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Contact Mechanics

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Contact Mechanics

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    1. Contact Mechanics

    2. SEM Image of Early Northeastern University MEMS Microswitch

    3. SEM of Current NU Microswitch

    4. Two Scales of the Contact Contact Bump (larger, micro-scale) Asperities (smaller, nano-scale)

    5. Basics of Hertz Contact

    6. Basics of Hertz Contact

    7. Basics of Hertz Contact

    8. Basics of Hertz Contact

    9. Hertz Contact Hertz Contact (1882)

    10. Assumptions of Hertz Contacting bodies are locally spherical Contact radius << dimensions of the body Linear elastic and isotropic material properties Neglect friction Neglect adhesion Hertz developed this theory as a graduate student during his 1881 Christmas vacation What will you do during your Christmas vacation ?????

    11. Onset of Yielding Yielding initiates below the surface when ?VM = ?Y which for Poissons ratio of 0.3 occurs when the average contact pressure is 1.07*?Y.

    12. Round Bump Fabrication Critical issues for profile transfer: Process Pressure Biased Power Gas Ratio

    13. Fully Plastic Single Asperity Contacts (Hardness Indentation) Contact pressure is uniform and equal to the hardness (H) Area varies linearly with force A=P/H Area is linear in the interference ? = a2/2R

    14. Nanoindenters

    15. Nanoindentation Test

    16. Depth-Dependent Hardness

    17. Surface Topography

    18. Contact of Surfaces

    19. Typical Contact

    20. Multi-Asperity Models (Greenwood and Williamson, 1966, Proceedings of the Royal Society of London, A295, pp. 300-319.) Assumptions All asperities are spherical and have the same summit curvature. The asperities have a statistical distribution of heights (Gaussian). Deformation is linear elastic and isotropic. Asperities are uncoupled from each other. Ignore bulk deformation.

    21. Greenwood and Williamson

    22. Greenwood & Williamson Model For a Gaussian distribution of asperity heights the contact area is almost linear in the normal force. Elastic deformation is consistent with Coulomb friction i.e. A ? P, F ? A, hence F ? P, i.e. F = ?N Many modifications have been made to the GW theory to include more effects ? many are not important. Especially important is plastic deformation and adhesion.

    23. Contacts With Adhesion (van der Waals Forces)

    24. Forces of Adhesion Important in MEMS Due to Scaling Characterized by the Surface Energy (?) and the Work of Adhesion (??) For identical materials Also characterized by an inter-atomic potential

    25. Adhesion Theories

    26. Two Rigid Spheres: Bradley Model

    27. JKR Model Johnson, K.L., Kendall, K., and Roberts, A.D., 1971, Surface Energy and the Contact of Elastic Solids, Proceedings of the Royal Society of London, A324, pp. 301-313. Includes the effect of elastic deformation. Treats the effect of adhesion as surface energy only. Tensile (adhesive) stresses only in the contact area. Neglects adhesive stresses in the separation zone.

    28. Derivation of JKR Model

    29. DMT Model

    30. Tabor Parameter: JKR-DMT Transition

    31. Adhesion Map

    32. Multi-Asperity Models With Adhesion Replace Hertz Contacts of GW Model with JKR Adhesive Contacts: Fuller, K.N.G., and Tabor, D., 1975, Proc. Royal Society of London, A345, pp. 327-342. Replace Hertz Contacts of GW Model with DMT Adhesive Contacts: Maugis, D., 1996, J. Adhesion Science and Technology, 10, pp. 161-175. Replace Hertz Contacts of GW Model with Maugis Adhesive Contacts: Morrow, C., Lovell, M., and Ning, X., 2003, J. of Physics D: Applied Physics, 36, pp. 534-540.

    33. Surface Tension

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