Chapter 4 FRAC TURE   TOUGHNESS

The Fundamentals Fracture = separation of body into two or more pieces due to application of static stress Tensile, Compressive Shear or torsional FAST FRACTURE _ In a balloon energy is stored: Compressed gas Elastic energy of Rubber membrane If more energy released than is absorbed crack advances Fails by fast fracture even though below yield stress Explosion of boilers, collapse of bridges

Modes of fracture DUCTILE BRITTLE Transgranular vs. intergranular fracture

‘’stress concentration’’ y x Stress trajectories Professor Inglis (1913) The birth of the term ‘’stress concentration’’ Large structures

 Griffith and his Energy criterion Crack propagates when favorable, i.e. system reduces its total energy Relaxed material behind crack = Elastic strain energy released Crack having surface energy (s) a  a = edge crack or 1/2 central crack

What about ductile materials But for v. ductile materials p >>> s Define the strain energy release rate Gc (IRWIN 1950) Hence Toughness or Strain energy release rate (Energy absorbed per unit area of crack)

Modes of fracture Fast fracture occurs when K=Kc Condition for fast fracture (for crack through center of a wide plate) Comes up a lot Hence give it symbol, K, Stress intensity factor Fast fracture occurs when K=Kc Modes of fracture

Stress intensity factor AND =

What about ductile materials  consider y (i. e What about ductile materials  consider y (i.e. y means direction not yield) Plastic zone

From: H.L.Ewalds, and R.J.H. Wanhill, Fracture Mechanics, 1991

From: H.L.Ewalds, and R.J.H. Wanhill, Fracture Mechanics, 1991

To be plane strain Plane strain fracture toughness

Critical flaw size (microns) Design using fracture mechanics Example: Compare the critical flaw sizes in the following metals subjected to tensile stress 1500MPa and K = 1.12 a. KIc (MPa.m1/2) Al 250 Steel 50 Zirconia(ZrO2) 2 Toughened Zirconia 12 Critical flaw size (microns) 7000 280 0.45 16 Where Y = 1.12. Substitute values SOLUTION

COMPRESSED AIR TANKS FOR A SUPERSONIC WIND TUNNEL From, M. Ashby, Engineering Materials 1, 2nd edition, 1996 COMPRESSED AIR TANKS FOR A SUPERSONIC WIND TUNNEL Supersonic wind tunnels in an Aerodynamic Lab, are powdered by a bank of large cylindrical pressure vessels. How can we design and check pressure vessels to make sure that they are safe? Vessels must be safe from plastic collapse or fail by fast fracture Also must not fail by fatigue Hoop stress in the wall of a cylindrical pressure vessel containing gas at pressure p: Provided that the wall is thin (t<<r) For general yielding For Fast Fracture

Yield before fracture Fracture before Yield Fatigue or stress corrosion Increases crack size to critical value

Easy to detect 10mm critical crack but not 1mm as for Al

If critical flaw size is less than thickness fast fracture NO WARNING For critical crack size 2a

R-curve behavior From: Brian Lawn, Fracture of brittle solids, 2nd edition, Cambridge university press) p.210, 1993