Lecture23 - ME 382 Lecture 23 13/iii/06 1 S TATISTICS OF F...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 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 ME 382 Lecture 23 13/iii/06 2 • If one flaw is critical entire material fails: ∴ Weakest-link statistics apply • If volume flaws responsible for fracture: P f ↑ as volume ↑ • If surface flaws responsible for fracture: P f ↑ as surface area ↑ • Strength of glass limited by surface flaws Fresh glass fibers are very strong because they are very small ( ≈ 1 GPa)...
View Full Document

This note was uploaded on 03/20/2011 for the course ME 382 taught by Professor Garikipati during the Winter '08 term at University of Michigan.

Page1 / 6

Lecture23 - ME 382 Lecture 23 13/iii/06 1 S TATISTICS OF F...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online