Antiplane shear analysis of a semi-infinite multi-layered monoclinic strip

Summary Elasticity solutions for a semi-infinite multi-layered monoclinic strip subject to antiplane shear deformation are presented. The solutions are obtained by the method of eigenfunction expansion in conjunction with Betti's reciprocity theorem. In particular, a compact closed-form solution for a two-layered strip loaded by a uniform shear stress at the end is obtained. The solution for the two-layered strip shows that at the interface the traction possesses a logarithmic singularity at the loaded end.     

Free end effect on the stress and displacement distributions in a cracked composite strip

Taking into account the marked anisotropic character of carbon fibre composite materials, a small parameter related to material properties is introduced. The stress field in a semi-infinite strip with a semi-infinite crack whose tip is close to the strip free end is investigated through a singular perturbation method. For slow crack propagation, the quasi-static character of the stress field is established. An accurate asymptotic solution is derived, which allows the interaction between the strip free end and the stress field around the crack tip to be studied. For the carbon–epoxy material investigated, this interaction becomes negligible when the distance between the crack tip and the strip free end is greater than 1.5h, where h is the strip half-height.     

Antiplane permeable edge cracks in a piezoelectric strip of finite width

A priezoelectric strip with permeable edge cracks normal to the strip boundaries is analyzed. Under uniform antiplane mechanical shear and inplane electric loading, the distribution of the entire electroelastic field in a cracked piezoelectric strip is determined in explicit analytic form via the conformal mapping technique. It is found that the strain and the electric displacement exhibit the same singularity as the stress near the crack tips, while the electric field is always uniform. The field intensity factors and the energy release rate are independent of the applied electric load for prescribed stress, and related to the applied electric load for prescribed strain.     

Asymptotic stress field in a cracked orthotropic strip

Christensen's theory of viscoelastic fracture allows the crack propagation velocity to be determined in terms of dissipation whose calculation requires the knowledge of the stress field in the vicinity of the crack tip: the simplest configuration leading to a constant velocity is that of a straight semi-infinite crack contained in an infinitely long strip whose clamped edges are displaced normal to the crack; although experimental data pertaining to this problem have been obtained for a number of materials, no analytical solution is available. When the material is highly anisotropic, an asymptotic solution involving a small parameter related to the ratio of shear modulus to the larger Young's modulus can be attempted. As the corresponding perturbation problem is singular, a matched asymptotic expansion has to be used: it is the sum of outer and inner approximations; both of these are solutions to simple boundary-value problems which can be solved in closed form. The so-constructed asymptotic solution is shown to agree with finite element results, even when the small parameter is as large as 0.2.     

A cracked elastic strip bonded to a rigid support

The elastostatic plane problem of an infinite strip containing a transverse crack is considered. It is assumed that one side of the strip is perfectly bonded to a rigid support whereas the other side is free of traction. The problem is formulated in terms of a singular integral equation. Internal crack, edge crack, crack terminating at the rigid support, and completely broken strip cases are considered in some detail. The singular integral equation is solved numerically by employing collocation schemes developed by Erdogan, Gupta and Cook. The stress intensity factor, which may be regarded as the most important fracture parameter, and the crack surface displacement are calculated for various crack geometries and given in graphical form.

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Résumé On considère le problème élastostatique et plan d'un feuillard infini comportant une fissure transversale. On suppose qu'un côté de la bande est parfaitement fixé à un support rigide tandis que l'autre côté est libre de contrainte. On formule le problème sous forme d'une équation intégrale singulière. On considère avec quelques détails la fissure interne, la fissure de coin, la fissure se terminant au support rigide et le cas de la bande complètement rompue. L'équation intégrale singulière est résolue numériquement en utilisant les schémas de collocation développés par Erdogan, Gupta et Cook. Le facteur d'intensité de contrainte qui peut être considéré comme le paramètre le plus important de rupture et le déplacement de surface de la fissure sont calculés pour diverses géométries de fissure; ils sont fournis sous une forme graphique.

     

Analytical beam theory for the in-plane deformation of a composite strip with in-plane curvature

The variational-asymptotic-method (VAM) provides a mathematically rigorous way to reduce a three-dimensional elasticity formulation to a one-dimensional beam theory without ad hoc assumptions. In this work, the VAM is employed to develop a beam theory to analyze the in-plane deformation of a laminated strip-beam with initial in-plane curvature. The cross-sectional stiffness constants and recovery relations for stress and strain are presented as analytical expressions. For the case of zero initial curvature, consistency of the expressions with those of plate theory is demonstrated. For strip-beams with initial curvature in the in-plane direction, results obtained show explicit dependence on the curvature. Results are verified by comparison with those obtained from VABS, the accuracy and consistency of which with three-dimensional finite elements has been reported in several published works. In addition to the internal consistency check this work provides and its utility in helping to validate VABS (which is based on the principles of VAM), it is hoped that the results obtained herein, since they are all analytical expressions, will help researchers and engineers validate the effect of initial curvature in their beam theories, whether existing or new.     

