Wave propagation analysis in laminated composite plates with transverse cracks using the wavelet spectral finite element method

This paper presents a newly developed wavelet spectral finite element (WFSE) model to analyze wave propagation in anisotropic composite laminate with a transverse surface crack penetrating part-through the thickness. The WSFE formulation of the composite laminate, which is based on the first-order shear deformation theory, produces accurate and computationally efficient results for high frequency wave motion. Transverse crack is modeled in wavenumber-frequency domain by introducing bending flexibility of the plate along crack edge. Results for tone burst and impulse excitations show excellent agreement with conventional finite element analysis in Abaqus (R). Problems with multiple cracks are modeled by assembling a number of spectral elements with cracks in frequency-wavenumber domain. Results show partial reflection of the excited wave due to crack at time instances consistent with crack locations. (C) 2014 Elsevier B.V. All rights reserved.

COMPUTATIONAL MODELING OF A MULTI-LAYERED PIEZO-COMPOSITE BEAM MADE UP OF MFC

The Variational Asymptotic Method (VAM) is used for modeling a coupled non-linear electromechanical problem finding applications in aircrafts and Micro Aerial Vehicle (MAV) development. VAM coupled with geometrically exact kinematics forms a powerful tool for analyzing a complex nonlinear phenomena as shown previously by many in the literature 3 - 7] for various challenging problems like modeling of an initially twisted helicopter rotor blades, matrix crack propagation in a composite, modeling of hyper elastic plates and various multi-physics problems. The problem consists of design and analysis of a piezocomposite laminate applied with electrical voltage(s) which can induce direct and planar distributed shear stresses and strains in the structure. The deformations are large and conventional beam theories are inappropriate for the analysis. The behavior of an elastic body is completely understood by its energy. This energy must be integrated over the cross-sectional area to obtain the 1-D behavior as is typical in a beam analysis. VAM can be used efficiently to approximate 3-D strain energy as closely as possible. To perform this simplification, VAM makes use of thickness to width, width to length, width multiplied by initial twist and strain as small parameters embedded in the problem definition and provides a way to approach the exact solution asymptotically. In this work, above mentioned electromechanical problem is modeled using VAM which breaks down the 3-D elasticity problem into two parts, namely a 2-D non-linear cross-sectional analysis and a 1-D non-linear analysis, along the reference curve. The recovery relations obtained as a by-product in the cross-sectional analysis earlier are used to obtain 3-D stresses, displacements and velocity contours. The piezo-composite laminate which is chosen for an initial phase of computational modeling is made up of commercially available Macro Fiber Composites (MFCs) stacked together in an arbitrary lay-up and applied with electrical voltages for actuation. The expressions of sectional forces and moments as obtained from cross-sectional analysis in closed-form show the electro-mechanical coupling and relative contribution of electric field in individual layers of the piezo-composite laminate. The spatial and temporal constitutive law as obtained from the cross-sectional analysis are substituted into 1-D fully intrinsic, geometrically exact equilibrium equations of motion and 1-D intrinsic kinematical equations to solve for all 1-D generalized variables as function of time and an along the reference curve co-ordinate, x(1).

A Study of Composite Beam with Shape Memory Alloy Arbitrarily Embedded under Thermal and Mechanical Loadings

The constitutive relations and kinematic assumptions on the composite beam with shape memory alloy (SMA) arbitrarily embedded are discussed and the results related to the different kinematic assumptions are compared. As the approach of mechanics of materials is to study the composite beam with the SMA layer embedded, the kinematic assumption is vital. In this paper, we systematically study the kinematic assumptions influence on the composite beam deflection and vibration characteristics. Based on the different kinematic assumptions, the equations of equilibrium/motion are different. Here three widely used kinematic assumptions are presented and the equations of equilibrium/motion are derived accordingly. As the three kinematic assumptions change from the simple to the complex one, the governing equations evolve from the linear to the nonlinear ones. For the nonlinear equations of equilibrium, the numerical solution is obtained by using Galerkin discretization method and Newton-Rhapson iteration method. The analysis on the numerical difficulty of using Galerkin method on the post-buckling analysis is presented. For the post-buckling analysis, finite element method is applied to avoid the difficulty due to the singularity occurred in Galerkin method. The natural frequencies of the composite beam with the nonlinear governing equation, which are obtained by directly linearizing the equations and locally linearizing the equations around each equilibrium, are compared. The influences of the SMA layer thickness and the shift from neutral axis on the deflection, buckling and post-buckling are also investigated. This paper presents a very general way to treat thermo-mechanical properties of the composite beam with SMA arbitrarily embedded. The governing equations for each kinematic assumption consist of a third order and a fourth order differential equation with a total of seven boundary conditions. Some previous studies on the SMA layer either ignore the thermal constraint effect or implicitly assume that the SMA is symmetrically embedded. The composite beam with the SMA layer asymmetrically embedded is studied here, in which symmetric embedding is a special case. Based on the different kinematic assumptions, the results are different depending on the deflection magnitude because of the nonlinear hardening effect due to the (large) deflection. And this difference is systematically compared for both the deflection and the natural frequencies. For simple kinematic assumption, the governing equations are linear and analytical solution is available. But as the deflection increases to the large magnitude, the simple kinematic assumption does not really reflect the structural deflection and the complex one must be used. During the systematic comparison of computational results due to the different kinematic assumptions, the application range of the simple kinematic assumption is also evaluated. Besides the equilibrium study of the composite laminate with SMA embedded, the buckling, post-buckling, free and forced vibrations of the composite beam with the different configurations are also studied and compared.

