Anisotropic Laminates Research Articles

Shaping Thermal Transport and Temperature Distribution via Anisotropic Carbon Fiber Reinforced Composites.

With the ongoing electrification of vehicles, thermal management is on everyone's lips. To prevent overheating in electronic systems, new design strategies for thermal dissipation are needed. Thermally anisotropic materials enable targeted directional heat transport due to their anisotropic thermal conduction. Laminates made of unidirectionally aligned carbon fibers in a polymer matrix can be tailored regarding their in-plane anisotropy. Exposing the laminates to a temperature gradient reveals that the thermal transport is determined by their anisotropic properties. The corresponding heat flow can be visualized by IR thermography. The combination of anisotropic laminate discs into composite materials, similar to building with toy bricks, enables precise control of heat transport in the macroscopic composite materials. Thus, we achieve control of heat flow at the level of the individual components. In addition, we show that the orientation of anisotropy relative to the temperature gradient is crucial to guide the heat flow selectively. We found that the ratio of thermal anisotropy, the amount and arrangement of anisotropic components, and their positioning in the composite strongly influence heat transport. By combining all these factors, we are able to locally control the heat flow in composites by creating materials to either dissipate heat or block heat transport. The proposed concept can be extended to different shapes of building blocks in two or three dimensions.

PA-LCR: A flexible ultrasonic characterization method

Abstract Critically refracted longitudinal (LCR) wave is demonstrated to be prominent in the characterization sensitivity of stress or surface/sub-surface defects. According to Snell’s law, however, its excitation seriously relies on the inclined angle of wedge, i.e., the first critical angle (θ CR). From this, it shows poor adaptability to the variations of wave velocity, especially for elastic anisotropic materials, e.g., carbon fibre reinforced plastic (CFRP) composites. An enhanced strategy based on the phased array ultrasonic, termed PA-LCR, is introduced here. It applies a wide angular distribution of energy to achieve beam steering, and then the beam is targeted at θ CR. LCR wave is successfully excited both in isotropic steel and anisotropic laminate, and the signal-to-noise ratio (SNR) is as high as 19.0-34.6 dB. With the same delay law, the wave can be excited within a wide wave velocity range about 6000 m/s for the steel, and about 3600 m/s for the CFRP laminate, for -6 dB amplitude. The performance of the LCR technique is strengthened by the proposed PA-LCR method.

Experimental evaluation of the use of cruciform specimens for biaxial stability analysis

Novel research is proposed about the suitability of cruciform specimens for estimating the stress-strain response and buckling modes of flat laminates under equibiaxial compression. The experimental challenge lies in determining whether the specimen design and test procedure can be adequate to observe geometric instability at the coupon scale with small dimensions of the tested region. Although the literature on composite buckling is extensive, the number of studies that include experimental biaxial testing of flat laminates is limited, particularly when considering strong flexural-torsional coupling. In this work the region of interest of the cruciform specimen consists of a carbon-fibre reinforced [∓45]S laminate with shape and boundary conditions close to a clamped square plate. For the first time, the buckling mode of an anisotropic laminate is observed in the central region of a cross-shaped specimen using 3D deflection surface data recorded by Digital Image Correlation. The effect of flexural-torsional coupling at the bifurcation onset is experimentally corroborated through the orientation of the buckling mode, which is analytically utilized to quantify the proportion between bending and twist moments. Non-linearities exhibited in the stress-strain evolution of the biaxially loaded region are verified to be independent of the response of the sample's arms. Furthermore, no previous experimental investigation has shown the differences in local strain gauge measurements induced by the stress state at the ply level. Additionally, this work adapts the method for strength reduction to estimate the real critical stress of a bi-compressed laminate.

Elastic bounds of the coupling tensor of anisotropic composite laminates: a polar approach

In the equivalent single-layer theories of anisotropic laminates, the coupling tensor B describes the relation between the in- and out-of plane behaviour of the plate. This tensor has some peculiar characteristics and in particular it is not defined, so it is normally considered as an unbounded tensor. We show in this paper a way to determine some relations between the polar invariants of B and those of the tensors describing the in- and out-of plane behaviours of the laminate, A and D , respectively. These relations constitute a set of bounds for the invariants of all the tensors of the laminate, A , B and D . It is hence shown that also the components of B must satisfy some conditions. Some peculiar cases, interesting for applications, are also considered.

