The Rapid Tearing of a Half Plane

1985 ◽  
Vol 52 (1) ◽  
pp. 51-56
Author(s):  
J. P. Dempsey ◽  
E. B. Smith
Keyword(s):  
Stress Intensity ◽  
Analytic Function ◽  
Conformal Mapping ◽  
Crack Propagation ◽  
Function Theory ◽  
Elastic Half Space ◽  
Intensity Factors ◽  
Crack Propagation Velocity ◽  
Crack Bifurcation ◽  
Mechanical Disturbances

The surface of an elastic half space is subjected to sudden antiplane mechanical disturbances. Crack initiation and subsequent crack instability are examined via two idealized problems; the first is concerned with instantaneous crack bifurcation and the second with instantaneous skew crack propagation. In either problem, crack propagation occurs at a constant subsonic velocity under an angle κπ with the normal to the surface. For the externally applied disturbances that are considered here, and for contstant crack-tip velocities, the particle velocity and τθz are functions of r/t and θ only, which allows Chaplygin’s transformation and conformal mapping to be used. The problems can then be solved using analytic function theory. For various values of the angle of crack propagation, the dependence of the elastodynamic stress intensity factors on the crack propagation velocity is investigated. For certain specific geometries, fully analytical solutions are derived to provide check cases.

The Calculation of Stress Intensity Factors and the Analysis of Propagation Characteristic of Crack at Hole

2011 ◽  
Vol 250-253 ◽  
pp. 1856-1861
Author(s):  
Li Jun Lu ◽  
Jian Ping Liu ◽  
Zhong Mei Li
Keyword(s):  
Stress Intensity ◽  
Crack Propagation ◽  
Stress Intensity Factors ◽  
Propagation Velocity ◽  
Propagation Characteristic ◽  
Propagation Model ◽  
Intensity Factors ◽  
Crack Propagation Velocity ◽  
Guyed Mast ◽  
Shape And Size

This paper focusing on the crack at hole of guyed-mast’s ear-plate connecting cables and shaft of guyed-mast, adopting two degree of freedom crack propagation model, track the crack propagation according to the increment of the deepest point and the surface point on the crack front of crack at hole of guyed-mast’s ear-plate. The stress intensity factors of I,II and III type crack with given shape and size have been calculated via finite element method, and a numerical method of calculating stress intensity factors with any shape and size crack has been proposed; furthermore according to modified I, II and III type compound crack propagation velocity formula on the basis of Paris crack propagation velocity formula, we analyzed the changing of crack shape parameter a/c with crack size parameter a/T of crack at hole of ear-plate connecting cable and shaft of guyed-mast by numerical integration method and obtained the propagation characteristic.

Two Analytical Solutions for Dynamic Crack Bifurcation in Antiplane Strain

1982 ◽  
Vol 49 (2) ◽  
pp. 366-370 ◽  
Author(s):  
P. Burgers ◽  
J. P. Dempsey
Keyword(s):  
Stress Intensity ◽  
Conformal Mapping ◽  
Crack Tip ◽  
Dynamic Crack ◽  
Antiplane Strain ◽  
Intensity Factors ◽  
Mode Iii ◽  
Constant Magnitude ◽  
Tip Velocity ◽  
Crack Bifurcation

A semi-infinite crack is subjected to constant magnitude, dynamic antiplane loading at time t = 0. At the same instant the crack is assumed to bifurcate and propagate normal to its original plane or to propagate without branching. For constant crack-tip velocities the stresses and particle velocity are functions of r/t and θ only, which allows Chaplygin’s transformaton and conformal mapping to be used to obtain two Riemann-Hilbert problems which can be solved analytically. Expressions for the elastodynamic Mode III stress-intensity factors are then computed as functions of the crack-tip velocity and some conclusions concerning crack initiation are drawn.

Elastodynamic Stress-Intensity Factors for Tearing of a Half Plane

1974 ◽  
Vol 41 (4) ◽  
pp. 1099-1105 ◽  
Author(s):  
J. D. Achenbach ◽  
V. K. Varatharajulu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Propagation ◽  
Propagation Velocity ◽  
Crack Propagation Velocity ◽  
Homogeneous Solutions ◽  
Static Solutions ◽  
Self Similar ◽  
Mechanical Disturbances

This paper is concerned with the propagation of a crack which emanates under an arbitrary angle from a free surface, when that surface is subjected to antiplane mechanical disturbances. The elastodynamic problem is solved by the method of homogeneous solutions, which is based on the observation that for the externally applied disturbances that are considered here the particle velocity is self-similar. The shear stress in the vicinity of the crack tip is determined, and a stress-intensity factor is computed. For various values of the crack propagation velocity the dependence of the stress-intensity factor on the angle of crack propagation is studied. As the velocity of crack propagation increases, the maximum value of the stress-intensity factor is still obtained for symmetrical crack propagation. The singularities at the corners of the wedge-shaped regions neighboring the propagating crack are also examined. It is shown that for small values of the crack propagation velocity, the elastodynamic results reduce to corresponding quasi-static solutions.

