A multi-objective optimization approach for design of blast-resistant composite laminates using carbon nanotubes

A reliable process for the design of blast-resistance composite laminates is needed. We consider here the use of carbon nanotubes (CNTs) to enhance the mechanical properties of composite interface layers. The use of CNTs not only enhances the strength of the interface but also significantly alters stress propagation in composite laminates. A simplified wave propagation simulation is developed and the optimal CNT content in the interface layer is determined using multi-objective optimization paradigms. The optimization process targets minimizing the ratio of the stress developed in the layers to the strength of that layer for all the composite laminate layers. Two optimization methods are employed to identify the optimal CNT content. A case study demonstrating the design of five-layer composite laminate subjected to a blast event is used to demonstrate the concept. It is shown that the addition of 2% and 4% CNTs by weight to the epoxy interfaces results in significant enhancement of the composite ability to resist blast.     

Optimum design of composite laminates for frequency constraints

A method for minimum thickness multilayer rectangular composite laminates is presented which is based on a layerwise optimization procedure under natural frequency limitations. In this method, all types of boundary conditions and their combinations can be taken into account. Analysis is based on the Ritz approximations, and no limitations exist on the number of layers that can be considered or the plate’s aspect ratio. Coupling of flexural and torsional stiffness terms need not be zero in any of the cases. Optimization constraints can be either limits on the fundamental frequency or separation between two natural frequencies. Hybrid combination of layers is also made possible in order to enhance the laminate economy, and a short cut procedure is recommended to save total computational efforts.

Examples are offered that illustrate the method’s capabilities, and the results are verified by comparison to some published ones.     

Mesh design in finite element analysis of post-buckled delamination in composite laminates

The role of mesh design in the post-buckling analysis of delamination in composite laminates is addressed in this paper. The determination of the strain energy release rate (SERR) along the crack front is central to the analysis. Frequently, theoretical analysis is limited to treatment of the problem in two dimensions, since considerable complexity is encountered in extending the analysis to three dimensions. However, many practical problems of embedded delamination in composite laminates are inherently three-dimensional in nature. Although in such cases, the finite element (FE) method can be employed, there are some issues that must be examined more closely to ensure physically realistic models. One of these issues is the effect of mesh design on the determination of the local SERR along the delamination front. There are few studies that deal with this aspect systematically. In this paper, the effect of mesh design in the calculation of SERR in two-dimensional (2D) and three-dimensional (3D) FE analyses of the post-buckling behavior of embedded delaminations is studied and some guidelines on mesh design are suggested. Two methods of calculation of the SERR are considered: the virtual crack closure technique (VCCT) and crack closure technique (CCT). The 2D analyses confirm that if the near-tip mesh is symmetric and consists of square elements, then the evaluation of the SERR is not sensitive to mesh refinement, and a reasonably coarse mesh is adequate. Despite agreement in the global post-buckling response of the delaminated part, the SERR calculated using different unsymmetrical near-tip meshes could be different. Therefore, unsymmetrical near-tip meshes should be avoided, as convergence of the SERR with mesh refinement could not be assured. While the results using VCCT and CCT for 2D analyses agree well with each other, these techniques yield different quantitative results when applied to 3D analyses. The reason may be due to the way in which the delamination growth is modeled. The CCT allows simultaneous delamination advance over finite circumferential lengths, but it is very difficult to implement and the results exhibit mesh dependency. Qualitatively, however, the two sets of results show similar distributions of Mode I and Mode II components of the SERR. This is fortunate, since the VCCT is relatively easy to implement.     

Thermal expansion behaviors of aluminum composite reinforced with carbon nanotubes

The coefficient of thermal expansion (CTE) of aluminum matrix composite reinforced with 1.0wt.% multi-wall carbon nanotubes (MWNTs) fabricated by cold isostatic pressing and hot squeeze technique was measured between 25 and 400 °C with a high-precision thermomechanical analyzer, and compared with those of pure aluminum and 2024Al matrix fabricated under the same processing. The results show that the CTE of the composite obviously reduces in relation to those of pure aluminum and 2024Al matrix due to the introduction of MWNTs. The addition of 1.0wt.% MWNTs to 2024Al matrix decreases the CTE by as much as 12% and 11% compared with those of pure aluminum and 2024Al matrix at 50 °C, respectively, which indicates that carbon nanotube reinforced metal matrix composite may be a promising materials with low CTE.     

