Evaluation of stress intensity factor under pure shear stress in orthotropic material

Various types of composite materials are currently being developed and used for automobiles, airplanes, ships and other structures in response to required service conditions which are getting increasingly more severe. Of growing importance under such circumstances is the study of stress analysis and fracture mechanics for these composite material structures. Particularly, the primary concern in design of structures and machines should be the initiation of cracks due to excessive deformation, delamination in material or other material defects. In evaluating safety, it is indispensable from the structural design point of view that K value should be known by an analysis conducted in advance. In this study, stress intensity factor (mode II) under a pure shear stress was obtained using the photoelastic method and caustic method and applying an isotropic material and orthotropic material (copper fibre epoxy composite (CFEC) developed by the authors), each containing the crack. Results were compared with theoretical values. As a result, this method was found useful and the effect of the direction of the primary axis of this material on the stress intensity factor was clarified.     

Symmetric loading of a Griffith crack by transient concentrated forces in an orthotropic material

Body forces are used to model the effect of fasteners and stiffeners. This paper contains results of a study that was undertaken to examine the effect of symmetric impact loading by concentrated body forces on a Griffith crack located in an orthotropic material. The integral transform method along with certain potential functions was used to obtain expressions for the stress intensity factor (SIF). Four different loading cases were considered. Numerical calculations show the typical overshoot in the dynamic SIF reaching values as much as 22% of the corresponding static SIF. The magnitude of the overshoot is affected by the material properties as well as the relative position between the crack and the body forces. In fact as the distance between the application of the body force and the crack increases, the magnitude of the peak value decreases. In addition, as the relative distance increases, the time at which the peak value of the overshoot occurs increases. Furthermore, the time interval over which the overshoot is maintained increases as the relative position increases. The results of the study imply that for stiffened or fastened orthotropic materials, the location of the fasteners or stiffeners may significantly affect the stress intensity factors.     

Analytical and numerical analysis of 3D grid-reinforced orthotropic composite structures

A comprehensive micromechanical investigation of 3D periodic composite structures reinforced with a grid of orthotropic reinforcements is undertaken. Two different modeling techniques are presented; one is based on the asymptotic homogenization method and the other is a numerical model based on the finite element technique. The asymptotic homogenization model transforms the original boundary value problem into a simpler one characterized by effective coefficients which are shown to depend only on the geometric and material parameters of a periodicity cell. The model is applied to various 3D grid-reinforced structures with generally orthotropic constituent materials. Analytical formula for the effective elastic coefficients are derived, and it is shown that they converge to earlier published results in much simpler case of 2D grid reinforced structures with isotropic constituent materials. A finite element model is subsequently developed and used to examine the aforementioned periodic grid-reinforced orthotropic structures. The deformations from the finite element simulations are used to extract the elastic and shear moduli of the structures. The results of the asymptotic homogenization analysis are compared to those pertaining to their finite element counterparts and a very good agreement is shown between these two approaches. A comparison of the two modeling techniques readily reveals that the asymptotic homogenization model is appreciably faster in its implementation (without a significant loss of accuracy) and thus is readily amenable to preliminary design of a given 3D grid-reinforced composite structure. The finite element model however, is more accurate and predicts all of the effective elastic coefficients. Thus, the engineer facing a particular design application, could perform a preliminary design (selection of type, number and spatial orientation of the reinforcements) and then fine tune the final structure by using the finite element model.     

Elastic stress transmission in cellular systems—Analysis of wave propagation

A closely packed array of thin-walled rings constitutes an idealisation of a cellular structure. Elastic waves propagating through such structures must do so via the ring (cell) walls. A theoretical investigation into the propagation of elastic stresses in thin-walled circular rings is undertaken to examine the nature of wave transmission. Three modes of motion, corresponding to shear, extensional and flexural waves, are established and their respective velocities defined by a cubic characteristic equation. The results show that all three waves are dispersive. By neglecting extension of the centroidal axis and rotary inertia, explicit approximate solutions can be obtained for flexural waves. Employment of Love's approach for extensional waves [Love AEH. A treatise on the mathematical theory of elasticity, 4th ed. New York: Dover Publications; 1944. p. 452–3] enables approximate solutions for shear waves to be derived. The three resulting approximate solutions exhibit good agreement with the exact solutions of the characteristic equation over a wide range of wavelengths. The effects of material property, ring wall thickness and ring diameter on the three wave modes are discussed, and the results point to flexural waves as the dominant means of elastic energy transmission in such cellular structures. Wave velocities corresponding to different frequency components determined from experimental results are compared with theoretical predictions of group velocity for flexural waves and good correlation between experimental data and theory affirms this conclusion.     

