Third Body Modeling Using a Combined Finite Discrete Element Approach

1. Third Body Modeling Using a Combined Finite Discrete Element Approach Benjamin Leonard Post-Doctoral Research Associate

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

3. 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 Contact Diagram of Third Body Wear

4. 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

5. 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

6. Compression of the Third Body • Shifting particles cause discontinuities in the force-deflection curve • Third body contact stiffness controls its effective elastic modulus Reaction Force from Third Body Compression of a Mass of Third Body Particles

7. 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 (a) (b) (c) Velocity Gradient Disposition of Platelets 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.

8. Effect of Platelet Length on the Velocity Gradient 1 • 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 2 4 7 Disposition of Platelets Velocity Gradient

9. 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 Finite Element Domain Variation in Platelet Length Loading of a Fretting Contact

10. 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 (b) (a) (d) (c) 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.

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

12. 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 120 particles 220 particles 320 particles 420 particles

13. 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

14. Effect of Platelet Length on Partial Slip Fretting Contacts 2 particles 14 particles 5 particles 10 particles • Longer platelets lead to formation of a thicker third body mass • Thicker third body masses are pushed further from the stick-slip zone interface Pressure Profile Frictional Shear Stress Particle Location After Loading

15. Wear Particles During Fretting Evolution 120k 160k 40k 80k • The wear particles group together due to the pressure and surface profile shape • Pressure is not longer uniform in the slip zone Pressure Subsurface Stress (σy) Groups of Clustered Wear Particles

16. 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