The Effect of Transverse Shear in a Cracked Plate Under Skew-Symmetric Loading

1979 ◽  
Vol 46 (3) ◽  
pp. 618-624 ◽  
Author(s):  
F. Delate ◽  
F. Erdogan
Keyword(s):  
Stress Intensity ◽  
Transverse Shear ◽  
Stress Intensity Factors ◽  
Orthotropic Materials ◽  
Shear Load ◽  
Intensity Factors ◽  
Mode Iii ◽  
Shear Loads ◽  
Elasticity Solutions ◽  
Symmetric Loading

The problem of an elastic plate containing a through crack and subjected to twisting moments or transverse shear loads is considered. By using a bending theory which allows the satisfaction of the boundary conditions on the crack surface regarding the normal and the twisting moments and the transverse shear load separately, it is found that the resulting asymptotic stress field around the crack tip becomes identical to that given by the elasticity solutions of the plane strain and antiplane shear problems. The problem is solved for uniformly distributed or concentrated twisting moment or transverse shear load and the normalized Mode II and Mode III stress-intensity factors are tabulated. The results also include the effect of the Poisson’s ratio and material orthotropy for specially orthotropic materials on the stress-intensity factors.

Singularities, interfaces and cracks in dissimilar anisotropic media

1990 ◽  
Vol 427 (1873) ◽  
pp. 331-358 ◽  
Keyword(s):  
Stress Intensity ◽  
Interface Crack ◽  
Stress Intensity Factors ◽  
Elastic Anisotropy ◽  
Homogeneous Medium ◽  
Interfacial Crack ◽  
Orthotropic Materials ◽  
Intensity Factors ◽  
Mode Iii ◽  
Crack Problems

For a non-pathological bimaterial in which an interface crack displays no oscillatory behaviour, it is observed that, apart possibly from the stress intensity factors, the structure of the near-tip field in each of the two blocks is independent of the elastic moduli of the other block. Collinear interface cracks are analysed under this non-oscillatory condition, and a simple rule is formulated that allows one to construct the complete solutions from mode III solutions in an isotropic, homogeneous medium. The general interfacial crack-tip field is found to consist of a two-dimensional oscillatory singularity and a one-dimensional square root singularity. A complex and a real stress intensity factors are proposed to scale the two singularities respectively. Owing to anisotropy, a peculiar fact is that the complex stress intensity factor scaling the oscillatory fields, however defined, does not recover the classical stress intensity factors as the bimaterial degenerates to be non-pathological. Collinear crack problems are also formulated in this context, and a strikingly simple mathematical structure is identified. Interactive solutions for singularity-interface and singularity interface-crack are obtained. The general results are specialized to decoupled antiplane and in-plane deformations. For this important case, it is found that if a material pair is non-pathological for one set of relative orientations of the interface and the two solids, it is non-pathological for any set of orientations. For bonded orthotropic materials, an intuitive choice of the principal measures of elastic anisotropy and dissimilarity is rationalized. A complex-variable representation is presented for a class of degenerate orthotropic materials. Throughout the paper, the equivalence of the Lekhnitskii and Stroh formalisms is emphasized. The article concludes with a formal statement of interfacial fracture mechanics for anisotropic solids.

Asymptotic Field Near the Tip of a Debonded Anticrack in an Anisotropic Elastic Material

2020 ◽  
Vol 73 (1) ◽  
pp. 76-83
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Stress Intensity ◽  
Elastic Material ◽  
Stress Intensity Factors ◽  
Orthotropic Materials ◽  
Intensity Factors ◽  
Power Type ◽  
Material Force ◽  
Real Power ◽  
Anisotropic Elastic ◽  
Anisotropic Elastic Material

Summary We use the sextic Stroh formalism to study the asymptotic elastic field near the tip of a debonded anticrack in a generally anisotropic elastic material under generalised plane strain deformations. The stresses near the tip of the debonded anticrack exhibit the oscillatory singularities $r^{-3/4\pm i\varepsilon }$ and $r^{-1/4\pm i\varepsilon }$ (where $\varepsilon $ is the oscillatory index) as well as the real power-type singularities $r^{-3/4}$ and $r^{-1/4}$. Two complex-valued stress intensity factors and two real-valued stress intensity factors are introduced to respectively scale the two oscillatory and two real power-type singularities. The corresponding three-dimensional analytic vector function is derived explicitly, and the material force on the debonded anticrack is obtained. Our solution is illustrated using an example involving orthotropic materials.

