Lecture19%20with%20slides

Lecture19%20with%20slides - Flaws in a solid δv m ⎧ ⎪...

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1 1 Lecture 19 Weibull statistics 2 δ v P s = exp δ V V o σ ( V ) S o m P s is the probability of survival σ (V) is the maximum normal stress in element δ V S o is the Weibull parameter (MPa) m is a “shape parameter” V o is a reference volume needed for dimensional purposes (say 1 m 3 ) Flaws in a solid 3 P s = exp 1 V o S o m m V () volume dV P s = exp 1 A o S o m m A area dA P s = exp V V o S o m Weibull probabilities for fracture Volume flaws Surface flaws Uniform tension (volume flaws) 4 P s = exp V V o S o m P s σ S o m = 0.5 median strength 1 0 Distribution of strengths in a uniaxial tensile test 5 Rank of specimen ( i ) Load (kN) Stress (MPa) P f i/N P s = 1 - P f 1 3.75 150 0.02 0.98 2 5.00 200 0.04 0.96 3 5.50 220 0.06 0.94 4 6.00 240 0.08 0.92 ..... ..... ..... ..... ....
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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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Lecture19%20with%20slides - Flaws in a solid δv m ⎧ ⎪...

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