Orthotropic Composite Materials Research Articles

Модель накопления повреждений в ортотропном композиционном материале

The paper presents a theoretical and experimental study of the influence of damage accumulation in composite material on the elastic fourth-rank tensor and on the strength under quasi-static, cyclic and dynamic loads. Layered polymer composites (glass or carbon fiber-reinforced plastic) are considered. This work aims to develop a mathematical model that accounts for the impact of damage in the composite material on the fourth-rank tensor of elastic properties. The constitutive relations for an orthotropic composite material are proposed, taking into account the accumulation of damage during tensile or shear loading. A numerical simulation using the finite element method is done for a periodicity cell for composite variants (unidirectional, layered, etc.) to determine the effective elastic properties. Quasi-static loading experiments were conducted on composite samples (carbon plastic) to validate the model and the degradation of elastic properties was determined by measuring the longitudinal sound speed. The full-scale experiments confirmed that damage accumulation in carbon fiber-reinforced plastic leads to the degradation of its effective elastic properties. In this connection, a technique was developed to take into account irreversible damage in an orthotropic composite material through the components of the ductility tensor, which may be helpful for the design and analysis of composite structures. The findings of the study could help with the creation of new materials with enhanced mechanical characteristics, as well as with raising the quality of already-existing materials. The developed mathematical model of orthotropic composite material can be used to enhance the structural strength properties and boost the application safety in a variety of industry.

Wiener–Hopf method to solve the anti-plane problem of moving semi-infinite crack in orthotropic composite materials

This paper contains the solution to the problem of a semi-infinite moving crack situated in an orthotropic strip bonded between two identical strips. The crack moves with a constant velocity, and the surface is under shear wave disturbance. We first examine the equations of elasticity, which include equilibrium equations and stress and displacement constitutive relations with the model-specific continuity and boundary conditions. Using the Fourier integral transform, the standard form for the Wiener–Hopf (W-H) equation is obtained, which is solved using the W-H method. The analytical expressions for the considered crack problem have been obtained for stress intensity factor (SIF), normalized stress intensity factor (NSIF), and stress magnification factor (SMF). The behavior of NSIF has been graphically presented for particular cases of composite materials for different crack propagation velocities and various depth ratios of the strips. The novelty of this paper lies in the analytic solutions using the W-H method for the semi-infinite moving crack problem under the influence of anti-plane shear waves. The pictorial presentations of normalized SIF clearly show their dependency on strip depths, crack propagation velocities and elastic constants.

Penalized anisotropy: Controlling anisotropy growth in concurrent optimization of topology and fiber orientation for orthotropic composite materials

The topology and fiber orientation of fiber-reinforced composite structures must be designed computationally to fully demonstrate their anisotropic mechanical properties. Optimization of the topology and fiber orientation is performed either sequentially or concurrently. In the sequential method, topology optimization is performed first, followed by fiber orientation optimization. This separated optimization process does not consider material anisotropy during the topology optimization process. The concurrent method has the potential to realize better results by considering the anisotropic properties during topology optimization. However, the concurrent method often obtains locally optimal solutions because of material anisotropy in the initial optimization process. A continuation approach for anisotropy, which starts with weak anisotropy and then improves the anisotropy gradually, resolves this issue. This paper proposes a new concurrent optimization that can control the growth of anisotropy. The growth of anisotropy affects the topology, which is used to determine a better structure. Optimization results were obtained serially by varying the growth of anisotropy, which allowed a highly optimal topology and fiber orientation to be explored by considering their anisotropic nature.