The discrete method of separation of variables for composite material problems

In this paper, we propose the discrete method of separation of variables for the numerical solutions of the composite material problems on a polygon. After a suitable transformation of coordinates, the original boundary value problem is reduced to a discontinuous coefficients problem on a semi-infinite strip. Then we get the semi-discrete approximation of the discontinuous coefficients problem which is equivalent to a boundary value problem of a system of ordinary differential equations (O.D.E's) with constant coefficients. After solving the boundary value problem of the system by a direct method, then the semi-discrete approximation of the original problem is obtained. Especially we can see that the semi-discrete approximation in form of separable variables naturally possesses the singularity of the original problem. Finally, the numerical examples show that our method is feasible and very effective for solving composite material problems numerically.     

The effect of a bump on wave propagation in a fluid-filled elastic tube

In the present work, treating the arteries as a thin walled prestressed elastic tube with variable cross-section, and using the longwave approximation, we have studied the propagation of weakly nonlinear waves in such a fluid-filled elastic tube by employing the reductive perturbation method. By considering the blood as an incompressible viscous fluid the evolution equation is obtained as the perturbed Korteweg-de Vries equation with variable coefficients. It is shown that this type of equations admit a solitary wave type of solution with variable wave speed. It is observed that, the wave speed gets smaller and smaller as we go away from the center of the bump. The wave speed reaches to its maximum value at the center of the bump.     

Comparison of different stress-state dependent cohesive zone models applied to thin-walled structures

Two different approaches that explicitly incorporate the stress triaxiality into cohesive zone models applicable to thin-walled structures are compared to identify the relative merits and limitation of these models. The number of model parameters involved, the ease of parameter determination and the predictive capabilities of the models over a wide range of thin-walled geometries are investigated. The first model, proposed recently by the authors, uses basic elastic–plastic constitutive equations combined with a model parameter depending on the average triaxiality in plane stress conditions. The second model incorporates stress-state through exponential dependence of cohesive strength on triaxiality, similar to plane strain studies earlier. The respective parameters for both models are identified and subsequently applied to several notched and precracked specimens. It is shown that in contrast to stress-state independent models, both constraint dependent models are able to predict well failure of a wide range of structures. While the model incorporating triaxiality dependent cohesive parameters has more parameters to be determined, it is not restricted to any specific stress condition and therefore can be extended to arbitrary three-dimensional stress-states.     

梁与正交各向异性板弯曲波的传递特性研究

以正交各向异性板与各向同性梁耦合系统弹性波传递特性为研究对象,基于弯曲波传播的动力学分析,推导出子系统间的功率流传递系数(power flow transmission coefficient,PTC)和耦合边界处的耦合损耗因子(coupling loss factor,CLF)表达式.计算分析了内损耗因子、频率和方向...     

The elastic displacement and stress in a material to promote reflection and transmission of an incoming wave

The conditions on elastic displacement and stress in a material that will promote reflection and transmission of an incoming wave are calculated. It is found, for example, that to optimize reflection and transmission, scalar potentials of the displacement in the wave and in the material will be related to rotations in planes perpendicular and parallel to the direction of propagation to the wave. When a pulse is constructed and its path analyzed through short distances, it is shown that abrupt transitions in tension and compression in a material will maximize reflection of the pulse. When strain energy is minimized where reflection and refraction are to occur, differences in tension and compression become prominent again. Finally, an approximate volume of material is calculated for an electron to harness the restoring forces in a material to balance the energy lost in inelastic scattering.     

Patterned structures fabricated on chalcogenide phase-change thin films by laser direct writing

In laser direct writing technology, the pattern is usually written in a photoresist. In this work, we use the chalcogenide phase change thin films as the laser direct writing materials, and patterned structures with different shapes and sizes were directly written with different laser wavelengths. Compared with traditional photoresist materials, the patterned structures can be directly formed in the chalcogenide phase change thin films without developing and etching procedures, and also can be directly written with different laser wavelengths. By tuning the laser parameters precisely, patterned structures with different sizes and shapes could be obtained as well. The analysis indicates that the formation mechanism of the patterned structure is mainly due to the volume expansion caused by material vaporization and the interior of the patterned structure is hollow with some solid leavings, and the chalcogenide phase change thin films are very good candidate materials for patterned structure formation.     

