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/Electrochemical/Cast_Stellite1_Sample2_Actual/OCP.cor filter=lfs diff=lfs merge=lfs -text
/Electrochemical/Cast_Stellite1_Sample3_Actual/OCP.cor filter=lfs diff=lfs merge=lfs -text
/Thesis.pdf filter=lfs diff=lfs merge=lfs -text
/.ipynb_checkpoints/Untitled-checkpoint.ipynb filter=lfs diff=lfs merge=lfs -text
/Thesis.bbl filter=lfs diff=lfs merge=lfs -text
*.jp*g filter=lfs diff=lfs merge=lfs -text
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\babel@toc {english}{}\relax
\contentsline {xpart}{Chapters}{2}{part.1}%
\addvspace {10\p@ }
\contentsline {xchapter}{Introduction}{2}{chapter.1}%
\addvspace {10\p@ }
\contentsline {xchapter}{Analytical Investigations}{9}{chapter.2}%
\addvspace {10\p@ }
\contentsline {xchapter}{Experimental Investigations}{12}{chapter.3}%
\addvspace {10\p@ }
\contentsline {xchapter}{Discussion}{13}{chapter.4}%

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\babel@toc {english}{}\relax
\contentsline {xpart}{Chapters}{2}{part.1}%
\addvspace {10\p@ }
\contentsline {xchapter}{Introduction}{2}{chapter.1}%
\addvspace {10\p@ }
\contentsline {xchapter}{Analytical Investigations}{9}{chapter.2}%
\addvspace {10\p@ }
\contentsline {xchapter}{Experimental Investigations}{12}{chapter.3}%
\addvspace {10\p@ }
\contentsline {xchapter}{Discussion}{13}{chapter.4}%

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{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.1}Paragraph 4: Synergistic Challenges in Applications Prone to Corrosion and Cavitation\hfill {}\textsc {ignore}}{\reset@font\mtcSfont 5}{section.1.1}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.2}Paragraph 5: Research and Development for Enhanced Corrosion and Cavitation Performance\hfill {}\textsc {ignore}}{\reset@font\mtcSfont 5}{section.1.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.3}Paragraph 6: Influence of HIPing\hfill {}\textsc {ignore}}{\reset@font\mtcSfont 5}{section.1.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.4}General Background}{\reset@font\mtcSfont 5}{section.1.4}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.5}Stellite 1}{\reset@font\mtcSfont 6}{section.1.5}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.6}Stellites}{\reset@font\mtcSfont 7}{section.1.6}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.7}Objectives and Scope of the Research Work}{\reset@font\mtcSfont 7}{section.1.7}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.8}Thesis Outline}{\reset@font\mtcSfont 7}{section.1.8}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.9}Literature Survey}{\reset@font\mtcSfont 7}{section.1.9}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.10}Cavitation Tests}{\reset@font\mtcSfont 7}{section.1.10}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.1}Paragraph 4: Synergistic Challenges in Applications Prone to Corrosion and Cavitation\hfill {}\textsc {ignore}}{\reset@font\mtcSfont 6}{section.1.1}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.2}Paragraph 5: Research and Development for Enhanced Corrosion and Cavitation Performance\hfill {}\textsc {ignore}}{\reset@font\mtcSfont 6}{section.1.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.3}Paragraph 6: Influence of HIPing\hfill {}\textsc {ignore}}{\reset@font\mtcSfont 6}{section.1.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.4}Paragraph: Cavitation Erosion Resistance}{\reset@font\mtcSfont 6}{section.1.4}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.5}General Background}{\reset@font\mtcSfont 6}{section.1.5}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.6}Stellite 1}{\reset@font\mtcSfont 8}{section.1.6}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.7}Stellites}{\reset@font\mtcSfont 8}{section.1.7}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.8}Objectives and Scope of the Research Work}{\reset@font\mtcSfont 8}{section.1.8}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.9}Thesis Outline}{\reset@font\mtcSfont 8}{section.1.9}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.10}Literature Survey}{\reset@font\mtcSfont 8}{section.1.10}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {1.11}Cavitation Tests}{\reset@font\mtcSfont 8}{section.1.11}}

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{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {2.1}Strain hardening}{\reset@font\mtcSfont 9}{section.2.1}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {2.2}Correlative empirical methods}{\reset@font\mtcSfont 9}{section.2.2}}

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{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.1}Materials and Microstructure}{\reset@font\mtcSfont 9}{section.3.1}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.1}Materials and Microstructure}{\reset@font\mtcSfont 12}{section.3.1}}

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{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.1}Experimental Test Procedure}{\reset@font\mtcSfont 10}{section.4.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.1.1}Hardness Tests}{\reset@font\mtcSSfont 10}{subsection.4.1.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.1.2}Cavitation}{\reset@font\mtcSSfont 10}{subsection.4.1.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.2}Relationships between cavitation erosion resistance and mechanical properties}{\reset@font\mtcSfont 10}{section.4.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.3}Influence of vibratory amplitude}{\reset@font\mtcSfont 10}{section.4.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.1}Experimental Test Procedure}{\reset@font\mtcSfont 13}{section.4.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.1.1}Hardness Tests}{\reset@font\mtcSSfont 13}{subsection.4.1.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.1.2}Cavitation}{\reset@font\mtcSSfont 13}{subsection.4.1.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.2}Relationships between cavitation erosion resistance and mechanical properties}{\reset@font\mtcSfont 13}{section.4.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.3}Influence of vibratory amplitude}{\reset@font\mtcSfont 13}{section.4.3}}

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** Packages :ignore_heading:
#+LaTeX_HEADER: \usepackage{multirow}
#+LaTeX_HEADER: \usepackage[flushleft]{threeparttable} % http://ctan.org/pkg/threeparttable
#+LaTeX_HEADER: \usepackage{booktabs,caption}
#+LaTeX_HEADER: \graphicspath{{expt/}}
#+LaTeX_HEADER: \usepackage{afterpage}
#+LaTeX_HEADER: \usepackage{pdflscape}
#+LaTeX_HEADER: \usepackage{booktabs,caption}
#+LaTeX_HEADER: \usepackage{longtable}
#+LaTeX_HEADER: \usepackage{threeparttablex}
#+LaTeX_HEADER: \usepackage[flushleft]{threeparttable}
#+LaTeX_HEADER: \usepackage{multirow}
#+LaTeX_HEADER: \usepackage{caption}
#+LaTeX_HEADER: \usepackage{booktabs} % Added for nicer rules
#+LaTeX_HEADER: \usepackage{textcomp}
#+LaTeX_HEADER: \usepackage{mathtools}
#+LaTeX_HEADER: \usepackage{graphicx} % include graphics
#+LaTeX_HEADER: \usepackage{fancyhdr} % layout
@ -28,7 +29,7 @@
#+LaTeX_HEADER: \usepackage[T1]{fontenc} % font
#+LaTeX_HEADER: \usepackage{csquotes}
#+LaTeX_HEADER: %\usepackage[defernumbers=true, sorting=none]{biblatex}
#+LaTeX_HEADER: \usepackage[style=ieee, backend=biber, maxbibnames=999]{biblatex}
#+LaTeX_HEADER: \usepackage[defernumbers=true, bibstyle=ieee, citestyle=numeric-comp, backend=biber, maxbibnames=999]{biblatex}
#+LaTeX_HEADER: \usepackage{setspace} % spacing
#+LaTeX_HEADER: % \usepackage[left=4cm,right=2cm,top=2cm,bottom=2cm]{geometry}
@ -172,9 +173,9 @@
#+LaTeX_HEADER: %% modified reference function
#+LaTeX_HEADER: %% https://tex.stackexchange.com/a/438998
#+LaTeX_HEADER: \newcommand\eref[1]{equation~(\ref{#1})}
#+LaTeX_HEADER: \newcommand\tref[1]{table~\ref{#1}}
#+LaTeX_HEADER: \newcommand\fref[1]{figure~\ref{#1}}
#+LaTeX_HEADER: \newcommand\eref[1]{Equation~(\ref{#1})}
#+LaTeX_HEADER: \newcommand\tref[1]{Table~\ref{#1}}
#+LaTeX_HEADER: \newcommand\fref[1]{Figure~\ref{#1}}
#+LaTeX_HEADER: %% 1.5 line spacing
#+LaTeX_HEADER: \setstretch{1.5}
@ -206,8 +207,7 @@
** Acronyms :ignore_heading:
#+LaTeX_HEADER: \newacronym{gcd}{GCD}{Greatest Common Divisor}
#+LaTeX_HEADER: \newacronym{lcm}{LCM}{Least Common Multiple}
** Packages 2 :ignore_heading:
@ -217,7 +217,7 @@
#+LaTeX: \pagestyle{empty}
# #+LaTeX: \input{preliminaries/1-titlepages}
#+BEGIN_LATEX
#+begin_export latex
\begin{center}
\vspace*{15pt}\par
\setstretch{1}
@ -263,8 +263,7 @@
The copyright in this thesis is owned by the author. Any quotation from the thesis or use of any of the information contained in it must acknowledge this thesis as the source of the quotation or information.