Dynamic mode-I delamination in composite DCB under impact loads with attunable dynamic effect

A dynamic mode-I energy release rate (ERR) of a double cantilever beam (DCB) under impact from a striker is derived for the first time for isotropic and orthotropic composite materials, accounting for DCB properties, a striker mass and an initial impact velocity. This is achieved in the context of structural vibration analysis by employing beam dynamics. It is found that the initial impact velocity determines the magnitude of the ERR, which is proportional to the velocity squared, while the delamination length ratio and the mass ratio between the striker and the DCB defines the time response. To understand the transient effect, a dynamic factor is defined as a function of the mass ratio. This factor decreases with an increasing striker mass, indicating a transition in the dynamic response from flexural-wave dominant to quasi-static-motion dominant, allowing an attunable dynamic effect. The developed theory is verified against the finite-element simulations for isotropic and orthotropic materials as well as experimental verification using published data. This work allows the measurements of fracture toughness under the impact load with the derived analytical solution. In addition, the developed theory can guide a design of impact tests and provide a fundamental understanding of impact-induced fracture for carbon-fiber-reinforced plastics.

Development of the statistical model failure of orthotropic composite materials

Development of the statistical model failure of orthotropic composite materials

Research of orthotropic composites failure taking into account their structural stochasticity

The object of the study is the construction of the reliability assessing algorithm for the orthotropic composite plate, taking into account the stochasticity of its structure under the conditions of plane deformation. The plate consists of a matrix and reinforcement elements. The main orthotropic directions of the material coincide with the directions of the loading. The conducted studies are based on the failure criteria expressed through the components of macro stresses. The hypothesis of the weakest link is used, which for the case of the statistical theory of strength sounds like this: the ultimate (failure) loading for an orthotropic composite plate is equal to the ultimate loading for its weakest element. Defects-cracks are characterized by independent random variables – the half-length and the orientation angle between the defect line and the axis of orthotropy with a higher modulus of elasticity. The proposed model of orthotropic composite material corresponds to known experimental studies epoxy phenolic fiberglass on the cord glass fiber. The distribution probabilities density of defect orientation takes into account their predominant orientation in the direction of reinforcement. On the basis of the obtained composite failure loading integral probability distribution function, the construction and study of the dependence of the plate failure probability diagrams for different number of cracks, structural inhomogeneity and type of applied loading was carried out. Complex application of the composite materials fracture mechanics deterministic solution and the methods of probability theory and mathematical statistics allows for a more adequate assessment of the composite materials reliability, taking into account the stochasticity of their structure. The main content of this work is the construction and analysis of dependence of stochastically defective reinforced composite materials failure probability diagrams. The obtained results make it possible to evaluate the reliability of orthotropic stochastically defective materials under conditions of plane deformation. The algorithm of a compatible combination of defectiveness and randomness of the orthotropic composite material structure makes it possible to qualitatively investigate its failure under various types of applied loading.

On the fracture toughness testing for single-edge notched bend specimen of orthotropic materials

Majority of the fracture toughness tests on orthotropic materials reported in the literature are based on the testing methods developed for isotropic materials since there is no available testing standards specifically dealing with orthotropic materials. In this study, a systematic two-dimensional finite element analyses (2D FEA) of orthotropic single-edge notched bend (SENB) specimens are performed to evaluate the stress intensity factor (SIF) and crack mouth opening displacement (CMOD), which are two key parameters used in the fracture toughness tests. The analysis matrix covers a wide range of material orthotropy. Highly accurate regression solutions for SIF, CMOD compliance and its inverse function were developed as functions of orthotropy parameters. Applications of the proposed equations on experimental data are presented and further discussed. The research outcome is expected beneficial to the standardization of the fracture toughness testing on orthotropic composite materials such as wood, bone and unidirectional fiber-reinforced polymer composites.

Harmonic analysis of annular sector sandwich plate using FEM

In present study, vibration and harmonic behaviors of annular sector sandwich plate of two orthotropic composite materials are analyzed using FEM technique. Sandwich plate made of two face sheet and one core sheet in middle has been modelled using an ANSYS APDL FEM tool. A suitable finite element model is developed and proposed based on first order shear deformation theory. The model has been discretized using appropriate elements i.e. 8-node solid 185 for core sheet and SOLSH190 for face sheet from the ANSYS element library. Effect of varying face sheet thickness is demonstrated on vibration as well as harmonic behaviors of sandwich plate and related findings are discussed briefly. Effect of sector angle has also been demonstrated. The authenticity of the proposed methodology has been verified by comparing the simulation results with available literature. It can be observed that the results obtained are in good propinquity and presently proposed model shows the results with adequate accuracy.

