- PDF ΔΩΡΕΑΝ Λήψη

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

µ υ ρ α

Coefficient of friction Coefficient of friction 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 20 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 Normal Load (N) 1.00 0.00 0 0.1 0.2 0.3 0.4 0.5 0.6 Sliding velocity (m/s)

= P F adh v F pl = + = τ + τ τ

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

ρ ρ = =

ρ ρ ρ µ µ

100 2.5 80 2 60 1.5 f = 0.85 k > 10-4 40 20 f = 0.4 f = 0.4 k < 10-6 f = 0.6 k < 10-6 k < 10-6 1 0.5 0 0 0 200 400 600 800 1000 Temperature (oc) ( C) Contact load (N) Contact Pressure (GPa)

σ π σ

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

σ σ f f f σ = ( ) ( ) ( ) = ( ) > = >

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

= ( ) 0.4 0.35 0.3 = 0.25 0.2 0.15 0.1 0.05 0 Circular contact (a = b) 0.0001 0.001 0.01 0.1 1 10 100 1000 = Line contact Line contact σ = =

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

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

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

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

Ξ [9] + Ξ

α µ µ ρ α

ω P ω

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

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-08 0 5 10 15 20 25 30 35 10 1 2.7 S c,m + 6 Ξ 0.1 0.01 0.1 1 10 100 Ξ

S c,m 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 Ξ

Coefficient of Friction 1 0.8 0.6 0.4 0.2 Normal Load (N) 50 f =0.7 Zirconia Silicon Carbide 0 0 10 20 30 40 50 60 Normal Load (N) f = 0.2 Alumina Silicon Nitride 100 Al 2 O 3 ZrO 2 0 0 0.01 0.1 1 10 Sliding Velocity (m/s) P V 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 Mean Contact Pressure (GPa)

α α µ

Coefficient of friction Coefficient of friction 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.25 0.2 0.15 0.1 0.05 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) 3Y-TZP + 5% wt CuO (Sintered at 1550 C) 3Y-TZP + 5% wt CuO (Sintered at 1500 C) Pure 3Y-TZP 0 0 0.05 0.1 0.15 0.2 0.25 Sliding Velocity (m/s)

' > ## # & 5@ ' $ ( ) 3 0 # 2 1 7 (a) 1 6 1 5 (c) 1 4 (b) 1 3 1! 1 1 (a) 1 2 1 1 311 2111 2311 * (c) (b) 5@ $ ) $ ) $ + &9) $ ) $ + 29) G ' 9/ + D 5@ $ ( &) 8 5@ 5 $ ( () # 3 9;

a b c d

Wear Track

Counts/s 20 10 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) 0 20 30 40 50 60 70 80 90 Position [ 2Theta]

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

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

+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 = + + = + +

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

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

β σ η 0.4 0.3 0.2 Measured Gaussian 0.1 0-5 0 σ 5 σ 0.5 0.4 0.3 Measured Gaussian 0.2 0.1 0-5 0 σ 5 σ β β σ ββ ββ

σ σ 3 2.5 2 1.5 1 0.5 0 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 3 2.5 2 1.5 1 0.5 0 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

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

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

( ) ( ) ( )( ) 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

ωω ω ω = ω ω ω ωω ωω µ

Indentation Depth (µm) 7 6 5 4 3 2 1 0 β = 1.59 mm t = 6 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) Contact Radius ( µm) 140 120 100 80 60 40 20 0 β = 1.59 mm t = 6 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N)

µ Indentation Depth ( x 0.0245 mm) 100 80 60 40 20 0 φ = 12.7 mm t = 1.2 µm Measured [13] Sherbiney's Model [13] Present model 0.1 1 10 100 Load ( x 0.453 Kg)

(Normal Load (N)) 2/3 Mean contact pressure (GPa) 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 12 10 8 6 4 2 0 β =100 µm t = 5 µm H layer /H substrate = 2 3 0 0.2 0.4 0.6 0.8 1 Indentation depth (µm) FEM Present Model FEM Present Model 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ω/t

β ω = + +

= + + + = + 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

Contact area Ratio (A tot /A nom ) Dimensionless separation (d/σ) 3 2.5 2 1.5 1 0.5 1.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

Contact area Ratio (A tot /A nom ) Dimensionless separation (d/σ) 3 2.5 2 1.5 1 0.5 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

Contact with substrate Contact with layer

τ = + τ + τ = + β β

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)

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

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

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

= 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

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

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

β µσ µη ηβσ η ηβσ

0.5 1 0.45 0.9 0.4 0.8 0.35 Measured [3] 0.7 0.3 0.6 Halling's Model 0.25 0.5 0.2 Present Model 0.4 0.15 Ratio of fully plastic to 0.3 total contact area 0.1 0.2 Present model 0.05 0.1 0 0 0.0001 0.001 0.01 0.1 1 10 100 Layer Thickness (µm) Coefficient of friction Plastic Contact Area Total Contact Area

Coefficient of friction 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 Measured [3] Halling's Model Present Model Ratio of fully plastic to total contact area Present model 0 0 0.0001 0.001 0.01 0.1 1 10 100 Layer Thickness (µm) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Plastic Contact Area Total Contact Area µ

µ µ ψ σβ

µ - µ

τ = = =

Wear Track ±

µ Indentation load (N) 0.6 0.5 0.4 0.3 0.2 0.1 0 0.0 0.5 1.0 1.5 2.0 2.5 Indentation depth (µm)

