An inverse procedure for identification of loads on composite laminates

An inverse procedure is presented to determine the transient line loads on a surface of composite laminate. The procedure recovers the time history as well as the distribution functions of the line loads based on the displacement responses at one receiving point. It is assumed that the time and spatial dependencies of the loading function are separable. The hybrid numerical method is used to obtain two kernel functions, dynamic Green's function as well as the response function of Heaviside step excitation of the composite laminates. The displacement response to a load with an arbitrary force function is expressed in a form of convolution, where the continuous convolution functions are spatially and temporally discretized. The loading functions are recovered by optimizing a set of proposed error (objective) functions. Numerical verifications were performed to identify loads on composite laminate for both concentrated and extended cases. Very good agreements have been obtained in terms of both load distribution and its magnitude, where calculation converged within a small number of iterations.     

Combined tension and bending testing of tapered composite laminates

A simple beam element used at Bell Helicopter was incorporated in the Computational Mechanics Testbed (COMET) finite element code at the Langley Research Center (LaRC) to analyze the responce of tappered laminates typical of flexbeams in composite rotor hubs. This beam element incorporated the influence of membrane loads on the flexural response of the tapered laminate configurations modeled and tested in a combined axial tension and bending (ATB) hydraulic load frame designed and built at LaRC. The moments generated from the finite element model were used in a tapered laminated plate theory analysis to estimate axial stresses on the surface of the tapered laminates due to combined bending and tension loads. Surfaces strains were calculated and compared to surface strains measured using strain gages mounted along the laminate length. The strain distributions correlated reasonably well with the analysis. The analysis was then used to examine the surface strain distribution in a non-linear tapered laminate where a similarly good correlation was obtained. Results indicate that simple finite element beam models may be used to identify tapered laminate configurations best suited for simulating the response of a composite flexbeam in a full scale rotor hub.The U.S. Government right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

Inversion of loading time history using displacement response of composite laminates: Three-dimensional cases

Summary An inverse procedure is proposed to reconstruct the time history of transient loads on the surface of composite laminates from the knowledge of dynamic displacement response at only one receiving point. A hybrid numerical method (HNM) is adopted as the forward solver to compute the dynamic displacement response of composite laminates subjected to arbitrary loads. By introducing a kernel displacement function — the dynamic displacement response of composite laminates excited by a point stepimpact load and the displacement response subjected to a load with an arbitrary force function are expressed in a form of convolution integral. The force history is reconstructed by employing an inversion algorithm, in which the least-squares optimization method being adopted to deconvolute the integral. Both point loads and loads with small spatial distribution are investigated and numerical verifications are given. The robustness of the procedure in the presence of noise is also investigated. Good agreements between the identified and true functions for all cases demonstrate the effectiveness of the present inverse procedure. The present inverse procedure is useful for determining impact loads on material surface using response on a point remote to the impact point.     

Low-velocity impact damage on dispersed stacking sequence laminates. Part I: Experiments

The stacking sequence design of composite laminates is often limited to combinations of 0°, 90°, and ±45° fibre angle plies. Furthermore, in order to comply to certain stiffness requirements, clustering of plies becomes unavoidable. Although such laminates might have the desired stiffness properties, they may show poor impact and/or compression-after-impact behaviour.A method to redesign the traditional stacking sequences such that the alternative laminates have improved damage resistance whilst keeping similar in-plane and bending stiffness properties as their original traditional stacking sequences is proposed. This method makes use of optimisation tools based on genetic algorithms. In the alternative laminates, the difference between fibre angles of two consecutive plies is maximised and allowed to vary in the 0–90° fibre angle range at intervals of 5°. Manufacturing of such laminates is practical nowadays as the industry is changing its production techniques into accurate automated fibre-placement and tape-laying technologies. A two-step approach is proposed for the design of laminates. In the first step, the optimal laminate is designed in the traditional fashion to cope with the expected quasi-static loads on the structure. The second step consists of redesigning this laminate to better withstand impact loads by dispersing its stacking sequence while keeping similar stiffness properties as in the first step.A traditional laminate and two dispersed stacking sequence alternative layups were tested under low-velocity impact and compression-after-impact loads in order to compare their impact resistance and damage tolerance characteristics. The evaluation of these laminates will also be carried out by the innovative numerical tools proposed in the follow-up of the present paper.     

