13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- curve lies in the region where plane stress conditions dominate. In that case the value of stress-optical constant corresponding to plane stress should to be used. In order to obtain caustics generated from the region of plane stress the radius of the initial curve of the caustic should be larger than a fraction of the specimen thickness. By taking this distance equal to half the specimen thickness we obtain d m z cK ⎟ > ⎠ ⎞ ⎜ ⎝ ⎛ 2/3 0 3.385 (4) Inequality (4) establishes a condition the quantities, z0, c, K, m, d should satisfy in order to obtain caustics generated by an initial curve that lies in the plane stress region Fig. 3 presents the variation of the critical (minimum) value of specimen thickness, z0, versus KI for a parallel light beam illuminating a notched Observe that the critical thickness z0 increases as the thickness of the specimen increases and KI decreases. Fig. 4 presents the variation of r0 versus stress intensity factor KI for a Plexiglas specimen of thickness d = 1 mm illuminated by a parallel light beam. The caustic is created by transmitted light rays (ct = 1.08x10-10m2N-1) and the reference screen is placed at distances z0 = 0.1,1 and 10 m from the specimen. KI varies up to 1 MPa√m corresponding to the value of fracture toughness of Plexiglas. In the same figure the line r0 = d/2 is drawn. Observe that r0 increases as KI and z0 are also increased. Only for the part of curves above the line r0 = d/2, does the radius of the initial curve lie in the region of plane stress. It is observed that the realm of validity of the method of caustics under conditions of plane stress increases with KI and z0. Figure 2. Variation of Kexp/Kth versus r/d for a = 15.5 mm, d = 4.5 mm and w = 47.5 mm (a) and w = 63.5 mm (b)
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