Uncertainty assessment approach for composite structures based on global sensitivity indices

The problem of uncertainty propagation in composite laminate structures is studied. An approach based on the optimal design of composite structures to achieve a target reliability level is proposed. Using the Uniform Design Method (UDM), a set of design points is generated over a design domain centred at mean values of random variables, aimed at studying the space variability. The most critical Tsai number, the structural reliability index and the sensitivities are obtained for each UDM design point, using the maximum load obtained from optimal design search. Using the UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on supervised evolutionary learning. Finally, using the developed ANN a Monte Carlo simulation procedure is implemented and the variability of the structural response based on global sensitivity analysis (GSA) is studied. The GSA is based on the first order Sobol indices and relative sensitivities. An appropriate GSA algorithm aiming to obtain Sobol indices is proposed. The most important sources of uncertainty are identified.

Uncertainty propagation in inverse reliability-based design of composite structures

An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.

Assessment of delamination in composite beams using shear horizontal (SH) wave mode

Interaction of Lamb waves with structural damage can lead to wave mode conversion. In this study, the shear horizontal (SH) wave, from the mode conversion of the fundamental symmetric Lamb wave (S0), was used for quantitative identification of delamination in composite beams, based on advanced signal processing using an inverse approach. SH wave propagation under various delamination conditions in CF/EP beams made of orthotropic plain woven fabrics was simulated, and signal characteristics were extracted in terms of the concept of digital damage fingerprints (DDF). With the aid of an artificial neural algorithm, the relation between the DDF of delamination-scattered SH mode and damage parameters was calibrated, whereby the occurrence, location and size of delamination in the composite beams were assessed. The approach was experimentally validated, and the results demonstrate the effectiveness of SH mode for quantitative damage evaluation of composite structures.

Desenvolvimento e implementação de algoritmo para análise de dutos fabricados ou reparados com material compósito carregados com pressão interna utilizando o método dos elementos finitos.

A integridade de dutos ganha importância à medida em que o desenvolvimento da indústria expande a malha para transportar líquidos e gases num contexto de aumento das exigências ambientais. Um importante aliado para manutenção da integridade de dutos são reparos de materiais compósitos. Estes materiais apresentam baixa densidade, capacidade de direcionar resistência de acordo com as direções das solicitações, execução de reparo a frio sem necessidade de interromper produção ou grande maquinário. Este trabalho tem como objetivo desenvolver e implementar um algoritmo de elementos finitos que permita avaliar os esforços e a resistência das paredes de um tubos fabricados ou reparados com laminados de material compósito carregados com pressão interna. Entre as vantagens de desenvolver um programa tem-se: agilidade de avaliação, menor custo com licença, menores exigências computacionais, possibilidade de desenvolver o programa e o melhor entendimento da modelagem dos fenômenos. Utiliza-se como entrada do programa o diâmetro do duto, pressão interna e parâmetros do laminado. A modelagem em elementos finitos é realizada a partir da teoria clássica de laminados. Aplicando o carregamento resultante da pressão interna, determina-se os deslocamentos e são calculadas as tensões e aplicado o critério de falha de Tsai-Hill em cada camada. Estudos experimentais e numéricos encontrados na literatura foram simulados com o programa gerado e os resultados para propriedades do laminado, tensões nos dutos e pressão de ruptura apresentam concordância com os resultados da literatura.O programa ainda tem sua estrutura modificada para encontrar a pressão de falha a partir dos dados do laminado. O programa implementado permite uma avaliação rápida de resistência do reparo e possibilita avaliar rapidamente a resposta a mudanças nos parâmetros de projeto do laminado.