On the mechanical and mathematical properties of the stiffness and compliance coupling tensors of composite anisotropic laminates

The problem of determining the general and relevant mechanical and mathematical properties of the stiffness, [Formula: see text], and compliance, [Formula: see text], tensors describing the bending-extension coupling of anisotropic laminates is addressed in this paper. A set of theoretical results is proposed, showing some peculiarities of these tensors, from the mathematical and mechanical point of view. The theoretical analysis and the mechanical results are obtained through an extensive use of the so-called polar formalism, introduced as early as 1979 by Prof. G. Verchery.

Guided wave skew velocity correction in anisotropic laminates

Guided ultrasonic wave propagation in anisotropic structures results in directional dependency of velocity and wave skewing effects that can impact the accuracy of damage detection. Phase and group velocities of the A0 guided wave mode, propagating in a unidirectional carbon fiber reinforced laminate, were investigated experimentally and through finite element analysis. A correction for the significant offset in phase and group velocities due to wave skewing effects is illustrated for both point and short line sources, achieving good agreement with theoretical calculations assuming planar wave fronts. The influence of the line excitation length on velocity measurements is discussed.

Multi-Layered and Homogenized Models for In-Plane Guided Wave Excitation, Sensing, and Scattering in Anisotropic Laminated Composites

The numerical evaluation of elastic guided wave (EGW) phenomena is an important stage in the development and configuration of ultrasonic-based non-destructive testing/structural health monitoring (NDT/SHM) systems. To reduce the computational costs, which are typical for EGW simulations in laminated composite structures, and to make the corresponding parametric analysis possible, the latter could be treated by employing an effective single-layer model with homogenized anisotropic material properties. The present study investigates the applicability of such an approach to simulate EGW excitation, propagation, scattering, and sensing in laminate composite structures, which are among the typical problems for ultrasonic-based NDT/SHM. To this end, two homogenized models have been implemented: the well-known static long-wave homogenization approach and the advanced Lamb wave homogenization method, where the effect of angular and frequency dispersion of EGWs is taken into account. To illustrate their performance, in-plane elastic guided wave excitation and sensing with surface-mounted piezoelectric transducers as well as wave scattering by a T-shaped stringer in cross-ply symmetric anisotropic laminates are examined by employing a recently developed semi-analytical hybrid approach. The limits of the applicability of both homogenized models are demonstrated and discussed via the comparison with the multi-layered model. The general conclusion from the obtained results is that only a qualitative, although computationally efficient, description of the EGW phenomena in the considered composites can be achieved using single-layer models.

A hybrid optimization algorithm for gate locations in the liquid composite molding process

It is costly to optimize the location of multiple injection gates through a trial and error-based method in the liquid composite molding, even though there are high fidelity physics-based numerical models. A hybrid optimization method called the Simulated Annealing Genetic Algorithm is proposed in this article, which uses the genetic algorithm to provide a global search for a predetermined time and then is further improved by the simulated annealing algorithm. The optimization results of multiple injection gates show that the number of convergence iterations using the Simulated Annealing Genetic Algorithm is less than that using the genetic algorithm, and the phenomenon becomes more obvious as the number of injection gates increases. The case shows that the Simulated Annealing Genetic Algorithm can solve the multiple injection gate configuration problems of highly anisotropic laminates without extra work. The optimization results are in good agreement with the experimental results.

Improved Unsupervised Learning Method for Material-Properties Identification Based on Mode Separation of Ultrasonic Guided Waves

Numerical methods, including machine-learning methods, are now actively used in applications related to elastic guided wave propagation phenomena. The method proposed in this study for material-properties characterization is based on an algorithm of the clustering of multivariate data series obtained as a result of the application of the matrix pencil method to the experimental data. In the developed technique, multi-objective optimization is employed to improve the accuracy of the identification of particular parameters. At the first stage, the computationally efficient method based on the calculation of the Fourier transform of Green’s matrix is employed iteratively and the obtained solution is used for filter construction with decreasing bandwidths providing nearly noise-free classified data (with mode separation). The filter provides data separation between all guided waves in a natural way, which is needed at the second stage, where a more laborious method based on the minimization of the slowness residuals is applied to the data. The method might be further employed for material properties identification in plates with thin coatings/interlayers, multi-layered anisotropic laminates, etc.

Experimental Investigation of Bubble Migration near Anisotropic Beams.