Interlaminar and intralaminar reinforcement of composite laminates with aligned carbon nanotubes

Three-dimensional reinforcement of woven advanced polymer–matrix composites using aligned carbon nanotubes (CNTs) is explored experimentally and theoretically. Radially-aligned CNTs grown in situ on the surface of fibers in a woven cloth provide significant three-dimensional reinforcement, as measured by Mode I interlaminar fracture testing and tension-bearing experiments. Aligned CNTs bridge the ply interfaces giving enhancement in both initiation and steady-state toughness, improving the already tough system by 76% in steady state (more than 1.5 kJ/m² increase). CNT pull-out on the crack faces is the observed toughening mechanism, and an analytical model is correlated to the experimental fracture data. In the plane of the laminate, aligned CNTs enhance the tension-bearing response with increases of: 19% in bearing stiffness, 9% in critical strength, and 5% in ultimate strength accompanied by a clear change in failure mode from shear-out failure (matrix dominated) without CNTs to tensile fracture (fiber dominated) with CNTs.     

Low-velocity impact and residual tensile strength analysis to carbon fiber composite laminates

In this paper, low-velocity impact characteristics and residual tensile strength of carbon fiber composite laminates are investigated by experimentally and numerically. Low-velocity impact tests and residual tensile strength tests are performed using an instrumented drop-weight machine (Instron 9250HV) and static test machine (Instron 5569), respectively. The finite element (FE) software, ABAQUS/Explicit is employed to simulate low-velocity impact characteristics and predict residual tensile strength of carbon fiber composites laminates. These numerical investigations create a user-defined material subroutine (VUMAT) to enhance the damage simulation which includes Hashin and Yeh failure criteria. The impact contact force and the tensile strength are accurately estimated using the present method. Two different tensile damage modes after different impact energies are observed. The degradation of residual tensile strengths can be divided to three stages for different impact energies, and amplitudes of degradation are affected by stacking sequences.     

考虑三维应力的复合材料层压板疲劳寿命分析

由于层间应力的存在,受面内载荷作用的复合材料层压板实际处于多轴应力状态。构建了由刚性元、弹簧元和二维板元构成的准三维有限元模型,结合单向板在典型应力状态下的疲劳试验结果和疲劳损伤模型,发展了一种考虑三维应力的、预测任意铺层多向层压板疲劳寿命的分析方法,包括应力分析、静力和疲劳累积损伤失效分析及材料性能退化3个主要部分,能够模拟面内和层间损伤产生、发展直至层压板整体破坏的完整过程,并得到疲劳寿命。对2种T300/QY8911多向铺层板进行了实际计算,寿命预测结果与试验结果吻合较好。      

Fracture of fatigue-loaded composite laminates

While the quasi-static fracture load of many composite laminates can be estimated with engineering accuracy, the fracture event itself has not been clearly characterized and is incompletely understood. When cyclic loading is present, the pre-fracture damage state is altered significantly, so that estimating strength (or residual strength) is greatly complicated. The present paper examines this complexity and attempts to assess the manner in which pre-fracture fatigue damage affects residual strength and the fracture event. It is found that the large strength reductions observed prior to failure at low load levels can be accounted for by internal stress redistribution and material degradation events. A careful chain of physical evidence in support of this approach is presented.     

Mode localization in composite laminates

We study free vibrations of monolithic and composite thin rectangular plates; the former are made of linear elastic, homogeneous, isotropic materials and the latter of fiber reinforced laminas. The plates are clamped on all four edges and interior points on a transverse normal to the plate midsurface are rigidly tied together and have either null displacements and null rotations (Type-I constraint) or only null transverse displacements (Type-II constraint). Depending upon the location of the point on the midsurface through which the transverse normal passes, modes localize in different regions of the plate. Plates of various aspect ratios (length/width) and stacking sequences of 0°, 45° and 90° leading to symmetric and anti-symmetric configurations about their midsurfaces are considered. The problem is studied using the first order shear deformable (or the Mindlin) plate theory. It is found that both the Type-I and Type-II constraints divide the plate into two vibrating regions with amplitudes of transverse vibration localized in a particular region on either side of the clamped interior points. It is found that the mode localization in laminates is governed by the mode localization characteristics of constituent laminas. For symmetric cross ply laminates the localization of modes is found to decrease with the increase in the number of 0° plies. For anti-symmetric cross ply laminates and those made of all 45° plies the mode localization is found to be independent of the number of plies. For isotropic plates made of a monolithic material the mode localization phenomenon is stronger for Type-I constraint compared to that for Type-II constraints. Also, for these plates the mode localization occurs when lumped masses are placed at these interior points. The significance of the work lies in providing an alternative and an economical way of annulling plate vibrations in selected parts of the plate, and confining the energy of vibration in desired regions of the plate.     

