Lecture17%20with%20slides

Lecture17%20with%20slides - When Does a Crack Propagate for...

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1 1 Lecture 17 Fracture-2 2 When Does a Crack Propagate for a Plate with a Crack in the Center? Crack propagates if above critical stress where E = modulus of elasticity γ s = specific surface energy a = one half length of internal crack For ductile => replace γ s by γ s + γ p where γ p is plastic deformation energy 2 1 2 / s c a E π γ = σ i.e., σ 0 > σ c 3 As crack propagates energy of system changes External loads may do work Strain energy stored in material may change G = a W U () Crack driving force: J/m 2 or N/m (strain) energy-release rate Resistance to crack propagation: Γ∼2 γ s J/m 2 or N/m toughness critical strain energy-release rate Theory on Crack Propagation 4 Design for strength K Ic = E Γ /1 ν 2 Material property: Loading parameter: Failure criterion: K I = E G 2 K I K Ic 5 Fracture Toughness Based on data in Table B5, Cal ister 7e . Composite reinforcement geometry is: f = fibers; sf = short fibers; w = whiskers; p = particles. Addition data as noted (vol. fraction of reinforcement): 1. (55vol%) ASM Handbook , Vol. 21, ASM Int., Materials Park, OH (2001) p. 606. 2. (55 vol%) Courtesy J. Cornie, MMC, Inc., Waltham, MA. 3. (30 vol%) P.F. Becher et al., Fracture Mechanics of Ceramics , Vol. 7, Plenum Press (1986). pp. 61-73. 4. Courtesy CoorsTek, Golden, CO. 5. (30 vol%) S.T. Buljan et al., "Development of Ceramic Matrix Composites for Application in Technology for Advanced Engines Program", ORNL/Sub/85-22011/2, ORNL, 1992. 6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci. Proc. , Vol. 7 (1986) pp. 978-82. Graphite/ Ceramics/ Semicond Metals/ Al oys Composites/ fibers Polymers 5 K Ic (MPa · m 0.5 ) 1 Mg al oys Al al oys Ti al oys Steels Si crystal Glass -soda Concrete Si carbide PC Glass 6 0.5 0.7 2 4 3 10 20 30 <100> <111> Diamond PVC PP
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Lecture17%20with%20slides - When Does a Crack Propagate for...

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