On the application of genetic algorithms for optimising composites against impact loading

A genetic algorithm (GA) was adopted to optimise the response of a composite laminate subject to impact. Two different impact scenarios are presented: low-velocity impact of a slender laminated strip and high-velocity impact of a rectangular plate by a spherical impactor. In these cases, the GA's objective was to, respectively, minimise the peak deflection and minimise penetration by varying the ply angles.

The GA was coupled to a commercial finite-element (FE) package LS DYNA to perform the impact analyses. A comparison with a commercial optimisation package, LS OPT, was also made. The results showed that the GA was a robust, capable optimisation tool that produced near optimal designs, and performed well with respect to LS OPT for the more complex high-velocity impact scenario tested.

Intralaminar toughness characterisation of unbalanced hybrid plain weave laminates

A numerical and experimental investigation on the mode-I intralaminar toughness of a hybrid plain weave composite laminate manufactured using resin infusion under flexible tooling (RIFT) process is presented in this paper. The pre-cracked geometries consisted of overheight compact tension (OCT), double edge notch (DEN) and centrally cracked four-point-bending (4PBT) test specimens. The position as well as the strain field ahead of the crack tip during the loading stage was determined using a digital speckle photogrammetry system. The limitation on the applicability of the standard data reduction schemes for the determination of intralaminar toughness of composite materials is presented and discussed. A methodology based on the numerical evaluation of the strain energy release rate using the J-integral method is proposed to derive new geometric correction functions for the determination of the stress intensity factor for composites. The method accounts for material anisotropy and finite specimen dimension effects regardless of the geometry. The approach has been validated for alternative non-standard specimen geometries. A comparison between different methods currently available for computing the intralaminar fracture toughness in composite laminates is presented and a good agreement between numerical and experimental results using the proposed methodology was obtained. 

Mode II delamination toughness of Z-pinned laminates

Mode II delamination toughness of z-pin reinforced composite laminates is investigated using finite element (FE) method. The z-pin pullout process is simulated by the deformation and breakage of non-linear springs. A critical shear stress criterion based on linear elastic fracture mechanics is used to simulate crack growth in an end-notched-flexure (ENF) beam made of z-pinned laminates. The mode II toughness is quantified by the potential energy release rate calculated using the contour integral method. This FE model is verified for an unpinned ENF composite beam. Numerical results obtained indicate that z-pins can significantly increase the mode II delamination toughness of composite laminate. The effects of design variables on the toughness enhancement of z-pinned laminates are also studied, which provides an important technological base and useful data to optimize and improve the z-pinning technique.

Melding: a new alternative to adhesive bonding

Melding, a novel method for joining composites is examined in this paper. The method uses Quickstep ™ technology to retain partially cured areas of a composite laminate, enabling subsequent bonding operations. The effect of melding on the mechanical properties of the composite has been investigated. Flexural testing of HexPly 914 indicates consistent properties throughout a melded section. Flexural strength values of 1.36±O.03 GPa compared to 1.35±O.03 GPa for a standard laminate were recorded. In order to achieve sufficient bond strength, the portion of the composite to be joined must have a significant proportion of uncured matrix. The ability of Hexply 914 prepreg to retain sufficient bonding potential to form a strong joint was also investigated. HexPly 914 Lap Shear results indicated no significant variation in strength values between co-cured and melded joins, with a recorded
strength value of 15.0±0. 7 MPa.

Compósitos poliméricos a base de fibras de licuri: efeitos da hibridização e do envelhecimento ambiental acelerado

