) or systems that would directly benefit from advancements in cavitation-resistant materials, improving reliability and performance across various sectors. + + + +\section{Stellites} +\section{Objectives and Scope of the Research Work} +\section{Thesis Outline} +\section{Literature Survey} +\section{Cavitation Tests} + +\chapter{Analytical Investigations} +\section{Introduction} +\section{Finite Element Model (FEM)} +\section{Model description} +\section{Model Validation} +\section{Result Analysis of Typical Load Case} + + + +\chapter{Experimental Investigations} + +\section{Introduction} + + +\section{X-ray diffraction technique of residual stress measurement} + +\section{Surface Roughness Measurements} +\section{Microhardness measurements} + + +\chapter{Discussion} + + + + +\chapter{Cavitation Erosion} +\chaptermark{Cavitation Erosion} % optional for veryy long chapter, you can rename what appear in the header + +%% have a mini table of content at the start of the chapter +{ +\hypersetup{linkcolor=black} +\minitoc +} + +%cite:@Franc2004265, @Romo201216, @Kumar2024, @Kim200685, @Gao2024, @20221xix, @Usta2023, @Cheng2023, @Zheng2022 + +Cavitation erosion presents a significant challenge in materials degradation in various industrial sectors, including hydroelectric power, marine propulsion, and nuclear systems, stemming from a complex interaction between fluid dynamics and material response \cite{francCavitationErosion2005, romoCavitationHighvelocitySlurry2012}. Hydrodynamically, the phenomenon initiates with the formation and subsequent violent collapse of vapor bubbles within a liquid, triggered by local pressures dropping to the saturated vapor pressure. These implosions generate intense, localized shockwaves and high-speed microjets that repeatedly impact adjacent solid surfaces \cite{gevariDirectIndirectThermal2020}. From a materials perspective, these impacts induce high stresses (100-1000 MPa) and high strain rates, surpassing material thresholds and leading to damage accumulation via plastic deformation, work hardening, fatigue crack initiation and propagation, and eventual material detachment. Mitigating this requires materials capable of effectively absorbing or resisting this dynamic loading, often under demanding conditions that may also include corrosion. + +Stellite alloys, cobalt-chromium formulations that contain carbon, tungsten and/or molybdenum, represent a critical class of materials renowned for their wear resistance in such harsh environments \cite{shinEffectMolybdenumMicrostructure2003}. Their performance stems from a composite-like microstructure combining a strong cobalt-rich matrix, strengthened by solid solutions of Cr and W/Mo, with hard carbide precipitates (e.g., M7C3, M23C6) that impede wear and crack propagation \cite{ahmedSlidingWearBlended2021a, crookCobaltbaseAlloysResist1994}. + +% Martensitic transformation +Crucially, the cobalt matrix often possesses a low stacking fault energy, facilitating a strain-induced martensitic transformation from a metastable face-centered cubic $\gamma$ phase to a hexagonal close-packed $\epsilon$ phase under the intense loading of cavitation. This transformation is a primary mechanism for dissipating impact energy and enhancing work hardening, contributing significantly to Stellite's characteristic cavitation resistance \cite{huangMicrostructureEvolutionMartensite2023, tawancyFccHcpTransformation1986}. + +HIPing is a thermo-mechanical material processing technique which involves the simultaneous application of pressure (up to 200 MPa) and temperature (2000 C), which results in casting densification, porosity closure, and metallurgical bonding. \cite{yuComparisonTriboMechanicalProperties2007} + +While commonly applied via casting or weld overlays, processing routes like Hot Isostatic Pressing (HIP) offer potential advantages such as