13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- ( ) ⎥ ⎦ ⎤ ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ± + ⎢⎣ ⎡ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = − θ ξ θ θ sin2 4 3 cos3 /2 3 2 cos 2 3 , 3/5 2/ 5 2/5 , , r t r t r t A X C A (7a) ( ) ( ) ⎥ ⎦ ⎤ ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ + ± + ⎢⎣ ⎡ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = − θ ξ θ θ 1 3cos2 4 1 sin3 /2 3 2 sin 2 3 , 3/5 2/5 2/ 5 , , r t r t r t A Y C A (7b) where: {( ( )} ( ) 1/2 2, , , 25 9cos2 32 1 7sin /2 sin3 /2 4 1 1 sin 4 1 ⎥⎦ ⎤ + + + ⎢⎣ ⎡ + ± =± θ ξ θ θ ξ θ ξ r t r t r t A (8) ( )1/2 , 0 , 2 π ε r t I r t z dc K C = (9) The equation of the initial curve is given by: 2/5 , 0 2 3 ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ = = r r C A r t (10) Equations (7) express the equations of the caustic curve for optically anisotropic materials. Two caustics are obtained corresponding to the plus and minus signs in equations. These caustics are referred to the two principal stress directions. Note that for r t,ξ = 0 equations (7) and (9) reduce to the equations of the caustic for optically isotropic materials. Fig. 7 shows the initial curves and respective caustics in a plate with crack subjected to tension made of birefringent materials with ξ = 0, 0.2, 0.4, 0.6, 0.8 and 1.0 [8]. Observe that as ξ increases the shapes of the initial curves and caustics are progressively distorted. The distance between the two caustics increases as ξ also increases. The value of ξdepends on the state of stress, being plane strain, plane stress or three-dimensional. Thus the experimental caustics obtained can be used for the determination of the triaxiality factor k and the subsequent calculation of the stress-optical constant for the correct determination of stress intensity factors.
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