Multiscale fiber-reinforced thermoplastic composites incorporating carbon nanotubes: A review

This article reviews recent literature on hierarchical thermoplastic-based composites that simultaneously incorporate carbon nanotubes (CNTs) and conventional microscale fibers, and discusses the structure–property relationships of the resulting hybrids. The mixing of multiple and multiscale constituents enables the preparation of materials with new or improved properties due to synergistic effects. By exploiting the outstanding mechanical, thermal and electrical properties of CNTs, a new generation of multifunctional high-performance composites suitable for a wide variety of applications can be developed.     

Modeling nonlinear rate dependent behaviors of composite laminates

Abstract

This study aims to propose a simple explicit model for predicting the nonlinear rate dependent behaviors of composite laminates. Using one parameter plastic potential to describe the flow rule, the viscoplasticity model is expressed as a single master effective stress‐effective plastic strain curve in the form of a power law with a rate dependent amplitude. Based on the viscoplasticity model together with the laminated plate theory, the incremental form of the constitutive formulation is derived to model the nonlinear rate dependent behaviors of composite laminates. Symmetric glass/ epoxy and graphite/epoxy composite laminates were tested at three different strain rates and the experimental results were then compared with the model predictions. It was indicated that the proposed constitutive model is effective in characterizing the nonlinear rate dependent behaviors of composite laminates at strain levels up to 1%.     

Layerwise modeling of progressive damage in fiber-reinforced composite laminates

This paper investigates the effects of discrete layer transverse shear strain and discrete layer transverse normal strain on the predicted progressive damage response and global failure of fiber-reinforced composite laminates. These effects are isolated using a hierarchical, displacement-based 2-D finite element model that includes the first-order shear deformation model (FSD), type-I layerwise models (LW1) and type-II layerwise models (LW2) as special cases. Both the LW1 layerwise model and the more familiar FSD model use a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the LW1 model includes discrete layer transverse shear effects via in-plane displacement components that are C ⁰ continuous with respect to the thickness coordinate. The LW2 layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects by expanding all three displacement components as C ⁰ continuous functions of the thickness coordinate. The hierarchical finite element model incorporates a 3-D continuum damage mechanics (CDM) model that predicts local orthotropic damage evolution and local stiffness reduction at the geometric scale represented by the homogenized composite material ply. In modeling laminates that exhibit either widespread or localized transverse shear deformation, the results obtained in this study clearly show that the inclusion of discrete layer kinematics significantly increases the rate of local damage accumulation and significantly reduces the predicted global failure load compared to solutions obtained from first-order shear deformable models. The source of this effect can be traced to the improved resolution of local interlaminar shear stress concentrations, which results in faster local damage evolution and earlier cascading of localized failures into widespread global failure.     

Buckling of the composite laminates containing through-the-width delaminations using different plate theories

The buckling behavior of the composite laminates with through-the-width delaminations is studied by using different plate theories. The analytical method is based on the CLPT, FSDT and HSDT plate theories. The formulation is developed on the basis of the Rayleigh–Ritz technique by the implementation of the simple polynomial series. The contact among sublaminates is handled. The three-dimensional FEM analysis is also performed by using ANSYS5.4 commercial software, and the results are compared with those obtained by the analytical models. The agreement between the results is very good.     

A new structural health monitoring system for composite laminates

The increasing use of composite laminates in safety critical structures has prompted the development of a robust structural health monitoring system for laminates, which uses metastable ferrous alloy inserts embedded within the laminate during component construction to provide an indication of the peak tensile strain encountered by the laminate. The metastable ferrous alloy insert has an austenitic crystal structure at room temperature, but upon application of strain, this transforms to a thermodynamically stable martensite, resulting in a change in magnetic susceptibility, which can be correlated with the peak strain experienced by the material (strain memory effect). This paper presents the test results that show that it is possible to manufacture a smart laminate in this fashion, and that sufficient strain is experienced by the insert to provide a significant change in magnetic susceptibility, thereby warning of a high strain level in the laminate. Various insert geometries and laminate thicknesses are also tested for their effect on the susceptibility measurements.     

