Lecture22-Notes - ME 382 Lecture 22 CRACK-TIP PLASTICITY...

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ME 382 Lecture 22 1 C RACK - TIP PLASTICITY Elastic solution predicts singular stress at crack tip: " yy = xx = K I / # r But ˜ H # Y , yielding and plastic zone at crack tip In plane stress [ σ zz = 0], radius of plastic zone: Y # K I / $ r p % r p # K I 2 2 $" Y 2 In plane strain [ σ zz = ν ( σ xx + σ yy )], radius of plastic zone: r p = 1 " 2 ( ) 2 2 K I % Y & ' ( ) * + 2 More accurate calculation with load shedding (plane strain): r p = 1 6 ! K I Y # $ % & ' ( 2 Size of plastic zone at fracture (in plane strain): r p * = 1 6 K Ic Y # $ % & ' ( 2 Examples: Mild steel: σ Y = 220 MPa; K Ic = 140 MPa m r p * = 43 mm Aluminum alloy: Y = 325 MPa; K Ic = 34 MPa m r p * = 1.2 mm Silicon nitride: Y = 8000 MPa; K Ic = 5.0 MPa m r p * = 41 nm As crack advances, material in plastic zone is unloaded, but plastic zone extends Energy dissipated by crack-tip plasticity Volume of material deforming in a plastic fashion as σ Y Energy dissipated as σ Y K Ic (approximately) as σ Y
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Lecture22-Notes - ME 382 Lecture 22 CRACK-TIP PLASTICITY...

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