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Understanding Fracture Mechanics in Tribology: Insights from M. S. Bobji's Seminar

This seminar, led by M. S. Bobji, delves into the critical importance of fracture mechanics in tribology, covering wear, erosion, and surface formation. Participants will explore various approaches including energy-based methods (energy release rate and J-integral), stress intensity factors, and crack tip opening displacements. The historical context of fracture mechanics, the relevance of Griffith’s energy balance approach, and the implications of fracture in various applications such as metal cutting and construction are discussed. Practical insights into fatigue fractures and their avoidance are also presented.

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Understanding Fracture Mechanics in Tribology: Insights from M. S. Bobji's Seminar

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  1. Seminar on Mokashi Imrankhan Sherkhan Guided by: M S Bobji

  2. Importance of Fracture Mechanics in Tribology • Wear • Erosion • Surface Formation

  3. Fracture Mechanics approach • Energy Based : Energy release rate(G) and J integral • Stress Based : Stress intensity factor (K) • Displacement Based : Crack tip opening displacement (CTOD)

  4. Modes of Crack Propagation

  5. Energy Approach

  6. Griffith’s Energy balance approach • First documented paper on fracture (1920) Considered as father of Fracture Mechanics

  7. Energy Approach Cont… • Surface energy Es = 2(2a B ᵞ) • ᵞ -Surface energy per unit area • B-Thickness of plate

  8. Energy Approach Cont.. • Total PE of Body with crack • U = UE – Uwork + US • Strain Energy • System always try to minimize its PE

  9. Thick plate is more resistant to fracture or thin?

  10. J Integral • J Integral over a closed loop = 0 • Path independent

  11. Displacement Approach

  12. Displacement Approach From Hooke’s law, displacement field can be obtained as

  13. Stress Approach

  14. Stress Intensity Factor for infinite plate for other geometry  can be obtained from : 1. handbook solution 2. approximate method 3. numerical method

  15. Stress near crack tip Plastic zone size

  16. Plastic Zone Shapes plane strain plane stress

  17. = 1 = 1 Mixed Loading where KIc, KIIc, KIIIc, ni (i = 1, 2, 3) – parameters that characterize material near the concentrator, determined experimentally

  18. Cont… (1) Diagrams of the deformed body limiting-equilibrium state the conditions of mixed (I+II), (I+III) fracture mechanisms Curve 1 – according to formula (1) when KIII = 0 and ni = 4, curve 2 according formula (1) when KIII = 0 and ni= 2 Curves 1 and 2 are plotted according to formula (1) when ni = 4 and ni=2 correspondingly

  19. FATIGUE FRACTURE

  20. Every Coin has two sides… • Useful Fracture • Metal cutting • Rock cutting in Mining • “Biting” of candies • Unwanted Fracture • Fracture of Liberty ships in World war II • Fracture of wheels, axles and rails

  21. Fracture Avoidance with Proper Use of Material • Pyramid of Egypt Schematic Roman Bridge Design • The primary construction material prior to 19th were timber, brick and mortar • Arch shape producing compressive stress  stone have high compressive strength

  22. Fracture Avoidance with Proper Use of Material (cont’) • Roof spans and windows were arched to maintain compressive loading

  23. REFERENCES A book on “Fracture Mechanics” by Prashant Kumar “Introduction to Fracture Mechanics” book by C. H. Wang

  24. Thank you for your attention

  25. Finite Element Analysis • Stress analysis near crack • Quarter point element • J- integral

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