microstructure refinement \cite{stoicaInfluenceHeattreatmentSliding2005} finer microstructures and enhanced fatigue resistance \cite{ahmedInfluenceReHIPingStructure2013, yuComparisonTriboMechanicalProperties2007}. + +HIPing of surface coatings results in microstructure refinement, which can yield improved fatigue and fracture resistance. + +HIPing leads to carbide refinement, which can yield improved impact toughness \cite{yuInfluenceManufacturingProcess2008}, and reduce carbide brittleness \cite{yuComparisonTriboMechanicalProperties2007}. + +Furthermore, HIP facilitates the consolidation of novel 'blended' alloys created from mixed elemental or pre-alloyed powders, providing a pathway to potentially tailor compositions or microstructures for optimized performance. However, despite the prevalence of Stellite alloys and the known influence of processing on microstructure and properties, the specific cavitation erosion behavior of HIP-consolidated Stellites, particularly these blended formulations, remains underexplored in academic literature. Given that erosion mechanisms in Stellites often involve interactions at the carbide-matrix interface \cite{szalaEffectNitrogenIon2021}, understanding how HIP processing and compositional blending affect these interfaces and the matrix's transformative capacity under cavitation, especially when potentially coupled with corrosion, constitutes a critical knowledge gap addressed by this research. + + +% Need to describe Stellite 1 +\section{Stellite 1} + +Stellite 1 is a high-carbon and high-tungsten alloy, making it suitable for demanding applications that require hardness & toughness to combat sliding & abrasive wear \cite{crookCobaltbaseAlloysResist1994} + + + + +\section{Experimental Test Procedure} + +\subsection{Materials and Microstructure} + +The HIPed alloy was produced via canning the gas-atomized powders at 1200C and 100 MPa pressure for 4h, while the cast alloys were produced via sand casting. +% Sieve analysis and description of powders + +% Refer to Table of chemical compositions of both cast and HIPed alloys. + +The microstructure of the alloys were observed via SEM in BSE mode, and the chemical compositions of the identified phases developed in the alloys were determined via EDS as well as with XRD under Cu $K_{\alpha}$ radiation. + +Image analysis was also conducted to ascertain the volume fractions of individual phases. + + +\subsection{Hardness Tests} + +The Vickers microhardness was measured using a Wilson hardness tester under loads of BLAH. Thirty measurements under each load were conducted on each sample. + +\subsection{Cavitation} + + +\section{Relationships between cavitation erosion resistance and mechanical properties} + +\section{Influence of vibratory amplitude} + +% Insert the whole spiel by that French dude about displacement and pressure (and then ruin it) +The pressure of the solution depends on the amplitude of the vibratory tip attached to the ultrasonic device. Under simple assumptions, kinetic energy of cavitation is proportional to the square of the amplitude and maximum hammer pressure is proportional to A. + +\begin{align} +x &= A sin(2 \pi f t) \\ +v &= \frac{dx}{dt} = 2 \pi f A sin(2 \pi f t) \\ +v_{max} &= 2 \pi f A \\ +v_{mean} &= \frac{1}{\pi} \int^\pi_0 A sin(2 \pi f t) = 4 f A \\ +\end{align} + +However, several researchers have found that erosion rates are not proportional to the second power of amplitude, but instead a smaller number. +Thiruvengadum \cite{thiruvengadamTheoryErosion1967} and Hobbs find that erosion rates are proportional to the 1.8 and 1.5 power of peak-to-peak amplitude. +Tomlinson et al find that erosion rate is linearly proportional to peak-to-peak amplitude in copper [3]. +Maximum erosion rate is approximately proportional to the 1.5 power of p-p amplitude [4]. +The propagation of ultrasonic waves