Mokashi Imrankhan Sherkhan Guided by: M S Bobji Seminar on

Importance of Fracture Mechanics in Tribology Wear Erosion Surface Formation

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)

Modes of Crack Propagation

Energy Approach

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

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

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

Thick plate is more resistant to fracture or thin?

J Integral  J Integral over a closed loop = 0  Path independent

Displacement Approach

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

Stress Approach

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

Stress near crack tip Plastic zone size

plane strain plane stress Plastic Zone Shapes

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

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)

FATIGUE FRACTURE

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

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

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

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

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