In order to resist bubble loading, anisotropic composite materials are the development direction of the future. The objective of this paper was to experimentally investigate the hydrodynamic performance of anisotropic laminate composite plates, with a focus on the effect of its anisotropic characteristics on single bubble migration. In these experiments, the bubble was generated in a transparent water tank filled with sufficiently degassed water by Joule heating at the connecting point of the electrodes through the discharge of a 6600 μF charge to 800 V, and a high-speed camera system with a recording speed of 40,000 frames per second was used to record the temporal evolution of bubble patterns and the dynamic responses of the laminated composite plates. The results are presented for two anisotropic cantilever composite beams with different ply angles, namely, 0° and 30°. Several variables, such as the shapes of the bubble, the curved trail of motion of the bubble center, bubble collapse time, and bubble initial standoff distances were extracted from the photographic images. The results showed that bubble migration near the 30° plate presents a curved bubble trail with an evident tilted angle during the collapse and rebound stages, which is very different from bubbles that all move vertically above the 0° plate. Furthermore, a characterization method for bubble migration was proposed to quantitatively describe the curved bubble trails and the deformation of the composite beams in temporal and spatial scales. This method shows that the curved bubble trails near the 30° plate are closely related to the dynamic response of composite beams, with a focus on the bending-twisting coupling effect.

A complex Fourier series solution for buckling of VAT composite laminates with elastically restrained edges

Variable Angle Tow (VAT) composites have general anisotropic characteristics, and their fiber orientation angle varies continuously along an arbitrary direction. Therefore, the investigation of their buckling performance is quite challenging. Different from the commonly used numerical methods, a new method called complex Fourier series solution is proposed to study the buckling of VAT laminates with elastically restrained edges. First the prebuckling analysis is achieved by introducing Airy’s stress function and expanding it into a complex Fourier series form. And the corresponding mid-plane internal forces with non-uniform distribution are determined. Based on classical laminated plate theory, the buckling analysis of VAT laminate is carried out. The transverse displacement is also expressed as a complex Fourier series. And the critical buckling load and buckling mode shape of VAT laminate are obtained. The accuracy of the presented complex Fourier series solution is verified by comparing with the existing results. The influence of fiber orientation angles, boundary stiffness and boundary conditions on the critical buckling load and buckling mode shape is investigated in numerical examples. Results show that boundary stiffness as well as fiber path have great influence on the critical buckling load and buckling mode shape of VAT laminate. By adjusting the fiber orientation angles and the translational stiffness of the elastically restrained boundary can effectively improve the critical buckling load of VAT laminate. This paper provides a new method for the analysis of general anisotropic laminates with in-plane variable stiffness and the present complex Fourier series solution can also be used as a benchmark for the verification of other numerical results.

Buckling analysis of symmetrically laminated composite plates including the effect of variable pre-stress field using the Ritz method

A buckling solution capable of accounting for prebuckling stress field heterogeneities is proposed. Oftentimes the same structural elements that restrict the out-of-plane displacement of the edges of a plate may also constrain their in-plane movements and cause heterogeneous prebuckling stress fields. The effect of these constraints and the consequent prebuckling stress field heterogeneity is vastly overlooked in the context of approximate analytical buckling solutions. The novelty of this work lies in basing the eigenvalue buckling analysis on a calculated prebuckling in-plane stress field. The in-plane stress field is determined by conducting a displacement-based linear elasticity analysis. In both elasticity and eigenvalue buckling analyses, the deformations of the anisotropic laminate were approximated using a first-order shear deformation theory. The equilibrium and instability equations were derived using the principle of stationary total potential energy and by employing the Ritz method. The derived formulation along with arbitrarily selected sets of boundary conditions was incorporated into a Matlab program and used for demonstrating the effect of in-plane constraints on prebuckling and buckling behavior of plates. Through a parametric study, the effect of the geometric configuration of plates on their buckling strength for selected symmetrical laminates was investigated.

An Experimental and Computational Study on the Low Velocity Impact-Induced Damage of a Highly Anisotropic Laminated Composite Panel

Abstract The low velocity impact (LVI)-induced damage of a highly anisotropic laminate [0/90/0/909]s has been studied experimentally and numerically. The purpose of the analyses of this laminate is that this stacking sequence resembles a sandwich composite panel, in the sense that the [0/90/0] outer layers serve as the “face sheet” while the inner 18 plies of 90 deg layers serve as the “core.” The LVI-induced damage pattern of this laminate is unique and referred to as the “kidney” shape. The “kidney” shape damage is caused by a strong interaction between matrix transverse cracking and delamination, hence is challenging to be computationally captured. The enhanced Schapery theory (EST) model has been improved with the capability to model material inelasticity, as well as a novel mixed-mode cohesive law, to tackle this problem. EST with inelasticity (EST-InELA) is shown to be able to predict load responses and damage morphology accurately and efficiently. The aim of this paper is to provide a challenging LVI case to examine and calibrate computational models.

