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18 α β χ φ() γ Γ θ θ Ξ Μ ν ν ρ σ σ σ σ σ σ τ ω ω ω

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23 µ υ ρ α

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25 Coefficient of friction Coefficient of friction Normal Load (N) Sliding velocity (m/s)

26 = P F adh v F pl = + = τ + τ τ

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28 Metal Transfer Metal Transfer $ ) $ ) $ ) $ % $ ), +- $ ), - $ ) 6. %, &-. 8 ;

29 = =

30

31 ρ ρ = =

32 ρ ρ ρ µ µ

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34 f = 0.85 k > f = 0.4 f = 0.4 k < 10-6 f = 0.6 k < 10-6 k < Temperature (oc) ( C) Contact load (N) Contact Pressure (GPa)

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38 α

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41 α

42 Ξ

43 σ π σ

44 2b 2a Circular contact Elliptical contact Line contact σ + σ = + π

45 σ σ f f f σ = ( ) ( ) ( ) = ( ) > = >

46 σ : [( + ) ] σ = = ( + ) ( + ) = ( + ) ( + ) σ σ = σ + σ σ σ = σ ( ) σ = +

47 = ( ) = Circular contact (a = b) = Line contact Line contact σ = =

48 Μ = ( + ) π Μ Circular contact Line contact (a/b) 0 + σ = π = ( π ) ( + ) = π Μ Μ = Line contact (a/b)

49 = ( θ ) θ = + θ θ { ( )} θ θ = θ φ + φ θ = θ = ρ = θ = θ =

50 ρ θ θ = ρ α σ = α ( ) α π ( ) = + α π απ Γ Γ = Ξ = Ξ

51 σ π { + σ } π σ α ( + ) + π + Γ π π + α + π π + Ξ π π

52 Ξ [9] + Ξ

53 α µ µ ρ α

54 ω P ω

55 Light source Spectral filter Aperture stop Field stop CCD Camera Beam splitter PZT movement Eyepiece Microscope objective Surface being measured Wear Track Mild Wear Wear Track Severe Wear

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58 Specific Wear Rate (mm 3 N -1 m -1 ) S c,m 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 ω Zirconia disc Alumina disc 1.E S c,m + 6 Ξ Ξ

59 S c,m Ξ

60 Coefficient of Friction Normal Load (N) 50 f =0.7 Zirconia Silicon Carbide Normal Load (N) f = 0.2 Alumina Silicon Nitride 100 Al 2 O 3 ZrO Sliding Velocity (m/s) P V Mean Contact Pressure (GPa)

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62 α

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67 α α µ

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77 Coefficient of friction Coefficient of friction Y-TZP + 5% wt CuO (Sintered at 1550 C) 3Y-TZP + 5% wt CuO (Sintered at 1500 C) Pure 3Y-TZP Sliding Velocity (m/s) 3Y-TZP + 5% wt CuO (Sintered at 1550 C) 3Y-TZP + 5% wt CuO (Sintered at 1500 C) Pure 3Y-TZP Sliding Velocity (m/s)

78 ' > ## # & 5@ ' $ ( ) 3 0 # (a) (c) 1 4 (b) 1 3 1! 1 1 (a) * (c) (b) 5@ $ ) $ ) $ + &9) $ ) $ + 29) G ' 9/ + D 5@ $ ( &) 8 5@ 5 $ ( () # 3 9;

79 a b c d

80 Wear Track

81

82 Counts/s Zr_hr96_1mmstep_I3_C13 Strongest peak of Cu 2 O Inside the wear track 0 20 Zr_hr96_1mmstep_I3_C15 10 Outside the wear track (Bulk) Position [ 2Theta]

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84 α

85

86 β = η φ +ω = πη βσ φ +ω = η β σ φ = + φ = π η σ σ, ω ω ω = β

87 ω ω = σ β = σ ω ω = ω ω = ω = πη βσ +ω ω ω + φ +ω ω ω ω ω

88 +ω ω = πη βσ +ω ω ω ω ω + φ ω ω ω ω Elastic Elastic-plastic Fully plastic ω πβω ω πβω ω = πη βσ φ ω = πη βσ φ ω = + + = + +

