The potentials: were proposed to solve the plane extension of an anisotropic panel containing a crack

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The potentials:

 P1 (21) A121 + 02 (22) = A222 Sa  2 (M4 - 4) 1 + / - 0 Sa 2(4 ) 22+2-a L

were proposed to solve the plane extension of an anisotropic panel containing a crack of length 2a (see Fig. 11.12). Recall that the constants A1 and A2 correspond to the uniform tension case, and for stress S in the y direction:

A (a + B) S = 2 [(2 - ) + (3-B)] . [ ( - B) -  (-B)] S +i (a +3-201) S A2 2 [(a-a) + (82-18) 26 [( - ) + (B 2

   Fig 11.12

18 AY a ^^ S S X

(a). Determine the general stress field and verify the far-field behavior.
(b). Show that the stress field is singular at each crack tip.
(c). Using the limiting procedures as related to Fig. 10.20, verify that the crack-tip stress field is given by (11.6.10).

Fig 10.20

1 a  AY ta a B B

Equation 11.6.10

x - dy = Txy = Sa, 1142 2r Re 11-1 Sa 2r Sa 2r Re Re 1 1 -14 - 1112 11-1 1 1 cos -  sine cos -  sine 14 1

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