Orthotropic Composites Research Articles

Omni-directional wavenumber dictionary modified imaging method for orthotropic composites damage detection using ultrasonic guided waves

The sparse reconstruction imaging method is promising for detecting damage in isotropic and quasi-isotropic materials. However, its effectiveness relies on an accurate dictionary. When applied to orthotropic materials without accounting for wavenumber directionality, the accuracy of the dictionary degrades, leading to inaccurate damage localization. To address this limitation, this paper presents an omnidirectional wavenumber dictionary modified imaging method for orthotropic composites damage detection. The omni-directional wavenumber dispersion curve of ultrasonic guided waves is calculated numerically by converting of elastic stiffness coefficient of orthotropic composites at various propagation angles. A modified propagation model, informed by the omni-directional wavenumber dispersion curve, enhances the precision of the acoustic field dictionary. Utilizing a coherent matched field processor, the method compares the scattered signal's envelope with the acoustic field dictionary's envelope to generate an ambiguity function, which in turn forms a damage image. Simulation and experimental results confirm the method's superiority in resolving damage localization inaccuracies and artifacts typically associated with orthotropic composites. The proposed method exhibits enhanced signal-to-noise ratio and lower positioning error, facilitating precise multi-damage detection in orthotropic composites compared to existing methods.

Nonlocal buckling analysis of five-layer laminated nanocomposites on kerr foundation: A refined zigzag theory approach

In this paper, the buckling analysis of a five-layer laminated nanocomposite resting on a Kerr foundation is presented. In order to describe the non-continuous behavior of composite plate through its thickness, the displacement field is determined using the Refined Zigzag Theory (RZT). Additionally, the constitutive relations of piezo electromagnetic isotropic materials, orthotropic composites, and Functionally Graded Porous Materials (FGPMs) are presented. With respect to Bi- and Uniaxial loading in the nanoplate, the Hamilton’s principle is utilized to derive the equation of motion of this nanoplate. To study the small-scale effect in nanoplates, both Nonlocal Eringen Theory and Nonlocal Strain Gradient Theory (NSGT) are employed to account for nonlocal effects. Finally, the coupled equations of motion are solved using the Differential Quadrature Method (DQM). This paper introduces the newly used Kerr foundation and its effect on the buckling analysis. It also investigates the influence of plate dimensions, piezo electromagnetic terms, boundary conditions, and loading on the dimensionless critical buckling load.

T-stress extraction in arbitrarily cracked orthotropic composites with the numerical manifold method and Stroh formalism

The escalating utilization of composites over the past decades has necessitated the fracture investigation of orthotropic materials. The T-stress, namely, the first non-singular term of the normal stress parallel to the crack in William’s expansion, is of great significance for fracture analysis. In this work, the numerical manifold method (NMM) is advanced to assess the T-stress of arbitrary-shaped cracks (including non-intersecting cracks and multi-branched cracks) in two-dimensional orthotropic composites. Attributing to the bi-cover systems, the NMM can conveniently discretize the physical domain and naturally accommodate the discontinuity across crack surface. Meanwhile, the singularity at crack tip can be well captured by the wise choice of local approximation function. Through the application of interaction integral technology in the NMM postprocessing, the T-stress is extracted with the Stroh-form auxiliary fields. The accuracy of the proposed method is verified by comparing with reference solutions and then applied to arbitrarily branched and intersecting cracks. The results indicate that the present approach has convincing accuracy and also considerable convenience in T-stress evaluation. Additionally, the impacts of material orientations, crack geometries and loading conditions on the T-stress are also investigated.

Investigation of two collinear cracks in fiber reinforced composites under thermal loading

The objective of this paper is to explore the transient behaviors of fiber reinforced composites with two embedded collinear cracks subject to a sudden thermal shock. The orthotropic composites with both the vertically oriented and horizontally aligned fibers are examined to present a systematic comparison. By means of the integral transform methodology and singular integral equations, the thermal and elastic governing equations are solved numerically to determine the transient thermal process and stress intensifications around the crack tips. Parametric investigations are carried out for fiber volume fractions and crack distances. The findings would be beneficial to a more thorough knowledge of fibrous composites’ fracture characteristics under thermal shocks, which helps material design and structural optimization of the composites with fiber reinforcements.

