Oblique Edge Research Articles

An edge crack problem in a semi-infinite plane subjected to concentrated forces

An oblique edge crack problem in a semi-infinite plane is discussed. The concentrated forces are applied on the edge crack face, or on the line boundary of the cracked semi-infinite plane. The rational mapping function approach is suggested to solve the boundary value problem and a solution in a closed form is obtained. Finally, several numerical examples with the calculated results are given.

Edge crack due to circular rigid punch in incomplete contact

A circular rigid punch with friction is assumed to be in contact with a half-plane and the punch has one end sliding on the half-plane and another end with a sharp corner. The contact length is determined by satisfying the finite stress condition at the sliding end of the punch. An oblique edge crack is assumed to be initiated near the end with the sharp corner where the infinite stresses exist. Coulomb's frictional force is assumed to act on the contact region. The cracked half-plane is mapped into a unit circle by using a rational mapping function and the problem is transformed into a standard Riemann–Hilbert problem, which is solved by introducing a Plemelj function. The contact length, the stress intensity factors of the crack and the resultant moment about the origin of the coordinates are calculated with different frictional coefficients and oblique angles of the crack. The stress distributions on the contact region are also shown.

Numerical Study of the Shock Wave Propagating through the Plenum Chamber with Borda's Mouthpiece.

In this paper, the shock wave propagating through the plenum chamber with Borda's mouthpiece was studied by numerical simulation. Computations were carried out by solving the two-dimensional compressible Navier-Stokes equations by using the total variation diminishing (TVD) scheme. Computations were performed for five types of the plenum chamber with Borda's mouthpiece [coaxial mouthpiece, off axis mouthpiece, oblique edge mouthpiece, no mouthpiece (coaxis, off axis)] and two incident shock Mach numbers (Ms=1.5, 2.0). The flow fields were numerically visualized by the pressure and vorticity contours, velocity vectors and sonic lines. The pressure distributions and time histories of the pressure contours in the wall and the axis of the duct were also studied, and the attenuating process of the shock front and the diminishing process of the nonuniformity of the shock front were explored.

Edge Preserving Interpolation of Digital Images Using Fuzzy Inference

This paper presents a novel edge preserving interpolation method for digital images. This new method reduces drastically the blurring and jaggy artifacts at the high-contrast edges, which are generally found in the interpolated images using conventional methods. This high performance is achieved by two proposed operations: a fuzzy-inference based edge preserving interpolator and a highly oblique edge compensation scheme developed based on an edge orientation detector. The former synthesizes the interpolated pixels to match the image local characteristics. Hence, edge sharpness can be retained. However, due to the small footage of the fuzzy interpolation method, it cannot avoid edge jaggedness along the highly oblique edges that have very sharp angles against one of the coordinates. Therefore, a segment matching technique is developed to identify precisely the orientation of the highly oblique edges. Combining these two techniques, we improve significantly the visual quality of the interpolated images, particularly at the high-contrast edges. Both the synthesized images (such as letters) and the natural scenes (captured by camera) have been tested and the results are very promising.

CIRCULAR RIGID PUNCH ON A SEMI-INFINITE PLANE WITH AN OBLIQUE EDGE CRACK SUBJECTED TO CONCENTRATED FORCES OR POINT DISLOCATIONS

A circular rigid punch is located on a semi-infinite plane with an oblique edge crack. The punch is acted by an eccentric load to keep the punch vertical, and frictional force is assumed to exist on the contact region. A pair of concentrated forces or point dislocations is assumed to act at arbitrary points in the semi-infinite plane. The analytical solution (Green function) is obtained by a rational mapping function and a complex variable method. To solve the problem, the complex stress functions are divided into two parts; one is the principal part, which corresponds to the fundamental solution of the semi-infinite plane with an oblique edge crack; the other is the holomorphic part of the problem, which can be derived explicitly. The stress intensity factors and resultant moment on the contact region to decide the position of the vertical load on the punch are shown.

The bending of set squares with one free oblique edge under a concentrated load

In the paper, the reciprocal theorem is applied to research on the bending of set square with one free oblique edge and two clamped edges under a concentrated load acting at any point. This method is simpler and general.