Singularity analysis of cracks in hybrid CNT reinforced carbon fiber composites using finite element asymptotic expansion and XFEM

The configuration of a crack with respect to the multi-material fiber reinforced composite joint determines the order of singularity of the stress solutions reproduced around the crack-tip. These solutions for different configurations of crack are obtained for carbon nano-tube (CNT) reinforced CFRP composite using an innovative finite element asymptotic analysis.Micro-cracks aligned with CNTs covered by interphase material in the reinforced polymer matrix (PMNC) may impinge upon the PMNC-Carbon fiber interface; and this investigation demonstrates that the CNT reinforcement increases the power of the stress field at the area surrounded by the crack-tip. Various CNT alignments have been considered with due concern on symmetric and anti-symmetric deviation of nanotubes on either side of the crack. The effect of notches is considered as well.Finally, the consistent singular mode shapes proposed are applies to efficiently increase the accuracy of the fracture analysis solutions for this category of orthotropic composite materials using a novel extended finite element (XFEM) approach named Direct-XFEM. Direct-XFEM reproduces the stress intensity factors (SIFs) directly, at a few additional degrees of freedom included in the local crack-tip area. The results indicate a notable improvement in contrast with the ordinary XFEM in the absence of the singular shape functions.

Poisson's ratio bounds in orthotropic materials. Application to natural composites: wood, bamboo and Arundo donax

The paper discusses the restrictions the positive definite character of the strain energy imposes to the values of the Poisson's ratios in a linear elastic orthotropic constitutive law. By exploiting the reciprocity principle and the conservation of energy, non-trivial constraints arise, leading to a particularly expressive form of the domain of existence, named Tetrahedron-Ellipsoid locus, in the space of three independent Poisson's ratios.The presented analysis establishes several notable restrictions for the elastic behavior of orthotropic composite materials, in all the cases in which there are great differences in the Young's moduli. For instance, near the edge of this locus, some Poisson ratios may belong to an interval not including the zero value; a very interesting peculiarity, perhaps not yet figured out in literature. In order to assess the coerciveness of the formulation, the results are applied to common wood essences, to several Italian growing species of bamboo and Arundo donax, natural composite functionally graded orthotropic materials. In the latter cases, an extensive experimental investigation is carried out to detect several Poisson's ratios, not studied in literature. Poisson ratios are obtained directly by strains measured by means of both physical strain gauges and Digital Image Correlation (DIC).

Устойчивость шарнирно-подвижно опертых перфорированных оболочек

The article considers sloping shell structures of rectangular design. The shells are made from orthotropic composite materials, articulated-movable supported on the contour, and weakened with holes. Two mathematical models of deformation of such structures have been developed: taking into account the discrete input of holes and with using the constructive anisotropy method. The shell stability calculation has been carried out, using three different geometries of shells which were made of 4 composite materials. Thus, altogether 12 structures have been investigated. It is shown that with an increase in the number of holes, the results obtained by the constructive anisotropy method coincide with the results obtained with the discrete introduction of holes.

Studies on the vibration of Japanese drum wood barrels under material property uncertainty

Unlike isotropic material such as steel, wood behaves as a highly orthotropic composite material. Due to measurement difficulty, only the longitudinal Young's modulus and the specific gravity of the wood were successfully measured at the time the wood barrel was made. In the experiments, mode shapes and modal resonance frequencies were measured. In the numerical modal analysis, the finite-element model of the drum was constructed using orthotropic conical shell elements which require more elastic constants than those being measured. A try-and-error method was used to estimate those unknown constants by comparing the computed and measured modal frequencies and shapes. It was found that the estimated value of the circumferential (cross-grain) Young's modulus, which was unknown at the beginning of the study, turns out to be crucial in determining the lower mode resonance frequencies. The usefulness of this analysis is that the estimated elastic constants can be used for updating the finite-element model which can then be used for calculating the higher order modes. These higher modes cannot be practically determined by measurements. [Work by 2nd author supported by Miyamoto Unosuke Shouten Co.]