A hybrid thermo-mechanical phase-field model for anisotropic brittle fracture

The phase-field modeling approach is integrated with the isogeometric-meshfree approach to investigate the coupled thermo-mechanical fracture behaviors of composite materials, accounting for material anisotropy. The present approach is formulated within a thermodynamic framework, exploring the effects of both thermal and mechanical factors on crack evolution. The crack driving force in composites is determined by the collective contributions from both fibers and the matrix. Moreover, a hybrid computational framework, enhanced with an adaptive mesh refinement technique, is proposed for the efficient implementation of thermo-mechanical fracture. Finally, simulations of the thermal deformation and fracture processes in both homogeneous and composite materials are implemented to verify the present approach. The impact of the weak material anisotropy, such as anisotropic thermal conductivity and material strength, along with the strong anisotropy coefficient on fracture patterns in orthotropic composites is also investigated. The simulation results demonstrate that the developed approach can predict complex failure patterns in composites under thermo-mechanical loading, thus offering insights for the design of composites.

Static and fatigue performance of non-circular rivet joints: Comparison between numerical modelling and preliminary testing

Alternative non-circular rivet joint geometries are investigated. An optimum non-circular rivet geometry based on a continuous change in the radius of curvature is proposed to minimise the stress concentration factor on structural components joined by rivets, which is the first time to be proposed to the best author’s knowledge. By-pass and bearing load cases are considered for both numerical analysis and a preliminary experimental programme. For isotropic materials, linear elastic analyses (for the stress concentration factors) and fully elastoplastic analyses are carried out in the numerical simulations. The experimental programme includes static tests (for both by-pass and bearing load cases) and fatigue tests (by-pass loading) for isotropic materials, whereas only static tests (for both by-pass and bearing load cases) are considered for orthotropic composites. The correlation of experimental and numerical results indicates that the reduction of the stress concentration factor plays an important role in improving fatigue behaviour and has almost no influence under static loading. Hence, the life of structural riveted components may increase, improving the life cycle of the entire structure in service.

Estimating the elastic constants of orthotropic composites using guided waves and an inverse problem of property estimation

The present research focusses on estimating the elastic constants of orthotropic laminates using ultrasonic guided waves (GWs) excited through Lead Zirconate Titanate (PZT) sensors and sensed using one-dimensional laser vibrometer. The elastic constants of a material are crucial for understanding its mechanical behaviour and are typically determined through experimental testing. However, this process can be time-consuming and expensive. We formulate this problem as an inverse problem of property estimation. Thus, in this work, the simulation models with PZT transducers have been employed for generating time series (TS) GWs for the orthotropic material. Then, an inverse machine learning model is trained using a TS dataset pertaining to different elastic constants generated using the simulations. The inverse model consists of deep neural networks and designing a loss function for the specific application. Limited number of unique sets of simulations were conducted. Out of available simulation data, 30% of the sets were used for validation. To further test the model, a blind experimental test was conducted, and the corresponding elastic constants were estimated with a mean absolute percentage error (MAPE) of 12.89% and standard deviation of 5.47%. The results demonstrate that formulation of property estimation as inverse problem is capable of accurately predicting the elastic constants of a material, by using a model solely trained on simulation and a very scare amount of data. This approach has the potential to significantly reduce the computational time for predicting the elastic constants, and thereby could have wide-ranging applications in materials science and engineering.

Mechanical modeling of arbitrarily perforated orthotropic composites with the numerical manifold method

With the widespread use of composites, analysis of their responses under various loadings is of significant importance. In this work, the mechanical behaviors of 2-D orthotropic composites with arbitrary holes are investigated by the numerical manifold method (NMM). Profiting from its unique dual cover systems, namely, the mathematical cover (MC) and the physical cover (PC), the NMM is able to model problems in arbitrarily-shaped physical domains with nonconforming MCs. The NMM global discrete equations are derived by the Galerkin method based on the governing equations, boundary conditions and also the NMM displacement approximations. To verify the convergence and also the accuracy of the proposed method, several numerical experiments are conducted through uniform MCs composed of square mathematical elements, and the results are in excellent agreement with the reference ones; besides, the effects of material principal direction and hole configurations on the mechanical behaviors of the orthotropic composites are also revealed.