may result in thermal energy absorption or into chemical energy, resulting in reduced power. For the purposes of converting data from studies that do not use an amplitude of 50um, a exponent factor of 1.5 has been applied. + + + + +\end{document} diff --git a/Chapters/Chapter1-Introduction.tex b/Chapters/Chapter1-Introduction.tex new file mode 100644 index 0000000..1ba040d --- /dev/null +++ b/Chapters/Chapter1-Introduction.tex @@ -0,0 +1,116 @@ +\documentclass[../Thesis]{subfiles} + +\begin{document} + +\chapter{Introduction} +\chaptermark{Chapter 1 title} % optional for veryy long chapter, you can rename what appear in the header + +{ +\hypersetup{linkcolor=black} +\minitoc +} +%% have a mini table of content at the start of the chapter + +\section{Start} +\subsection{Basic Info} +\subsubsection{This Is A Subsubsection} +Subsubsection should not be numbered, nor indicated in the table of contents. The config options are tocdepth and secnumdepth, you can find them in the config file. + +\paragraph{Paragraph Title} +I studied \cite{C08} and that was fun. I also looked at \cite{C02} \footnote{you should do footnotes like this. More details here \url{https://www.overleaf.com/learn/latex/Footnotes}}. + +I also wrote this \cite{C05}. But the most fun thing was reading \cite{C01} + +URI should be included like this \url{https://github.com/jackred/Heriot_Watt_Thesis_Template}. + +\subsection{Equation} +Equations placed on separate lines from the text should be numbered whether or not they are referred to in the text. Numbering should appear in round brackets at the right hand side of the page and be ordered consecutively either throughout the thesis as (1) etc, or in each chapter (1.1) etc. Equations should be referred to in the text as equation(1) etc.\par +\bigskip +Believe it or not, this is the equation for the canonical version of PSO, using the inertia factor, first proposed in 1998. +\begin{equation} + V_{i} = wV_{i} + c_{1} * U(0,1) * (P_{i} - X_{i}) + c_{2} * U(0,1) * (L_{i} - X_{i}) + \label{eqn:velocityInertia} +\end{equation} + +% you refer an equation like this +And here you have the constriction factor equation, which have the same role as the inertia factor defined in \eref{eqn:velocityInertia}, but is used differently. Proposed in 1999. +\begin{equation} + \chi = \dfrac{2}{|2 - \phi - \sqrt{\phi^{2} - 4\phi}|} + \label{eqn:velocityConstriction} +\end{equation} + +Was I just lazy and copied the equation of my Master Thesis? Not at all. Look, here is the gravity equation for PSO2011, proposed, as the name suggest, in 2011. +\begin{equation} + G_{i} = \dfrac{X_{i} + (X_{i}+U(0,1)c(P_{i}-X_{i})) + (X_{i}+U(0,1)c(L_{i}-X_{i}))}{3} + \label{eqn:gravityVelocity2011} +\end{equation} + +\clearpage % aesthetic purpose + +\subsection{Tables} +Tables, figures etc. shall be numbered either consecutively throughout the thesis–Table 1, Figure 1 etc., or within individual chapters Chapter –Table1.1, but not within sections or subsections. With in the text tables should be referred to as table 1etc. + +\begin{table}[H] + \centering + \begin{tabular}{llllll} + D10 & min & max & median & std & average \\ + f1 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 \\ + f3 & 4.40E-02 & 1.37E+08 & 3.49E+05 & 2.18E+07 & 6.46E+06 \\ + f8 & 2.01E+01 & 2.05E+01 & 2.03E+01 & 8.44E-02 & 2.03E+01 \\ + f9 & 1.51E+00 & 6.96E+00 & 4.54E+00 & 1.21E+00 & 4.53E+00 \\ + f15 & 1.41E+02 & 1.04E+03 & 7.16E+02 & 2.26E+02 & 6.64E+02 \\ + f20 & 1.26E+00 & 3.82E+00 & 3.02E+00 & 5.67E-01 & 2.93E+00 \\ + f21 & 1.00E+02 & 4.00E+02 & 4.00E+02 & 1.05E+02 & 3.33E+02 \\ + f22 & 8.79E+01 & 8.30E+02 & 4.83E+02 & 2.00E+02 & 4.91E+02 \\ + f25 & 2.04E+02 & 2.23E+02 & 2.15E+02 & 3.73E+00 & 2.15E+02 + \end{tabular} + \rule{35em}{0.5pt} + \caption[Example table]{Summary Statistics for the 10 dimensional case of PSO 2007 with a ring neighborhood