508L3.31.1.07

508L3.31.1.07 - Mechanics of Earthquakes and Faulting...

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Unformatted text preview: Mechanics of Earthquakes and Faulting Mechanics of Earthquakes and Faulting Energy balance for crack propagation Stress intensity factors Static & dynamic fracture mechanics Critical energy release rate Process zone Crack models Failure Criteria 31 Jan. 2007 22 23 21 r r G is Energy flow to crack tip per unit new crack area G = 1 - h ( ) 2 m g I v ( ) K I 2 + g II v ( ) K II 2 [ ] + 1 2 m g III v ( ) K III 2 G = G critical = 2 g Critical energy release rate u 2 D u 1 D u 3 4 1 - h ( ) m r ' 2 p g I v ( ) K I g II v ( ) K II g III v ( ) K III 1 - h ( ) G is a material property --the fracture energy G = K / E = 2 , where K is the critical stress intensity factor (also known as the Static vs. dynamic fracture mechanics, relativistic effects u 2 D u 1 D u 3 4 1- h ( ) m r ' 2 p g I v ( ) K I g II v ( ) K II g III v ( ) K III 1- h ( ) g I ( ) = g II ( ) = g III ( ) =1 Static g I v ( ) and = g II v ( ) , as v C R g III v ( ) = 1 1- h 2 / C s 2 , as v C s Dynamic crack propagation 22 23 21 v 1 2 r r r Stress field is singular at the crack tip. because we assumed perfectly sharp crack but real materials cannot support infinite stress 22 s 21 s 23 tip 1 2 pr K I K II K III K I = pc s Process zone (Irwin) to account for non-linear zone of plastic flow and cracking Size of this zone will depend upon crack velocity, material properties and crack geometry Energy dissipation in the crack tip region helps to limit the stresses there (why?) 22 23 21 r r Fault tip stresses, process zone Slip. u x Boxcar function, assuming infinite material strength Elastic model (Eshelby) Dugdale Small-scale yielding e.g., depth-averaged co-seismic or post-seismic slip distribution; geologic data on the relationship between fault slip and fault length Crack tip stress field, real materials r Singular crack (Eshelby)...
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508L3.31.1.07 - Mechanics of Earthquakes and Faulting...

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