Adaptive phase-field modeling of fracture in orthotropic composites

An adaptive phase-field method is developed and applied to model fracture propagation in orthotropic composites. The proposed approach extends the work of Muixí et al. (2020) to orthotropic composites through following modifications: (a) elastic tensor is evaluated in the global coordinate system from a given engineering stiffness matrix in the principal material coordinates, (b) strain energy density is additively decomposed into fiber and matrix-dominated modes, and (c) a penalized second-order structural tensor is introduced in the phase-field equation facilitating preferential damage growth along the fiber orientation. The developed approach is validated through several benchmark examples and available experimental results.Several numerical failure experiments are conducted varying fiber orientation, adhesive layer thickness, shear modulus, and fracture toughness. A large increase in ductility and peak-load carrying capacity is observed for laminate configurations where the fibers are oriented such that the principal material coordinates and the global coordinates are aligned. An increase in the adhesive layer’s fracture toughness increases the macroscopic ductility and prevents catastrophic failure of laminate. The results of this study provide valuable insights into the failure mechanisms in orthotropic composites.

Influence of plate thickness on the results of residual stresses determination by through hole drilling in orthotropic composites of different fiber orientation

The main objective of this study is to characterize residual stress in composite orthotropic plates using hole drilling method. The values of hole diameter increment in the principal anisotropic directions, which were obtained from electronic speckle-pattern interferometry on the external surface of the specimen, serve as the initial experimental information. The theoretical foundation of the approach is based on S. G. Lekhnitsky's analytical solution, which describes a stress concentration along the edge of the central open hole in a rectangular orthotropic plate under tension in principal anisotropy directions. The transitional model, that is essential link for deriving residual stress components from initial experimental data, provides the unequivocally solution to the properly posed inverse problem. Firstly, the validation of the transitional model regarding prescription of residual stress values for specific plies within a specimen’s thickness is based on calibration experiments. These experiments yield data for unidirectional and cross-ply composite plates of three different thicknesses. The results demonstrate that the values of principal residual stress components for cross-ply composite material are independent of plate thickness. This means that the transition model, based on the measurements of deformation responses to through hole drilling on the external plate face, can be reliably implemented to characterize the maximal residual stress values present in the middle plane of the composite plate. An investigation into the effect of hole diamter values on the determination of residual stress is conducted for cross-ply and angle-cross-ply composites. It is shown that a hole of diameter of 3.2 mm provides the most reliable results.

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.

Determination of fracture toughness and traction–separation relation in Mode I/II of a natural quasi-brittle orthotropic composite using multi-specimen approach

The fracture behavior of quasi-brittle naturally occurring composites is characterized by the presence of fracture process zone (FPZ), which is attributed by crack bridging and micro-cracking in wood. The FPZ limits the use of existing standards for fracture toughness. Also, the repeated loading–unloading approach using single specimen is difficult due to crack face interference. Further, the crack growth monitoring is difficult since the crack tip may be buried inside FPZ. So far, the compliance based beam method (CBBM) has offered a reasonable solution to these challenges. However, the CBBM is not an absolutely independent approach as it uses elastic constant and compliance determined from other experiments. Naturally occurring materials, like wood, exhibits large variations in its properties. Therefore, the use of parameters from multiple other experiments decreases the confidence in measured fracture toughness. Considering this, the present work evaluates the fracture toughness attributed by critical energy release rate of New Zealand Pine wood. Firstly, the research method follows a stand-alone multi-specimen approach to evaluate fracture toughness without any requirement for crack growth monitoring. Secondly, it experimentally establishes the traction–separation relation for both Mode I and II. This work has a general applicability to other natural quasi-brittle orthotropic solids like bone.

