\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
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%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.




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