\end{flushleft}
\end{center}
#+END_LATEX
#+end_export
** Abstract :ignore_heading:
@ -272,7 +271,7 @@ The copyright in this thesis is owned by the author. Any quotation from the thes
# also read the comment below, for table of content and other
# #+LaTeX: % \pagestyle{preliminary}
#+BEGIN_LATEX
#+begin_export latex
\clearpage
\begin{center}
\LARGE\textbf {Abstract}
@ -281,11 +280,11 @@ The copyright in this thesis is owned by the author. Any quotation from the thes
\noindent
In accordance with the Academic Regulations the thesis must contain an abstract preferably not exceeding 200 words, bound in to precede the thesis. The abstract should appear on its own, on a single page. The format should be the same as that of the main text. The abstract should provide a synopsis of the thesis and shall state clearly the nature and scope of the research undertaken and of the contribution made to the knowledge of the subject treated. There should be a brief statement of the method of investigation where appropriate, an outline of the major divisions or principal arguments of the work and a summary of any conclusions reached. The abstract must follow the Title Page.
#+END_LATEX
#+end_export
** Dedication & Acknowledgements :ignore_heading:
#+BEGIN_LATEX
#+begin_export latex
\clearpage
\begin{center}
\LARGE\textbf {Dedication}
@ -294,9 +293,7 @@ In accordance with the Academic Regulations the thesis must contain an abstract
If a dedication is included then it should be immediately after the Abstract page.\par
I don't what it is actually.
#+END_LATEX
#+BEGIN_LATEX
\clearpage
\begin{center}
\LARGE\textbf {Acknowledgements}
@ -304,22 +301,49 @@ I don't what it is actually.
\vspace{5pt}
\noindent I wanna thanks all coffee and tea manufacturers and sellers that made the completion of this work possible.
#+END_LATEX
#+end_export
** COMMENT Declaration :ignore_heading:
#+LaTeX: \clearpage
#+LaTeX: % % read about declaration in file
#+LaTeX: % % \input{Preliminaries/5-declaration}
#+LaTeX: \includepdf[pages=-]{preliminaries/5-declaration.pdf}
#+LaTeX:
** TOC, Tables, Figures, Glossary :ignore_heading:
#+LaTeX: {
#+LaTeX: \setstretch{1}
#+LaTeX: \hypersetup{linkcolor=black}
#+LaTeX: \tableofcontents
*** Tables :ignore_heading:
#+LaTeX: \listoftables % optional
*** Figures :ignore_heading:
#+LaTeX: \listoffigures % optional
*** Glossary :ignore_heading:
# #+LaTeX_HEADER: \newacronym{gcd}{GCD}{Greatest Common Divisor}
# #+LaTeX_HEADER: \newacronym{lcm}{LCM}{Least Common Multiple}
#+LaTeX_HEADER: \newacronym{sem}{SEM}{Scanning Electron Microscope/Microscopy}
#+LaTeX_HEADER: \newacronym{edx}{EDX}{Energy-Dispersive X-ray}
#+LaTeX_HEADER: \newacronym{xrd}{XRD}{X-ray Diffraction}
#+LaTeX_HEADER: \newacronym{hv}{HV}{Hardness Vickers Scale}
#+LaTeX_HEADER: \newacronym{hip}{HIP}{Hot Isostatically Pressed}
#+LaTeX_HEADER: \newacronym{fcc}{FCC}{Face Centred Cubic}
#+LaTeX_HEADER: \newacronym{hcp}{HCP}{Hexagonal Close Packed}
#+LaTeX_HEADER: \newacronym{se}{SE}{Secondary Electrons}
#+LaTeX_HEADER: \newacronym{bse}{BSE}{Backscatter Electrons}
#+LaTeX_HEADER: \newacronym{pdf}{PDF}{Powder Diffraction File}
#+LaTeX: \glsaddall % this is to include all acronym. You can do a sort of citation for acronym and include only the one you use, Look at the glossary package for details.
#+LaTeX: \printnoidxglossary[type=\acronymtype, title=Glossary] % optional
#+LaTeX: }
*** COMMENT Our own publications
#+LaTeX: {
#+LaTeX: %% put your publications in BibMine.bib
#+LaTeX: %% They will be displayed here
#+LaTeX: \begin{refsection}[BibMine.bib]
@ -339,7 +363,10 @@ I don't what it is actually.
** Introduction
*** Paragraph 1: Introduction to Stellite Alloys for Hostile Environments :ignore_heading:
*** Paragraph: Cavitation :ignore_heading:
*** Paragraph: Introduction to Stellite Alloys for Hostile Environments :ignore_heading:
#+BEGIN_COMMENT
- [X] What they are and where they came from.
@ -350,29 +377,27 @@ I don't what it is actually.
Stellite 6 with nominal composition
#+END_COMMENT
Stellites are a cobalt-base superalloy used in aggresive service environments due to retention of strength, wear resistance, and oxidation resistance at high temperature \cite{ahmedStructurePropertyRelationships2014}.
Originating in 1907 with Elwood Haynes's development of alloys like Stellite 6, Stellites quickly found use in orthopedic implants, machine tools, and nuclear components, and new variations on the original CoCrWC and CoCrMoC alloys are spreading to new sectors like oil & gas and chemical processing \cite{malayogluComparingPerformanceHIPed2003, ahmedStructurePropertyRelationships2014}.
Stellites are cobalt-base superalloys used in aggresive service environments due to retention of strength, wear resistance, and oxidation resistance at high temperature \cite{ahmedStructurePropertyRelationships2014, shinEffectMolybdenumMicrostructure2003}. Originating with Elwood Haynes's development of alloys like Stellite 6 in the early 1900s \cite{hasanBasicsStellitesMachining2016}, stellites quickly found use in medical implants & tools, machine tools, and nuclear components, and new variations on the original CoCrWC and CoCrMoC alloys are spreading to new sectors like oil & gas and chemical processing \cite{malayogluComparingPerformanceHIPed2003, ahmedStructurePropertyRelationships2014, raghuRecentDevelopmentsWear1997}.
*** Paragraph: Impact of Composition, Microstructure, and Processing on Corrosion and Cavitation Performance :ignore_heading:
Stellites generally contain 25-33 wt Cr, 4-18 W/Mo, 0.1-3.3 wt C, and optional trace elements of Fe, Ni, Si, P, S, B, Ln, Mn, as seen in Table \ref{tab:stellite_composition} \cite{ahmedMappingMechanicalProperties2023, alimardaniEffectLocalizedDynamic2010, ashworthMicrostructurePropertyRelationships1999, bunchCorrosionGallingResistant1989, davis2000nickel, desaiEffectCarbideSize1984, ferozhkhanMetallurgicalStudyStellite2017, pacquentinTemperatureInfluenceRepair2025, ratiaComparisonSlidingWear2019, zhangFrictionWearCharacterization2002}. The microstructure of Stellite alloys consists of a CoCr(W,Mo) matrix with solid solution strengthening, with hard carbide phases, usually with Cr (e.g., $M_{7}C_{3}$, $M_{23}C_{6}$), and W/Mo (e.g. $MC$, $M_{6}C$ ); the proportion and type of carbides depend on carbon content and the relative amounts of carbon with carbide formers (Cr, W, Mo), as well as processing routes. In addition to the solid solution toughness and carbide hardness, the stress-induced FCC tp HCP phase transformation of the Co-based solid solution further increases wear resistance through work hardening.
#+BEGIN_COMMENT
- [X] What they are and where they came from.
