Effect Of Material Orthotropy Research Articles

SH-waves interaction with crack at orthotropic interface

ABSTRACT The problem of diffraction of SH-waves by two coplanar Griffith cracks situated at the interface of two different orthotropic media has been analyzed. Fourier transform and integral equation method have been used to solve this problem. The expressions for the stress intensity factors (SIFs) around the crack tips are obtained. Numerical values of SIF and the crack opening displacement for several orthotropic materials have been calculated and plotted graphically to show the effect of material orthotropy.

The effect of buffer-layer on the steady-state energy release rate of a tunneling crack in a wind turbine blade joint

The effect of a buffer-layer on the steady-state energy release rate of a tunneling crack in the adhesive layer of a wind turbine blade joint, loaded in tension, is investigated using a parametric 2D tri-material finite element model. The idea of embedding a buffer-layer in-between the adhesive and the basis glass fiber laminate to improve the existing joint design is novel, but the implications hereof need to be addressed.The results show that it is advantageous to embed a buffer-layer near the adhesive with controllable thickness- and stiffness properties in order to improve the joint design against propagation of tunneling cracks. However, for wind turbine blade relevant material combinations it is found more effective to reduce the thickness of the adhesive layer since the stiffness mismatch between the existing laminate and the adhesive is already high. The effect of material orthotropy was found to be relatively small for the blade relevant materials.

Non-singular antiplane fracture theory within nonlocal anisotropic elasticity

In the present paper, the distributed dislocation technique is applied for the analysis of anisotropic materials weakened by cracks. Eringen's theory of nonlocal elasticity of Helmholtz type is employed. The non-singular screw dislocation within anisotropic elasticity is distributed to model cracks of mode III. The corresponding dislocation density functions are evaluated using the proper crack-face boundary conditions. The nonlocal stress field within a plane weakened by cracks is determined. The crack opening displacement is also discussed within the framework of nonlocal elasticity. The stress singularity of the classical linear elasticity is removed by the introduction of the nonlocal theory of elasticity. The general anisotropic case and the special case of orthotropic material are studied. The effect of material orthotropy is presented for a crack which is not necessarily aligned with the principal orthotropy direction.

Displacement potential solution of stiffened composite struts subjected to eccentric loading

The elastic behavior of stiffened struts of orthotropic composite material is investigated under an eccentric loading using displacement potential formulation. Solutions are obtained for different aspect ratios of the strut where the fibers are assumed to be directed along the axis of the struts. Solutions of stresses and displacements of boron/epoxy composite struts are presented numerically in the form of graphs. The effects of material orthotropy and different stiffeners on the elastic field are also investigated. Finally, some of the results of the present solution are compared with the corresponding finite element predictions, which, in turn, establishes the soundness as well as reliability of the present analysis of the composite struts.

Free Vibration of Laminated Composite Circular Arches by Dynamic Stiffness Analysis

The dynamic stiffness method for studying the vibration characteristics of the laminated composite shallow circular arches is introduced in this article. The exact dynamic stiffness matrix is formulated from the analytical solutions of the governing differential equations of motion of the laminated circular arches, based on second-order shear deformation theory. The application of the present method is illustrated by miscellaneous numerical examples, in which the effects of material orthotropy, the lamination scheme, the curvature ratio, length-to-thickness ratio, and boundary condition upon the natural frequencies of the composite arches are investigated. Compared to those solutions available in the literature, the numerical results demonstrate the accuracy and effectiveness of the present method.

Failure Initiation and Progression in Internally-Pressurized Elliptical Composite Cylinders

The article addresses the influences of the noncircular geometry and material orthotropy on the predictions of initial material failure, and the extent and spatial distribution of subsequent failures, within the walls of internally-pressurized laminated composite cylinders with elliptical cross sections. The work is focused on the potential for leakage through the cylinder walls due to the accumulation of matrix cracking and fiber breakage within the layers. The predictions are based on numerical analyses using the finite-element code STAGS. Three different graphite-epoxy lamination sequences, a quasi-isotropic, a circumferentially stiff, and an axially stiff lamination sequence, are considered to investigate the effects of material orthotropy. Three different failure criteria and several material degradation schemes are considered to determine the sensitivity of the predictions to these steps in the analyses. It is shown that the spatial location of and pressure level to produce the initial failure, which occurs in the form of matrix cracking, is highly dependent on the lamination sequence. The pattern of failure accumulation due to increased pressure levels following initial failure is also dependent on the lamination sequence. No leakage is predicted for pressures to the level to produce first fiber failure. However, leakage is predicted for just a slight increase in pressure beyond that pressure, and the leakage pressure level and location are virtually independent of lamination sequence. The location of the first matrix failure and the spatial pattern of subsequent failures are not overly sensitive to the failure criterion used or the details of material degradation scheme employed. The pressure levels to produce the first matrix and first fiber failures are dependent on the failure criterion used.

