Fracture Mechanics Homework


6.11 For 260° temper, 2a = 1.32 mm; for 425° temper, 2a = 4.02 mm.

6.13 For the range of Kic's, 44 MPa root meters gives the max crack size, 
which is 2a = 1.49 mm.

6.15 Max stress without exceeding yield with FOS is Sy/2.5 = 130.0 MPa.  
Max nominal stress permitted by Kic and crack size is 370.8 MPa.  FOS against 
cracking is 2.85.  Another way to look at it is that the stress intensity 
factor with the max stress of 130 MPa is (130) x Sqrt(Pi x 0.003) = 12.62 MPa 
root(M).  The 2024-T351 has a fracture toughness of 36 MPa root(M), so the 
FOS is 36/12.62 = 2.85 .  Since the safety factor for yielding is lower than 
the safety factor guarding against crack propagation, the safety factor for 
the pressure vessel is still 2.5.

Handout 
Nominal stress without crack is Mc/I.  M = 24x62500 lb.in. (the bending stress 
at the crack, not the max at the wall); I = 166.7 in^4; c = 5 in., so 
Stress = 45 KSI.  From Appendix C Figure C.4, with lc/b = 0.3/10 = 0.03, and 
on the Pure bending line, Y = 1.085.  Ki = 47,400 psi root in.  FOS = 1.24.
  
Check for yielding, nominal stress with crack has I = 152.1 in^4 and c = 9.7/2", 
for stress = 47,827 psi.  Yield FOS is 130/47.8 = 2.72.