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

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 ) -Surface energy per unit area B-Thickness of plate

8. Energy Approach Cont..  Total PE of Body with crack U = U E – U work + U S  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. From Hooke’s law, displacement field can be obtained as Displacement Approach

13. Stress Approach

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

15. Stress near crack tip Plastic zone size

16. plane strain plane stress Plastic Zone Shapes

17. Mixed Loading where K Ic, K IIc, K IIIc, n i (i = 1, 2, 3) – parameters that characterize material near the concentrator, determined experimentally = 1

18. Cont… 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 K III = 0 and n i = 4, curve 2 according formula (1) when K III = 0 and n i = 2 Curves 1 and 2 are plotted according to formula (1) when n i = 4 and n i =2 correspondingly (1)

19. FATIGUE FRACTURE

22. 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

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

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

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

27. Finite Element Analysis Stress analysis near crack  Quarter point element J- integral