Edge effects of uniformly loaded cross-ply composite laminates

Interlaminar stresses resulting from bending of rectangular cross-ply composite laminates are determined using a layer wise laminate theory. Two types of laminates are considered. First a fully simply supported laminate subjected to bi-directional bending is analyzed. The results obtained from this theory are compared with those of the published three-dimensional elasticity solutions to verify the validity and accuracy of the present theory. Then laminates with two edges simply supported and the other two edges free are examined. The results indicate the presence of significant interlaminar stresses near the free edges.     

Reinforcing effect of carbon nanotubes on PEEK composite filled with carbon fibre

Abstract

The main objective of the present paper is to develop high wear resistance carbon fibre reinforced polyether ether ketone composite with addition of multiwall carbon nanotubes. These compounds were well mixed in a batch mixer, and compounded polymers were fabricated into sheets of known thickness by compression moulding. Samples were tested for wear resistance with respect to different concentration of fillers. The wear resistance properties of these samples depend on filler aspect ratio. Wear resistance of composite with 20 wt-% of carbon fibre increases when multiwall carbon nanotubewas introduced. The worn surface features have been examined using scanning electron microscope. Photomicrographs of the worn surfaces revealed higher wear resistance with the addition of carbon nanotube. Also better interfacial adhesion between carbon and vinyl ester in carbon reinforced vinyl ester composite was observed.     

Analysis of free edge effects in composite laminates

Extensive work has been done in the field of free edge effects in composite laminates. The present paper reviews the modelling as well as the experimental work on this class of boundary value problems. The modelling techniques developed by a number of investigators and the experimental validation of the predictions made through these models are discussed.     

The enhanced growth of multi-walled carbon nanotubes using an atmospheric pressure plasma jet

The growth of multi-walled carbon nanotube (MWCNT) forests was investigated using an atmospheric pressure plasma jet (APPJ) system with a mixture of helium and acetylene gases. The MWCNT forests grown on Fe catalyst were compared with those grown on Ni. The growth of MWCNT forests using Fe as the catalyst was better than the growth of MWCNT forests using Ni. The MWCNT forests grown using Fe catalyst and with a plasma power of 30 W were about 17 ± 9% taller than for the plasma off. We were unable to grow MWCNTs using Ni catalyst with the plasma power off; but curly MWCNTs were grown using Ni catalyst if the plasma power was 30 W. It is found that MWCNT growth is enhanced using an APPJ. The height of the forests produced using this APPJ system was also better than that reported by other researchers using either CVD or PECVD systems.     

Response of multilayered composite laminates to dynamic surface loads

A theoretical investigation of the response of multilayered composite laminates to concentrated and distributed dynamic surface loads is carried out. Each layer of the laminate is assumed to be transversely isotropic and dissipative with arbitrarily oriented symmetry axis. The dissipative property of the material is modeled approximately through the introduction of a frequency-dependent damping function. A multiple transform technique is used to calculate the spectra and time histories of the displacements and stresses produced by a variety of dynamic loads, and the quantitative features of the waves produced in the laminate are determined. The methodology developed in this work is expected to be useful in the prediction of the response of composite laminates to impact loads and also in the characterization of acoustic emission (AE) sources in these materials under static and dynamic loads.     

Fracture toughness improvement of CFRP laminates by dispersion of cup-stacked carbon nanotubes

Several techniques are introduced to enhance the interlaminar fracture toughness of CFRP laminates using cup-stacked carbon nanotubes (CSCNTs). Prepared CSCNT-dispersed CFRP laminates are subject to Double Cantilever Beam (DCB) and End Notched Flexure (ENF) tests in order to obtain mode-I and mode-II interlaminar fracture toughness. The measured fracture toughnesses are compared to that of CFRP laminates without CSCNT to evaluate the effectiveness of CSCNT dispersion for the improvement of fracture toughness. All CSCNT-dispersed CFRP laminates exhibit higher fracture toughness, and specifically, CSCNT-dispersed CFRP laminates with thin epoxy interlayers containing short CSCNTs have three times higher fracture toughness than CFRP laminates without CSCNT. SEM observation of fracture surfaces is also conducted to investigate the mechanisms of fracture toughness improvement. Crack deflection mechanism is recognized in the CSCNT-dispersed CFRP laminates, which is considered to contribute the enhancement of interlaminar fracture toughness.