Evaluation of fatigue behavior on repaired carbon fiber/epoxy composites

The continuous use of structural polymer composites in aeronautical industry has required the development of repairing techniques of damages found in different types of laminates. The most usually adopted procedure to investigate the repair of composite laminates has been by repairing damages simulated in laminated composite specimens. This work shows the influence of structural repair technique on mechanical properties of a typical carbon fiber/epoxy laminate used in aerospace industry. When analyzed by tensile test, the laminates with and without repair present tensile strength values of 670 and 892 MPa, respectively, and tensile modulus of 53.0 and 67.2 GPa, respectively. By this result, it is possible to observe a decrease of the measured mechanical properties of the repaired composites. When submitted to fatigue test, it is observed that in loads higher than 250 MPa, this laminate presents a low life cycle (lower than 400,000 cycles). The fatigue performance of both laminates is comparable, but the non-repaired laminate presented higher tensile and fatigue resistance when compared with the repaired laminate.     

Post-impact compressive strength of curved GFRP laminates

Low velocity impacts to fibre reinforced plastic composites cause a pattern of damage consisting in general of delamination, fibre breakage and matrix cracking. Such damage is accidental and may go unnoticed; therefore composite structures must be designed assuming impact damage exists. Previous work on flat composite laminates has resulted in a reasonable understanding of the mechanisms of compressive strength reduction. There are, however, many instances where curved laminates are used in structures where impact is likely. Furthermore, due to the mechanisms of strength reduction, it may be expected that curvature would have a significant effect on the behaviour of the laminates.The work described here consists of experimental measurement of the post-impact compressive strength of curved GFRP laminates. The laminates were of 8 plies of 0.3 mm thick pre-impregnated glass fibre/epoxy tape in a (0, ±45, 0°)_s lay-up. Each laminate was 200 mm in length by 50 mm wide with the plane of curvature normal to the length. Laminates were impacted on the convex surface of the laminate by dropping a steel mass from 1 m vertically above it.Impacted laminates were loaded in compression and the out-of-plane displacements of the top and bottom surfaces were recorded. Final failure was typically due to fibre breakage occurring through the centre of the impacted area of the laminate. Possible differences in the impact response, and measurable differences in the sizes of the impact damage area, were found to arise from these curvatures, and differences were observed in their post-impact buckling behaviour. However, perhaps unexpectedly, the post-impact compressive strength for a curved laminate was found to be similar to that for a flat laminate. The failure loads for the impact damage laminates are shown to be comparable with those for laminates containing artificial delaminations.     

Optimization of laminated composites subject to uncertain buckling loads

Optimal design of composite laminates under buckling load uncertainty is presented. The laminates are subjected to biaxial compressive loads and the buckling load is maximized under worst case in-plane loading which is computed using an anti-optimization approach. The magnitudes of the in-plane loads are not known a priori resulting in load uncertainty subject to the only constraint that the loads belong to a given uncertainty domain. Results are given for continuous and discrete fibre orientations which constitute the optimization problem coupled to load anti-optimization problem leading to a nested solution method. It is observed that the stacking sequence of a laminate designed for a deterministic load case only differs considerably from that of a robust laminate designed taking load uncertainties into account. Consequently the buckling load carried by a deterministic design is considerably less than the one carried by a robust design when both are subjected to uncertain loads.     

混杂薄膜天线层的双稳态复合材料层板力电性能

给出了既有双稳态特性又具有天线功能的多功能复合材料层板设计与分析方法。基于非线性层板理论和Rayleigh-Ritz法,建立了双稳态混杂层板构型预报理论模型,并通过有限元计算和实验进行了验证。研究了薄膜天线混杂非对称双稳态复合材料层板的临界载荷及电磁性能,分析了铺层方式对双稳态混杂层板稳定构型、临界载荷和电磁性能的影响。结果表明：双稳态混杂层板通过转变其稳定构型实现天线主辐射方向在俯仰面内偏转30°,实现方向图可重构,扩大天线波束的扫描范围。铺层方式对层板构型和反射系数影响较大,当天线辐射层铺设在层板表面且聚酰亚胺薄膜厚度大于0.2 mm时,其双稳态特性消失,没有出现分叉现象,且其中心频率会左移大约0.2 GHz。     

Non‐linear dynamic stability analysis of composite laminates under periodic in‐plane compressive loads

This work deals with the investigation of the non‐linear instability behaviour of the composite laminates subjected to periodic in‐plane/axial load, through the finite element formulation with dynamic response analysis. Here, C¹ eight‐noded shear‐flexible plate element, based on a new kind of kinematics which allows to exactly ensure the continuity conditions for displacements and stresses at the interfaces between the layers of the laminate, and also the boundary conditions at the top and bottom surfaces of the laminate, is employed. The non‐linear governing equations obtained are solved using the Newmark direct integration method coupled with a modified Newton–Raphson iteration procedure. The analysis brings out various characteristic features of the dynamic stability such as existence of beats, their dependency on the forcing frequency, and the typical character of vibrations in the different regions. Numerical results are also presented to highlight the influence of ply‐angle and lay‐up of the laminate on dynamic stability behaviour of the composite laminates. Copyright © 1999 John Wiley & Sons, Ltd.     