Analysis of a crack approaching a circular hole in cross-ply laminates under biaxial loading

The problem of a crack approaching a circular hole in cross-ply laminates under uniaxial and biaxial loading is investigated in this paper. The effects of material orthotropy, geometry [R/d and a/d], and loading conditions on crack tip singularity are investigated. The stress intensity factors are obtained by the modified mapping collocation method. The present results for an isotropic infinite plate show good agreement with existing solutions. The results for cross-ply laminates show that the stress intensity factors strongly depend on material orthotropy, geometry, and loading condition. The stress intensity factors for cross-ply laminates exist between those for θ=0° and those for θ=90° in the whole range of crack length and decrease as the percentage of 0° plies increases. In the range of small crack length the stress intensity factors for biaxial tension are higher than those for uniaxial tension. In the range of large crack length the stress intensity factors for uniaxial tension are higher than those for biaxial tension.

Diffraction of elastic waves by four rigid strips embedded in an infinite orthotropic medium

In the present paper, the elastodynamic response of four coplanar rigid strips embedded in an infinite orthotropic medium due to elastic waves incident normally on the strips is analyzed. The resulting mixed boundary-value problem is solved by an integral-equation method. The normal stress and the vertical displacement are derived in closed analytic form. Numerical values of stress-intensity factors at the edges of the strips and vertical displacements at point in the plane of the strips for several orthotropic materials are calculated and plotted graphically to show the effect of material orthotropy.

Stress analysis of an orthotropic material under diametral compression

The diametral compression test is commonly used to determine the tensile strength of brittle materials. For isotropic materials a simple relation based on specimen geometry and the applied load at failure is used to calculate the tensile strength. Previous to this work the effect of material orthotropy and material orientation on the specimen stress state had not been completely determined. In this study, both isotropic and orthotropic specimens were analyzed using a finite element analysis and experimentally verified by strain gage and photoelastic measurements. Further, this work investigated the effect of the applied load area on the specimen stress state. Results of this work show that there is a significant difference between the theoretical calculations based on the assumption of material isotropy when compared to an orthotropic material. This difference can be as much as 45 percent depending on the degree of orthotropy and the orientation. It was also determined that the applied load area and material orientation significantly influence the specimen stress state. An applied load area of 8 percent of the circumference was found to reduce the stresses in the applied load region.

Classification of crack-tip isochromatics in orthotropic composites

Classification of crack-tip isochromatics in unidirectional orthotropic composites, when the crack is parallel to the fibre and perpendicular to the fibre direction, is considered for mode I, mode II and mixed-mode type of loadings. The knowledge of the mode of fracture helps in identifying the appropriate governing equation to evaluate the Stress Intensity Factor (SIF) from the experimental fringe patterns. The effect of material orthotropy, change of material and a/ w ratio in influencing the geometry of the fringe loops is studied in detail for mode I type of loading. Typical experimental fringe patterns are obtained by photo-orthotropic elasticity for mode I, mode II and mixed-mode loadings. The inclusion of the term σ ox to the σ x stress term introduced by Mojtahed and Zachary is validated. The necessity for developing a higher order theory in evaluating the SIF from experimental fringe loops when the crack tip is closer to a free boundary is emphasised.

Diffraction of elastic waves by two parallel rigid strips embedded in an infinite orthotropic medium

The elastodynamic response of a pair of parallel rigid strips embedded in an infinite orthotropic medium due to elastic waves incident normally on the strips has been investigated. The mixed boundary value problem has been solved by the Integral Equation method. The normal stress and the vertical displacement have been derived in closed form. Numerical values of stress intensity factors at inner and outer edges of the strips and vertical displacement at points in the plane of the strips for several orthotropic materials have been calculated and plotted graphically to show the effect of material orthotropy.

The role of material orthotropy in fracture specimens for composites

Guided by the orthotropy rescaling technique and other available analytic results, a systematic analysis is conducted for commonly used fracture specimens to investigate the role of material orthotropy in fracture behavior of unidirectional composites. Included are notched bars, delamination beams and hybrid sandwiches, of many varieties All numerical calibrations are presented with fitting formulae in the relevant parameter regimes. The effect of material orthotropy on fracture behavior of unidirectional composites is thus quantified, which significantly reduces the complexities involved in both experimental investigation and theoretical modelling. A summary of the orthotropy rescaling concepts, with some extensions, is also included.

On a finite element model for the analysis of through cracks in laminated anisotropic cylindrical shells

A finite element model for the analysis of laminated composite cylindrical shells with through cracks is presented. The analysis takes into account anisotropic elastic behaviour, bending-extensional coupling and transverse shear deformation effects. The proposed finite element model is based on the approach of dividing a cracked configuration into triangular shaped singular elements around the crack tip with adjoining quadrilateral shaped regular elements. The parabolic isoparametric cylindrical shell elements (both singular and regular) used in this model employ independent displacement and rotation interpolation in the shell middle surface. The numerical comparisons show the evidence to the conclusion that the proposed model will yield accurate stress intensity factors from a relatively coarse mesh. Through the analysis of a pressurised fibre composite cylindrical shell with an axial crack, the effect of material orthotropy on the crack tip stress intensity factors is shown to be quite significant.