Numerical calculations of elastic wave propagation in anisotropic thin films deposited on substrates

In this work, we present a generalized numerical model to study the dispersion curves of elastic waves in anisotropic thin layer/substrate systems. Dispersion curves as a function of wave frequency for different propagation angles are calculated. The nature of the mode (Rayleigh or Love) is identified by analyzing the polarization of the three-dimensional displacement field. This numerical model has been applied to the system Au(0 0 1)/Ni(0 0 1).     

Preliminary study on cost optimisation of aircraft composite structures applicable to liquid moulding technologies

This paper details the initial development of a method for determining the associated recurring labour costs for the manufacture of a aircraft component that will form the basis for a computerised methodology for determining the optimum manufacturing method for a component design. The research focuses on the flow of process steps to manufacture an aircraft component for the vacuum-assisted resin transfer moulding and resin transfer moulding manufacturing process. The methodology developed is based on applying MIT cost equations to process steps from which cost variables and constants are established to represent an estimated costing of the aircraft structure. This research will assist in providing a swifter and more accurate conceptual design/manufacturing system that includes an analysis of cost and will assist the production of trade studies that consider the manufacture of aircraft components using cost-effective technologies, such as liquid moulding.     

Clamping effects on the dynamic characteristics of composite machine tool structures

Substituting composite structures for conventional metallic structures has many advantages for structural dynamic characteristics because composite materials have the higher specific stiffness and damping characteristics than conventional materials. However, the dynamic characteristics such as the fundamental natural frequency and damping of composite structures are influenced much by their joints. In this work, the effects of clamping conditions on the dynamic characteristics of cantilever type composite machine tool structures with clamped joint were investigated to increase the natural frequency and damping of structures. In order to improve the shear property of the clamping part of composite machine tool bar, a new method for the clamping part was developed with metal core or sleeve inserted in the composite body at the clamping part. From the finite element and experimental results, suitable clamping conditions for the maximum dynamic stiffness were obtained for the composite structures with clamped joint.     

The transfer length in concrete structures repaired with composite materials: a survey of some analytical models and simplified approaches

This work focuses on the closed-form solutions for the shear distribution that takes place in the adhesive between composite and concrete in RC structures repaired with composite plates. Three different loading cases are studied. It is shown that the exact shear stress distributions, which are rather complicated, can be simplified to provide very similar expressions in the three studied cases. The main parameters that govern the shear distribution are then clearly highlighted. This leads to an easy understanding of the influence of some geometrical and material parameters on the shear distribution, as illustrated through a parametric study.     

On the static equilibrium of an elastic orthotropic medium with an arbitrarily oriented elliptical crack

We analyze the problem of the stress distribution in an elastic orthotropic medium with an arbitrarily oriented elliptical crack. To construct the problem solution, the Willis approach is used which is based on the triple Fourier transformation of spatial variables and Fourier-image of Green’s function for an infinite anisotropic space. The investigation results in special cases are compared with the data of other authors. The effect of the elliptical crack orientation in an orthotropic space on the distribution of the stress intensity factors along its contour is studied. __________ Translated from Problemy Prochnosti, No. 4, pp. 146–159, July–August, 2007.     

The effect of second principal stress on the fatigue propagation of mode I surface crack in Al2O3/Al alloy composites

Using a plate made of A2017-T6 metal matrix composites reinforced with 10 volume % and 20 volume % Al₂O₃ particles and Al alloy possesses the same composition as matrix alloy, the crack propagation rate da/dN of a mode I surface crack by the simultaneous action of plane bending and cyclic torsion are studied. And the effects of crack tip opening stress σ_top, crack opening displacement COD, biaxial stress ratio C (=second principal stress/first principal stress) and the surface roughness of crack section are examined. When stress intensity factor range ΔK is lower than the specific level, da/dN decreases with the increase of volume fraction of Al₂O₃ in C=0 and C=−0.55. But, da/dN of Al alloy becomes minimum in C=−1 and the effect of Al₂O₃ particles disappears. σ_top rises with the increase of volume fraction of Al₂O₃ particles and the decline of C. On the other hand, COD doesn’t always rise with the decline of C. These phenomena can be explained by the residual compressive stress formed at the surface layer of the specimen by the fatigue test and the surface roughness of crack section.     