Stress intensity factors in novel specimens for crack propagation under loading conditions II+III in polymers

2020 ◽  
Author(s):  
Ondrej Slávik ◽  
Pavel Hutař ◽  
Michael Berer ◽  
Anja Gosch ◽  
Tomáš Vojtek ◽  
...  
Keyword(s):  
Stress Intensity ◽  
Crack Propagation ◽  
Stress Intensity Factors ◽  
Loading Conditions ◽  
Intensity Factors

Analysis of Crack Propagation in Roller Bearings Using the Boundary Integral Equation Method—A Mixed-Mode Loading Problem

1988 ◽  
Vol 110 (3) ◽  
pp. 408-413 ◽  
Author(s):  
L. J. Ghosn
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Crack Propagation ◽  
Boundary Integral Equation ◽  
Stress Intensity Factors ◽  
High Speed ◽  
Roller Bearing ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Intensity Factors

Crack propagation in a rotating inner raceway of a high-speed roller bearing is analyzed using the boundary integral method. The model consists of an edge plate under plane strain condition upon which varying Hertzian stress fields are superimposed. A multidomain boundary integral equation using quadratic elements was written to determine the stress intensity factors KI and KII at the crack tip for various roller positions. The multidomain formulation allows the two faces of the crack to be modeled in two different subregions making it possible to analyze crack closure when the roller is positioned on or close to the crack line. KI and KII stress intensity factors along any direction were computed. These calculations permit determination of crack growth direction along which the average KI times the alternating KI is maximum.

Crack Propagation in Rolling Line Contacts

1992 ◽  
Vol 114 (4) ◽  
pp. 690-697 ◽  
Author(s):  
H. Salehizadeh ◽  
N. Saka
Keyword(s):  
Stress Intensity ◽  
Crack Propagation ◽  
Stress Intensity Factors ◽  
Mode Ii ◽  
Pure Mode ◽  
Intensity Factors ◽  
Crack Face ◽  
Normal Loading ◽  
Line Contacts ◽  
Crack Growth Model

The stress intensity factors for short straight and branched subsurface cracks subjected to a Hertzian loading are calculated by the finite element method. The effect of crack face friction on stress intensity factors is considered for both straight and branched cracks. The calculations show that the straight crack is subjected to pure mode II loading, whereas the branched crack is subjected to both mode I and mode II, with ΔKI/ΔKII < 0.25. Although KI is small, it strongly influences KII by keeping the branched crack faces apart. Based on the ΔKII values and Paris’s crack growth model, the number of stress reversals required to grow a crack in a rolling component from an initial threshold length to the final spalling length was estimated. It was found that the crack propagation period is small compared with the expected bearing fatigue life. Therefore, crack propagation is not the rate controlling factor in the fatigue failure of bearings operating under normal loading levels.

Elastodynamic Stress-Intensity Factors for a Crack Near a Free Surface

1981 ◽  
Vol 48 (3) ◽  
pp. 539-542 ◽  
Author(s):  
J. D. Achenbach ◽  
R. J. Brind
Keyword(s):  
Stress Intensity ◽  
Half Space ◽  
Stress Intensity Factors ◽  
Elastic Half Space ◽  
Mode I ◽  
Dimensionless Frequency ◽  
Subsurface Crack ◽  
Intensity Factors ◽  
Time Harmonic ◽  
Crack Tips

Elastodynamic Mode I and Mode II stress-intensity factors are presented for a subsurface crack in an elastic half space. The plane of the crack is normal to the surface of the half space. The half space is subjected to normal and tangential time-harmonic surface tractions. Numerical results show the variation of KI and KII at both crack tips, with the dimensionless frequency and the ratio a/b, where a and b are the distances to the surface from the near and the far crack tips, respectively. The results are compared with corresponding results for a crack in an unbounded solid.

On the Influence of the Corner Singularity on Kinking Mixed-Mode Crack Propagation

2007 ◽  
Vol 348-349 ◽  
pp. 585-588
Author(s):  
Henning Schütte ◽  
Kianoush Molla-Abbasi
Keyword(s):  
Stress Intensity ◽  
Crack Propagation ◽  
Crack Growth ◽  
Stress Intensity Factors ◽  
Mixed Mode ◽  
Small Scale ◽  
Intensity Factors ◽  
Plastic Energy ◽  
Mixed Mode Crack ◽  
The Impact

The aim of the presentation is to highlight the influence of the kink, developing at the beginning of mixed-mode crack growth, on the propagation behavior of the crack. Le et al. [1] have shown that the variational principle of a body containing a crack results in the principle of maximum energy release rate incorporating the stress intensity factors of the kinked crack. Here the influence of the kink and the kinking angle, resulting in a singular field around the corner, on the crack growth is analyzed. The generalized stress intensity factors at the kinks corner are computed with the help of a FEM strategy. The influence of these on the T-stresses and the plastic energy dissipated at the kink is determined using a small scale yielding approach. The impact of these results on mixed-mode crack propagation is discussed.

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