+ [ ] Main alloying elements and ref to tab:stellite_composition
+ [ ] Describe the microstructure briefly
+ [ ] Carbon grades
#+END_COMMENT
The main alloying elements in Stellite alloys are cobalt (Co), chromium (25-33 wt% Cr), tungsten (0-18 wt% W), molybdenum (0-18 wt% Mo), carbon (0.1-3.3 wt% C), and trace elements iron (Fe), nickel (Ni), silicon (Si), phosphorus (P), sulphur (S), boron (B), lanthanum (La), & manganese (Mn); \tref{tab:stellite_composition} summarizes the nominal and measured composition of commonly used Stellite alloys \cite{ahmedMappingMechanicalProperties2023, alimardaniEffectLocalizedDynamic2010, ashworthMicrostructurePropertyRelationships1999, bunchCorrosionGallingResistant1989, davis2000nickel, desaiEffectCarbideSize1984, ferozhkhanMetallurgicalStudyStellite2017, pacquentinTemperatureInfluenceRepair2025, ratiaComparisonSlidingWear2019, zhangFrictionWearCharacterization2002}. Stellite alloys possess a composite-like microstructure, combining a cobalt-rich matrix strengthened by solid solutions of chromium, tungsten, & molybdenum, with hard carbide phases with carbide formers Cr (of carbide type $\textrm{M}_{7}\textrm{C}_{3}$ & $\textrm{M}_{23}\textrm{C}_{6}$) and W/Mo (of carbide type $\textrm{MC}$ & $\textrm{M}_{6}\textrm{C}$), that impede wear and crack propagation \cite{ahmedSlidingWearBlended2021a, crookCobaltbaseAlloysResist1994}. The proportion and type of carbides depend on carbon content and the relative amounts of carbon with carbide formers (Cr, W, Mo), which greatly influence alloy performance and intended applications; high carbon alloy (>1.2 wt%) have greater carbide formation and are primarily used for wear resistance, low carbon alloys (<0.5 wt%) are used for enhanced corrosion resistance, while medium carbon alloys (0.5 wt% - 1.2 wt%) are used in applications requiring a combination of wear and corrosion resistance \cite{davis2000nickel}.
# In addition to the solid solution toughness and carbide hardness, the stress-induced FCC \textrightarrow{} HCP phase transformation of the Co-based solid solution further increases wear resistance through work hardening.
**** Table: Show the table of stellite compositions :ignore_heading:
# \begin{landscape}
# \begin{table}
# \caption{Stellite Compositions}
# \label{tab:stellite_composition}
# \begin{threeparttable}
# \begin{table}{lllllllllllllllll}
#+BEGIN_LATEX
#+begin_export latex
\afterpage{%
\begin{landscape}
\begin{ThreePartTable}
\centering
\caption{Stellite Compositions}
\label{tab:stellite_composition}
@ -381,9 +406,9 @@ Stellites generally contain 25-33 wt Cr, 4-18 W/Mo, 0.1-3.3 wt C, and optional t
% \toprule & \multicolumn{2}{c}{Base} & \multicolumn{2}{c}{Refractory} & Carbon & \multicolumn{8}{c}{Others} & \multicolumn{3}{c}{} \\
\toprule
Alloy &
\textbf{Alloy} &
\textbf{Co} & \textbf{Cr} & \textbf{W} & \textbf{Mo} & \textbf{C} & \textbf{Fe} &
\textbf{Ni} & \textbf{Si} & \textbf{P} & \textbf{S} & \textbf{B} & \textbf{Ln} &
\textbf{Ni} & \textbf{Si} & \textbf{P} & \textbf{S} & \textbf{B} & \textbf{La} &
\textbf{Mn} & \textbf{Ref} & \textbf{Process Type} & \textbf{Observation} \\
\midrule
@ -505,25 +530,87 @@ Stellite 19
% & 37.2 & 33 & & 18 & 2.5 & 3 & 3 & 1.5 & & & 0.3 & & 1.5 & \cite{davis2000nickel} & \multicolumn{2}{c}{Nominal composition} \\
\end{longtable}
\begin{TableNotes}
\begin{tablenotes}
\small
\item[a] Hot Isostatic Pressing
\item[b] Inductively coupled plasma atomic emission spectroscopy
\item[c] Shielded metal arc welding
\item[d] Gas tungsten Arc Welding
\item[e] Plasma transfered Arc Welding
\end{TableNotes}
\end{tablenotes}
\end{ThreePartTable}
\end{landscape}
#+END_LaTeX
}
#+end_export
*** Paragraph: Co phases :ignore_heading:
The Co solid solution in Stellites is a metastable fcc crystal with a very low stacking fault energy.
\cite{davis2000nickel, frenkMicrostructuralEffectsSliding1994}
# One of the main applications of Stellite alloys can be wear and erosion resistance, which results from various carbides and Co solid solution [1], [7]. Cobalt imparts to its alloys an unstable fcc crystal structure with a very low stacking fault energy.
# The cubic FCC phase of cobalt (ICDD 00-015-0806)
# The hexagonal HCP phase of cobalt (ICDD 01-071-4239)
# The wear resistance of Stellite alloys benefits from the strain-induced face-centered cubic (FCC) to hexagonal closepacked (HCP) transformation of Co \cite{collierTribologicalPerformanceMolybdenum2020, ahmedFrictionWearCobaltBase2017}
# I *love* this paragraph
# https://doi.org/10.1016/j.surfcoat.2018.11.011
# The ε-Co and γ-Co phase are the main phases in Co alloys [39]. According to the phase diagram, the ε-Co phase is more stable at room temperature [40]. However, the γ-Co to ε-Co transformation rarely occurs under normal cooling conditions, and as a result, the γ-Co phase is generally retained at room temperature [39], as we found in the as-deposited Stellite 6 coatings. Nevertheless, this transformation can be triggered athermally (e.g. quenching from temperature of γ-Co) [25,41], isothermally (e.g. aging at temperatures between 650 °C and 950 °C) [35,42,43], or by strain [30,31]. In this study, the thermal fatigue process was achieved by quenching, with heating temperatures of up to 650 °C, and the crack tip introduced severe plastic deformation, all conditions that promote the γ-Co to ε-Co transformation.
*** Paragraph: Stellite 1 :ignore_heading:
# Stellite 1 is a high-carbon and high-tungsten CoCrWMoCFeNiSiMn alloy, making it suitable for tribological applications such as valve seating, wear pads in gas turbines, bearing sleeves, slurry pumps, ball bearings and expeller screws. Stellite 1 alloy is labeled as CoCrW alloy in this paper. Stellite 21 is a low-carbon, high-molybdenum alloy used in applications such as forging and hot-stamping dies and valve trims in the chemical industry (Ref 1, 2).
*** Paragraph: Tungsten & Molybdenum :ignore_heading:
# Tungsten is primarily utilized in Stellite alloys to provide solid solution strength and carbide formation but can be replaced by Mo which also partitions to the carbides.
# Tungsten (W) and molybdenum (Mo) have a similar function in providing additional strength to Co solid solution matrix of Stellite alloys due to large atomic size, that is, they impede dislocation flow when present as solute atoms\cite{boeckRelationshipsProcessingMicrostructure1985}.
Tungsten (W) and molybdenum (Mo) serve to provide additional strength to the matrix, when present in a small amount (<4 wt%), by virtue of their large atomic size that impedes dislocation flow when present as solute atoms. When present in large quantities, W and Mo also participate in formation of W-rich or Mo-rich carbides during alloy solidification
\cite{davis2000nickel}
\cite{raghuRecentDevelopmentsWear1997}
*** Paragraph: Tungsten Carbide :ignore_heading:
There are two main phases in the tungsten-carbon system: the hexagonal $\textrm{WC}$ (ICDD Card# 03-065-4539, COD:2102265), denoted as $\delta-\textrm{WC}$, and multiple variations of hexagonal-close-packed \textrm{W}_2\textrm{C}$ (ICDD:00-002-1134, COD:1539792) \cite{kurlovPhaseEquilibriaWC2006}.
# There are two hexagonal carbides in the tungsten – carbon system (Fig. 2): the monocarbide, WC, and the subcarbide [12070-13-2], W 2 C. The hexagonal WC, also called a-WC, decomposes at its incongruent melting point of 2776 C. Its range of homogeneity is extremely narrow: from 49.5 to 50.5 mol % C \cite{tulhoffCarbides2000}
# Several stable tungsten carbide phases in the WC phase diagram. They consist of the S phase with simple hexagonal structure (prototype: WC), γ phase with face-centred-cubic structure (prototype: NaCl), and β phase with hexagonal-close-packed structure (prototype: PbO2). Both β and β phases are nonstoichiometric with a solubility of C wt.% in approximate ranges of 2.2∼3.0 and 3.6∼3.9, respectively. The S phase is a stoichiometric compound. For the sake of convenience, we represent the β, γ and δ phases by their corresponding compounds W2C, WC1-x and WC, respectively. \cite{gubischTribologicalCharacteristicsWC1x2005}
The precipitation of the tungsten-rich phase $M_6C$ is closely related to the decomposition of the MC carbide, and the $M_6C$ only occurs in the vicinity of the MC \cite{jiangSecondaryM6CPrecipitation1999}, as $M_6C$ carbides form only when the tungsten and.or molybdenum content exceeds 4-6 a/o.