Effects of fiber ellipticity and orientation on dynamic stress concentrations in porous fiber-reinforced composites

Interaction of time harmonic fast longitudinal and shear incident plane waves with an elliptical fiber embedded in a porous elastic matrix is studied. The novel features of Biot dynamic theory of poroelasticity along with the classical method of eigen-function expansion and the pertinent boundary conditions are employed to develop a closed form series solution involving Mathieu and modified Mathieu functions of complex arguments. The complications arising due to the non-orthogonality of angular Mathieu functions corresponding to distinct wave numbers in addition to the problems associated with appearance of additional angular dependent terms in the boundary conditions are all avoided by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. A MATHEMATICA code is developed for computing the Mathieu functions in terms of complex Fourier coefficients which are themselves calculated by numerically solving appropriate sets of eigen-systems. The analytical results are illustrated with numerical examples in which an elastic fiber of elliptic cross section is insonified by a plane fast compressional or shear wave at normal incidence. The effects of fiber cross sectional ellipticity, angle of incidence (fiber two-dimensional orientation), and incident wave polarization (P, SV, SH) on dynamic stress concentrations are studied in a relatively wide frequency range. Limiting cases are considered and fair agreements with well-known solutions are established.     

Surface acoustic wave characterization of a thin, rough polymer film

Laser generated surface acoustic waves (SAW) in a heterodyne diffraction scheme is a powerful technique for elastic characterization of thin films and it is frequently used on samples of high optical quality. We show that the method can also be effectively used in difficult conditions, on rough samples. Measurements are presented on a 3 µm thick film of polymer, spin-coated on steel, and on the same sample after addition of an aluminum coating. The experimental data are interpreted using a model assuming a stack of perfect layers. The analyses show good consistency within the SAW results for both configurations, and consistency with nano-indentation results, cross-validating both approaches.     

Influence of damaged area on lamb wave propagation in composite plate

The influence of a specified damage on transient propagation of Lamb wave in a composite laminated plate is studied by finite element analysis. The finite element formulation is developed for the laminated plate with embedded or surface-bonded piezoelectric layers. A higher order laminate model is used to describe the displacement field of both composite laminate and piezoelectric layer. The damaged area is modeled by a localized loss of stiffness and quantified by a degradation coefficient . Piezoelectric materials act as both actuators and sensors for generating and receiving Lamb waves. Numerical results show that the waveform, wave peaks and the arrival time of the transmitted Lamb wave are distinctly correlated with quantified degradation coefficient of the damaged area, which are helpful to damage detection for a composite laminated plate in a new way.Tel (Res).: 86-29-88242204, Tel (Off).: 86-29-88213623-8026     

Influence of boundary condition on the sound velocity in granular assembly: Spiral tube versus cylinder

The properties of elastic wave propagation in granular assemblies have become a subject of immense interest in recent years, however, the influence of different confinements on the sound velocity is seldom investigated. This study provides a method to determine the contact point between spherical, super-ellipsoidal particles and complex boundaries, in order to investigate how the anisotropy induced by particle shape or boundary affects velocity. Taking cylinder and spiral tube confinements as examples, the falling process of spherical and super-ellipsoidal assemblies are simulated to verify the validation by the discrete element method (DEM). The convergence of the kinetic energy during the falling process and the equilibrium state with zero residual kinetic energy guarantees the stability and correctness. On the basis, elastic wave propagation of spherical and super-ellipsoidal systems in spiral tube and cylindrical confinements under different pressures are modelled, and sound velocities are calculated. The effective medium theory (EMT), granular solid hydrodynamics (GSH), and elastic stiffness are used to interpret the relationship between velocity and stress in cylindrical confinement. However, the results in the spiral tube deviate from EMT and GSH, which means the boundary affects velocity significantly. The difference of velocity between spiral tube and cylinder is qualitatively explained from the perspective of anisotropy of contact force distribution in the system. The simulation results show that anisotropy introduced by the curved surface affects the acoustic properties greatly. The method used for spiral boundary is also suitable for other complicated confinements.