89 β

90 ω ω = d Mean plane z 1 z 4 z 3 z i z 2 ω ω ω β 1 β 2 β 3 β 4 β i ( ω ) ω <ω ( ω ) ( ω ) ω ( ω ) < ω <ω ( ω ) ( ω ) = ( ω ) ω( ω ) < ω ( ) = πβω ω ( ) ω ω ω ω + ω = πβω ω ω ω ω ( ) = πβω ω

91 ( ω ) ω <ω ( ω ) ( ω ) = ( ω ) ω ( ω ) < ω <ω( ω ) ( ω ) ω( ω ) < ω = β ω ω ω = ω ω = = = β σ

92 β σ η Measured Gaussian σ 5 σ Measured Gaussian σ 5 σ β β σ ββ ββ

93 σ σ E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E Deterministic Model Statistical Model [3] Ε Deterministic Model Statistical Model [3] Statistical Model [7] 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 Ε

94 ω

95 ω ω ω ω ξ Normal approach ω P FP Elayer, Hlayer, Esubstrate, Hsubstrate, Layer Thickness (t) layer substrate ω = + ξω Normal approach ω FP P Eeff (ω) Heff(ω) eff (ω) ξω = ( ξω) + π π ω ( ω) + ξω ξω ξω ξω + ξω ξω = ω ω = β ω

96 βω ( ) ( ξ( ω) ) ω = + ξω = π ξω π + ξω ( ξω) + ξω ω ω ω ω ω = ω + ω ω = πβω ω = ωβ ω ω ( ) σ ω ω = + σ

97 ( ) ( ) ( )( ) ω ω = + σ σ σ ω ω = πβω ω = ωω ω ω ω ω ω = β ω ω ω ω = ω ω ω ω ω ω ω ω + ω = πβω ωω ωω ωω ωω

98 ωω ω ω = ω ω ω ωω ωω µ

99 Indentation Depth (µm) β = 1.59 mm t = 6 µm El-Shafei et al. Present Model Normal Load (N) Contact Radius ( µm) β = 1.59 mm t = 6 µm El-Shafei et al. Present Model Normal Load (N)

100 µ Indentation Depth ( x mm) φ = 12.7 mm t = 1.2 µm Measured [13] Sherbiney's Model [13] Present model Load ( x Kg)

101 (Normal Load (N)) 2/3 Mean contact pressure (GPa) β =100 µm t = 5 µm H layer /H substrate = Indentation depth (µm) FEM Present Model FEM Present Model ω/t

102 β ω = + +

103 = = + d Asperities mean plane z 1 z 4 z 3 z i z 2 Layer Thickness (t) E layer ; H layer ; v layer E substrate ; H substrate ; v substrate d Asperities mean plane z 1 z 4 z 3 z i z 2 E eff (ω i ) H eff (ω i ) v eff (ω i ) β 1 β 1 β 2 β 2 β 3 β 3 σ β 4 β 4 β i β i

104 Contact area Ratio (A tot /A nom ) Dimensionless separation (d/σ) E+00 1.E-01 1.E-02 1.E-03 1.E-04 Case-1 t = t = t = t = t= 0 µm 0.1 µm 0.25 µm 0.5 µm µm 0 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 Dimensionless load (P tot /(E * t=0a nom )) Case-1 1.E-05 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 t = t = t = t = t = Dimensionless load (P tot /(E * t=0a nom )) 0 µm 0.1 µm 0.25 µm 0.5 µm µm σ

105 Contact area Ratio (A tot /A nom ) Dimensionless separation (d/σ) Case-2 t = t = t = t = t = 0 µm 0.25 µm 0.5 µm 1 µm µm 0 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E+00 1.E-01 1.E-02 Dimensionless load (P tot /(E * t=0a nom )) 1.E-03 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 Dimensionless load (P tot /(E * t=0a nom )) Case-2 t = t = 0.25 µm t = t = t = 0 µm 0.5 µm 1 µm µm σ

