Lateral constraint at an open crack tip

1980 ◽  
Vol 16 (4) ◽  
pp. R199-R205
Author(s):  
L. P. Harrop
Keyword(s):  
Crack Tip ◽  
Open Crack ◽  
Lateral Constraint

scholarly journals Scattering on a square lattice from a crack with a damage zone

2020 ◽  
Vol 476 (2235) ◽  
pp. 20190686 ◽  
Author(s):  
Basant Lal Sharma ◽  
Gennady Mishuris
Keyword(s):  
Asymptotic Approximation ◽  
Damage Zone ◽  
Crack Tip ◽  
Square Lattice ◽  
Open Crack ◽  
Matrix Kernel ◽  
Link Type ◽  
Damaged Zone ◽  
Sharp Crack ◽  
Appl Math

A semi-infinite crack in an infinite square lattice is subjected to a wave coming from infinity, thereby leading to its scattering by the crack surfaces. A partially damaged zone ahead of the crack tip is modelled by an arbitrarily distributed stiffness of the damaged links. While an open crack, with an atomically sharp crack tip, in the lattice has been solved in closed form with the help of the scalar Wiener–Hopf formulation (Sharma 2015 SIAM J. Appl. Math. , 75 , 1171–1192 ( doi:10.1137/140985093 ); Sharma 2015 SIAM J. Appl. Math. 75 , 1915–1940. ( doi:10.1137/15M1010646 )), the problem considered here becomes very intricate depending on the nature of the damaged links. For instance, in the case of a partially bridged finite zone it involves a 2 × 2 matrix kernel of formidable class. But using an original technique, the problem, including the general case of arbitrarily damaged links, is reduced to a scalar one with the exception that it involves solving an auxiliary linear system of N  ×  N equations, where N defines the length of the damage zone. The proposed method does allow, effectively, the construction of an exact solution. Numerical examples and the asymptotic approximation of the scattered field far away from the crack tip are also presented.

scholarly journals On stationary and moving interface cracks with frictionless contact in anisotropic bimaterials

1993 ◽  
Vol 443 (1919) ◽  
pp. 563-572
Keyword(s):  
Crack Problem ◽  
Stress Singularity ◽  
Crack Tip ◽  
Substantial Part ◽  
Open Crack ◽  
Interface Cracks ◽  
Complete Representation ◽  
Crack Tip Fields ◽  
Out Of Plane ◽  
Anisotropic Bimaterials

The asymptotic structure of near-tip fields around stationary and steadily growing interface cracks, with frictionless crack surface contact, and in anisotropic bimaterials, is analysed with the method of analytic continuation, and a complete representation of the asymptotic fields is obtained in terms of arbitrary entire functions. It is shown that when the symmetry, if any, and orientation of the anisotropic bimaterial is such that the in-plane and out-of-plane deformations can be separated from each other, the in-plane crack-tip fields will have a non-oscillatory, inverse-squared-root type stress singularity, with angular variations clearly resembling those for a classical mode II problem when the bimaterial is orthotropic. However, when the two types of deformations are not separable, it is found that an oscillatory singularity different than that of the counterpart open-crack problem may exist at the crack tip for the now coupled in-plane and out-of-plane deformation. In general, a substantial part of the non-singular higher-order terms of the crack-tip fields will have forms that are identical to those for the counterpart open-crack problem, which give rise to fully continuous displacement components and zero tractions along the crack surfaces as well as the material interface.