Single-edge cracked strip under three-point load

The problem of a strip of an elastic solid having a crack of unit length normal to one edge and subjected to a bending moment resulting from three-point loading is solved using integral transform method. The stress intensity factor is calculated for many values of the width of the strip.     

A finite strip analysis of cracked laminates

As a step towards the construction of a comprehensive model for damaged composites, the deformation of transversely cracked laminates is analysed. The approach is based on a generalised plane strain approach and uses the finite strip method which allows general lay-ups of laminates rather than just cross-ply to be considered. General loading is treated. In addition, the method permits a more flexible control to be exercised between accuracy and the extensiveness of the calculations than can be achieved using existing analyses. This method could be integrated with the finite element analysis of structures to allow for changes in the effective material properties of locally damaged regions. Results produced by the approach are compared with those available in the literature and good agreement is demonstrated.     

Thermal shock of a cracked strip: Effect of temperature-dependent material properties

The problem of a strip containing an edge crack and an interior crack subjected to a thermal shock on one edge and insulated on the other is solved in order to analyze the difference between using temperature-dependent material properties and constant ones. For this purpose two brittle materials, ceramics and glass, are each subjected to a thermal shock. The results show that in general, using constant material properties over large temperature ranges can lead to considerable underestimation of the maximum stress intensity factors. The difference in the results is dependent on the variation of the thermal diffusivity and the thermal expansion coefficient with temperature for a given material. Also, this difference varies for different crack lengths and different thermal shock conditions at the boundary.     

Torsional deformation behavior of cracked gold nano-wires

The presence of in-homogeneity or defects in materials cannot be ignored. There is great need to understand the influence of defects on the mechanical response of nano-materials. In this study, atomistic simulations have been used to investigate the mechanical response of gold nano-wires under twisting. Simulations show that nano-wires have different elastic properties when defects are present. Embedded cracks of different sizes have been created in nano-wires to quantify in-homogeneity. The inter-atomic interactions are represented by employing an embedded-atom potential. The effect of different sizes of crack on potential energy, torque and stresses for investigating the mechanical response of a nano-wire is part of the whole investigation. It is predicted from our simulation that the presence of a crack and dimensions of the crack control the torsional response of gold nano-wires. Deviation in the behavior of gold nano-wires from continuum expectations is also discussed. The comparison of results of atomistic simulations is made with a linear elasticity model (of healthy and cracked nano-wires) to get deep insights into the nano-scale behavior of nano-wires.     

Local compliance of composite cracked bodies

In many circumstances material flaws are present in structures made of anisotropic composites. Such cracks can be detected by vibrational analysis based on the variation of the local compliance as the crack gradually grows. Accordingly, the variation of the mixed term in the energy release rate equation is studied at various angles of inclination of the material axes of symmetry. The significance of this term on the local flexibility of a centrally-cracked plate is discussed by presenting a numerical example for a graphite-fiber reinforced polyimide composite. The prospect of crack diagnosis of composite components on the basis of coupled deformation modes due to the crack presence is signified by analyzing the compliance matrix of a prismatic beam containing a central crack.     

Dynamics of cracked composite material structures

As the result of this work models of the finite cracked beam element, delaminated beam element, and also delaminated plate element have been developed. These models have been used for the analysis of the influence of the fatigue cracks and delaminations on the dynamic characteristics of the constructions made of unidirectional composite materials. The method of modelling cracks and delaminations presented in this work enables its easy modification according to specific cases of damage (i.e. oblique crack, two-side crack, inside crack, multiple delaminations etc.). The results obtained from numerical calculations of the presented models are in good agreement with the known influence of damage parameters like: the position and the depth of the crack or the length and the position of the delamination on the natural frequencies. Simultaneously, a strong influence of the material parameters on these changes has been observed, which does not exist in the case of isotropic materials.     

Determination of SIF in a cracked plane orthotropic strip by the Wiener-Hopf technique

The stress intensity factor for a long cracked strip was determined within the context of the linear orthotropic clasticity. The body had the form of an infinite strip containing a semi-infinite crack at the middle distance of the strip faces. Fourier transforms in combination with the Wiener-Hopf technique were employed to evaluate asymptotically the cleavage stress and its intensity at the crack tip.

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Résumé On détermine le facteur d'intensité d'entaille relatif à une longue bande fissurée, dans un contexte d'élasticité linéaire et orthotrope. On considère un corps ayant la forme d'une bande infinie et comportant une fissure semi-infinie à mi-distance des faces de la bande. On recourt à une transformée de Fourier en combinaison avec la technique de Wiener-Hopf pour évaluer par voie asymptotique la tension de clivage et son intensité à l'extrémité de la fissure.

     

Effects of electric boundary conditions on electroelastic field in a cracked piezoelectric strip

Effects of electric boundary conditions on electroelastic field in a cracked piezoelectric strip are examined. Attention is focussed on an antiplane shear central crack normal to the strip surfaces. By decoupling equations and using the conformal mapping technique, expressions for electroelastic field in the piezoelectric strip are determined under the assumptions of an impermeable, permeable, or conducting crack, respectively. Comparison for the singularity near the crack tips among the obtained electroelastic fields is made.