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110 Contact with substrate Contact with layer

111 τ = + τ + τ = + β β

112 πβω πβω ω ω ω = ω = ω = πβ ω ω = ω Contact area Elastic Elastic-Plasitic Plastic Elastic Elastic-Plasitic Plastic Static Moving static ω c1 2πβ i ω i static ω c2 dynamic ω c2 πβ i ω i (Moving asperity) (Static asperity) Indentation depth (ω)

113 ω = β ω ωω ω ω = ω ω ωω ωω ω = ω ω ( ω ) = ( ω ) + ( ω ) + ( ω ) = P tot = Surface Properties Given P Guess d P ie + P iep + ie iep P tot = P No P tot > P ip No Yes P ip Yes Stop Reduce the value of d Increase the value of d

114 ω ω ω t i ω is Layer Substrate 2a il 2a is = = = = = =

115 ω ω = + ω ω = β ω ω ω ω = ω ω ω ω ω ω πβ ω + ω ω ω ω ω = πβω = + ω = β ω = ω = = = πβω

116 = ω > ω ω ω ω < ω ω ω < ω = = πβω ω > ω ω ω ω = = + + = + τ τ τ = τ + τ + τ + + τ + τ + τ + τ

117 v β i θ i ω i θ θ θ θ = π θ θ θ = ω β ω β ω π ω < β ω β

118 θ θ θ = χω π θ χω ω > ω ω χω = ω < ω < ω ω ω < ω = + = =

119 β µσ µη ηβσ η ηβσ

120 Measured [3] Halling's Model Present Model Ratio of fully plastic to 0.3 total contact area Present model Layer Thickness (µm) Coefficient of friction Plastic Contact Area Total Contact Area

121 Coefficient of friction Measured [3] Halling's Model Present Model Ratio of fully plastic to total contact area Present model Layer Thickness (µm) Plastic Contact Area Total Contact Area µ

122 µ

123 µ µ ψ σβ

124 µ - µ

125

126

127 τ = = =

128 -

129 Wear Track ±

130 µ Indentation load (N) Indentation depth (µm)

131 γ γ

132 β β σβ µσµ

133 γ µ γ γ γ γ γ γ γ γ γ γ

134 $ ) (+ &9 & βdβ $ % $ < 9 ) 0 ' 0 γ # 3 < ; $ & 5@ 0 ' + D 5N 2 8N

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139 γ

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141 R 1 R 1 a R 2 R 2 = υ υ = +

142 = = + δ) δ = = π = Z R x1 R y1 b a Y R y2 R x2 X δ)

143 = α = β δ = γ = α κ π ( ) γ κ β κ π π ( ) π ( ) ( ) π ( ) + ( ) π( )

144 π ( ) + ( ) π ( λ) ( ) κ + + ( λ) λ = κ λ = < λ = π = R 1 R 2 b

145 π = π = =

146

147 = = ( ) = ( )

148 π = ( ) α = αα = ε ε ε ε ε ν = ν =

149 Indentation Depth (µm) β = 3.7 mm t = 0 µm El-Shafei et al. Present Model Normal Load (N) Contact Radius ( µm) β = 3.7 mm t = 0 µm µ El-Shafei et al. Present Model Normal Load (N)

150 Indentation Depth (µm) Indentation Depth (µm) Indentation Depth (µm) β = 3.7 mm t = 1.5 µm El-Shafei et al. Present Model Normal Load (N) β = 3.7 mm t = 3 µm Normal Load (N) β = 1.59 mm t = 0 µm El-Shafei et al. Present Model Normal Load (N) El-Shafei et al. Present Model Contact Radius ( µm) Contact Radius ( µm) Contact Radius ( µm) β = 3.7 mm t = 1.5 µm El-Shafei et al. Present Model Normal Load (N) β = 3.7 mm t = 3 µm El-Shafei et al. Present Model Normal Load (N) β = 1.59 mm t = 0 µm El-Shafei et al. Present Model Normal Load (N)