*** Paragraph: Chromium carbide :ignore_heading:
Although M23C6 can precipitate as primary carbide during solidification, it is most commonly found in secondary carbides along grain boundaries.
M7C3 is a metastable pseudo-eutectic carbide that typically forms at lower carbon-chromium ratios and effectively transforms into secondary M23C6 upon heat treatment.
In addition to being a carbide former, chromium provides solid solution strengthing and corrosion/oxidation resistance to the cobalt-based matrix.
The Cr7C3 carbide is unstable at high temperatures and transforms to M_{23}C_{6} upon heat treatment. Under further temperature and time, Cr_{23}C_{6} partially transforms to Cr_6C \cite{mohammadnezhadInsightMicrostructureCharacterization}.
$$ 2Cr_{7}C_{3} + 9Cr \rightarrow Cr_{23}C_{6} $$
$$ Cr_{23}C_{6} + 13Cr \rightarrow 6Cr_{6}C $$
$$ 23Cr_{7}C_{3} \rightarrow 7Cr_{23}C_6 + 27C $$
$$ 6C + 23Cr \rightarrow Cr23C6 $$
# \end{tabular}
# \begin{tablenotes}
# \item[*] The footnote text.
# \item[a] Another footnote.
# \end{tablenotes}
# \end{threeparttable}
# \end{table}
# \end{landscape}
*** Paragraph 2: Fundamental Mechanisms of Corrosion and Cavitation Resistance :ignore_heading:
@ -538,12 +625,33 @@ Stellite 19
The remarkable ability of Stellite alloys to withstand these specific challenges stems from key metallurgical features. Their corrosion resistance is primarily attributed to a high chromium content, typically 20-30 wt.%, which promotes the formation of a highly stable, tenacious, and self-healing chromium-rich passive oxide film on the material's surface; this film acts as a barrier isolating the underlying alloy from the corrosive environment. Alloying elements such as molybdenum and tungsten can further enhance this passivity, particularly improving resistance to localized corrosion phenomena like pitting and crevice corrosion in aggressive media. Concurrently, their outstanding cavitation resistance is largely derived from the unique behavior of the cobalt-rich matrix, which can undergo a stress-induced crystallographic transformation from a face-centered cubic (fcc) to a hexagonal close-packed (hcp) structure. This transformation, often facilitated by mechanical twinning, effectively absorbs the intense, localized impact energy from collapsing cavitation bubbles and leads to significant work hardening, thereby impeding material detachment and erosion.
Antony suggests that the cavitation-erosion resistance of Stellites derives from the matrix phase and is enhanced by the strain-induced fcc \textrightarrow hcp allotropic transformation \cite{antonyWearResistantCobaltBaseAlloys1983}.
*** Paragraph: Lit review of corrosion :ignore_heading:
The aqueous oxidation of Stellite 6 alloy was investigated in a 1979 study using X-ray Photoelectron Spectroscopy (XPS) \cite{mcintyreXRayPhotoelectronSpectroscopic1979}. Specimens were exposed to pH 10 water at 285°C. To understand the oxidation behavior, the study measured dissolved oxygen concentration against exposure duration.
The high-temperature corrosion resistance of stellite coatings is attributable to the formation of cobalt & chromium surface \cite{cesanekDeteriorationLocalMechanical2015}.
Heathcock et al found that carbides are selectively eroded, with the carbide-matrix interface acting as initiating erosion site \cite{heathcockCavitationErosionCobaltbased1981}.
*** Paragraph 4: Synergistic Challenges in Applications Prone to Corrosion and Cavitation :ignore:
*** Paragraph 5: Research and Development for Enhanced Corrosion and Cavitation Performance :ignore:
*** Paragraph 6: Influence of HIPing :ignore:
Compared with the case alloys, the HIPed alloys had relatively finer, rounded, and distributed carbides.
*** Paragraph: Cavitation Erosion Resistance
The primary result of an erosion test is the cumulative mass loss versus time, which is then converted to volumetric loss and mean depth of erosion (MDE) versus time for the purposes of comparison between materials of different densities. The calculation of the mean depth of erosion for this test method should be performed in conformity with ASTM G-32.
*** General Background
# \section{General Background}
@ -578,7 +686,6 @@ Compared with the case alloys, the HIPed alloys had relatively finer, rounded, a
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}.
@ -616,6 +723,182 @@ Stellite 1 is a high-carbon and high-tungsten alloy, making it suitable for dema
# \section{Model Validation}
# \section{Result Analysis of Typical Load Case}
*** Strain hardening
# \cite{berchicheCavitationErosionModel2002}
Cavitation bubble collapse induce a work hardening of the material surface, comparable to that obtained in conventional peening \cite{swietlickiEffectsShotPeening2022}, characterized by the thickness of the hardened layers and the shape of the strain profile below the surface.
The strain profile within the material can usually be modeled by the following power law:
\begin{equation}
\epsilon\left(x\right) = \epsilon_s {\left( 1 - \frac{x}{L} \right)}^{\theta}
\end{equation}
where $\epsilon\left(x\right)$ is the strain at depth $x$ from the eroded surface, $\epsilon_s$ is the failure rupture strain on the eroded surface, $L$ is the thickness of the hardened layer, and $\theta$ is the shape factor of the power law.
After each cycle, the thickness of the hardened layer $L$ and the surface strain $\epsilon_s$ will increase continuously until damage is initiated at the surface ($\epsilon_s$ reaches the failure rupture strain $\epsilon_R$), at which point the strain profile is in steady-state.
\begin{equation}
\epsilon_R = \epsilon_{mean} {\left( 1 - \frac{\Delta L }{L+ \Delta L} \right)}^{\theta}
\end{equation}
*** Correlative empirical methods
Empirical methods are common for addressing complex cavitation erosion, involving lab tests to correlate cavitation erosion resistance with mechanical properties.
**** Karimi and Leo
The Karimi and Leo phenomenological model describes cavitation erosion rate as a function of
Karimi and Leo
**** Noskievic
Noskievic formulated a mathematical relaxation model for the dynamics of the cavitation erosion using a differential equation applied to forced oscillations with damping:
\begin{equation}
\frac{\mathrm{d}^2 v }{\mathrm{d}t^2} + 2 \alpha \frac{\mathrm{d} v }{\mathrm{d}t} + \beta^2 v = I
\end{equation}
where $I$ is erosion intensity, which can vary linearly with time, $v = \frac{\mathrm{d} v }{\mathrm{d}t}$ is erosion rate, $\alpha$ is strain hardening or internal friction of material during plastic deformation, and $\beta$ is coefficient inversely proportional to material strength. The general solution of equation can be written as:
\begin{equation}
v = a f_0 \left( \delta, \tau \right) + b f_1 \left( \delta, \tau \right)
\end{equation}
\begin{equation*}
f_0\left(\ \delta,\tau \right) = \begin{cases*}
1 - \mathrm{exp}{ \left( - \delta \tau \right) } \left[ \dfrac{\delta}{\omega} \mathrm{sin} \left(\omega \tau\right) + \mathrm{cos}{\left( \omega \tau \right)} \right]
& \text{if} -1 < \delta < 1; \delta \neq 0 \\
1 - \dfrac{1}{ {{\delta_0}^2} - 1} \left[ \delta_0^2 \mathrm{exp}{\left( -\dfrac{\tau}{\delta_0}}\right) - \mathrm{exp}{\left(- \delta_0 \tau\right)} \right]
& \text{if} \delta > 1 \\
1 - \mathrm{cos}{\left( \tau \right)}
& \text{if} \delta = 0 \\
1 - \left(1 + \tau \right) \mathrm{exp} \left( - \tau \right)
& if \delta = 1
\end{cases*}
\end{equation*}
\begin{equation*}
f_1\left(\ \delta,\tau \right) = \begin{cases*}
1 - \dfrac{2\delta}{\tau} \left[ 1 - {\mathrm{exp}\left(-\delta \tau\right)} {\left[ {\mathrm{cos} \omega \tau} + {\epsilon \mathrm{sin} \omega \tau} \right]} \right]
& \text{if} -1 < \delta < 1; \delta \neq 0 \\
1 - \dfrac{1}{\tau} \left( 2 \delta - \dfrac{1}{\delta_0 \left( \delta_0^2 - 1 \right)} \left[\mathrm{exp}{\left( -\delta_0 \tau \right) - \delta^4 \mathrm{exp}{\left( - \dfrac{\tau}{\delta_0} \right)} \right] \right)
& \text{if} \delta > 1 \\
1 - \dfrac{ \mathrm{sin}{\left( \tau \right)} }{\tau}
& \text{if} \delta = 0 \\
1 - \dfrac{2 \left[ 1 - \mathrm{exp}\left(-\tau\right) \right]}{\tau} + \mathrm{exp} \left( - \tau \right)
& if \delta = 1
\end{cases*}
\end{equation*}
\begin{equation*}
\delta = \dfrac{\alpha}{\beta},\quad
\tau = \beta t,\quad
\epsilon = \dfrac{\delta^2 - 0.5}{\delta \sqrt{ 1 - \delta^2 } },\quad
\omega = \sqrt{1 - \delta^2},\quad
\delta_0 = \delta + \sqrt{ \delta^2 - 1 }
\end{equation*}
***** Noskievic python function :noexport:ignore:
#+NAME: noskievic
#+BEGIN_SRC python :exec no :exports none
def noskievic(t, alpha, beta, a, b):
"""
Calculates the erosion rate (v) based on Noskievic's relaxation model.