Experimental investigation of delamination buckling of stitched composite laminates

In the current investigation, effects of through-the-thickness stitching with two different types of aramid threads, Kevlar^® and Twaron^® threads, on the buckling loads of delaminated glass/epoxy composite laminates are studied. Buckling loads are predicted based on the Southwell, Vertical displacement and Membrane strain plot methods by using the experimental data. From the Southwell, Vertical displacement and Membrane strain plot methods it is observed that stitching either by Kevlar^® or Twaron^® threads is effective in improving the buckling strength of glass/epoxy composite laminates when the delamination length is greater than 0.5L, L being the length of the laminate. For long delaminations, Kevlar^® stitched glass/epoxy composite laminate is best in retaining its buckling strength when re-loading is done. Southwell plot method tends to overestimate the buckling loads as the data obtained from this method are influenced by the breakages in the glass/epoxy composite laminate buckling test specimens.     

基于改进模拟退火算法的复合材料层合板频率优化

针对复合材料层合板频率优化问题,结合可行规则法和直接搜索模拟退化算法,提出了一种自适应模拟退火(SA)改进算法。层合板优化目标是基频、频率带隙以及给定基频和带隙约束的层合板厚度。设计变量包括铺层角度和铺层数两种离散变量。改进算法的自适应新点产生模块采用依赖温度的动态调整搜索半径,改善了直接搜索模拟退化(DSA)算法易陷入局部极值的缺陷,而可行规则法的引入提高了SA算法求解约束问题的效率和简易性。采用Ritz法进行频率响应分析以考虑弯扭耦合影响。不同铺层数、角度增量和长宽比时的层合板3类算例结果显示:改进算法能有效求解层合板频率优化,可获得更多或更好的铺层顺序全局优化解。     

The effect of extension/twist anisotropy on compression buckling in cylindrical shells

The study of axial compression buckling of isotropic cylinders has received much attention by various researchers over the years. It is commonly acknowledged that the presence of minute imperfections significantly reduces potential buckling loads in comparison with classical linear predictions. This approach, of including geometric imperfections, has been extended by a significant, yet fewer, number of researchers to composite cylindrical shells. As the current study shows, imperfections may not be the only major factor for the discrepancy between experimental and linear buckling loads. Flexural/twist anisotropy, present in most balanced, symmetric laminates with angle-ply layers, is shown to play a significant role in reducing buckling loads from those predicted by classical analysis. Indeed, the assumption of deflections in the form of a double sine series appears to be questionable for such laminates. A recently reported classically linear analysis that included the effects of flexural/twist coupling on buckling loads has been further developed to include the effects of extension/twist coupling. It is shown that buckling loads can be improved by making the laminate antisymmetric rather than symmetric, for the class of quasi-isotropic laminates, whilst retaining a spiral mode shape.     

Buckling and free vibration of non-homogeneous composite cross-ply laminated plates with various plate theories

Various theories of homogeneous laminated plates are extended to study the buckling and free vibration behavior of non-homogeneous rectangular composite laminates. The equations governing the dynamic response of non-homogeneous composite laminates are deduced. Numerical results for the natural frequencies and critical buckling loads of symmetric cross-ply laminates are presented. The influences of the degree of non-homogeneity, aspect ratio, thickness ratio and in-plane orthotropy ratio on the natural frequencies and critical buckling loads are investigated. The results obtained for homogeneous cases are compared with their counterparts in the literature. The study concludes that the classical plate theory is inadequate for predicting the structural response of non-homogeneous laminates, and that the free vibration and the state of the stability are affected strongly by the degree of nonhomogeneity.     

Analysis of unsymmetric CFRP–metal hybrid laminates for use in adaptive structures

The potential of using multistable composite materials for adaptive structures is currently receiving interest from the aerospace community because they possess more than one single equilibrium configuration. Unsymmetric CFRP laminates are studied which have an inner isotropic metallic layer. These hybrid laminates are studied using analytical, finite element and experimental techniques. The thermal contraction of the isotropic layer upon cool down from cure induces large in-plane thermal loads which act remotely from the laminate’s neutral plane, increasing snap-through moments and out-of-plane displacements. The curvatures of the hybrid laminates can be doubled compared to pure unsymmetric CFRP laminates.     

