Additions to Thesis

.gitattributes

@@ -595,5 +595,6 @@
 /xrd_phase/1-s2.0-S1359645410007007-main.pdf filter=lfs diff=lfs merge=lfs -text
 /xrd_phase/25032132-MIT.pdf filter=lfs diff=lfs merge=lfs -text
 /xrd_phase/Influence_of_a_Partial_Substitution_of_Co_by_Fe_on.pdf filter=lfs diff=lfs merge=lfs -text
+/Figures/nairExceptionallyHighCavitation2018a_strainHardening.jpg filter=lfs diff=lfs merge=lfs -text
 *.jp*g filter=lfs diff=lfs merge=lfs -text
 *.tif filter=lfs diff=lfs merge=lfs -text

Thesis.org

@@ -361,6 +361,14 @@ I don't what it is actually.
 
 ** Introduction
 
+*** Cavitation
+
+# Cavitation erosion (CE) is a common mechanism of material deterioration in hydrodynamic environments, and many components are subjected to serious CE, such as propellers, impellers, turbines, centrifugal-chambers and valves [1], [2], [3]. \cite{houCavitationErosionMechanisms2020}
+# Cavitation is generally induced by rapid pressure variations or high-frequency vibrations in liquid environments, and is associated with the formation, growth and collapse of bubbles [4], [5], [6], [7]. \cite{houCavitationErosionMechanisms2020}
+# When such bubbles implode in the proximity of a solid surface, powerful micro-jets and/or shock waves with high speeds and impact pressures are produced that can cause the fatigue, fracture and material depletion [8], [9], [10]. \cite{houCavitationErosionMechanisms2020}
+# As a result, pits can form on component surfaces that are exposed to repeated loading and then can coalesce and form deep cavities, thereby leading to CE and the eventual failure of components [11], [12], [13]. \cite{houCavitationErosionMechanisms2020}
+
+
 *** TODO Paragraph: Cavitation :ignore_heading:
 *** Paragraph: Introduction to Stellite Alloys for Hostile Environments :ignore_heading:
 
@@ -902,9 +910,18 @@ Molybdenum and tungsten have favorable effects on the selective oxidation of chr
 *** Strain hardening
 
 
+
+# The present paper is a contribution to this subject. It presents a model of prediction of the erosion damage applicable to ductile materials only. Other limitations of the model will be pointed out along the presentation. The originality of this work lies in the fact that the proposed model is fully predictive and involves no parameters to be adjusted on the basis of experimental data. It is based upon the original work of Karimi and Leo @5#.
+
+# Interesting tidbit? Maybe not actually something to include
+# comparable to that obtained in conventional peening \cite{swietlickiEffectsShotPeening2022},
+
+
+
+Cavitation bubble collapse induce a work hardening of the ductile material's surface, characterized by the thickness of the hardened layers and the shape of the strain profile below the surface.
 # \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.
+This analysis was first proposed by Karimi & Leo in 1987 \cite{karimiPhenomenologicalModelCavitation1987} and adapted by Berniche et al in 2002 \cite{berchicheCavitationErosionModela}, and Franc \cite{francIncubationTimeCavitation2009} in 2009.
 
 The strain profile within the material can usually be modeled by the following power law:
 
@@ -912,19 +929,67 @@ The strain profile within the material can usually be modeled by the following p
 \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.
+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, $\theta$ is the shape factor of the power law. The parameters $L$ and $\theta$ are determined from the microhardness measurements on cross sections of the cavitation affected region.
 
-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.
+
+# Tensile tests done by Rehan, in order to give us K and n
+# \cite{ahmedMappingMechanicalProperties2023}
+# The tensile tests were carried out on an Instron tensometer following the BS EN 10,002 standard [29]. The dumbbell-shaped specimens, with 25 mm gauge length and 4 mm diameter, were used in this investigation. The tests were conducted at 0.05 mm/min, equalling a strain rate of 0.000033 s−1. Three tests were conducted on each alloy. The fracture sections were examined via SEM.
+
+
+
+The strain hardening effect after erosion tests was calculated from the following formula:
 
 \begin{equation}
-\epsilon_R = \epsilon_{mean} {\left(  1 - \frac{\Delta L }{L+ \Delta L}  \right)}^{\theta}
+\Delta{}HV = \dfrac{{HV}_{x} - {HV}_{0}}{{HV}_{0}} \cdot 100 \%
 \end{equation}
 
+where ${HV}_{x}$ is the hardness at a distance below the cavitation crater, while HV_0 is the initial hardness.
+
+# 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}
+
+
+
+
+
 
 
 # Let's talk more about Woodford
 In Woodford's investigations on the $\gamma$\textrrightarrow$\epsilon$ transformation on the surface of cobalt-base alloys during cavitation erosion, the transformed layer was found to extend to a depth of 25 to 50 \um \footnote{Converted from the original 1e-3 to 2e-3 \cite{woodfordCavitationerosionlnducedPhaseTransformations1972}}.
 
+**** Data for strain hardening :ignore:
+
+#+CAPTION: Microhardness HV_0.01 of Al0.1CoCrFeNi HEA \cite{nairExceptionallyHighCavitation2018a}
+|                  x |                  y |
+| 15.025380710659899 |  339.3103448275862 |
+| 29.949238578680202 |  277.2413793103448 |
+|  44.87309644670051 |  212.0689655172414 |
+| 59.974619289340104 | 230.34482758620692 |
+|  74.89847715736042 | 203.10344827586206 |
+|  89.82233502538071 | 203.44827586206895 |
+| 104.74619289340102 | 195.86206896551724 |
+|  120.0253807106599 | 195.86206896551724 |
+| 135.12690355329948 | 187.58620689655174 |
+|  150.2284263959391 | 155.86206896551724 |
+|  164.9746192893401 | 153.10344827586206 |
+
+#+CAPTION: Microhardness HV_0.01 of 316LSS \cite{nairExceptionallyHighCavitation2018a}
+|                  x |                  y |
+| 14.847715736040609 | 288.62068965517244 |
+|  29.77157360406091 | 251.72413793103448 |
+|   45.0507614213198 |                240 |
+| 59.974619289340104 | 219.31034482758622 |
+|  74.89847715736042 | 227.24137931034483 |
+|  89.82233502538071 |  228.9655172413793 |
+|  104.9238578680203 | 221.72413793103448 |
+|  120.0253807106599 | 218.27586206896552 |
+| 135.48223350253807 | 224.82758620689657 |
+| 149.87309644670052 | 225.86206896551727 |
+|  165.1522842639594 | 224.48275862068965 |
 
 *** Correlative empirical methods