4020-F2011-HW13Solutions

# 4020-F2011-HW13Solutions - MSE 4020 HW13-SOLUTION Problem...

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1 MSE 4020 HW13-SOLUTION 11/26/2011 Problem 1. (a) Using 70°F curve as the master curve, we can estimate shift factors for different temperatures with reference to 70°F as follows: log a(73 ° F) = 0 log a(115 ° F) = ! 2.8 log a(185 ° F) = ! 4.7 log a(212 ° F) = ! 6.3 Fitting these data by Cubic spline interpolation, we have the follow plot:

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(b) The stress state of a thin walled tube is: ! "" = P # r t ! zz = P # r 2t ! rr = 0 \$ % ' ( equivalent stress ! = 1 2 ! "" ) ! rr ( ) 2 + ! "" ) ! zz ( ) 2 + ! zz ) ! rr ( ) 2 * + , - . / 0 1 2 \$ % ' 1/2 = 3 2 ! "" equivalent strain 3 = 2 3 3 "" ! = E r (t) # 3 ( 3 2 ! "" = E r (t) # 2 3 3 "" ( 3 "" = 3 4 # 1 E r (t) # ! "" = 3 4 # 1 E r (t) # P # r t T = 170 ° F ! log a(170 ° F) = " 4.2 t(170 ° F) = 10 # 365 # 24 = 8.46 # 10 4 hrs t(73 ° F) = t(170 ° F) a(170 ° F) ! log t(73 ° F) = log t(170 ° F) " log a(170 ° F) = 4.95 + 4.2 = 9.15 ! E r (10 9.15 ) = 0.63 # 10 5 psi \$ %% ( ) max = 0.01 P = 100 psi ! r
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4020-F2011-HW13Solutions - MSE 4020 HW13-SOLUTION Problem...

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