Identification of Elastic Properties of Composites by Inversion of Ultrasonic Guided Wave Data

Given the inherent manufacturing variabilities and potential for in-service damage of composite parts, the identification of the elastic properties of composites is important to ensuring the safety and the proper performance of the part. The primary objective of this manuscript is to determine, nondestructively, the elastic properties of composite parts, whether as in-situ components that are part of a larger system, or as laboratory coupons. The proposed technique is based on multimode and dispersive ultrasonic guided waves propagating along a single direction, and the inversion of their phase velocity dispersion curves. The inversion procedure utilizes an efficient Semi-Analytical Finite Element method to solve the forward problem, and a Simulated Annealing algorithm as the optimization tool. The method is particularly well-suited for the characterization of composite laminates. In particular, the manuscript presents experimental evidence of the effectiveness of this technique, that was suggested earlier in a solely numerical work previously conducted by the authors. The test results show that reasonable accuracy can be obtained in the identification of four in-plane and three out-of-plane engineering constants of a quasi-isotropic laminate and a highly anisotropic laminate utilizing the single wave propagation direction. Non-obvious sensitivities of certain wave modes to particular constants are explained on the basis of stress coupling phenomena that are revealed by the SAFE wave propagation models. The study gives experimental evidence of the suitability of ultrasonic guided wave inversion schemes to identify the engineering constants of laminated composites, with the potential to properly characterize parts in-situ, because of the insensitivity of guided waves to boundary conditions located outside of the transmitter–receiver path.

Convex or non-convex? On the nature of the feasible domain of laminates

This work investigates two aspects linked to the nature of the feasible domain of anisotropic laminates. In the first part of the paper, proofs are given on the non-convexity of the feasible domain for full anisotropic and for membrane-orthotropic laminates, either in the lamination parameters space or in the polar parameters one. Then, adopting the polar formalism, some particular cases are studied, providing analytical expressions of new narrower bounds, in terms of polar parameters of the membrane stiffness tensor. For a particular case, the exact expression of the membrane stiffness tensor feasible domain is determined. In the second part of the paper, a discussion on the necessary and sufficient condition to get membrane/bending uncoupled and/or homogeneous laminates is presented. It is proved that, when the distinct orientations within the stack are two, quasi-triviality represents a necessary and sufficient condition to achieve uncoupling and/or quasi-homogeneity. This work disproves the common belief of the convexity of the feasible domain in the lamination parameters space and fosters new ideas to face the problem of the determination of the feasible domain of laminates.

A macro‐element strategy based upon spectral finite elements and mortar elements for transient wave propagation modeling. Application to ultrasonic testing of laminate composite materials

SummaryProposing efficient numerical modeling tools for high‐frequency wave propagation in realistic configurations, such as the one appearing in ultrasonic testing experiments, is a major challenge, especially in the perspective of inversion loops or parametric studies. We propose a numerical methodology addressing this challenge and based upon the combination of the spectral finite element method and the mortar element method. From a prior decomposition of the scene of interest into “macro‐elements,” we show how one can improve the performances of the standard finite element procedures in terms of memory footprint and computational load. Additionally, using this decomposition, we are able to efficiently reconstruct important modeling features on‐the‐fly, such as orientations of anisotropic materials or splitting directions of perfectly matched layers formulations, altogether in a robust and efficient manner. We believe that this strategy is particularly suitable for parametric studies and sensitivity analysis. We illustrate our strategy by simulating the propagation of an ultrasonic wave into an immersed and curved anisotropic laminate 3D specimen flawed with an internal circular delamination of varying size, thus showing the efficiency and the robustness of our approach.

