Lecture23 - ME 382 Lecture 23 STATISTICS OF FRACTURE Very...

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ME 382 Lecture 23 13/iii/06 1 S TATISTICS OF F RACTURE Very brittle materials have very small critical flaw sizes E.g., Consider a ceramic with K Ic 1 MPa m ( σ Y 1-4 GPa) Crack length for a “useful” strength of 150 MPa? Assume loading parameter for fracture: K I ! " # a Critical crack size for fracture when σ f = 150 MPa a cr ! K Ic 2 "# f 2 = 10 12 " $ 2.25 $ 10 16 ! 14 μ m Critical crack length grain size & random natural defects Difficult to measure size of strength-limiting flaw (problem is both small size, and the fact that there are lots of flaws of similar sizes) Use statistical methods to determine probability of failure Weakest-link statistics Consider a chain made up of many brittle links Probability of failure of each link: P f = 0.3 / link Probability of survival of each link: P s = 1 - P f = 0.7 For 1 link: P f = 0.3, P s = 0.7 For 2 links: P s = 0.7 x 0.7 = 0.49 ( P f = 0.51) For n links: P s = 0.7 n P f = 1 - (0.7) n P f as n A general feature of non-redundant systems: P f as size Brittle materials are full of flaws
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ME 382 Lecture 23 13/iii/06 2 If one flaw is critical entire material fails: Weakest-link statistics apply
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