Analysis of the properties of orthotropic composites in terms of their use in airframe repairs

The aim of the research was to determine the basic strength properties of orthotropic composites in terms of their use in the repair of aircraft airframes. The objects of the tests were three types of composites reinforced with carbon fibers: produced using the wet method with a thickness of 2.5 mm, commercial with a thickness of 2 mm and commercial with a thickness of 7.3 mm. Specimens cut out from the first two types of materials were subjected to a static tensile test with a force applied in the direction of the fibers and at an angle of 45°, which enabled the determination of tensile strength and modulus of elasticity. Specimens made of 7.3 mm thick composite were subjected to four-point bending and tensile tests to determine Young's modulus, compression and impact strength, also taking into account two directions of load application. The values of stresses and Young's modulus determined in this way indicate much lower strength and stiffness of orthotropic composites apart from the reinforcement fibers’ directions, which is the basis for replacing them with quasi-isotropic composites in repairs of aircraft airframes.

Dynamic Characterization of Hexagonal Microstructured Materials with Voids from Discrete and Continuum Models.

The mechanical response of materials such as fiber and particle composites, rocks, concrete, and granular materials, can be profoundly influenced by the existence of voids. The aim of the present work is to study the dynamic behavior of hexagonal microstructured composites with voids by using a discrete model and homogenizing materials, such as micropolar and classical Cauchy continua. Three kinds of hexagonal microstructures, named regular, hourglass, and skew, are considered with different length scales. The analysis of free vibration of a panel described as a discrete system, as a classical and as a micropolar continuum, and the comparison of results in terms of natural frequencies and modes show the advantage of the micropolar continuum in describing dynamic characteristics of orthotropic composites (i.e., regular and hourglass microstructures) with respect to the Cauchy continuum, which gives a higher error in frequency evaluations for all three hexagonal microstructured materials. Moreover, the micropolar model also satisfactorily predicts the behavior of skewed microstructured composites. Another advantage shown here by the micropolar continuum is that, like the discrete model, this continuum is able to present the scale effect of microstructures, while maintaining all the advantages of the field description. The effect of void size is also investigated and the results show that the first six frequencies of the current problem decrease by increasing in void size.

Crush simulations of composite energy absorbing structural systems

A recently developed material model for orthotropic composites is demonstrated by modeling an energy absorbing crush event used in the development of automotive components. The material model (MAT213) provides a wide variety of capabilities such as tension/compression asymmetric behavior, visco-elastic/plastic behavior, damage modeling, rate and temperature effects with the ability to support these features in shell and solid finite elements. Data from limited laboratory testing of composite coupons is used to construct the material model input. Data from laboratory conducted crush testing is used to validate the material model. The predictions from the explicit finite element (FE) simulations are compared against the laboratory data as well as a popular constitutive model used in the automotive industry (MAT058). Results show that even with incomplete material data to build the constitutive model, MAT213 yields superior results that match experimental validation data reasonably well.

Torsional wave propagation on a penny-shaped crack in an orthotopic layer sandwiched between two rigid discs bonded by an orthotropic elastic half-space

The mechanical stability of the interface of two materials determines the stress behavior of the interface. So, observation of failure analysis in orthotropic composites with penny-shaped crack and circular disc in orthotropic materials due to the presence of torsional waves play a major role in structural design. The present article concerns the study of the torsional wave propagation of a penny-shaped crack in an orthotropic layer and two circular discs bonded between the layer and half-spaces. A general solution for the system is presented as a set of dual integral equations using the Hankel transform technique. Using Abel's transform method, the equations have been transformed into Fredholm integral equations of the second kind, which have been solved numerically to compute the stress intensity factors (SIFs) near the rims of crack and discs. Numerical results are obtained using material constants of two orthotropic mediums to demonstrate the impact of material non-homogeneity, normalized disc radius, and layer depth on SIFs and portrayed by virtue of graphs. The analysis of the physical quantity SIF in the present model leads to speculation about the stability of composites against the propagation of cracks in layered engineering solids by surveilling geometric parameters of orthotropic materials and layer depth.

