Oblique Edge Crack Research Articles

Teh hypersingular lntegral equation method in the analysis of mixed mode crack problems. (The extended body force method using chebychev polynomials.)

In this paper, the hypersingular integral equation method (HIEM) is applied to calculate the stress intensity factors of the mixed mode crack problems. The stress fields induced by "two kinds of displacement discontinuity" are used as fundamental solutions. Then, the problem is formulated as a system of integral equations with the singularity of the form of (ζ-χ)-2. In the numerical calculation, two kinds of unknown-functions are approximated by the products of the weight functions and Chebychev polynomials. As examples, the stress intensity factors of the oblique edge crack in the semi-infinite plate are treated. The calculation shows that the HIEM gives rapidly converging numerical results even for extremely oblique edge crack.

Stress intensity factor for an oblique edge crack in symmetric two-dimensional projections

An integral transform method is used to obtain stress-distributions in cracked symmetric two-dimensional projections extending out of the half-plane. These projections are similar to such concrete cases as gear teeth. In this study, the case of a crack normal to the boundary has been considered. Integral equations methods have been used to calculate mode I and II stress intensity factors. Results have been obtained through numerical integration for a given boundary equation. They are shown graphically for typical values of shape parameters. Although a particular shape has been assumed, equations and numerical results may be useful in evaluating fatigue and fracture strength of mechanical elements such as gears.

Blunting phenomena in cracked ductile plates under mixed mode conditions

The mode of blunting of the tips in cracked ductile plates was experimentally and graphically studied by assuming plane-stress conditions in the cracked plates and small scale yielding developed at the crack front. The material is supposed to be elastic-perfectly plastic, plastically incompressible. Oblique edge cracks, of different angles β of obliquity, created mixed mode conditions of loading. The experimental study was executed in a scanning electron microscope and the specimens used were made of polycarbonate. By applying a progressively increasing tensile load to an initially sawn oblique edge-crack, the various steps of development of blunting of crack tips was recorded and studied. The experimental results checked with the results derived by tracing the slip-line field for the various angles β of obliquity and for plane-stress conditions. Experimental evidence helped to form the respective slip-line fields for blunted cracks and indicated that the forms of blunting for plane-stress are different from the “Japanese-sword” types of blunting for plane strain. The forms of the plastically deformed crack tips indicated the certain existence of corners which supported previous assumptions of very rapid radial stress changes resembling to stress jumps. It was also shown that the positions of these tail-jumps in σ rr -stresses coincided with the deformed flanks of the blunted cracks thus yielding a reasonable explanation of these lines being coincident with the deformed boundaries.

A two dimensional investigation on plates with oblique equal and unequal parallel edge cracks subjected to tension

This paper reports on an attempt to investigate the stress intensity factors of equal and unequal oblique parallel edge cracks subjected to tension. The effects of the variation of the length of the cracks, angle of inclination, and crack spacings on the stress intensity factors (opening and sliding modes) were studied. Experimental observations show that, for crack spacings equal or larger than the length of the equal oblique parallel edge cracks, the size of the caustics for the cracks in the loaded specimen approach that of a single oblique edge crack with the same angle of inclination.

Stress analysis of a semi-infinite plate with an oblique edge crack

A semi-infinite plate with an oblique edge crack is analyzed as a thin plate bending problem and a plane elastic problem. The rational mapping function of the sum of fractional expressions and the complex variable method are used. Closed solutions are obtained for these respective problems. Stress distributions, stress intensity factors are investigated for loads causing transverse bending, twisting and uniform tension. The relations between the stress intensity factors and the angle of the oblique edge crack are also investigated.