Screech tones from rectangular jets with spanwise oblique shock-cell structures

Understanding screech is especially important for the design of advanced aircraft because screech can cause sonic fatigue failure of aircraft structures. Although the connection between shock-cell spacing and screech frequency is well understood, the relation between non-uniformities in the shock-cell structures and the resulting amplitude, mode, and steadiness of screech have remained unexplored. This paper addresses the above issues by intentionally producing spanwise (larger nozzle dimension) variations in the shock-cell structures and studying the resulting spanwise screech mode. The spanwise-oblique shock-cell structures were produced using imperfectly expanded convergent–divergent rectangular nozzles (aspect ratio = 5) with non-uniform exit geometries. Three geometries were studied: (a) a nozzle with a spanwise uniform edge, (b) a nozzle with a spanwise oblique (single-bevelled) edge, and (c) a nozzle that had two spanwise oblique (double-bevelled) cuts to form an arrowhead-shaped nozzle. For all nozzles considered, the screech mode was antisymmetric in the transverse (smaller nozzle dimension) direction allowing focus on changes in the spanwise direction. Three types of spanwise modes were observed: symmetric (I), antisymmetric (II), and oblique (III). The following significant results emerged: (i) for all cases the screech mode corresponds with the spanwise shock-cell structure, (ii) when multiple screech modes are present, the technique presented here makes it possible to distinguish between coexisting and mutually exclusive modes, (iii) the strength of shocks 3 and 4 influences the screech source amplitude and determines whether screech is unsteady. The results presented here offer hope for a better understanding of screech and for tailoring shock-containing jets to minimize fatigue failure of aircraft components.

An oblique edge crack and an internal crack in a semi-infinite plane acted on by concentrated force at arbitrary position

A semi-infinite plane with an oblique edge crack and an internal crack acted on by a pair of concentrated forces at arbitrary position is studied. The problem can be divided into two particular parts; one is the half plane with the edge crack acted on by the concentrated forces; the other is the half plane with the edge cracked subjected to distributed dislocations on the line of the internal crack. The traction components along the line of the internal crack induced by the distributed dislocations must be of the same magnitude and in the opposite direction to the traction components resulting from the first part, the condition is used to establish the boiunary integral equation of the problem, in which the fundamental solutions of the edge cracked half plane plays an important part, and the dislocation distributions on the line of the internal crack can be determined by solving the boundary integral equation numerically. Since the properties of the half plane and edge crack have been reflected analytically by the fundamental solution of the edge crack have been reflected necessary to perform numerical computation on the surface of the half plane so that the method is presented in this paper is of high precision and less computation.

Stress intensity factors of an oblique edge crack subjected to normal and shear tractions

Stress intensity factors (SIFs) were obtained for an oblique crack under normal and shear traction and remote extension loads. The oblique crack was modeled as the pseudodislocation. The stress field due to tractions was solved by the Flamant solution. The SIR of Mode I and Mode II ( K Iand K II) were then obtained. Finite element analysis was performed with ABAQUS and compared with the analytical solutions. The analytical solutions were in good agreement with the results of FEM. From investigating SIFs and their ranges, the following results were obtained. The growth rate of an oblique edge crack decreased due to the reduction in the SIF ranges. The crack driving force depended on the obliquity, the normal traction and the ratio of crack to traction length. The peak value of shear traction was found as a key parameter to accelerate the crack growth.

Fundamental solutions for half plane with an oblique edge crack

An elastic half plane with an oblique edge crack is considered in this paper. A pair of concentrated forces or point dislocations is assumed to act at an arbitrary point in the half plane. The half plane with an edge crack is first mapped into a unit circle by a rational mapping function so that the following analysis can be carried out on the mapped plane analytically. Then the complex stress functions are derived by separating the whole problem into two parts; one is the principal part corresponding to the infinite plane acted on by concentrated forces or dislocations, the other is the holomorphic part, which can be determined by making use of the property of regularity of complex stress functions. The stress intensity factors of the crack can be calculated with different inclined angles of the crack, and the displacement and stress components at an arbitrary position in the half plane can be expressed explicitly.

A General Mechanics and Dynamics Model for Helical End Mills

The mechanics and dynamics of helical end milling processes are integrated to a general model. The chip removal geometry is evaluated by considering the true kinematics of the operation and chatter vibrations. The cutting forces are predicted by transforming shear angle, shear stress and friction angle stored in an orthogonal cutting data base to local oblique edge segments along the helical flutes. The general model allows prediction of cutting forces, vibrations, dimensional surface errors and chatter stability lobes for a class of helical end mills. The model is verified experimentally on cylindrical and ball end mills with complex helix geometry.