Guided wave time-reversal imaging of macroscopic localized inhomogeneities in anisotropic composites

Estimation of damage position and extent in the inspected structure is among the emerging problems of active structural health monitoring (SHM) with elastic guided waves. Unlike conventional non-destructive testing (NDT) techniques, which assume continuous surface scanning, SHM systems operate only with data from a limited number of sensors. Nevertheless, in the case of isotropic (metal) plate-like structures, computational time-reversal techniques have proved to be effective for estimating in situ the location and size of wave sources and/or local scatterers within the SHM concept. With composite plates, the reconstruction procedure faces additional difficulties associated with the complexity of wave phenomena caused by their lamination and anisotropy. In this article, we present an extension of the time reversal technique for the case of composite laminate plate-like structures. This technique relies on the simulation of the reversed guided waves generated by reciprocal surface loads applied at a sparse set of measurement points of a real sensor network. The proposed implementation is based on the far-field asymptotics for guided waves generated in arbitrarily anisotropic laminate waveguides by a prescribed source, which have been derived from the path integral representations in terms of Green’s matrix for the structures considered. The performance of this approach has been experimentally tested on cross-ply carbon fiber-reinforced plastic plates showing reliable and adequate results for both active (piezoactuators) and passive (artificial defects) source characterization.

Integration of multiple passive load mitigation technologies by automated design optimization—The case study of a medium‐size onshore wind turbine

AbstractThe present work considers the application to a medium‐size onshore wind turbine of passive load mitigation technologies, first individually and then integrated together. The study is conducted with the help of a comprehensive automated design optimization procedure, which eases the generation and comparison of consistent solutions, each satisfying the same overall requirements. Passive load mitigation is here obtained by inducing bend‐twist coupling to the blades. The coupling is generated by rotating the fibers of anisotropic laminates, by the aerodynamic sweeping of the blade and by offsetting the spar caps in opposite directions on the pressure and suction sides. The first two solutions yield significant benefits, while the third, for this particular wind turbine, is ineffective. In addition, the typical power losses associated with bend‐twist coupled blades are reduced by a novel regulation strategy that varies the fine pitch setting in the partial load region. After having considered each load mitigation technology by itself, fiber rotation and sweeping are combined together and used to design a rotor with a larger swept area. The final design generates cost of energy savings thanks to a large‐diameter, highly coned, soft‐in‐bending rotor that results in lower turbine costs and a higher energy capture compared with the baseline design.

A framework for FFT-based homogenization on anisotropic lattices

In order to take structural anisotropies of a given composite and different shapes of its unit cell into account, we generalize the basic scheme in homogenization by Moulinec and Suquet to arbitrary sampling lattices and tilings of the d-dimensional Euclidean space. We employ a Fourier transform for these lattices by introducing the corresponding set of sample points, the so called pattern, and its frequency set, the generating set. The pattern and the generating set represent the anisotropy of both the shape of the unit cell and the chosen preferences in certain sampling directions. In several cases, this Fourier transform is of lower dimension than the space itself. For the so called rank-1-lattices it reduces to a one-dimensional Fourier transform having the same leading coefficient as the fastest Fourier transform implementation available. We illustrate the results using the generalized basic scheme on an anisotropic laminate and on a generalized ellipsoidal Hashin structure. For both we give an analytical solution to the elasticity problem, in two- and three dimensions, respectively. We then illustrate the possibilities of choosing a pattern. Compared to classical grids this introduces both a reduction of computation time and a reduced error of the numerical method. It also allows for anisotropic subsampling, i.e. choosing a sub lattice of a pixel or voxel grid based on anisotropy information of the material at hand.

An experimental study on mechanical response of single-lap bolted CFRP composite interference-fit joints

This paper reports an experimental study on mechanical response of single-lap bolted composite interference-fit joints in their entire life span. Particular focus was given to interface behavior, bearing response, strain distribution and out-of-plane deformation under varying multiple parameters including interference-fit percentage, tightening torque and stacking sequence. The 3D digital image correlation system was used to characterize development of strain concentration and deformation. Microscopy studies on coupled interface and bearing plane were conducted to understand the damage mechanism. It‘s found that the bolt-inserting can act as cold expansion which facilitates forming tightly coupled interface and prohibits inclination of bolt. The linear phase of stress-strain behavior is prolonged by tightening torque which inhibits delamination growth in bearing plane, induces friction force to balance external load and postpones bolt-to-hole bearing action. The strain around the hole goes through a switch from release of residual pressure on tensile side to squeezing on bearing side. During the switch the interface keeps tightly coupled without delay in load take-up. Strain concentration bands were observed in the joints with highly anisotropic laminates, whereas it is localized around bolt-hole in quasi-isotropic laminates. The joint structure possesses its own response characteristics which are beyond extrapolation from ply properties.