Crack front elastic stress state for three-dimensional crack problems

1984 ◽  
Vol 25 (2) ◽  
pp. 121-131 ◽  
Author(s):  
D. N. Fenner ◽  
M. J. Abdul Mihsein
Keyword(s):  
Stress State ◽  
Crack Front ◽  
Elastic Stress ◽  
Three Dimensional ◽  
Crack Problems

Three-Dimensional Finite Element Analysis of Elastic-Plastic Crack Problems

1981 ◽  
Vol 103 (3) ◽  
pp. 214-218 ◽  
Author(s):  
B. V. Kiefer ◽  
P. D. Hilton
Keyword(s):  
Finite Element ◽  
Normal Stress ◽  
Crack Front ◽  
Stress Component ◽  
Three Dimensional ◽  
Specimen Thickness ◽  
Element Analysis ◽  
Finite Element Program ◽  
Elastic Plastic ◽  
Crack Problems

A three-dimensional, elastic-plastic finite element program is developed and applied to analyze the stress field in a plate containing a through crack. The center cracked plate is subjected to uniform tensile loading which results in mode I opening of the crack surfaces. Transverse variations of the opening tensile stress component and of the effective stress (von Mises) in the vicinity of the crack front are presented. They clearly demonstrate the three-dimensional nature of this problem with distributions that depend on specimen thickness. For thinner plates, the plastic deformation concentrates near the plate surfaces while the normal stress is largest in the plate interior. In thicker plates the deformation and normal stress fields are more uniform in the plate interior near the crack front, but they develop a rapid boundary layer-type variation in the vicinity of the plate surfaces.

scholarly journals An Analysis of Crack Trapping by Residual Stresses in Brittle Solids

1993 ◽  
Vol 60 (1) ◽  
pp. 175-182 ◽  
Author(s):  
A. F. Bower ◽  
M. Ortiz
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Crack Front ◽  
Three Dimensional ◽  
Crack Plane ◽  
Three Dimensional Model ◽  
Brittle Solids ◽  
Crack Problems ◽  
Monolithic Ceramics ◽  
Toughness Enhancement

The residual stress distribution in a brittle polycrystalline solid may have a significant influence on its toughness. Grains in a state of residual compression are less likely to be fractured by a growing crack and may trap the crack front or be left behind as bridging particles (Evans et al., 1977). This paper estimates the toughness enhancement due to intergranular residual stresses, using a three-dimensional model. The residual stress is approximated as a doubly sinusoidal distribution acting perpendicular to the plane of an initially straight semi-infinite crack. An incremental perturbation method developed by Bower and Ortiz (1990) for solving three-dimensional crack problems is extended here to cracks loaded by nonuniform remote stresses. It is used to calculate the shape of the semi-infinite crack as it propagates through the doubly sinusoidal residual stress. It is shown that the local regions of compression may trap the crack front and give rise to some transient toughening. In addition, if the residual stress exceeds a critical magnitude, pinning particles may be left in the crack wake. However, for practical values of residual stress and grain size, the predicted toughness enhancement is insignificant. Furthermore, the analysis cannot account for the large bridging zones observed in experiments. It is concluded that the R-curve behavior and bridging particles observed in monolithic ceramics are caused by mechanisms other than residual stresses acting perpendicular to the crack plane.

First-Order Variation in Elastic Fields Due to Variation in Location of a Planar Crack Front

1985 ◽  
Vol 52 (3) ◽  
pp. 571-579 ◽  
Author(s):  
J. R. Rice
Keyword(s):  
Weight Function ◽  
Half Plane ◽  
Crack Front ◽  
Function Theory ◽  
Three Dimensional ◽  
Plane Crack ◽  
Elastic Fields ◽  
First Order ◽  
Crack Problems ◽  
Order Variation

The problem explained in the title is formulated generally and given an explicit solution for tensile loadings opening a half-plane crack in an infinite body. For the half-plane crack, changes in the opening displacement between the crack surfaces and in the stress-intensity factor distribution along the crack front are calculated to first order in an arbitrary deviation of the crack-front position from a reference straight line. The deviations considered lie in the original crack plane. The results suggest that in the presence of loadings that would induce uniform conditions along the crack front, if it were straignt, small initial deviations from straightness should reduce in size during quasistatic crack growth if of small enough spatial wavelength but possibly enlarge in size if of longer wavelength. The solution methods rely on elastic reciprocity, in terms of a three-dimensional version of weight function theory for tensile cracks, and on direct solution of elastic crack problems. The weight function is derived for the half-plane crack by solving for the first-order variation in the elastic displacement field associated with arbitrary variations of the crack front from a straight reference line. Also, a new three-dimensional weight function theory is developed for planar cracks under general mixed-mode loading involving tension and shears relative to the crack, the connection between weight functions and the Green’s function for crack problems is shown, and some results are given for the half-plane crack on the variations of elastic fields for variation of crack-front location in the presence of general loadings including shear.

The Enriched Element for Finite Element Analysis of Three-Dimensional Elastic Crack Problems

1980 ◽  
Vol 102 (4) ◽  
pp. 347-352 ◽  
Author(s):  
P. D. Hilton ◽  
B. V. Kiefer
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Stress Intensity ◽  
Crack Front ◽  
Three Dimensional ◽  
Crack Edge ◽  
Element Analysis ◽  
Front Solution ◽  
Penny Shaped Crack ◽  
Crack Problems

An improved procedure for enriching three-dimensional isoparametric elements with the asymptotic crack front solution is described. Results from finite element calculations, involving these enriched elements, for the three-dimensional problems of a straight crack in plane strain and an axisymmetric penny-shaped crack which demonstrate the high degree of accuracy attainable are presented. Some finite-element solutions for through-crack and surface flaw problems are then reported showing the influence of a free surface on the variation of the stress intensity along the crack edge. Special treatments of the crack front-free surface stress intensity are implemented and the results discussed.

Shape and energies of a dynamically propagating crack under bending

2003 ◽  
Vol 18 (10) ◽  
pp. 2379-2386 ◽  
Author(s):  
Dov Sherman ◽  
Ilan Be'ery
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Front ◽  
Three Dimensional ◽  
Strain Energy Release ◽  
Governing Parameter ◽  
Propagating Crack ◽  
Front Shape

We report on the exact shape of a propagating crack in a plate with a high width/thickness ratio and subjected to bending deformation. Fracture tests were carried out with brittle solids—single crystal, polycrystalline, and amorphous. The shape of the propagating crack was determined from direct temporal crack length measurements and from the surface perturbations generated during rapid crack propagation. The shape of the crack profile was shown to be quarter-elliptical with a straight, long tail; the governing parameter of the ellipse axes is the specimen's thickness at most length of crack propagation. Universality of the crack front shape is demonstrated. The continuum mechanics approach applicable to two-dimensional problems was used in this three-dimensional problem to calculate the quasistatic strain energy release rate of the propagating crack using the formulations of the dynamic energy release rate along the crack loci. Knowledge of the crack front shape in the current geometry and loading configuration is important for practical and scientific aspects.

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