This model describes the dynamics of cavitation erosion using a differential
equation applied to forced oscillations with damping. The general solution
for the erosion rate (v) is given by:
v = a * f0(delta, tau) + b * f1(delta, tau)
where delta = alpha / beta and tau = beta * t. The functions f0 and f1
have different forms depending on the value of delta.
Args:
t (float): Time.
alpha (float): Material parameter representing strain hardening or
internal friction of the material during plastic
deformation (α).
beta (float): Material parameter, a coefficient inversely proportional
to material strength (β).
a (float): Coefficient for the f0 component in the general solution.
b (float): Coefficient for the f1 component in the general solution.
Returns:
float: The calculated erosion rate (v) at the given time t.
Notes:
The intermediate parameters used in the model are:
- delta (δ) = alpha / beta
- tau (τ) = beta * t
- omega (ω) = sqrt(1 - delta^2) (for -1 < delta < 1, delta != 0)
- delta_0 (δ₀) = delta + sqrt(delta^2 - 1) (for delta > 1)
- epsilon (ε) = (delta^2 - 0.5) / (delta * sqrt(1 - delta^2)) (for -1 < delta < 1, delta != 0)
The functions f0(delta, tau) and f1(delta, tau) are piecewise
functions dependent on the value of delta:
- Case 1: -1 < delta < 1 and delta != 0
- Case 2: delta > 1
- Case 3: delta = 0
- Case 4: delta = 1
This implementation should handle these cases internally to compute
f0 and f1 correctly.
"""
import numpy as np
d = alpha/beta
tau = beta*t
if np.isclose(d,0.0):
print("d=0")
f0 = 1 - np.cos(tau)
f1 = 1 - ((np.sin(tau))/(tau))
elif np.isclose(d,1.0):
print("d=1")
f0 = 1 - (1 + tau)*np.exp(-tau)
f1 = 1 - 2*((1 - np.exp(-tau))/(tau)) + np.exp(-tau)
elif -1 < d and d < 1:
e = (d**2 - 0.5)/(d*np.sqrt(1 - d**2))
w = np.sqrt(1 - d**2)
f0 = 1 - np.exp(-d*tau)*((d/w)*np.sin(w*tau) + np.cos(w*tau))
f1 = 1 - ((2*d)/(tau))*(1 - np.exp(-d*tau)*( np.cos(w*tau) + e*np.sin(w*tau) ))
elif d > 1:
d_0 = d + np.sqrt(d**2 - 1)
f0 = 1 - (1/(d_0**2 - 1))*(d_0**2 * np.exp(-tau/d_0) - np.exp(-d_0 * tau))
f1 = 1 - (1/tau)*(2*d - (1/(d_0*(d_0**2-1)))*( np.exp(-d_0*tau) - d**4*np.exp(-tau/d_0) ) )
else:
raise ValueError("d is not within bounds")
return a*f0 + b*f1
#+END_SRC
**** Hoff and Langbein equation
Hoff and Langbein proposed a simple exponential function for the rate of erosion, representing the normalized erosion rate requiring only the
A simple exponential function for the rate of erosion was proposed by Hoff and Langbein,
$$ \frac{ \dot{e} }{ \dot{e_{max}} } = 1 - e^{\frac{-t_i}{t}} $$
$\dot{e}$ - erosion rate at any time t
$\dot{e_{max}}$ - Maximum of peak erosion rate
$t_i$ - incubation period (intercept on time axis extended from linear potion of erosion-time curve)
$t$ - exposure time
**** L Sitnik model
$$ V = V_o {\left[ ln\left( \frac{t}{t_o} + 1 \right) \right]} ^ {\beta} $$
$$ \dot{V} = \frac{\beta V_o}{t + t_o} {\left[ ln \left( \frac{t}{t_o} + 1 \right) \right]}^{\beta - 1}$$
V_o > 0
t_o > 0
\beta >= 1
** Experimental Investigations
*** Materials and Microstructure
@ -647,21 +930,13 @@ The Vickers microhardness was measured using a Wilson hardness tester under load
# \chapter{Cavitation Erosion}
\section{Experimental Test Procedure}
\subsection{Hardness Tests}
\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)
@ -681,20 +956,12 @@ Maximum erosion rate is approximately proportional to the 1.5 power of p-p ampli
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.
* COMMENT Appendix :ignore_heading:
** Cavitation :noexport:
#+LaTeX: \pagestyle{chapter}
#+LaTeX: \subfile{Chapters/Cavitation}
#+LaTeX: \subfile{Chapters/Chapter1-Introduction}
#+LaTeX: \subfile{Chapters/Chapter2}
#+LaTeX: \subfile{Chapters/Chapter3}
#+LaTeX: \appendix
#+LaTeX: \subfile{Appendices/Appendix1}
* COMMENT Publications :ignore_heading:
#+LaTeX: %% add publications in pdf format
#+LaTeX: \clearpage
@ -702,8 +969,7 @@ The propagation of ultrasonic waves may result in thermal energy absorption or i
#+LaTeX: \addcontentsline{toc}{chapter}{\thechapter\ \ \ \ Publication 1}
#+LaTeX: \includepdf[pages=-]{Publications/Publication1.pdf}
* Bibliography :noexport:
* Bibliography :ignore_heading:
# using biblatex rather than bibtex to easily have further reading and references

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Thesis.tex
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@ -1,4 +1,4 @@
% Created 2025-05-12 ن 00:31
% Created 2025-05-12 ن 08:48
% Intended LaTeX compiler: pdflatex
\documentclass[11pt]{report}
\usepackage[utf8]{inputenc}
@ -12,16 +12,17 @@
\usepackage{amssymb}
\usepackage{capt-of}
\usepackage{hyperref}
\usepackage{multirow}
\usepackage[flushleft]{threeparttable} % http://ctan.org/pkg/threeparttable
\usepackage{booktabs,caption}
\graphicspath{{expt/}}
\usepackage{afterpage}
\usepackage{pdflscape}
\usepackage{booktabs,caption}
\usepackage{longtable}
\usepackage{threeparttablex}
\usepackage[flushleft]{threeparttable}
\usepackage{multirow}
\usepackage{caption}
\usepackage{booktabs} % Added for nicer rules
\usepackage{textcomp}
\usepackage{mathtools}
\usepackage{graphicx} % include graphics
\usepackage{fancyhdr} % layout
\usepackage[english]{babel}
@ -29,7 +30,7 @@
\usepackage[T1]{fontenc} % font
\usepackage{csquotes}
%\usepackage[defernumbers=true, sorting=none]{biblatex}
\usepackage[ backend=biber, maxbibnames=999]{biblatex}
\usepackage[defernumbers=true, bibstyle=ieee, citestyle=numeric-comp, backend=biber, maxbibnames=999]{biblatex}
\usepackage{setspace} % spacing
% \usepackage[left=4cm,right=2cm,top=2cm,bottom=2cm]{geometry}
@ -149,9 +150,9 @@ filecolor = black % url which open local files
}
%% modified reference function
%% https://tex.stackexchange.com/a/438998
\newcommand\eref[1]{equation~(\ref{#1})}
\newcommand\tref[1]{table~\ref{#1}}
\newcommand\fref[1]{figure~\ref{#1}}
\newcommand\eref[1]{Equation~(\ref{#1})}
\newcommand\tref[1]{Table~\ref{#1}}
\newcommand\fref[1]{Figure~\ref{#1}}
%% 1.5 line spacing
\setstretch{1.5}
%% The title of Thesis
@ -176,9 +177,17 @@ filecolor = black % url which open local files
\newcommand{\monthDate}{September}
%% Year of submission
\newcommand{\yearDate}{2042}
\newacronym{gcd}{GCD}{Greatest Common Divisor}
\newacronym{lcm}{LCM}{Least Common Multiple}
\usepackage{subfiles}
\newacronym{sem}{SEM}{Scanning Electron Microscope/Microscopy}
\newacronym{edx}{EDX}{Energy-Dispersive X-ray}
\newacronym{xrd}{XRD}{X-ray Diffraction}
\newacronym{hv}{HV}{Hardness Vickers Scale}
\newacronym{hip}{HIP}{Hot Isostatically Pressed}
\newacronym{fcc}{FCC}{Face Centred Cubic}
\newacronym{hcp}{HCP}{Hexagonal Close Packed}
\newacronym{se}{SE}{Secondary Electrons}
\newacronym{bse}{BSE}{Backscatter Electrons}
\newacronym{pdf}{PDF}{Powder Diffraction File}
\date{}
\title{}
\hypersetup{
@ -196,7 +205,6 @@ filecolor = black % url which open local files
\pagestyle{empty}
\begin{LATEX}
\begin{center}
\vspace*{15pt}\par
\setstretch{1}
@ -242,10 +250,8 @@ filecolor = black % url which open local files
The copyright in this thesis is owned by the author. Any quotation from the thesis or use of any of the information contained in it must acknowledge this thesis as the source of the quotation or information.
