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.

Mixed Mode Stress Singularities in Anisotropic Composites

1999 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Stress Intensity ◽  
Asymptotic Solution ◽  
Stress Intensity Factors ◽  
Stress Singularity ◽  
Free Edge ◽  
Complex Conjugate ◽  
Circular Path ◽  
Intensity Factors ◽  
Element Analysis ◽  
Anisotropic Elastic

Abstract Multi-material wedges composed of fully anisotropic elastic sectors generally show intrinsic coupling of the anti-plane and in-plane modes of deformation. Each anisotropic sector has three complex conjugate pairs of material eigensolutions whose form of expression depends on five distinct types of anisotropic materials. Continuity of the displacements and the tractions across the sector interfaces and the traction-free conditions on two exterior boundary edges determine an infinite sequence of eigenvalues and eigensolutions of the multi-material wedge. These eigensolutions are linearly combined to match the traction-boundary data (generated by global finite element analysis of the structure) on a circular path encircling the singularity. The analysis method is applied to a bimaterial wedge near the free edge of a four-layer angle-ply laminate, and to a trimaterial wedge surrounding the tip of an embedded oblique crack in a three-layer composite. Under a uniform temperature load, the elasticity solution based on the eigenseries yields interfacial stresses that are significantly different from the asymptotic solution (given by the first term of the eigenseries), even as the distance from the singularity decreases to subatomic scales. Similar observations have been found previously for isotropic and orthotropic multi-material wedges. This raises serious questions with regard to characterizing the criticality of stress singularity exclusively in terms of the asymptotic solution and the associated stress intensity factors or generalized stress intensity factors.

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.

Mixed-Mode Stress Intensity Factors in a Homogeneous Orthotropic Medium Loaded by a Frictional Sliding Rigid Flat Stamp

2018 ◽  
Vol 774 ◽  
pp. 179-184 ◽  
Author(s):  
K.B. Yilmaz ◽  
Mehmet Ali Güler ◽  
Boray Yildirim
Keyword(s):  
Stress Intensity ◽  
Half Plane ◽  
Stress Intensity Factors ◽  
Mixed Mode ◽  
Orthotropic Materials ◽  
Geometrical Parameters ◽  
Orthotropic Medium ◽  
Intensity Factors ◽  
Flat Punch ◽  
Mode Stress

In this study, the crack problem for a homogeneous orthotropic medium loaded by a sliding rigid flat punch is considered. The homogeneous orthotropic medium is assumed to be a half-plane and is subjected to both normal and tangential forces through the sliding action of the punch. The crack on the homogeneous orthotropic medium is supposed to a depth of and is parallel to the direction of the normal force. The effect of the geometrical parameters and coefficient of friction on the mixed-mode stress intensity factors (mode I and mode II) is investigated using a computational approach using the finite element method. Augmented Lagrange method is used for the contact algorithm between the rigid flat punch and homogeneous orthotropic half-plane. This study may provide insight to the engineers in understanding the crack mechanisms in orthotropic materials in a comprehensive way and to identify early crack propagations under frictional loadings accurately.

Transient Stress Intensity Factors of an Interfacial Crack Between Two Dissimilar Anisotropic Half-Spaces, Part 1: Orthotropic Materials

1984 ◽  
Vol 51 (1) ◽  
pp. 71-76 ◽  
Author(s):  
A.-Y. Kuo
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Jacobi Polynomials ◽  
Interfacial Crack ◽  
Orthotropic Materials ◽  
Intensity Factors ◽  
Orthotropic Solids

Transient response of an interfacial crack between two dissimilar elastic, orthotropic solids is investigated. The interfacial crack is excited by tractions suddenly applied on the crack surfaces. Governing equations, boundary conditions, and continuity conditions along the interface are reduced to a singular integral equation. Solution of the singular integral equation is obtained by the use of Jacobi polynomials. Expressions for stress intensity factors at the crack tip are given. As a sample problem, an interfacial crack in a 0 deg/90 deg fiber-reinforced composite solid excited by a suddenly applied uniform pressure on the crack surfaces is studied.

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