ch5 wear mechanisms - MIT OpenCourseWare · 2 Delamination Wear Mechanisms • 1. Plastic...

1

Chapter 4 and 5 Wear Mechanisms

2

Delamination Wear Mechanisms

•

1. Plastic deformation of the surface 2. Crack nucleation at the sub-surface due to

plastic deformation 3. Crack propagation from these nucleated cracks

due to plastic deformation 4. Creation of loose wear sheets

Four mechanisms of delamination wear

3

Plastic Deformation of a Semi-Infinite Elastoplastic Solid

Governing equations 1. Equilibrium condition 2. Yield condition 3. Constitutive relationships for elastic and plastic

deformation 4. Geometric compatibility


( )

U

p o

q o

z

x

S tat io na ry ri g i d

El as tic-P erfe ctl y Pl as tic

4


• Mises Flow Rule (Yield Criterion)

3 3

− J ' 2 = 1 ∑∑(σ '

ijσ ' ij )=

1σ

2 = k2

2 i =1 j=1 3

5


Conversion of the time derivative to gradients:

d 'ε( ij; ij;W)=U ( ij; ij;W)dt ∂x

'σ∂'ε'σ

8


Residual Stress Calculation

σ( ) = f1 (z )xx r

σ( ) = f2 ( z )zz r

σ( ) = ν [ f1 (z ) + f2 ( z )]yy r

σ( ) = f3 ( z )xz r

9


Residual Stress Calculation -- Equilibrium Equations∂ ( σ ) ∂ ( σ xz ) r = 0xx r +

∂ x ∂ z

∂ ( σ ) ∂ ( σ zz ) r = 0xz r +∂ x ∂ z

f 3 = c 1

f 2 = c 2

( σ ) = f ( z )xx r

( σ yy ) = ν f ( z )r

( σ ) = 0zz r

( σ ) = 0xz r

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Residual Stress Calculation -- Equilibrium Equations

1− 2νε (σ zz )' rzz r( ) = −

2(1 −ν )G

( ) = −(σ xz )

' rγ xz r G

σ xx r σ xx

ν ( )' r( ) = ( )'

r −1− ν

σzz

σ σ( ) = σ yy' ν ( )' ryy r zz( )r −

1 −ν11

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Crack Nucleation

• 1. Energy criterion 2. Strength criterion

• critical flaw size for crack nucleation, which is satisfied by most flaws in engineering materials.

Crack nucleation criteria

Because of the energy criterion, there is a

13

Crack Nucleation

• multi-phase metals. It takes only 100 to 1,000 cycles. Therefore, it is not the rate-controlling mechanism in these multi-phase metals.

Crack nucleation occurs rather readily in

14

Crack Nucleation

• the sub-surface is very difficult. Therefore,

be the primary wear mechanism. Wear by plowing of the surface by wear particles may be the primary wear-rate controlling mechanism.

In single phase metals, crack nucleation at

in these metals, delamination wear may not

Crack Nucleation

Imaginary sphere

A B

Deformed sphere of the Imaginary sphere

(a) (b)

Figure 4.36

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Criteria for Crack Nucleation Energy Criterion and Strength Criterion

Stra

in, e

Energy criterion

Strength criterion

d*

Particle size, d Figure 4.37

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Rigid Cylinder under a General State of Stress

x

z

τmax

σr r

φ

θ

Figure 4.38

17

Crack Nucleation

Strength criterion

( )σ kk max ≥ σ i

Energy criterion E s

before − E s after ≥ A ∆ γ

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19

Crack Nucleation

d c

St rain

P articl e si ze

Ene rgy C rit er i o n

St re n g th Cr it e ri o n

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Contour of σrr under a sliding contact (normalized with respect to k)

Graphs removed for copyright reasons. Tribophysics. EnglewoodSee Figures 4.39-4.41 in [Suh 1986]: Suh, N. P.

Cliffs NJ: Prentice-Hall, 1986. ISBN: 0139309837.

21

Depth of Void Nucleation Region as a function of µ and p0

Graph removed for copyright reasons. See Figure 4.42 in [Suh 1986].

22

Number of passes required for crack nucleation and the depth of crack nucleation at p0=4k


23

Number of passes required for crack nucleation and the depth of crack nucleation at p0=6k


24

Crack Propagation

• classified in terms of three modes.

direction.

In fracture mechanics, crack propagation is

1. The load is applied perpendicular to the crack. 2. The load is applied parallel to the crack direction. 3. The load is applied transversely to the crack

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Crack Propagation

• is due to a combined loading of compression and shear on the crack -compressive stress on the crack and shear deformation at the crack tip.

However, crack propagation in sliding wear

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Crack Propagation

• wear conditions is very slow, being about 30 microns per cycle of crack-tip sliding.

• multi-phase metals is controlled by the crack propagation rate.

The rate of crack propagation under sliding

Therefore, the delamination wear of many

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Sliding Wear at Low Speeds

•

∆(CTSD) ~ 0.003 µm

Crack propagation rate controls the delamination wear rate.

F α

maximum

Tension

r

Compression

maximum

Crack

θ

Constant

shear stress

Constant

shear stress

28

29

Variation of plastically deformed zone around crack under a moving asperity

(a=10µm, d=0.5 a, µ=0.25, po=4k=980 MPa)

Plots removed for copyright reasons. See Figure 4.48 in [Suh 1986].

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Shear strain vs. distance from the left crack tip when plastic elements are used.

Ph.D. Thesis, MIT, 1981.

Source: Sin, H-C. “Surface Fraction and Crack Propagation in Delamination Wear.”

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Shear strain vs. distance from the right cracktip when plastic elements are used.



32

Shear strain as a function of distance from the left tip for different depths of crack location



Figure 4.52

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Void and crack formation in annealed OFHC copper

Figure 4.53

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Subsurface deformation and crack formation in Fe solid solution

Typical plot of the crack extension per cycle versus the logarithm of the change in the stress intensity factor

da/d

N (m

m/c

ycle

)

10-2 Final failure

10-4

10-6

1

m B

A

1

C

Kc

Threshold ∆K0

∆K)mda/dN = C(

log ∆K Figure 4.47

35

36

Void formation around inclusions and crack propagation from these voids near the surface

in annealed Fe-1.3% Mo

Photos removed for copyright reasons. See Figure 4.35 in [Suh 1986].

Subsurface crack under a moving asperity

L R-θc Ld

C

Figure 5.8 Subsurface crack under a moving asperity

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Model of wearing specimen

Figure 5.9 Model of wearing specimen and slider

Slider

∆L

dD

lC

Specimen

λ

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Worn surface of pure iron

dimpled appearance of wear crater

Photo removed for copyright reasons.

(a) sheet formation, (b) shear dimples beneath the wear sheet in (a), ©

See Figure 5.7 in [Suh 1986].

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Fretting Wear


41



42

removed for copyright reasons. Sequence of graphs and photos

See Figures 5.12-5.23 in [Suh 1986].

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