\end{flushleft}
\end{center}
\end{LATEX}
\begin{LATEX}
\clearpage
\begin{center}
\LARGE\textbf {Abstract}
@ -254,10 +260,8 @@ The copyright in this thesis is owned by the author. Any quotation from the thes
\noindent
In accordance with the Academic Regulations the thesis must contain an abstract preferably not exceeding 200 words, bound in to precede the thesis. The abstract should appear on its own, on a single page. The format should be the same as that of the main text. The abstract should provide a synopsis of the thesis and shall state clearly the nature and scope of the research undertaken and of the contribution made to the knowledge of the subject treated. There should be a brief statement of the method of investigation where appropriate, an outline of the major divisions or principal arguments of the work and a summary of any conclusions reached. The abstract must follow the Title Page.
\end{LATEX}
\begin{LATEX}
\clearpage
\begin{center}
\LARGE\textbf {Dedication}
@ -266,9 +270,7 @@ In accordance with the Academic Regulations the thesis must contain an abstract
If a dedication is included then it should be immediately after the Abstract page.\par
I don't what it is actually.
\end{LATEX}
\begin{LATEX}
\clearpage
\begin{center}
\LARGE\textbf {Acknowledgements}
@ -276,32 +278,43 @@ I don't what it is actually.
\vspace{5pt}
\noindent I wanna thanks all coffee and tea manufacturers and sellers that made the completion of this work possible.
\end{LATEX}
{
\setstretch{1}
\hypersetup{linkcolor=black}
\tableofcontents
\listoftables % optional
\listoffigures % optional
\glsaddall % this is to include all acronym. You can do a sort of citation for acronym and include only the one you use, Look at the glossary package for details.
\printnoidxglossary[type=\acronymtype, title=Glossary] % optional
}
\clearpage
\pagestyle{chapter}
\part{Chapters}
\label{sec:org82d3bd9}
\label{sec:orga0be3a3}
\chapter{Introduction}
\label{sec:org2e0b8b2}
Stellites are a cobalt-base superalloy used in aggresive service environments due to retention of strength, wear resistance, and oxidation resistance at high temperature \cite{ahmedStructurePropertyRelationships2014}.
Originating in 1907 with Elwood Haynes's development of alloys like Stellite 6, Stellites quickly found use in orthopedic implants, machine tools, and nuclear components, and new variations on the original CoCrWC and CoCrMoC alloys are spreading to new sectors like oil \& gas and chemical processing \cite{malayogluComparingPerformanceHIPed2003, ahmedStructurePropertyRelationships2014}.
\label{sec:org4e058f3}
Stellites generally contain 25-33 wt Cr, 4-18 W/Mo, 0.1-3.3 wt C, and optional trace elements of Fe, Ni, Si, P, S, B, Ln, Mn, as seen in Table \ref{tab:stellite_composition} \cite{ahmedMappingMechanicalProperties2023, alimardaniEffectLocalizedDynamic2010, ashworthMicrostructurePropertyRelationships1999, bunchCorrosionGallingResistant1989, davis2000nickel, desaiEffectCarbideSize1984, ferozhkhanMetallurgicalStudyStellite2017, pacquentinTemperatureInfluenceRepair2025, ratiaComparisonSlidingWear2019, zhangFrictionWearCharacterization2002}. The microstructure of Stellite alloys consists of a CoCr(W,Mo) matrix with solid solution strengthening, with hard carbide phases, usually with Cr (e.g., \(M_{7}C_{3}\), \(M_{23}C_{6}\)), and W/Mo (e.g. \(MC\), \(M_{6}C\) ); the proportion and type of carbides depend on carbon content and the relative amounts of carbon with carbide formers (Cr, W, Mo), as well as processing routes. In addition to the solid solution toughness and carbide hardness, the stress-induced FCC tp HCP phase transformation of the Co-based solid solution further increases wear resistance through work hardening.
Stellites are cobalt-base superalloys used in aggresive service environments due to retention of strength, wear resistance, and oxidation resistance at high temperature \cite{ahmedStructurePropertyRelationships2014, shinEffectMolybdenumMicrostructure2003}. Originating with Elwood Haynes's development of alloys like Stellite 6 in the early 1900s \cite{hasanBasicsStellitesMachining2016}, stellites quickly found use in medical implants \& tools, machine tools, and nuclear components, and new variations on the original CoCrWC and CoCrMoC alloys are spreading to new sectors like oil \& gas and chemical processing \cite{malayogluComparingPerformanceHIPed2003, ahmedStructurePropertyRelationships2014, raghuRecentDevelopmentsWear1997}.
\begin{LATEX}
The main alloying elements in Stellite alloys are cobalt (Co), chromium (25-33 wt\% Cr), tungsten (0-18 wt\% W), molybdenum (0-18 wt\% Mo), carbon (0.1-3.3 wt\% C), and trace elements iron (Fe), nickel (Ni), silicon (Si), phosphorus (P), sulphur (S), boron (B), lanthanum (La), \& manganese (Mn); \tref{tab:stellite_composition} summarizes the nominal and measured composition of commonly used Stellite alloys \cite{ahmedMappingMechanicalProperties2023, alimardaniEffectLocalizedDynamic2010, ashworthMicrostructurePropertyRelationships1999, bunchCorrosionGallingResistant1989, davis2000nickel, desaiEffectCarbideSize1984, ferozhkhanMetallurgicalStudyStellite2017, pacquentinTemperatureInfluenceRepair2025, ratiaComparisonSlidingWear2019, zhangFrictionWearCharacterization2002}. Stellite alloys possess a composite-like microstructure, combining a cobalt-rich matrix strengthened by solid solutions of chromium, tungsten, \& molybdenum, with hard carbide phases with carbide formers Cr (of carbide type \(\textrm{M}_{7}\textrm{C}_{3}\) \& \(\textrm{M}_{23}\textrm{C}_{6}\)) and W/Mo (of carbide type \(\textrm{MC}\) \& \(\textrm{M}_{6}\textrm{C}\)), that impede wear and crack propagation \cite{ahmedSlidingWearBlended2021a, crookCobaltbaseAlloysResist1994}. The proportion and type of carbides depend on carbon content and the relative amounts of carbon with carbide formers (Cr, W, Mo), which greatly influence alloy performance and intended applications; high carbon alloy (>1.2 wt\%) have greater carbide formation and are primarily used for wear resistance, low carbon alloys (<0.5 wt\%) are used for enhanced corrosion resistance, while medium carbon alloys (0.5 wt\% - 1.2 wt\%) are used in applications requiring a combination of wear and corrosion resistance \cite{davis2000nickel}.