The gradual replacement of conventional materials by the ones called composite materials is becoming a concern about the response of these composites against adverse environmental conditions, such as ultraviolet radiation, high temperature and moist. Also the search for new composite using natural fibers or a blend of it with synthetic fibers as reinforcement has been studied. In this sense, this research begins with a thorough study of microstructural characterization of licuri fiber, as a proposal of alternative reinforcement to polymeric composites. Thus, a study about the development of two composite laminates was done. The first one, involving only the fiber of licuri and the second comprising a hybrid composite based of fiber glass E and the fiber of licuri, in order to know the performance of the fiber when of fiber across the hybridization process. The laminates were made in the form of plates using the tereftálica ortho-polyester resin as matrix. The composite laminate made only by licuri fiber had two reinforcing fabric layers of unidirectional licuri and the hybrid composite had two reinforcing layers of unidirectional licuri fabric and three layers of fiber short glass-E mat. Finally, both laminates was exposed to aging acceleration in order to study the influence of environmental degradation involving the mechanical properties and fracture characteristics thereof. Regarding the mechanical properties of composites, these were determined through uniaxial tensile tests, uniaxial compression and three bending points for both laminates in original state, and uniaxial tensile tests and three bending points after accelerated aging. As regards the study of structural degradation due to aging of the laminates, it was carried out based on microscopic analysis and microstructure, as well as measuring weight loss. The characteristics of the fracture was performed by macroscopic and microscopic (optical and SEM) analysis. In general, the laminated composites based on fiber licuri showed some advantages in their responses to environmental aging. These advantages are observed in the behavior related to stiffness as well as the microstructural degradation and photo-oxidation processes. However, the structural integrity of this laminate was more affected in case the action of uniaxial tensile loads, where it was noted a lower rate of withholding his last resistance property

Desenvolvimento de um laminado compósito híbrido a base de fibras de vidro/licurí

This research work is based, in search of reinforcement s vegetable alternative to polymer composites. The idealization of making a hybrid composite reinforced with vegetable fibers licuri with synthetic fibers is a pioneer in this area. Thus was conceived a hybrid composite laminate consisting of 05 (five) layers being 03 (three) webs of synthetic fibers of glass and E-02 (two) unidirectional fabrics of vegetable fibers licuri. In the configuration of the laminate layers have alternating distribution. The composite laminate was manufactured in Tecniplas Commerce & Industry LTD, in the form of a card through the manufacturing process of hand lay up. Licuri fibers used in making the foil were the City of Mare Island in the state of Bahia. After cooking and the idealization of the hybrid composite laminate, the objective of this research work has focused on evaluating the performance of the mechanical properties (ultimate strength, stiffness and elongation at break) through uniaxial tensile tests and three point bending. Comparative studies of the mechanical properties and as well as among other types of laminated hybrid composites studied previously, were performed. Promising results were found with respect to the mechanical properties of strength and stiffness to the hybridization process idealized here. To complement the entire study were analyzed in terms of macroscopic and microscopic characteristics of the fracture for all tests.

Estudo da presença de entalhes semicirculares em compósitos poliméricos híbridos

Composite materials have a wide application in various sectors, such as the medical field in the manufacture of prostheses, in automotive and aerospace. Thus it is essential to the development of new composite and a better understanding in the face of various loading conditions and service. Several structural elements are manufactured in the presence of geometric discontinuity (notch, hole, etc ) in their longitudinal sections and/or cross-cutting, and these affect the mechanical response of these elements. The objective is to study the mechanical response of laminated polymer matrix hybrid composites reinforced with glass fiber/jute in a uniaxial tensile test. The mechanical response takes in account both the influence of the presence of a geometric discontinuity (semicircular notches) and the orientation of fibers in the layers (anisotropy). The semicircular notches are located in longitudinal section (with a reduction in cross section) of the same. In this analysis, the anisotropy is characterized by types of configurations (with different orientations of fibers in the outer layers). A comparative study of mechanical properties with and without the presence of notches is developed. Both configurations consist of four layers of woven jute fiber bidirectional and a central layer of bidirectional woven glass fibers. In addition to the mechanical properties was also studied the characteristics of the fracture developed in each composite laminate. The results showed that in the comparative study, the anisotropy and the presence of semicircular notches directly influences the mechanical behavior of laminates composites, mainly in reducing the tensile strength, and well as the final characteristics of the fracture

Damping behavior of hygrothermally conditioned carbon fiber/epoxy laminates

Carbon fiber reinforced polymer composites have been used in wide variety of applications including, aerospace, marine, sporting equipment as well as in the defense sector due to their outstanding properties at low density. In many of their applications, moisture absorption takes place which may result in a reduction in mechanical properties even at lower temperature service. In this work, the viscoelastic properties, such as storage modulus (E′) and loss modulus (E″), were obtained through vibration damping tests for three carbon fiber/epoxy composite families up to the saturation point (6 weeks). Three carbon fiber/epoxy composites having [0/0] s, [0/90] s, and [±45] s orientations were studied. During vibration tests the storage modulus (E′) and loss modulus (E″) were monitored as a function of moisture uptake, and it was observed that the natural frequencies and E′ values decreased with the increase during hygrothermal conditioning due to the matrix plasticization. © 2007 Wiley Periodicals, Inc.