Weaker singular integral equation approach for an oblique edge crack problem of half-plane

Weaker singular integral equation approach for an oblique edge crack problem of half-plane

Effect of blade configuration, knife action, and intraocular pressure on keratotomy incision depth and shape.

For the same diamond blade extension, uphill (centripetal) radial keratotomy incision direction achieves greater depth and consequently greater refractive effect than downhill (centrifugal) incisions. To determine which factors may account for this difference, two uphill and two downhill incisions were made with a double-edged diamond blade set to 90% central pachometry in 26 human donor eyes at 15 or 60 mm Hg. Uphill incisions made with the perpendicular blade had greater mean incision depth than downhill incisions made with the oblique blade at 15 mm Hg (83.6 +/- 3.9% and 68.2 +/- 5.2%) (p < 0.0005) and at 60 mm Hg (86.3 +/- 3.1% and 79.7 +/- 1.7%) (p < 0.0005). Uphill and downhill incisions both made with the perpendicular blade had equal depth (85.4 +/- 4.9% and 83.7 +/- 3.5%) (p > 0.1). The perpendicular blade edge created a straight, and the oblique edge an S- or J-shaped, histological incision configuration. Corneal profile pictures taken during each incision showed the knife to tilt opposite of the incision direction and to move at a constant angle to the limbal plane, producing a smaller optical clear zone (OCZ) in the posterior stroma than intended with uphill incisions. Greater refractive effect with uphill incisions may be explained by the perpendicular blade being more effective in incising corneal lamellae, and the creation of a smaller posterior OCZ. Intraocular pressure variations during surgery may affect achieved incision depth of downhill, but not of uphill, incisions.

Numerical solutions of the singular integral equations in the crack analysis using the body force method

In this paper, numerical solutions of the singular integral equations of the body force method in the crack problems are discussed. The stress fields induced by ‘two kinds of displacement discontinuity’ are used as fundamental solutions. Then, the problem is formulated as a hypersingular integral equation with the singularity of the form r2. In the numerical calculation, two kinds of unknown functions are approximated by the products of the fundamental density function and the Chebyshev polynomials. As examples, the stress intensity factors of the oblique edge crack, kinked crack, branched crack and zig-zag crack are analyzed. The calculation shows that the present method gives accurate results even for the extremely oblique edge crack and kinked crack with extremely short bend which has been difficult to analyze by the previous method using the approximation by the products of the fundamental density function and the stepped functions etc.

Some variant forms of the Poggendorff illusion and their implications for an explanation

When with six widely different figures subjects adjusted one 45° oblique bar or edge so that it appeared to be collinear with another, large misalignment errors of about the same size occurred in all figures, including one figure that consisted of two bars only (Experiment 1). When the ends of these bars were angled at 45° to their axes and vertical in the figure, the errors were consistently greater than when the ends were square and oblique in the figure (Experiment 2). As well as calling into question some recent explanations of Poggendorff-type misalignment effects, these results suggest an alternative, more general explanation in terms of physical misalignment relative to a figure axis. This axis can be defined by elongated bars or lines, the ends of oblique bars, the direction of movement of the adjustable bar, or a combination of these.

Weight functions of oblique edge and center cracks in finite bodies

The finite element method for the determination of weight functions in a two-dimensional mixed mode cracked body with finite dimension is presented. The generalized form of the crack-face weight functions for modes I and II are successfully demonstrated by using the least squares fitting procedure. Explicit weight functions are presented for plates of finite width and length containing edge and central cracks. The stress intensity factors KI and KII can be obtained for any arbitrary loading from the weight functions. Comparison of the calculated results with some solutions by other workers from the literature confirms the efficiency and accuracy of the weight function method.

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.

Aberrant right subclavian artery: further observations.

One hundred one posteroanterior and 89 lateral chest radiographs were reviewed of patients with proven aberrant right subclavian artery. The patients were 17-96 years old. Three findings were noted on the posteroanterior radiograph: an oblique edge extending to the right from the aortic knob (60%); demonstration of the vessel through the lucency of the tracheal air column (43%) with sharp margins (29%) or as a tubular opacity without sharp margins (14%); and a "mass" effect at the medial right clavicular area (32%). Three findings were noted on the lateral radiograph: retrotracheal opacity (79%), aortic arch obscuration (62%), and posterior tracheal imprint (49%). Two of these findings (tubular opacity and mass effect) are reported as new observations in patients with aberrant right subclavian artery.