Lecture18%20with%20slides

# Lecture18%20with%20slides - Yield or fracture? t P P 2b 2a...

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1 1 Lecture 18 Fracture-3 2 Yield or fracture? 2a 2b t P P a b t P P 3 a P P Example 10 mm 50 mm Aluminum alloy: K Ic = 30.0 MPa m; σ Y = 300 MPa Fracture: K I = f ( a / b ) F 1 2 3 S g π a Onset of yield: a (m) (b-a) m a/b f (a/b) P Y (kN) P F (kN) P Failure (kN) 0 0.050 0 1.122 150 & 0.0025 0.0475 0.005 0.045 0.1 1.209 101 99.0 0.010 0.040 0.2 1.380 68.6 61.3 0.020 0.030 2 Y () = (2 ) Y bat P ab σ + 4 5 Fracture of Pressure Vessels (often known as: explosions ) 6 April 28, 1988 24,000 feet above Hawaii . .......

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VK250 Lecture 18 Fracture III Fail by Yield or Fracture? Load to cause onset of yield YY (2 -2 ) Pb a t σ = Fully plastic force or moment Fully plastic force or moment for given = / ab α (a) 0 = 2 (1 ) Y t (b) 2 2 0 =( 1 ) 4 Y bt M (c) 2 0 = 1 2(1 ) Y t σα ⎡⎤ −−+ + ⎣⎦ (d) 2 0 = 2 2 1 Y t +− + Center crack Edge crack 32 () 1 2 ( 2) = 2( ) ( ) ( ) M ba P abP tb a b at b a t + += −− ) 2 Y = ( ) /(2 ) Y a t a b −+ (Derivation: M = Pa /2
2 7 Design of pressure vessels t R σ zz σ zz σ θθ σ θθ σ rr crack along length σ rr =− P /2 0; θθ = PR / t ; zz = PR t Design against yield: Design against fracture: - 2 a t a K I π a 8 yield fracture a T a PR / t 2 Y 3 Transition between fracture and yield
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## This note was uploaded on 09/15/2010 for the course MATSCIE 250 taught by Professor Yalisove during the Fall '08 term at University of Michigan.

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Lecture18%20with%20slides - Yield or fracture? t P P 2b 2a...

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