\afterpage{%
\begin{landscape}
\begin{ThreePartTable}
\centering
\caption{Stellite Compositions}
\label{tab:stellite_composition}
@ -310,9 +323,9 @@ Stellites generally contain 25-33 wt Cr, 4-18 W/Mo, 0.1-3.3 wt C, and optional t
% \toprule & \multicolumn{2}{c}{Base} & \multicolumn{2}{c}{Refractory} & Carbon & \multicolumn{8}{c}{Others} & \multicolumn{3}{c}{} \\
\toprule
Alloy &
\textbf{Alloy} &
\textbf{Co} & \textbf{Cr} & \textbf{W} & \textbf{Mo} & \textbf{C} & \textbf{Fe} &
\textbf{Ni} & \textbf{Si} & \textbf{P} & \textbf{S} & \textbf{B} & \textbf{Ln} &
\textbf{Ni} & \textbf{Si} & \textbf{P} & \textbf{S} & \textbf{B} & \textbf{La} &
\textbf{Mn} & \textbf{Ref} & \textbf{Process Type} & \textbf{Observation} \\
\midrule
@ -434,34 +447,90 @@ Stellite 19
% & 37.2 & 33 & & 18 & 2.5 & 3 & 3 & 1.5 & & & 0.3 & & 1.5 & \cite{davis2000nickel} & \multicolumn{2}{c}{Nominal composition} \\
\end{longtable}
\begin{TableNotes}
\begin{tablenotes}
\small
\item[a] Hot Isostatic Pressing
\item[b] Inductively coupled plasma atomic emission spectroscopy
\item[c] Shielded metal arc welding
\item[d] Gas tungsten Arc Welding
\item[e] Plasma transfered Arc Welding
\end{TableNotes}
\end{tablenotes}
\end{ThreePartTable}
\end{landscape}
\end{LATEX}
}
The Co solid solution in Stellites is a metastable fcc crystal with a very low stacking fault energy.
\cite{davis2000nickel, frenkMicrostructuralEffectsSliding1994}
Tungsten (W) and molybdenum (Mo) serve to provide additional strength to the matrix, when present in a small amount (<4 wt\%), by virtue of their large atomic size that impedes dislocation flow when present as solute atoms. When present in large quantities, W and Mo also participate in formation of W-rich or Mo-rich carbides during alloy solidification
\cite{davis2000nickel}
\cite{raghuRecentDevelopmentsWear1997}
There are two main phases in the tungsten-carbon system: the hexagonal \(\textrm{WC}\) (ICDD Card\# 03-065-4539, COD:2102265), denoted as \(\delta-\textrm{WC}\), and multiple variations of hexagonal-close-packed \textrm{W}\textsubscript{2\textrm}\{C\}\$ (ICDD:00-002-1134, COD:1539792) \cite{kurlovPhaseEquilibriaWC2006}.
The precipitation of the tungsten-rich phase \(M_6C\) is closely related to the decomposition of the MC carbide, and the \(M_6C\) only occurs in the vicinity of the MC \cite{jiangSecondaryM6CPrecipitation1999}, as \(M_6C\) carbides form only when the tungsten and.or molybdenum content exceeds 4-6 a/o.
Although M23C6 can precipitate as primary carbide during solidification, it is most commonly found in secondary carbides along grain boundaries.
M7C3 is a metastable pseudo-eutectic carbide that typically forms at lower carbon-chromium ratios and effectively transforms into secondary M23C6 upon heat treatment.
In addition to being a carbide former, chromium provides solid solution strengthing and corrosion/oxidation resistance to the cobalt-based matrix.
The Cr7C3 carbide is unstable at high temperatures and transforms to M\textsubscript{23}C\textsubscript{6} upon heat treatment. Under further temperature and time, Cr\textsubscript{23}C\textsubscript{6} partially transforms to Cr\textsubscript{6C} \cite{mohammadnezhadInsightMicrostructureCharacterization}.
$$ 2Cr_{7}C_{3} + 9Cr \rightarrow Cr_{23}C_{6} $$
$$ Cr_{23}C_{6} + 13Cr \rightarrow 6Cr_{6}C $$
$$ 23Cr_{7}C_{3} \rightarrow 7Cr_{23}C_6 + 27C $$
$$ 6C + 23Cr \rightarrow Cr23C6 $$
The remarkable ability of Stellite alloys to withstand these specific challenges stems from key metallurgical features. Their corrosion resistance is primarily attributed to a high chromium content, typically 20-30 wt.\%, which promotes the formation of a highly stable, tenacious, and self-healing chromium-rich passive oxide film on the material's surface; this film acts as a barrier isolating the underlying alloy from the corrosive environment. Alloying elements such as molybdenum and tungsten can further enhance this passivity, particularly improving resistance to localized corrosion phenomena like pitting and crevice corrosion in aggressive media. Concurrently, their outstanding cavitation resistance is largely derived from the unique behavior of the cobalt-rich matrix, which can undergo a stress-induced crystallographic transformation from a face-centered cubic (fcc) to a hexagonal close-packed (hcp) structure. This transformation, often facilitated by mechanical twinning, effectively absorbs the intense, localized impact energy from collapsing cavitation bubbles and leads to significant work hardening, thereby impeding material detachment and erosion.
Antony suggests that the cavitation-erosion resistance of Stellites derives from the matrix phase and is enhanced by the strain-induced fcc \textrightarrow hcp allotropic transformation \cite{antonyWearResistantCobaltBaseAlloys1983}.
The aqueous oxidation of Stellite 6 alloy was investigated in a 1979 study using X-ray Photoelectron Spectroscopy (XPS) \cite{mcintyreXRayPhotoelectronSpectroscopic1979}. Specimens were exposed to pH 10 water at 285°C. To understand the oxidation behavior, the study measured dissolved oxygen concentration against exposure duration.
The high-temperature corrosion resistance of stellite coatings is attributable to the formation of cobalt \& chromium surface \cite{cesanekDeteriorationLocalMechanical2015}.
Heathcock et al found that carbides are selectively eroded, with the carbide-matrix interface acting as initiating erosion site \cite{heathcockCavitationErosionCobaltbased1981}.
\section{Paragraph 4: Synergistic Challenges in Applications Prone to Corrosion and Cavitation\hfill{}\textsc{ignore}}
\label{sec:org3496e89}
\label{sec:org6e56f58}
\section{Paragraph 5: Research and Development for Enhanced Corrosion and Cavitation Performance\hfill{}\textsc{ignore}}
\label{sec:org95f97c6}
\label{sec:org771c866}
\section{Paragraph 6: Influence of HIPing\hfill{}\textsc{ignore}}
\label{sec:org7bb1376}
\label{sec:orgc7253a3}
Compared with the case alloys, the HIPed alloys had relatively finer, rounded, and distributed carbides.
\section{Paragraph: Cavitation Erosion Resistance}
\label{sec:orgc39e335}
The primary result of an erosion test is the cumulative mass loss versus time, which is then converted to volumetric loss and mean depth of erosion (MDE) versus time for the purposes of comparison between materials of different densities. The calculation of the mean depth of erosion for this test method should be performed in conformity with ASTM G-32.
\section{General Background}
\label{sec:orgcf64eda}
\label{sec:orgf417579}
\%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}.
@ -491,12 +560,110 @@ Stellite 1 is a high-carbon and high-tungsten alloy, making it suitable for dema
\section{Literature Survey}
\section{Cavitation Tests}
\chapter{Analytical Investigations}
\label{sec:orgbc9a8d0}
\label{sec:org701ceff}
\section{Strain hardening}
\label{sec:orgae434ab}
Cavitation bubble collapse induce a work hardening of the material surface, comparable to that obtained in conventional peening \cite{swietlickiEffectsShotPeening2022}, characterized by the thickness of the hardened layers and the shape of the strain profile below the surface.
The strain profile within the material can usually be modeled by the following power law:
\begin{equation}
\epsilon\left(x\right) = \epsilon_s {\left( 1 - \frac{x}{L} \right)}^{\theta}
\end{equation}
where \(\epsilon\left(x\right)\) is the strain at depth \(x\) from the eroded surface, \(\epsilon_s\) is the failure rupture strain on the eroded surface, \(L\) is the thickness of the hardened layer, and \(\theta\) is the shape factor of the power law.