Mode III Stress Intensity Factors of Surface Crack in Round Bars

2011 ◽  
Vol 214 ◽  
pp. 192-196 ◽  
Author(s):  
Al Emran Ismail ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Mariyam Jameelah Ghazali ◽  
Ruslizam Daud
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Depth ◽  
Crack Tip ◽  
Bending Moment ◽  
Surface Cracks ◽  
Intensity Factors ◽  
Mode Iii ◽  
Element Analysis ◽  
Proposed Model

This study presents a numerical investigation on the stress intensity factors (SIF), K of surface cracks in round bars that were obtained under pure torsion loadings or mode III. ANSYS finite element analysis (FEA) was used to determine the SIFs along the crack front of surface cracks embedded in the solid circular bars. 20-node isoparametric singular elements were used around the crack tip by shifting the mid-side node ¼-position close to a crack tip. Different crack aspect ratio, a/b were used ranging between 0.0 to 1.2 and relative crack depth, a/D were ranged between 0.1 to 0.6. Mode I SIF, KI obtained under bending moment was used to validate the proposed model and it was assumed this proposed model validated for analyzing mode III problems. It was found that, the mode II SIF, FII and mode III SIF, FIII were dependent on the crack geometries and the sites of crack growth were also dependent on a/b and a/D.

Mode-III Stress Intensity Factors of an Arbitrarily Oriented Crack Crossing Interface in a Layered Structure

2013 ◽  
Vol 29 (4) ◽  
pp. 643-651 ◽  
Author(s):  
C. K. Chao ◽  
L. M. Lu
Keyword(s):  
Stress Intensity ◽  
Layered Structure ◽  
Stress Intensity Factors ◽  
Singular Integral Equations ◽  
Linear Interpolation ◽  
Plane Elasticity ◽  
Intensity Factors ◽  
Mode Iii ◽  
Line Segments ◽  
Arbitrarily Oriented Crack

ABSTRACTThe problem of a layered structure containing an arbitrarily oriented crack crossing the interface in anti-plane elasticity is considered in this paper. The fundamental solution of displacements and stresses is obtained in a series form via the method of analytical continuation in conjunction with the alternating technique. A dislocation distribution along the prospective site of a crack is used to model a crack crossing the interface and the singular integral equations with logarithmic singular kernels for a line crack are then established. The crack is approximated by several line segments and the linear interpolation equation with undetermined coefficients was applied for the dislocation function along line segments. Once the undetermined dislocation coefficients are solved, the mode-III stress intensity factors KIII at two crack tips can be obtained for various crack inclinations with different material property combinations. All the numerical results are checked to achieve a good approximation that demonstrates the accuracy and the efficiency of the proposed method.

Mode II and mode III stress singularities and intensities at a crack tip terminating on a transversely isotropic-orthotropic bimaterial interface

1994 ◽  
Vol 444 (1922) ◽  
pp. 447-460 ◽  
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Transversely Isotropic ◽  
Bimaterial Interface ◽  
Mode Ii ◽  
Stress Singularities ◽  
Intensity Factors ◽  
Mode Iii ◽  
Orthotropic Media

In a recent paper (referred to as I) we obtained inter alia , the stress and displacement fields at the tips of a transverse crack in an isotropic medium sandwiched between orthotropic media under in-plane loading (mode II). The crack was lying wholly within the isotropic medium so that the singularity at the crack tip was of the usual inverse square root type. In this paper, the analysis is extended to the case when the tip of the crack terminates on the transversely isotropic-orthotropic bimaterial interface and the nature of the singularity at the crack tip depends on the elastic properties of both media. The analysis is performed for both inplane (mode II) and out-of-plane (mode III) shear loading. General solutions are obtained for the crack tip stress singularities and corresponding stress intensity factors, together with the influence of the elastic properties and geometry of the media upon the stress field. These solutions are specialized to the limiting case when the crack terminates on the interface between dissimilar isotropic media in order to demonstrate consistency with published results. As in I, the solutions are used to investigate the influence of ply angle θ upon the stress singularities in [± θ /90°] s fibre-reinforced composite laminates. For this analysis, the outer angle-ply sublaminates are treated macroscopically as homogeneous orthotropic media whose elastic constants are obtained using the classical lamination approximation. Calculations are also carried out to study the variation of stress intensity factors with the ply angle and outer sublaminate thickness.

Three-Dimensional Mode Separation to Obtain Stress Intensity Factors

2006 ◽  
Author(s):  
Pei Gu ◽  
R. J. Asaro
Keyword(s):  
Stress Intensity ◽  
Crack Propagation ◽  
Stress Intensity Factors ◽  
Three Dimensional ◽  
Integral Approach ◽  
Mode I ◽  
Mode Ii ◽  
Intensity Factors ◽  
Mode Iii ◽  
Mode Separation

For mixed-mode loading at a crack tip under small-scale yielding condition, mode I, mode II and mode III stress intensity factors control the crack propagation. This paper discusses three-dimensional mode separation to obtain the three stress intensity factors using the interaction integral approach. The 2D interaction integral approach to obtain mode I and mode II stress intensity factors is derived to 3D arbitrary crack configuration for mode I, mode II and mode III stress intensity factors. The method is implemented in a finite element code using domain integral method and numerical examples show good convergence for the domains around the crack tip. A complete solution for the three stress intensity factors is obtained for a bar with inclined crack face to the cross-section from numerical calculations. The solution for the bar is plotted into curves in terms of a set of non-dimensional parameters for practical engineering purpose. From the solution, mode mixity along the crack front and its implication to the direction of crack propagation is discussed.

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