November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

Benjamin LeonardPost-Doctoral Research Associate

Third Body Modeling Using a Combined Finite Discrete Element Approach

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

Outline

• Motivation• Objectives• Combined Finite-Discrete Element Model• Sliding Plates• Fretting Contacts• Summary and Conclusions

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

Motivation• Third body particles play an important role in many industrial applications

– Wear debris– External objects

• The fretting phenomenon is caused by small scale reciprocating motion leading to failure from fatigue or wear– Due to the small scale motions the third body effect is large in fretting

In Situ Photograph of a Fretting ContactDiagram of Third Body Wear

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

Objectives

• Develop a numerical model for fretting wear which includes third body effects

• Study the effects of various parameters– Loading – Surface roughness– Coatings

• Develop a stress based approach for modeling fretting wear

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

Modeling of the Third Body• The “third body” is composed of loose wear particles or external

debris inside a contact• In the FDEM the third body is modeled using loose spherical particles

– Third body particles interact with first bodies– Third body particles interact with each other

Motion of Third Body Particles in the FDEM

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

Compression of the Third Body

• Shifting particles cause discontinuities in the force-deflection curve

• Third body contact stiffness controls its effective elastic modulus 0 0.1 0.2 0.3 0.4

0

2

4

6

8

10

12

Deflection (m)

Forc

e (m

N/

m)

k=10k=15k=20k=25

Compression of a Mass of Third Body Particles

Reaction Force from Third Body

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

Friction and the Velocity Gradient• The velocity

gradient between two surfaces depends on their coefficients of friction

• By varying the coefficient of friction no slip conditions can be achieved on each surface

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

Y (y

/L)

Velocity (V/V0)

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

Y (y

/L)

Velocity (V/V0)

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

Y (y

/L)

Velocity (V/V0)

The effect of lower surface coefficient of friction on the velocity gradient for μ of (a) 0.2, (b) 0.3 and (c) 0.4.

Velocity GradientDisposition of Platelets

(a)

(b)

(c)

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL) Velocity GradientDisposition of Platelets

-0.2 0 0.2 0.4 0.6 0.8 1 1.20

0.1

0.2

0.3

Y (y

/L)

Velocity (V/V0)

-0.2 0 0.2 0.4 0.6 0.8 1 1.20

0.1

0.2

0.3

Y (y

/L)

Velocity (V/V0)

-0.2 0 0.2 0.4 0.6 0.8 1 1.20

0.1

0.2

0.3

Y (y

/L)

Velocity (V/V0)

• With unlinked particles, the third body behaves as a Newtonian fluid

• Regions of the third body clump together when platelets interlock– This effect grows

larger as platelets become longer

– The velocity gradient is not constant with time

-0.2 0 0.2 0.4 0.6 0.8 1 1.20

0.1

0.2

0.3

Y (y

/L)

Velocity (V/V0)

1

2

4

7

Effect of Platelet Length on the Velocity Gradient

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

The Third Body in a Fretting Contact• Third body particles can be

introduced into worn fretting contacts

• Wear particles (individual and platelets) have been placed into the worn slip zones at the edge of the contact

0.675 0.68 0.685 0.69 0.695 0.7 0.7050

2

4

6x 10

-3

X (x/b)

Y (y

/b)

0.675 0.68 0.685 0.69 0.695 0.7 0.7050

2

4

6x 10

-3

X (x/b)

Y (y

/b)

0.675 0.68 0.685 0.69 0.695 0.7 0.7050

2

4

6x 10

-3

X (x/b)

Y (y

/b)

0.675 0.68 0.685 0.69 0.695 0.7 0.7050

2

4

6x 10

-3

X (x/b)

Y (y

/b)

0 0.2 0.4 0.6 0.8 1-1

-0.5

0

0.5

1

time (t/tsimulation)

P/P

max

, /

max

Normal LoadDisplacement

Loading of a Fretting Contact

Finite Element Domain

Variation in Platelet Length

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

The Effect of Particle Size in a Fretting Contact

• The maximum pressure and force carried by a single particle increases with diameter

• The pressure in the stick zone does not vary significantly from a single particle

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

Distance (x/b)P

ress

ure

(P/P

h)

The effect of particle size on the contact pressure for diameters of (a) 0.1 μm, (b) 0.2 μm, (c) 0.4 μm and (d) 0.6 μm.