Analytical and experimental studies on the low-velocity impact response and damage of composite laminates under in-plane loads with structural damping effects

In this paper, low-velocity impact response and damage of composite laminates under in-plane loads are analytically and experimentally investigated. The authors recently proposed a modified displacement field of plate theory, considering the effect of initially loaded in-plane strain, and used a finite element program to analyze the structural behavior of the composite laminate. In this study, the program is upgraded to account for the structural damping effect of the laminate. A pendulum type impact test system and an in-plane loading fixture are constructed for the experimental study. The analytical and experimental impact behaviors are compared at different impact energy levels for cases with an initial in-plane tensile load and a compressive load, as well as cases without the initial in-plane load. The results show good correspondence between the analytical and experimental impact force histories. The effect of the initial in-plane load reduces for higher impact energies. The numerical estimation of the damaged area is in good agreement with the results from C-scanning experiments.     

平面编织复合材料层压板低速冲击后的压缩失效

采用超声C扫描检测、断口分析、有限元分析等方法研究低速冲击损伤对G803/5224与G827/5224两种平面编织复合材料层压板失效行为的影响。结果表明,低速冲击后压缩载荷作用下,G803/5224层压板最终为剪切分层失效,G827/5224层压板最终为剪切屈曲失效,两种层压板低速冲击后压缩的失效模式与未受损伤层压板基本相同。建立了平面编织复合材料层压板的损伤扩展与失效模型,该模型的计算结果与试验结果吻合较好,可用于平面编织复合材料层压板的失效仿真。     

Reliability-based optimization of fibrous laminated composites

This paper is concerned with the optimum design of multiaxial fiber reinforced laminate systems under probabilistic conditions of loads and material properties. A multiaxially laminated composite is treated as a structural system with each ply contained in the composite as one element. The Tsai-Wu failure criterion is adopted as the limit state function of a unidirectional ply. It is assumed that the system failure occurs when any one of the plies in a laminate system fails. The multiple-check-point method is successfully applied to evaluate the system reliabilities of multiaxial laminates under probabilistic in-plane stresses. An optimization problem is defined to find the optimal number of fiber orientation axes, optimum orientation angles, and optimum ply ratios which yield the highest system reliability.     

Interfacial fracture toughness measurement using indentation

Recent models have been developed for relating fracture toughness to indentation strengths for brittle monolithic materials. Thus, indentation may provide a simple and non-destructive means to measure fracture toughness. The indentation technique is further explored to evaluate the interfacial toughness in this work. When microindentations at loads ranging from 50 g to 4 kg were placed close to the interface of an aluminium/aluminum composite laminate, the interface stayed intact. In contrast, the interface of a niobium silicide/niobium laminate indented under similar conditions was found to debond, indicating a weaker interface. However, a Rockwell indenter at loads ranging from 60 to 150 kg were sufficient to debond the interfaces of two of the aluminum composite/aluminum laminates. Finally, the interfacial toughness is correlated to the indenter load and the delamination length along the interface. A power-law relationship was found between the load and the delamination length.     

Multicontinuum Failure Analysis of Composite Structural Laminates

Damage in a composite typically begins at the constituent level and may, in fact, be limited to only one constituent in some situations. Accurate predictions of constituent damage at points in a laminate provide a genesis for progressively analyzing failure of a composite structure from start to finish. In this article we develop an efficient constituent-based failure analysis for composite structural laminates. Continuum-based (phase-averaged) constituent stress and strain fields are computed in a finite-element environment without a computational time penalty. Constituent stress-based failure criteria are developed and used to construct a progressive failure algorithm in which one constituent is allowed to fail while the other constituent remains intact, e.g., matrix cracking. The proposed failure algorithm was used to predict failure of a variety of laminates under uniaxial and biaxial loads. The results were shown to be superior to comparable single-continuum failure analyses and in good agreement with experimentally determined failure loads.     

Lateral buckling analysis of thin-walled laminated channel-section beams

The lateral buckling of a laminated composite beam with channel section is studied. A general analytical model applicable to the lateral buckling of a channel-section composite beam subjected to various types of loadings is derived. This model is based on the classical lamination theory, and accounts for the material coupling for arbitrary laminate stacking sequence configuration and various boundary conditions. The effects of the location of applied loading on the buckling capacity are also included in the analysis. A displacement-based one-dimensional finite element model is developed to predict critical loads and corresponding buckling modes for a thin-walled composite beam with arbitrary boundary conditions. Numerical results are obtained for thin-walled composites under central point load, uniformly distributed load, and pure bending with angle-ply and laminates. The effects of fiber orientation, location of applied load, and types of loads on the critical buckling loads are parametrically studied.