Introduction to Fracture Mechanics phần 3 docx

Plane Crack Problem Airy Stress Function

For the plane problem, the equations of equilibrium are

satisfied when the stress components are expressed by

the Airy stress function xthrough

, ,

1 1 2 2

x x x

rr













   

21

, , 2 2 2 r r r r

rr 









   



. 1 



 













  

 

x

r r

r

Using these definitions for the stresses and Hooke’s

law, the strains can be expressed in terms of . x