13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- The Effect of the Changing State of Stress Around the Crack Tip on the Determination of Stress Intensity Factors by the Method of Caustics Emmanuel Gdoutos* Civil Engineering, Democritus University of Thrace, GR-671 00 Xanthi, Greece * egdoutos@civil.duth.gr Abstract The state of stress in the vicinity of the crack tip changes from plane strain at the tip to plane stress at a critical distance (about half the specimen thickness) from the tip through an intermediate region where the state of stress is three-dimensional. In the optical method of caustics, the caustic is the image of a circle on the specimen centered at the crack tip, and, therefore, yields information on the stress state along this circle. In the method conditions of plane stress are assumed along this circle. This condition imposes restrictions on the geometrical dimensions of the optical arrangement, specimen thickness, crack length and applied loads for the correct determination of stress intensity factors. In the present work the limits of applicability of the method of caustics are studied. The use of optically anisotropic materials is introduced to obtain a double caustic which provides the correct state of stress (plane strain, plane stress or three-dimensional) along the initial curve. When the state of stress is known the proper values of stress-optical constants can be used for the correct determination of stress intensity factors. Keywords Cracks, Stress intensity factors, The method of caustics, Triaxial state of stress 1. Introduction The optical method of caustics is sensitive to stress gradients, and it has extensively been used for the determination of stress intensity factors in crack problems [1-6]. According to the method the stress singularity at the crack tip is transformed to an optical singularity. A highly illuminated curve, so-called caustic, is obtained on a viewing screen at a distance from the crack tip. The dimensions of the caustic are related to the state of stress near the crack tip. Thus the stress intensity factor which governs the stress field can be determined by measuring characteristic dimensions of the caustic, usually, its diameter perpendicular to the crack. The method is based on the assumption that the state of stress near the crack tip is plane stress. However, experimental and analytical solutions have shown that the state of stress changes from plane strain near the crack tip to plane stress away from the tip through an intermediate region where the stress state is three-dimensional. The changing state of stress results to changing values of stress-optical constants which enter in the equations for the determination of stress intensity factors. In the present work the method of caustics is critically reviewed, and its limits of applicability are studied. Furthermore, the use of optically anisotropic material is introduced for the determination of stress intensity factors. 2. The Optical Method of Caustics In the optical method of caustics a specimen is illuminated by a light beam and the reflected or transmitted rays undergo a change of their optical path dictated by the stress field (Fig. 1). The change of the optical path is caused by the variation of the thickness and refractive index as the specimen is loaded. At stress gradients resulting at crack tips, the reflected or transmitted rays generate a highly illuminated three-dimensional surface in space. When this surface is intersected by a reference screen, a bright curve, the so-called caustic curve, is formed. For transparent
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