(a) (b)

(c) (d)

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

Effect of A Small Number of Particles on a Fretting Contact

• As the number of particles increase, the maximum pressure decreases

• The outermost (4th) particle does not come into contact due to curvature of the surface

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

Distance (x/b)P

ress

ure

(P/P

h)

The effect of (a) 2, (b) 4, (c) 6, and (d) 8 of particles with diameters of 0.6 μm on contact pressure.

(a) (b)

(c) (d)

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

The Effect of Increasing Numbers of Particles on the Pressure Profile

• Increasing the number of particles has several effects:– The total force carried by the slip zone increases– The pressure in the slip zone decreases

• Frictional shear stress in the slip zones is not uniform on each side of the contact

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.5-1

-0.5

0

0.5

1

Distance (x/b)

She

ar S

tress

(q/P

h)

-1.5 -1 -0.5 0 0.5 1 1.5-1

-0.5

0

0.5

1

Distance (x/b)

She

ar S

tress

(q/P

h)

-1.5 -1 -0.5 0 0.5 1 1.5-1

-0.5

0

0.5

1

Distance (x/b)

She

ar S

tress

(q/P

h)

-1.5 -1 -0.5 0 0.5 1 1.5-1

-0.5

0

0.5

1

Distance (x/b)

She

ar S

tress

(q/P

h)

120 particles 220 particles 320 particles 420 particles

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

Wear Particles at the Stick Zone-Slip Zone Interface

• The normal force (red arrows) from the first bodies result in a net lateral force on the third bodies (blue arrow) pushing them away from the edge of the stick zone (green circle)

Initial disposition of wear particles in the Hertzian fretting contact (120 particles).

The stick zone-slip zone interface in a fretting contact

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

Effect of Platelet Length on Partial Slip Fretting Contacts

• Longer platelets lead to formation of a thicker third body mass• Thicker third body masses are pushed further from the stick-slip zone interface

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.5

-0.4

-0.2

0

0.2

0.4

0.6

Distance (x/b)

She

ar S

tress

(q/P

h)

-1.5 -1 -0.5 0 0.5 1 1.5

-0.4

-0.2

0

0.2

0.4

0.6

Distance (x/b)

She

ar S

tress

(q/P

h)

-1.5 -1 -0.5 0 0.5 1 1.5

-0.4

-0.2

0

0.2

0.4

0.6

Distance (x/b)

She

ar S

tress

(q/P

h)

-1.5 -1 -0.5 0 0.5 1 1.5

-0.4

-0.2

0

0.2

0.4

0.6

Distance (x/b)

She

ar S

tress

(q/P

h)

2 particles 5 particles 10 particles 14 particles

Particle Location After Loading

Frictional Shear Stress

Pressure Profile

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

Wear Particles During Fretting Evolution

• The wear particles group together due to the pressure and surface profile shape

• Pressure is not longer uniform in the slip zone

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Distance (x/b)

Pre

ssur

e (P

/Ph)

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Distance (x/b)

Pre

ssur

e (P

/Ph)

40k 80k 120k 160k

Subsurface Stress (σy)

Pressure

Groups of Clustered Wear Particles

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November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

Summary and Conclusions

• A model of the third body has been created using the combined finite discrete element method

• Third body properties can be controlled using size, spring stiffness and platelet length

• Longer platelets interlock forming thicker third body masses• The third body supports load and takes the stress off the edge

of the stick zone in fretting contacts• Loose third body particles tend to clump together in fretting

contacts which may lead to platelet formation