151 Indentation Depth (µm) Indentation Depth (µm) Indentation Depth (µm) β = 1.59 mm t = 1.5 µm El-Shafei et al. Present Model Normal Load (N) β = 1.59 mm t = 3 µm Normal Load (N) β = 1.59 mm t = 6 µm El-Shafei et al. Present Model Normal Load (N) El-Shafei et al. Present Model Contact Radius ( µm) Contact Radius ( µm) Contact Radius ( µm) β = 1.59 mm t = 1.5 µm El-Shafei et al. Present Model Normal Load (N) β = 1.59 mm t = 3 µm El-Shafei et al. Present Model Normal Load (N) β = 1.59 mm t = 6 µm El-Shafei et al. Present Model Normal Load (N)

152 Indentation Depth (µm) Indentation Depth (µm) β = 1.59 mm t = 9 µm El-Shafei et al. Present Model Normal Load (N) β = 1.59 mm t = 12 µm El-Shafei et al. Present Model Normal Load (N) Contact Radius ( µm) Contact Radius ( µm) β = 1.59 mm t = 9 µm El-Shafei et al. Present Model Normal Load (N) β = 1.59 mm t = 12 µm El-Shafei et al. Present Model Normal Load (N) µ

153 Indentation Depth ( x mm) Indentation Depth ( x mm) φ = 12.7 mm t = 1.2 µm Measured [13] Sherbiney's Model [13] Present model Load ( x Kg) φ = 25.4 mm t = 1.2 µm Measured [13] Sherbiney's Model [13] Present model Load ( x Kg)

154 Indentation Depth ( x mm) Indentation Depth ( x mm) φ = 12.7 mm t = 15 µm Measured [13] Sherbiney's Model [13] Present model Load ( x Kg) φ = 25.4 mm t = 15 µm Measured [13] Sherbiney's Model [13] Present model Load ( x Kg)

155 µ µ µ βµ µ βµ µ µ µ

156 µ µ µ βµ βµ µ βµ µ µ

157 µ µ µ βµ β β µ µ µ

158 µ µ µ µ β β µ µ

159 (Normal Load (N)) 2/3 (Normal Load (N)) 2/3 (Normal Load (N)) 2/ β =100 µm t = 1 µm H layer /H substrate = β =100 µm t = 2 µm H layer /H substrate = 2 3 Indentation depth (µm) FEM Present Model β =100 µm t = 5 µm H layer /H substrate = 2 3 Indentation depth (µm) FEM Present Model Indentation depth (µm) FEM Present Model

160 (Normal Load (N)) 2/3 Mean contact pressure (GPa) Mean contact pressure (GPa) β =100 µm t = 10 µm H layer /H substrate = 2 FEM Present Model Indentation depth (µm) β µ µ β µ µ ω/t FEM Present Model ω/t FEM Present Model

161 Mean contact pressure (GPa) Mean contact pressure (GPa) Mean contact pressure (GPa) β µ µ β µ µ ω/t β µ µ ω/t FEM Present Model FEM Present Model ω/t FEM Present Model

162 Mean contact pressure (GPa) Mean contact pressure (GPa) β µ µ β µ µ FEM Present Model ω/t FEM Present Model ω/t

Π Ο Λ Ι Τ Ι Κ Α Κ Α Ι Σ Τ Ρ Α Τ Ι Ω Τ Ι Κ Α Γ Ε Γ Ο Ν Ο Τ Α

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< = ) Τ 1 <Ο 6? <? Ν Α <? 6 ϑ<? ϑ = = Χ? 7 Π Ν Α = Ε = = = ;Χ? Ν !!! ) Τ 1. Ο = 6 Μ 6 < 6 Κ = Δ Χ ; ϑ = 6 = Σ Ν < Α <;< Δ Π 6 Χ6 Ο = ;= Χ Α

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