of 4. I know you don't know what it means. But at least you have an example of a table. More info here \url{https://www.overleaf.com/learn/latex/Tables}} + \label{tab:PSO_2007_D10_R4} +\end{table} + + +\subsection{Figures} +Because I think you are very interested in PSO (or I am just very lazy) here is a nice figure explaining how PSO 2006 works. +\begin{figure}[H] + \centering + \includegraphics[]{Figures/pso2006.png} + \rule{35em}{0.5pt} + \caption[SPSO 06/07 movement]{SPSO 2006 and 2007 particle's position update. $X'_{i}$ and $X"_{i}$ are temporary point to explain the second and third terms of equation \ref{eqn:velocityInertia}.} + \label{fig:schemaPSO2006Update} +\end{figure} + + +\clearpage % aesthetic purpose + +And while we are at it, look at the 2011 version, that you can't probably understand without the context, but eh, it's a figure to illustrate how to put some. We can see it is different than \fref{fig:schemaPSO2006Update} +\begin{figure}[H] + \centering + \includegraphics[]{Figures/pso2011.png} + \rule{35em}{0.5pt} + \caption[SPSO 2011 movement]{SPSO 2011 particle's position update. $X'_{i}$ is generated inside the hyper-sphere of center $G_{i}$.} + \label{fig:schemaPSO2011Update} +\end{figure} + +I placed my figure right after the text, but you will usually use other option to place them, such as \textit{htpb}. More info \url{https://www.overleaf.com/learn/latex/Positioning_of_Figures}. + +\begin{figure}[H] + \centering + \rotatebox{90}{\includegraphics[width=22cm]{Figures/rk4_0-100_dt-0-0001}} + \rule{35em}{0.5pt} + \caption[Sideways picture]{How to put a very big picture sideways. It is in French but who cares?} + \label{fig:veryBigFigure} +\end{figure} + + +\begin{landscape} +\begin{figure}[!h] + \centering + \includegraphics[width=\linewidth]{Figures/rk4_0-100_dt-0-0001} + \caption{How to put a figure in landscape instead} + \label{fig:verybigfigure2} +\end{figure} +\end{landscape} + + +\end{document} diff --git a/Chapters/Chapter2.tex b/Chapters/Chapter2.tex new file mode 100644 index 0000000..9681b78 --- /dev/null +++ b/Chapters/Chapter2.tex @@ -0,0 +1,22 @@ +\documentclass[../Thesis]{subfiles} +\begin{document} + +\chapter{Some Very Informative Text} +\chaptermark{Title of The Chapter} + +{ +\hypersetup{linkcolor=black} +\minitoc +} + +\section{Information} +\subsection{This is a test} + +Let's just have the equation of Charged PSO to see how equation are numbered through Chapter (spoil, per chapter): +\begin{equation} + V_{i} = wV_{i} + c_{1} * U(0,1) * (P_{i} - X_{i}) + c_{2} * U(0,1) * (L_{i} - X_{i}) + a_{i} \label{eqn:velocityChargedUpdate} +\end{equation} +Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Congue eu consequat ac felis donec et odio pellentesque. Sem fringilla ut morbi tincidunt augue interdum. Imperdiet massa tincidunt nunc pulvinar sapien et ligula. Urna condimentum mattis pellentesque id nibh tortor. Fringilla est ullamcorper eget nulla facilisi etiam dignissim. Vel turpis nunc eget lorem dolor sed viverra ipsum nunc. Volutpat est velit egestas dui id ornare arcu odio. Pretium nibh ipsum consequat nisl vel pretium lectus. Aenean et tortor at risus viverra adipiscing at. Vivamus arcu felis bibendum ut tristique et egestas quis. Sollicitudin aliquam ultrices sagittis orci. Vulputate sapien nec sagittis aliquam malesuada bibendum. + + +\end{document} \ No newline at end of file diff --git a/Chapters/Chapter3.tex b/Chapters/Chapter3.tex new file mode 100644 index 0000000..67f58fb --- /dev/null +++ b/Chapters/Chapter3.tex @@ -0,0 +1,16 @@ +\documentclass[../Thesis]{subfiles} +\begin{document} + +\chapter{Conclusion} +\chaptermark{This is the end, skyfall} + +{ +\hypersetup{linkcolor=black} +\minitoc +} + +\section{This is the end} + + +You have to finish your Thesis. I know it's sad, but all things come to end. +\end{document} \ No newline at end of file