β β σβ µσµ

γ µ γ γ γ γ γ γ γ γ γ γ

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

R 1 R 1 a R 2 R 2 = υ υ = +

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

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

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

π = π = =

= = ( ) = ( )

π = ( ) α = αα = ε ε ε ε ε ν = ν =

Indentation Depth (µm) 3.5 3 2.5 2 1.5 1 0.5 0 β = 3.7 mm t = 0 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) Contact Radius ( µm) 120 100 80 60 40 20 0 β = 3.7 mm t = 0 µm µ El-Shafei et al. Present Model 0 20 40 60 Normal Load (N)

Indentation Depth (µm) Indentation Depth (µm) Indentation Depth (µm) 3.5 3 2.5 2 1.5 1 0.5 0 4 3.5 3 2.5 2 1.5 1 0.5 0 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 β = 3.7 mm t = 1.5 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) β = 3.7 mm t = 3 µm 0 20 40 60 Normal Load (N) β = 1.59 mm t = 0 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) El-Shafei et al. Present Model Contact Radius ( µm) Contact Radius ( µm) Contact Radius ( µm) 160 140 120 100 80 60 40 20 0 160 140 120 100 80 60 40 20 0 120 100 80 60 40 20 0 β = 3.7 mm t = 1.5 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) β = 3.7 mm t = 3 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) β = 1.59 mm t = 0 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N)

Indentation Depth (µm) Indentation Depth (µm) Indentation Depth (µm) 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 6 5 4 3 2 1 0 7 6 5 4 3 2 1 0 β = 1.59 mm t = 1.5 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) β = 1.59 mm t = 3 µm 0 20 40 60 Normal Load (N) β = 1.59 mm t = 6 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) El-Shafei et al. Present Model Contact Radius ( µm) Contact Radius ( µm) Contact Radius ( µm) 120 100 80 60 40 20 0 120 100 80 60 40 20 0 140 120 100 80 60 40 20 0 β = 1.59 mm t = 1.5 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) β = 1.59 mm t = 3 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) β = 1.59 mm t = 6 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N)

Indentation Depth (µm) Indentation Depth (µm) 7 6 5 4 3 2 1 0 8 7 6 5 4 3 2 1 0 β = 1.59 mm t = 9 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) β = 1.59 mm t = 12 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) Contact Radius ( µm) Contact Radius ( µm) 160 140 120 100 80 60 40 20 0 160 140 120 100 80 60 40 20 0 β = 1.59 mm t = 9 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) β = 1.59 mm t = 12 µm El-Shafei et al. Present Model 0 20 40 60 Normal Load (N) µ

Indentation Depth ( x 0.0245 mm) Indentation Depth ( x 0.0245 mm) 100 80 60 40 20 0 100 80 60 40 20 0 φ = 12.7 mm t = 1.2 µm Measured [13] Sherbiney's Model [13] Present model 0.1 1 10 100 Load ( x 0.453 Kg) φ = 25.4 mm t = 1.2 µm Measured [13] Sherbiney's Model [13] Present model 0.1 1 10 100 Load ( x 0.453 Kg)

Indentation Depth ( x 0.0245 mm) Indentation Depth ( x 0.0245 mm) 100 80 60 40 20 0 120 100 80 60 40 20 0 φ = 12.7 mm t = 15 µm Measured [13] Sherbiney's Model [13] Present model 0.1 1 10 Load ( x 0.453 Kg) φ = 25.4 mm t = 15 µm Measured [13] Sherbiney's Model [13] Present model 0.1 1 10 100 Load ( x 0.453 Kg)

µ µ µ βµ µ βµ µ µ µ

µ µ µ βµ βµ µ βµ µ µ

µ µ µ βµ β β µ µ µ

µ µ µ µ β β µ µ

(Normal Load (N)) 2/3 (Normal Load (N)) 2/3 (Normal Load (N)) 2/3 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 β =100 µm t = 1 µm H layer /H substrate = 2 3 0 0.2 0.4 0.6 0.8 1 β =100 µm t = 2 µm H layer /H substrate = 2 3 Indentation depth (µm) FEM Present Model 0 0.2 0.4 0.6 0.8 1 β =100 µm t = 5 µm H layer /H substrate = 2 3 Indentation depth (µm) FEM Present Model 0 0.2 0.4 0.6 0.8 1 Indentation depth (µm) FEM Present Model

(Normal Load (N)) 2/3 Mean contact pressure (GPa) 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 Mean contact pressure (GPa) 8 7 6 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1 0 β =100 µm t = 10 µm H layer /H substrate = 2 FEM Present Model 0 0.2 0.4 0.6 0.8 1 1.2 Indentation depth (µm) β µ µ 0 1 2 3 4 β µ µ ω/t FEM Present Model 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 ω/t FEM Present Model

Mean contact pressure (GPa) Mean contact pressure (GPa) Mean contact pressure (GPa) 9 8 7 6 5 4 3 2 1 0 12 10 12 10 8 6 4 2 0 8 6 4 2 0 β µ µ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 β µ µ ω/t 0 0.1 0.2 0.3 0.4 β µ µ ω/t FEM Present Model FEM Present Model 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ω/t FEM Present Model

Mean contact pressure (GPa) Mean contact pressure (GPa) 12 10 8 6 4 2 0 14 12 10 8 6 4 2 0 β µ µ β µ µ FEM Present Model 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ω/t FEM Present Model 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ω/t