Moisture transport in laminated wood and bamboo composites bonded with thin adhesive layers – A numerical study

Sustainable materials such as laminated wood and bamboo composites are increasingly being used in the construction of green buildings across the world. Such products may be exposed to cyclic environmental conditions and exhibit moisture-induced damage. Predicting the moisture profile variation with time is the first step towards understanding the performance of such products under combined mechanical and environmental loads. The main objective of this study is to develop and validate an efficient, physically-based tool to elucidate the transient moisture transport in layered orthotropic composites made from wood and bamboo. To ensure the capability of the framework in capturing the essential moisture transport mechanisms, a comprehensive literature review was conducted to determine the most critical parameters in moisture transport phenomena in laminated panels. Thermal moisture analogy theory was used for simulating the moisture transport across the composite material cross-section. The analogy approach was first verified based on a simple one-dimensional (1-D) analytical model. Then, moisture profiles in various small laminated composite panels were predicted using a three-dimensional (3-D) finite element model developed in ANSYS Workbench©. Unlike previous studies, the moisture adsorption curve of the material was used instead of employing surface emission coefficient to estimate moisture flux at the surfaces. Results were compared against experimental data for validation purposes. A series of parametric studies were conducted using the validated model to highlight quantitatively the effect of glue line and the constituents’ (i.e. wood/bamboo and adhesive) physical properties on the moisture transport across the composite panel. The model predictions showed a remarkably good description of the data reported in the literature. For the first time, the results showed that the choice of adhesive along with the combination of wood/bamboo physical properties can significantly affect the panel’s moisture profile even after 14 days under similar environmental conditions.

Evaluating SIFs in finite orthotropic composites from experimentally determined stress coefficients

Unlike with isotropy materials, determining stress intensity factors in orthotropic composites is complicated as they can depend on constitutive properties and principal material directions. Acknowledging the above, this paper develops a novel technique to evaluate stress intensity factors in finite, plane-stressed, orthotropic composites. Upon substantiating the numerical reliability of the approach, KI is determined experimentally in a finite tensile loaded double-edge cracked [013/905/013] graphite-epoxy composite laminate from displacement-evaluated stress coefficients. Only a single DIC-measured displacement field is need. Advantages of the method include applicability beyond a laboratory environment and to other structural shapes, loads and crack configurations, wide acceptable range of stress coefficients and highly arbitrary source locations of the measured input data. Unlike purely numerical or theoretical approaches, the method does not require knowing the external loading. This is significant as loads are often unknown in practice. Results are verified independently.

Maximum principal strain criterion for fracture in orthotropic composites under combined tensile/shear loading

A strain-based criterion is presented in this paper to investigate mixed-mode I/II fracture behavior in orthotropic materials. The maximum principal strain component, in the vicinity of a crack existing in an orthotropic medium, is formulated considering the T-stress effect as well as the singular terms. The criterion predicts the onset of mixed-mode I/II fracture when the maximum principal strain reaches its critical value. The role of T-stress, calculated for an orthotropic domain, in the mixed-mode I/II fracture toughness assessment is explored theoretically. Along with other criteria, the accuracy of the proposed criterion is evaluated by predicting the fracture test data in the literature for wood species and laminated composites. The developed criterion is shown to be superior to other criteria in predicting the onset of mixed-mode I/II fracture in orthotropic materials.

Inversion of elastic constants of composite materials by single test based on virtual fields method

In this paper, a method of obtaining four elastic constants of orthotropic composites by single tensile test is proposed. The principle of this method is to obtain the full field strain on the surface of the specimen through the tensile test of the specimen with a specific geometry, and to invert the measured in-plane strain field into the virtual fields method (VFM) to obtain the elastic constants. Based on the deformation field data generated by finite element numerical simulation, the effects of design parameters such as effective length, notch position, notch size and fillet radius on the identification results of elastic parameters of V-notch tensile specimen are studied. The results show that the inversion results of symmetrical V-notch specimen with 50 mm length, 12 mm notch size and 3.1 mm fillet radius are the best, and the sum of absolute relative errors of four elastic constants is less than 3%, which verifies the feasibility of the method.