Stress Intensity Factor of an Edge Crack in Composite Media (original) (raw)

2011, International Journal of Fracture

The problem of an edge crack under normal point loading terminating perpendicular to the surface of an orthotropic strip of finite thickness bonded to another orthotropic finite strip is considered. Expressing the displacements and stresses in plane strain condition in terms of harmonic functions, the problem is reduced to a pair of integral equations solved by the Hilbert transform technique. The analytical expression of stress intensity factor (SIF) at the crack tip for large thickness of the strips is calculated, which corresponds to the weight function of a crack under normal point loading. The effects of elastic constants, different locations of normal point loading on the crack surface and length of the crack in the composite material are analyzed numerically.

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Symmetric Edge Cracks in an Orthotropic Strip Under Normal Loading

International Journal of Fracture, 2008

The problem of two edge cracks of finite length, situated symmetrically in an orthotropic infinite strip of finite thickness h 2 , under normal point loading has been discussed. The displacements and stresses in plane strain conditions are expressed in terms of two harmonic functions. The problem is addressed by seeking the solution of a pair of simultaneous integral equations with Cauchy type singularities solved by finite Hilbert Transform technique. For large h , analytical expression for the stress intensity factor at the crack tip is obtained.

Thermal stress intensity factor for an edge crack in orthotropic composite media

Composites Part B: Engineering, 2018

The purpose of this article is to determine the thermal stress intensity factor (SIF) of an edge crack situated in an orthotropic strip of finite thickness h bonded to an orthotropic half plane, under thermal and mechanical loadings. The problem is reduced to a singular integral equation of the first kind. The integral equation is converted to a pair of the singular integral equations using asymptotic expansion method. The analytical expression of the stress intensity factor at the edge crack tip is found for concentrated point loading. The numerical values of SIF are computed for different point loading for various crack lengths and different ratios of thermal conductivities for different particular cases when the composite orthotropic material is the mixture of Steel-Myler and E-Glass epoxy. The significant feature of the article is the pictorial presentations of the variations of SIF due to the effect of ratios of thermal conductivities of both the materials.

Study of Semi-Infinite Crack in a Sandwiched Orthotropic Strip

Journal of Mechanics, 2020

ABSTRACTThe problem of semi-infinite crack situated in an orthotropic strip sandwiched between two identical half planes has been considered. The considered boundary value problem has been solved to convert it into the standard Wiener-Hopf equation by using Fourier transform technique, which has been solved to obtain analytical expressions for stress intensity factor and crack opening displacement. The variations of stress intensity factors and crack opening displacement are displayed graphically for different pair of orthortropic materials and for various depth of the strip of the composite media.

Influence of Initial Stresses on Stress Intensity Factors at Crack Tips in a Composite Strip

2004

The influence of initial tension or compression along cracks on the stress intensity factor (SIF) at crack tips under the action of additional normal forces on crack edges is studied for infinite bodies. A strip made of a composite material is considered. The strip ends are simply supported, and the strip contains a crack whose edges are parallel to its face planes. The strip is first stretched or compressed along crack edges, and then additional uniformly distributed normal forces are applied to the crack edges. The influence of the initial tension (compression) on the SIF caused by the additional normal forces is studied. The corresponding boundary-value problems are modelled with the use of the three-dimensional linearized theory of elasticity. All the investigations are carried out numerically by employing the finite-element method. The values of SIF are calculated by the energy release method.

Dynamic stress intensity factors of an interfacial crack in orthotropic elastic strips under impact loading conditions

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2018

The present article deals with the investigation of elasto-dynamic response of a finite crack under normal and shear impact loading situated at the interface of two semiinfinite orthotropic strips. Laplace and Fourier Integral transforms are employed to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane which are solved using iterations in the low frequency domain. The analytical expressions of stress intensity factors of the crack at the interface problem are found. To determine time dependence of the parameters, these equations are inverted to yield the dynamic stress intensity factors for some fiber-reinforced orthotropic composite materials using Bellman method and the method given by H. Dubner and J. Abate. The results are depicted through graphs for different particular cases.

Elastostatic analysis of edge cracked orthotropic strips

Acta Mechanica, 2003

The elastostatic problem of an edge cracked orthotropic strip is considered. The crack possesses a semi-infinite length. The crack surfaces are subjected to opening mode I fracture, by a concentrated force action, while the strip surfaces are traction free. Fourier transforms and asymptotic analyses are employed to reduce the problem to a first kind singular integral equation. The stress intensity factor is determined in a closed form expression. The effects of geometric and elastic characteristics of the strip on the values of the stress intensity factor are explained.

Effect of Thermomechanical Loading on an Edge Crack of Finite Length in an Infinite Orthotropic Strip

Mechanics of Composite Materials, 2019

The purpose of this article is to determine the effect of thermal loadings on the stress intensity factor of an edge crack of finite length in an orthotropic infinite strip of finite thickness under mechanical loading. Analytical expressions of the stress intensity factor at the crack tip in point and arbitrary constant loadings are found. Numerical values of the factor at any arbitrary location on the crack face due to mechanical loading and effects of thermal loadings are computed for various crack lengths in an orthotropic material composite, and the results are presented in the form of graphs. The effects of thermal conductivity parameters on the stress intensity factor for different particular cases are also shown graphically.

Stress intensity factors and weight functions for a corner crack in a finite thickness plate

Engineering Fracture Mechanics

The failure of cracked components is governed by the stresses in the vicinity of the crack tip. The singular stress contribution is characterised by the stress intensity factor K. Stress intensity factors depend on the geometry of the component and on the special loading conditions (tension, bending, thermal stresses,...). A procedure for their determination is the weight function technique where the weight functions are only dependent on the crack geometry. Stress intensity factors and weight functions are reported for many practical problems in handbooks. In this report new solutions for stress intensity factors and weight functions are compiled in form of tables or approximate relations.

Dynamic stress intensity factors around two parallel cracks in an infinite-orthotropic plane subjected to incident harmonic stress waves

International Journal of Solids and Structures, 1997

The time-harmonic problem of determining stresses around two parallel cracks in an infinite orthotropic plane is studied. Incident stress waves impinge on the two cracks normal to their surfaces. The Fourier transform technique is used to reduce the boundary conditions to four simultaneous integral equations which are then solved by expanding the differences in the crack surface displacements in a series. The unknown coefficients in the series are calculated using the Schmidt method. Numerical calculations are carried out for the dynamic stress intensity factors in a boron-epoxy composite material, a carbon fiber reinforced plastic, a modulite II graphite-epoxy composite and an isotropic material.

The Influence of the Initial Stresses on Stress Intensity Factor of Mode II at the Crack Tips in a Composite Strip

The influence of the initial finite stretching or compressing of the strip containing a single crack on the Energy Release Rate (ERR) and on the SIF of mode II at the crack tips is studied by the use of the Three-Dimensional Linearized Theory of Elasticity. In the present paper these investigations are developed for a strip made from composite material. It is assumed that the ends of the strip are simply supported and this strip contains a crack whose edges are parallel to the face planes. It is supposed that the strip is stretched or compressed along the crack edges and after this stretching (compressing) the edges of the crack are loaded by additional uniformly distributed tangential (sliding) forces. Corresponding Boundary Value Problems were formulated with the use of the Three- Dimensional Linearized Theory of Elasticity. All investigations are carried out numerically by employing the FEM. The numerical results on the influence of the initial stresses on the values of the ERR a...

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