Stressed deformed condition of orthotropic spherical shell, lowered by two circular hole

Methods of calculating the shell structures from composite materials and studying the concentration of strains near the holes are devoted to a rather large number of works. However, most of the research was carried out within the framework of the classical Kirchhoff-Love hypothesis, which does not take into account the interlayer and lateral shifts characteristic of composite materials. Application of finite elements method to solve the problems on orthotropic shells of composites, weakened by several holes is reported within the improved theory of Timoshenko type. A numerical algorithm has been developed using the finite element method and a software package has been implemented on a computer that makes it possible to solve problems of stress concentration near two apertures in shells of composite materials. Shearing parameter has been studied for its influence on stress concentration near two circular holes internal pressure for orthotropic spherical shells. Specific results are presented for the cases of large and small holes, taking into account the rigidity of the reinforcing elements. Thus, this software package can be applied to the calculation of the elements of shell structures from orthotropic composite materials weakened by several holes.

Failure analysis of orthotropic composite material under thermo-elastic loading by XFEA

Present work describes the crack growth characteristics in orthotropic composite materials by utilizing extended finite element analysis under combined thermal–mechanical loading conditions. In combined system, temperature and displacement approximations are extrinsically governed by additional functions to define discontinuity profile across crack surface. In present work, two step simulation methodologies are adopted where thermal discrete equations are solved for thermo-elastic problems to obtain temperature distribution in domain. Thereafter, these results acts as load input criterion for elastic discrete equations. Post process of simulation, SIFs at crack tips are calculated using interaction integral approach for few orthotropic composites with preexisted crack.

Stress concentration factor near loaded hole contacting with the bolt in the monolayer of orthotropic composite material

Purpose. To suggest a method to predict the stress concentration factor near loaded hole contacting with the bolt in the monolayer of orthotropic composite material to be independent of difficult calculations. And to verify the factor with use results of numerical calculations using the finite element method in contact formulation. Methodology. The analysis of known outcomes in the literature is carried out. Several assumptions have been formulated about the changes of stress concentration factor depending on the ratio of the hole diameter to the plate width, as well as on orthotropy in the plate material. Assumptions are confirmed by calculated results, graphs. The finite element method was used. Results. A formula is proposed that predicts the stress concentration factor without carrying out difficult calculations of contact problems using known approximations for an isotropic material and the Lekhnitsky-Soldatov solution for a stretched orthotropic infinite plate with an empty hole. Using the results of numerical calculations of contact boundary problems with the finite element method the proposed formula was verified, its good accuracy was shown in the practically applicable range of the ratio of the hole diameter to the plate width. Originality. A four-step method is developed - simple formulas that allow rapid prediction of the stress concentration factor near loaded hole contacting with the bolt in a monolayer of orthotropic composite material using only of the elastic characteristics of the plate material, proven approximations and simple solutions.

Extended meshless moving Kriging method for crack propagation analyzing in orthotropic media

Orthotropic composite material is the particular type of anisotropic materials and their products have been extensively used in a wide range of engineering applications. Study on mechanical behaviors of such materials under working conditions is very essential. In this study, an extended meshfree moving Kriging interpolation method (namely as X- MK) is presented for crack analyzing in 2D orthotropic materials models. The Gaussian function is used for constructing the moving Kriging shape functions. Typical advantages of the MK shape function are the high-order continuity and the satisfaction of the Kronecker’s delta property. To calculate the stress intensity factors (SIFs), interaction integral method is used with orthotropic auxiliary fields. Several numerical tests including static SIFs calculating and crack propagation predicting are performed to verify the accuracy of the present approach. The obtained results are compared with available refered results and they have shown a very good performance of the present method.

