~~ Fmcture M ec~~c~ Vol. 39, No. 5, pp.875-885, 1991 oot3-7944/91 $3.00 + 0.00 Printi in Great Britain. @ 1991 Pergamoo Press plc. A STUDY OF THE THREE-DIMENSIONAL REGION AT CRACK TIPS BY THE METHOD OF CAUSTICS E. I. MELETIS and WEIJI HUANG Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 708036413, U.S.A. and E. E. GDGUTOS School of Engineering, Demo&us University of Thrace, GR-67100 Xanthi, Greece Ahatraet-A thorough investigation of the three-dimensional region around the border of a straight through-crack in a plate was undertaken by the method of caustics. A series of experiments were performed on 209OAl alloy fatigue precracked double cantilever beam specimens of various thicknesses. The power and potential of the method of caustics in studying the ~r~dimension~ nature of the stress field in crack problems was demonstrated. It was found that in the immediate vicinity of the crack tip and for specimen thicknesses larger than a critical thickness, a region exists that is under strong “plane strain” inguence. The size of this region increases initially with specimen thickness and finally reaches a limiting value. Following the “plane strain” region which surrounds the crack tip, three-dimensional stress conditions hold in the vicinity of the crack tip up to a critical distance which depends on the thickness of the plate. Beyond this critical distance plane stress conditions dominate. The value of the effective thickness of the specimen which contributes to the formation of the caustic was found to increase by receding from the crack tip and it finally reaches the actuaI specimen thickness. The results of the present study shed light onto the complicated problem of the state of stress around cracks and establish the limits of applicability of the method of caustics in crack problems. 1. I~RODU~ON THE STRESS BIBLD in the neighborhood of a straight or curved crack is inherently three-dimensional. The stress intensity factor, which is a measure of the strength of the stress and displacement fields, is not constant but varies along the crack front. However, for mathematical convenience the situation is usually idealized as plane stress or plane strain and the solution of the problem is obtained within the framework of the two-dimensional theory of elasticity. Conditions of plane stress dominate in very thin plates where it can be assumed that the transverse stress to the plane of the plate is zero through the plate thickness. On the other hand, in thick plates the state of stress is primarily one of plane strain. Generally speaking, the stress state in cracked plates changes from conditions approaching plane stress near the plate surfaces to plane strain at the mid thickness. An extensive amount of work has been devoted to the study of the thr~m~sional nature of the stress field in cracked plates. Sih and coworkers[l-31 performed a thorough study of three-dimensional crack problems. They expressed the local stress field near the crack front in a form analogous to the two-dimensional case in terms of three stress intensity factors which are independent of the local coordinates, and are dependent only on the crack geometry, the form of loading and the location along the crack border. This result is fundamental in analysing the fracture behavior of cracks and provides uniform expressions for the local stresses under various geometrical and loading conditions where only the values of stress intensity factors differ. A great variety of stress solutions for internal and external cracks in three dimensions, also including the effects of material anisotropy and inhomogeneity, is provided in the book by Kassir and Sih[4]. The above analytical solutions are mainly concerned with bodies of infinite extent. However, when the dimensions of the body become finite, great mathematical difficulties arise and numerical or experimental methods are used. For example, Kobayashi and coworker@, 6] dete~in~ stress intensity factor variations along the periphery of a semi-elliptical crack in a plate of finite thickness under various loading conditions. The finite element method has also been extensively used in the investigation of the three-dimensional character of crack problems. Special three-dimensional elements were introduced in which the inverse square root singularity of the stress field in the 875