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Lecture20-Notes

# Lecture20-Notes - ME 382 Lecture 20 LINEAR-ELASTIC FRACTURE...

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ME 382 Lecture 20 1 L INEAR - ELASTIC FRACTURE MECHANIC s Fundamental loading parameter for elastic fracture: G (energy-release rate) Fundamental material property for elastic fracture: Γ (toughness) Failure criterion: G Γ Loading parameter for design against fracture: K I = E G / 1 ν 2 ( ) Mode-I stress-intensity factor (MPa m) Material property for design against fracture: K Ic = E Γ / 1 2 ( ) Mode-I plane-strain fracture toughness Failure criterion: K K Ic The “mode-I” denotes a loading condition in which the crack is opened only Only mode-I (fracture by a normal stress) considered in ME382 Another perspective on the stress-intensity factor: Linear elasticity predicts singular stresses at a crack tip

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ME 382 Lecture 20 2 σ rr θθ τ r θ Χ Ψ Ϊ Ω Ϊ Ϋ ά Ϊ έ Ϊ = K 1 2 π r ( ) 1/2 cos / 2 ( ) 1 + sin 2 / 2 ( ) [ ] cos 3 /2 ( ) ( ) cos 2 ( ) Χ Ψ Ϊ Ω Ϊ Ϋ ά Ϊ έ Ϊ In particular, note that ahead of the crack ( θ = 0 ° ) = K I r In real materials, yielding occurs at crack tip so K I does not actually describe stress at crack tip. However, K I
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Lecture20-Notes - ME 382 Lecture 20 LINEAR-ELASTIC FRACTURE...

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