THE sraxss distribution in a plate into which a crack is generated has been studied by many investigators. The most earlier contri&tuions are due to Inglis[ll, who studied the stresses around an elliptic hole in an iu8nite plate and to Westergaard [2], who treated the crack problem by the complex. variable technique. W-0
[3] gave the stress components at the crack tip in a power series form whose coe8lcients can be calculated from the bou&ry conditions aud made some intelliit observations on the near to crack-tip stress field.
Substantial progress in fracture mechanics has been made for the determination of the stress distribution at the close vicinity of the crack tip. This stress field is controlled by a constant, the stress intensity factor K*, which is a function of loading and the geometric co&umtion of the cracked plate. Several tkmtiud and experimental techniques have been developed for the determination of the sttess intensity factor.
~~y,thisq~~mgybe&~ininfU3iteplatcsbytheclassicrlcontn'butionby Westergaard[2],whileforplateswith8nitewidthsubstantialworkhasbeendonebyIsida[4,5]and Bowie and Neal[6] among others. Paris and Sih[71 gave a thorough review for the problem of cracks. Generally, the results infinite width plates are presented as correction factors for the stress intensity factor for the corresponding case of an infmite plate with the same crack.
Experimentally, Post [8] and Wells and Post were the first to study the stress distribution for a stationary as well as for a running crack, by classical photoelasticity and interferometry. IrwinflO], in a discussion of Ref. 9, pointed out that the stress intensity factor can be calculated by measuring the distance between the crack tip and the farthest point on a given fringe loop in the typical isochromatic pattern near the crack tip, as well as the corresponding angle of inclination of this line to the crack axis. Post and Wells in their authors' closure showed thata small error in measuring the distance and the angle inlluences considerably the determination of K.
In order to eliminate uncertainties in the calculation of K, Bradley and Kobayashi [ 111, as well as Smith and his co-workers [G-14] and Cheng [ 151 introduced the idea of making more than one measurements at the stress field near the crack tip and they used statistical procedures to evaluate accurately K.
Following a statement by Vitvitskii ef cf. [ 16j in their recent Russian publication, we may quote that: "New (experimental) methods have been used recently in investigating plastic zones: optical, based on the use of moire patterns, distortion of the image on a deformed surface, interferometry, and holography; metallographic, involving etching of the deformed xone with subsequent microscopic study. Still, these have not been sufllcient to determine the field of deformation at a small zone about the head of a crack because of the high gradients. An exception may be the caustic method, the possibilities of which in the presence of plastic xones have not yet been adequately studied. There is new promise, especially in the study of small plastic xones and fine changes of material structure in the vicinity of the crack head, in electron microscopy and X-ray photography. However, the use of these methods has not yet led to any essentially new results from the view point of fracture mechanics".