After each cycle, the thickness of the hardened layer \(L\) and the surface strain \(\epsilon_s\) will increase continuously until damage is initiated at the surface (\(\epsilon_s\) reaches the failure rupture strain \(\epsilon_R\)), at which point the strain profile is in steady-state.
\begin{equation}
\epsilon_R = \epsilon_{mean} {\left( 1 - \frac{\Delta L }{L+ \Delta L} \right)}^{\theta}
\end{equation}
\section{Correlative empirical methods}
\label{sec:orga1e98e9}
Empirical methods are common for addressing complex cavitation erosion, involving lab tests to correlate cavitation erosion resistance with mechanical properties.
\begin{enumerate}
\item Karimi and Leo
\label{sec:org2cce5b5}
The Karimi and Leo phenomenological model describes cavitation erosion rate as a function of
Karimi and Leo
\item Noskievic
\label{sec:org2309ffd}
Noskievic formulated a mathematical relaxation model for the dynamics of the cavitation erosion using a differential equation applied to forced oscillations with damping:
\begin{equation}
\frac{\mathrm{d}^2 v }{\mathrm{d}t^2} + 2 \alpha \frac{\mathrm{d} v }{\mathrm{d}t} + \beta^2 v = I
\end{equation}
where \(I\) is erosion intensity, which can vary linearly with time, \(v = \frac{\mathrm{d} v }{\mathrm{d}t}\) is erosion rate, \(\alpha\) is strain hardening or internal friction of material during plastic deformation, and \(\beta\) is coefficient inversely proportional to material strength. The general solution of equation can be written as:
\begin{equation}
v = a f_0 \left( \delta, \tau \right) + b f_1 \left( \delta, \tau \right)
\end{equation}
\begin{equation*}
f_0\left(\ \delta,\tau \right) = \begin{cases*}
1 - \mathrm{exp}{ \left( - \delta \tau \right) } \left[ \dfrac{\delta}{\omega} \mathrm{sin} \left(\omega \tau\right) + \mathrm{cos}{\left( \omega \tau \right)} \right]
& \text{if} -1 < \delta < 1; \delta \neq 0 \\
1 - \dfrac{1}{ {{\delta_0}^2} - 1} \left[ \delta_0^2 \mathrm{exp}{\left( -\dfrac{\tau}{\delta_0}}\right) - \mathrm{exp}{\left(- \delta_0 \tau\right)} \right]
& \text{if} \delta > 1 \\
1 - \mathrm{cos}{\left( \tau \right)}
& \text{if} \delta = 0 \\
1 - \left(1 + \tau \right) \mathrm{exp} \left( - \tau \right)
& if \delta = 1
\end{cases*}
\end{equation*}
\begin{equation*}
f_1\left(\ \delta,\tau \right) = \begin{cases*}
1 - \dfrac{2\delta}{\tau} \left[ 1 - {\mathrm{exp}\left(-\delta \tau\right)} {\left[ {\mathrm{cos} \omega \tau} + {\epsilon \mathrm{sin} \omega \tau} \right]} \right]
& \text{if} -1 < \delta < 1; \delta \neq 0 \\
1 - \dfrac{1}{\tau} \left( 2 \delta - \dfrac{1}{\delta_0 \left( \delta_0^2 - 1 \right)} \left[\mathrm{exp}{\left( -\delta_0 \tau \right) - \delta^4 \mathrm{exp}{\left( - \dfrac{\tau}{\delta_0} \right)} \right] \right)
& \text{if} \delta > 1 \\
1 - \dfrac{ \mathrm{sin}{\left( \tau \right)} }{\tau}
& \text{if} \delta = 0 \\
1 - \dfrac{2 \left[ 1 - \mathrm{exp}\left(-\tau\right) \right]}{\tau} + \mathrm{exp} \left( - \tau \right)
& if \delta = 1
\end{cases*}
\end{equation*}
\begin{equation*}
\delta = \dfrac{\alpha}{\beta},\quad
\tau = \beta t,\quad
\epsilon = \dfrac{\delta^2 - 0.5}{\delta \sqrt{ 1 - \delta^2 } },\quad
\omega = \sqrt{1 - \delta^2},\quad
\delta_0 = \delta + \sqrt{ \delta^2 - 1 }
\end{equation*}
\item Hoff and Langbein equation
\label{sec:org36031ea}
Hoff and Langbein proposed a simple exponential function for the rate of erosion, representing the normalized erosion rate requiring only the
A simple exponential function for the rate of erosion was proposed by Hoff and Langbein,
$$ \frac{ \dot{e} }{ \dot{e_{max}} } = 1 - e^{\frac{-t_i}{t}} $$
\(\dot{e}\) - erosion rate at any time t
\(\dot{e_{max}}\) - Maximum of peak erosion rate
\(t_i\) - incubation period (intercept on time axis extended from linear potion of erosion-time curve)
\(t\) - exposure time
\item L Sitnik model
\label{sec:org2511802}
$$ V = V_o {\left[ ln\left( \frac{t}{t_o} + 1 \right) \right]} ^ {\beta} $$
$$ \dot{V} = \frac{\beta V_o}{t + t_o} {\left[ ln \left( \frac{t}{t_o} + 1 \right) \right]}^{\beta - 1}$$
V\textsubscript{o} > 0
t\textsubscript{o} > 0
\(\beta\) >= 1
\end{enumerate}
\chapter{Experimental Investigations}
\label{sec:orgd1434a3}
\label{sec:orgd786c5f}
\section{Materials and Microstructure}
\label{sec:org51ee073}
\label{sec:org74c8cac}
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
@ -510,19 +677,12 @@ Image analysis was also conducted to ascertain the volume fractions of individua
The Vickers microhardness was measured using a Wilson hardness tester under loads of BLAH. Thirty measurements under each load were conducted on each sample.
\chapter{Discussion}
\label{sec:org03afda8}
\label{sec:orgc2d24d7}
\section{Experimental Test Procedure}
\subsection{Hardness Tests}
\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)
@ -540,4 +700,10 @@ Thiruvengadum \cite{thiruvengadamTheoryErosion1967} and Hobbs find that erosion
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.
\label{Bibliography}
\printbibliography[title={References}, heading=bibintoc, resetnumbers=true]
\end{document}

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@ -19,16 +19,6 @@ Steller \cite{} noted the poor agreement beween
Steller [72,73] observed that often there was poor agreement between cavitation resistance of materials measured in different types of test rigs and this proved to be a stumbling block in the prediction of material performance in the prototype.
* Phase Transformation
The Cr7C3 carbide is unstable at high temperatures and transforms to M_{23}C_{6} upon heat treatment. Under further temperature and time, Cr_{23}C_{6} partially transforms to Cr_6C \cite{mohammadnezhadINSIGHTMICROSTRUCTURECHARACTERIZATION2018}.
2M_{7}C_{3} + 9M \rightarrow M_{23}C_{6}
M_{23}C_{6} + 13M \rightarrow 6M_{6}C
* Grain size
@ -37,29 +27,6 @@ ASTM E112
Heyn Lineal Interceot Procedure
* Stellite Introduction
mp-1221498
Chromium provides superior hot oxidation and corrosion resistance by forming resilient Cr2O3 scales.
many cobalt-based alloys, most of its service strength relies on generating and controlling MC, M7C3, and M23C6 carbide particles within grains, interdendritic spaces, and grain boundaries.
M7C3 is a metastable pseudo-eutectic carbide typically formed at lower carbon-chromium ratios and effectively transforms into secondary M23C6 upon heat treatment according to the following reactions: [4]
$$ 23Cr_{7}C_{3} \rightarrow 7Cr_{23}C_6 + 27C $$
$$ 6C + 23Cr \rightarrow Cr23C6 $$
* FCC to HCP Transformation
# I *love* this paragraph
# https://doi.org/10.1016/j.surfcoat.2018.11.011
# The ε-Co and γ-Co phase are the main phases in Co alloys [39]. According to the phase diagram, the ε-Co phase is more stable at room temperature [40]. However, the γ-Co to ε-Co transformation rarely occurs under normal cooling conditions, and as a result, the γ-Co phase is generally retained at room temperature [39], as we found in the as-deposited Stellite 6 coatings. Nevertheless, this transformation can be triggered athermally (e.g. quenching from temperature of γ-Co) [25,41], isothermally (e.g. aging at temperatures between 650 °C and 950 °C) [35,42,43], or by strain [30,31]. In this study, the thermal fatigue process was achieved by quenching, with heating temperatures of up to 650 °C, and the crack tip introduced severe plastic deformation, all conditions that promote the γ-Co to ε-Co transformation.
* Strain Energy
@ -83,36 +50,6 @@ CavitationErosionBehaviourSteelPlateScroll
* Karimi and Leo
The Karimi and Leo phenomenological model describes cavitation erosion rate as a function of
Karimi and Leo
* Hoff and Langbein equation
Hoff and Langbein proposed a simple exponential function for the rate of erosion, representing the normalized erosion rate requiring only the
A simple exponential function for the rate of erosion was proposed by Hoff and Langbein,
$$ \frac{ \dot{e} }{ \dot{e_{max}} } = 1 - e^{\frac{-t_i}{t}} $$
$\dot{e}$ - erosion rate at any time t
$\dot{e_{max}}$ - Maximum of peak erosion rate
$t_i$ - incubation period (intercept on time axis extended from linear potion of erosion-time curve)
$t$ - exposure time
* L Sitnik model
$$ V = V_o {\left[ ln\left( \frac{t}{t_o} + 1 \right) \right]} ^ {\beta} $$
$$ \dot{V} = \frac{\beta V_o}{t + t_o} {\left[ ln \left( \frac{t}{t_o} + 1 \right) \right]}^{\beta - 1}$$
V_o > 0
t_o > 0
\beta >= 1
* Timeline latex