Preparation and Performance Test of Orthotropic Piezoelectric Composite Material Ultrasonic Phased Array Transducer

Preparation and Performance Test of Orthotropic Piezoelectric Composite Material Ultrasonic Phased Array Transducer

Scale Effects in Orthotropic Composite Assemblies as Micropolar Continua: A Comparison between Weak- and Strong-Form Finite Element Solutions.

The aim of the present work was to investigate the mechanical behavior of orthotropic composites, such as masonry assemblies, subjected to localized loads described as micropolar materials. Micropolar models are known to be effective in modeling the actual behavior of microstructured solids in the presence of localized loads or geometrical discontinuities. This is due to the introduction of an additional degree of freedom (the micro-rotation) in the kinematic model, if compared to the classical continuum and the related strain and stress measures. In particular, it was shown in the literature that brick/block masonry can be satisfactorily modeled as a micropolar continuum, and here it is assumed as a reference orthotropic composite material. The in-plane elastic response of panels made of orthotropic arrangements of bricks of different sizes is analyzed herein. Numerical simulations are provided by comparing weak and strong finite element formulations. The scale effect is investigated, as well as the significant role played by the relative rotation, which is a peculiar strain measure of micropolar continua related to the non-symmetry of strain and work-conjugated stress. In particular, the anisotropic effects accounting for the micropolar moduli, related to the variation of microstructure internal sizes, are highlighted.

Constitutive Equations for Hyperelastic Materials Based on the Upper Triangular Decomposition of the Deformation Gradient

The upper triangular decomposition has recently been proposed to multiplicatively decompose the deformation gradient tensor into a product of a rotation tensor and an upper triangular tensor called the distortion tensor, whose six components can be directly related to pure stretch and simple shear deformations, which are physically measurable. In the current paper, constitutive equations for hyperelastic materials are derived using strain energy density functions in terms of the distortion tensor, which satisfy the principle of material frame indifference and the first and second laws of thermodynamics. Being expressed directly as derivatives of the strain energy density function with respect to the components of the distortion tensor, the Cauchy stress components have simpler expressions than those based on the invariants of the right Cauchy-Green deformation tensor. To illustrate the new constitutive equations, strain energy density functions in terms of the distortion tensor are provided for unconstrained and incompressible isotropic materials, incompressible transversely isotropic composite materials, and incompressible orthotropic composite materials with two families of fibers. For each type of material, example problems are solved using the newly proposed constitutive equations and strain energy density functions, both in terms of the distortion tensor. The solutions of these problems are found to be the same as those obtained by applying the polar decomposition-based invariants approach, thereby validating and supporting the newly developed, alternative method based on the upper triangular decomposition of the deformation gradient tensor.

Thermal-mechanical crack propagation in orthotropic composite materials by the extended four-node consecutive-interpolation element (XCQ4)

A numerical study of thermal-mechanical crack growth in orthotropic composite materials by the recently developed extended nodal gradient finite element method is presented. The extended four-node consecutive-interpolation quadrilateral element (XCQ4) used in this work is the conventional four-node quadrilateral element, but it is enhanced by additional terms of averaged nodal gradients to smoothen the derivative fields and increase the accuracy of solution, while keeping the same total number of degrees of freedom (DOFs) as that of the traditional element. Inspired by enrichment partition-of-unity method, the singularity and discontinuity of temperature, heat flux, and displacements due to the presence of crack are mathematically described through known enrichment functions. Once the stress fields are obtained, stress intensity factors (SIFs) can thus be evaluated by interaction integral technique. The SIFs are then used to predict crack growth direction. Unlike isotropic media, material orientation plays a critical role and that has to be considered when modeling the evolution of crack in orthotropic composite materials under thermo-mechanical loading condition. In addition, we introduce for the first time an improved way for the enriched approximation of discontinuous temperature field in cracked orthotropic media by taking into account the effect of material orientation. Several numerical examples for thermo-mechanical fracture problems in orthotropic composites with both isothermal and adiabatic loading conditions are analyzed to show the accuracy and performance of the present XCQ4. The computed results of the SIFs are compared with reference solutions derived from experiments, the standard extended four-node quadrilateral element (XQ4), and other numerical methods available in literatures.