Effects of Local Energy Loss on the Dynamic Response of a Cylindrical Bar With a Penny Shape Crack

2002 ◽  
Author(s):  
A. Vaziri ◽  
H. Nayeb-Hashemi
Keyword(s):  
Dynamic Response ◽  
Energy Loss ◽  
Crack Opening ◽  
Crack Tip ◽  
Strain Energy Release ◽  
Open Crack ◽  
Local Energy ◽  
Opening Displacement ◽  
Resonant Frequencies ◽  
Penny Shape Crack

The effects of a penny shape in a cylindrical bar on its axial dynamic response are obtained, considering the local energy loss at the crack tip. The crack is taken to be normal to the bar axis and the bar is subjected to a harmonic axial load. The bar material is assumed to be viscoelastic perfectly plastic. The penny shape crack is assumed an open crack, for simplicity of calculations. The local flexibility is calculated by using the strain energy release rate. The local damping due to the crack presence is related to the plastic zone and the crack opening displacement. The results show that the bar material damping does not affect the lower resonant frequencies significantly, however, it decreases the amplitude of response. It is observed that for the range of crack length studied here, the system resonant frequencies and the system amplitude are little affected by considering the local energy loss at the crack tip. Furthermore, the results show that that the system resonant frequencies are not sensitive to the presence of a small penny shape crack. However, with increasing radius of the penny shape crack, resonant frequencies of the system decrease drastically. The results also indicate that the resonant frequencies are more sensitive to the crack location than its size.

Simulation and Contrast Analysis of tem Images of Cracks

1990 ◽  
Vol 48 (1) ◽  
pp. 578-579
Author(s):  
D. Goyal ◽  
A. H. King
Keyword(s):  
Displacement Vector ◽  
Crack Tip ◽  
Perfect Crystal ◽  
Operating Conditions ◽  
Displacement Fields ◽  
Fringe Contrast ◽  
Orthogonal Geometry ◽  
Moire Fringe ◽  
Moiré Fringe

TEM images of cracks have been found to give rise to a moiré fringe type of contrast. It is apparent that the moire fringe contrast is observed because of the presence of a fault in a perfect crystal, and is characteristic of the fault geometry and the diffracting conditions in the TEM. Various studies have reported that the moire fringe contrast observed due to the presence of a crack in an otherwise perfect crystal is distinctive of the mode of crack. This paper describes a technique to study the geometry and mode of the cracks by comparing the images they produce in the TEM because of the effect that their displacement fields have on the diffraction of electrons by the crystal (containing a crack) with the corresponding theoretical images. In order to formulate a means of matching experimental images with theoretical ones, displacement fields of dislocations present (if any) in the vicinity of the crack are not considered, only the effect of the displacement field of the crack is considered.The theoretical images are obtained using a computer program based on the two beam approximation of the dynamical theory of diffraction contrast for an imperfect crystal. The procedures for the determination of the various parameters involved in these computations have been well documented. There are three basic modes of crack. Preliminary studies were carried out considering the simplest form of crack geometries, i. e., mode I, II, III and the mixed modes, with orthogonal crack geometries. It was found that the contrast obtained from each mode is very distinct. The effect of variation of operating conditions such as diffracting vector (), the deviation parameter (ω), the electron beam direction () and the displacement vector were studied. It has been found that any small change in the above parameters can result in a drastic change in the contrast. The most important parameter for the matching of the theoretical and the experimental images was found to be the determination of the geometry of the crack under consideration. In order to be able to simulate the crack image shown in Figure 1, the crack geometry was modified from a orthogonal geometry to one with a crack tip inclined to the original crack front. The variation in the crack tip direction resulted in the variation of the displacement vector also. Figure 1 is a cross-sectional micrograph of a silicon wafer with a chromium film on top, showing a crack in the silicon.

A new type of cracks adding to Griffith–Irwin cracks

2019 ◽  
Vol 485 (2) ◽  
pp. 162-165
Author(s):  
V. A. Babeshko ◽  
O. M. Babeshko ◽  
O. V. Evdokimova
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Tip ◽  
Stress Concentrations ◽  
New Type

The distinctions in the description of the conditions of cracking of materials are revealed. For Griffith–Irwin cracks, fracture is determined by the magnitude of the stress-intensity factor at the crack tip; in the case of the new type of cracks, fracture occurs due to an increase in the stress concentrations up to singular concentrations.

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