Nonlinear Analysis of Angle‐Ply Composite and Sandwich Laminates

A refined higher order shear deformation theory for linear and geometrically nonlinear behavior of fiber‐reinforced angle‐ply composite and sandwich laminates is established. Laminae material is assumed to be linearly elastic, homogeneous and isotropic/orthotropic. The theory accounts for nonlinear quadratic variation of transverse shear strains through the thickness of the laminate and higher order terms in Green's strain vector in the sense of von Karman. A simple C0 finite‐element formulation of this theory is then presented with a total Lagrangian approach, and a nine node Lagrangian quadrilateral element is chosen with nine degrees of freedom per node. Numerical results are presented for linear and geometrically nonlinear analyses of multilayer angle‐ply composite and sandwich laminates. The theory is shown to predict displacements and stresses more accurately than first‐order shear deformation theory. The results are compared with available closed‐form and numerical solutions of plate theories and three‐dimensional finite‐element solutions. New results are also generated for future evaluations.     

Delamination Characteristics around Hole in Laminates with Softening Strip

Graphite/epoxy laminates with and without a softening strip around a hole were investigated. The softening strip is a portion of the graphite critical ply, which is replaced by a glass/epoxy composite. Analysis was conducted with finite element methods: The in‐plane stress distribution was found using a planform two‐dimensional model and interlaminar stress distributions around a hole were obtained from a through‐thickness quasi‐three‐dimensional model. The variation of strain‐energy release rate for a delamination occurring at the critical interface was investigated. The finite element results indicate that the inplane and interlaminar stress distributions, as well as the strain‐energy release rates, are significantly reduced for laminates with a softening strip.     

Optimal Hybridization of Symmetric, Cross‐Ply Laminates against Biaxial Buckling

Optimal ratio of the thickness of the inner layers made of a low‐stiffness fiber‐reinforced material to the total laminate thickness is determined for sandwich hybrid laminates, with the objective of maximizing the buckling load for a given laminate thickness. The sandwich plate is constructed as a symmetric, cross‐ply laminate with outer layers made of a high‐stiffness fiber composite material and inner layers made of a low‐stiffness fiber‐composite material. The fiber orientations of high‐ and low‐stiffness materials (0° or 90°) are determined optimally, noting that the orientations of outer and inner layers affect the maximum buckling load in the case of hybrid laminates. The relative stiffness of outer layers to inner layers is shown to affect the optimal level of hybridization. The optimal laminate configurations are shown to be sensitive to the relative magnitudes of biaxial buckling loads as well as to the changes in the aspect ratio.     

Finite-Element Formulation for Analysis of Laminated Composites

This paper presents a multilayered∕multidirector and shear-deformable finite-element formulation of shells for the analysis of composite laminates. The displacement field is assumed continuous across the finite-element layers through the composite thickness. The rotation field is, however, layerwise continuous and is assumed discontinuous across these layers. This kinematic hypothesis results in independent shear deformation of the director associated with each individual layer and thus allows the warping of the composite cross section. The resulting through-thickness strain field is therefore discontinuous across the different material sets. Numerical results are presented to show the performance of the method.     

薄铺层复合材料薄壁管轴压屈曲行为研究

在薄壁结构的应用中,屈曲稳定性是影响其承载性能的关键因素,为研究减薄铺层厚度对复合材料薄壁结构局部屈曲行为的影响,本文采用不同厚度(0.125、0.055和0.020 mm)的预浸料制备复合材料薄壁管,实验测试了其在轴压下的局部屈曲行为.实验结果表明,随着铺层厚度减薄,实验采用的正交和均衡两种铺层方式的复合材料薄壁管局部屈曲载荷均随之提高,而屈曲失效模式没有发生改变.力学分析表明,铺层厚度减薄后,管壁弯曲刚度的改变和层间剪切应力分布对薄壁管局部屈曲载荷提高有重要影响.采用薄铺层制备复合材料薄壁结构件能够有效提高其局部屈曲能力.      

Analysis of Impact Response of Composite Laminates under Prestress

An analytical solution for the impact response is obtained for the central impact of mass on a simply supported laminated composite plate under prestresses based on the Fourier series expansion and Laplace transform technique. A linearized version of the elastoplastic contact law proposed was used in the analytical formulation to consider permanent indentation during the impact. Permanent indentation including damage effects was included in the elastoplastic contact law. The effects of initial stresses on the contact force, plate center displacement, as well as strain time histories are presented. It is shown that higher initial stresses increase the maximum value of the contact force but reduce the plate central displacement. Effects of impactor velocity, mass, interlaminar shear strength of the laminates, and plate thickness on the contact force and dynamic response of the plate under tensile prestresses are also discussed.     

Design∕Control Optimization of Cross‐Ply Laminates Under Buckling and Vibration

The optimal layer thicknesses and optimal feedback control function are determined for a symmetric, cross‐ply laminate. The objectives of the optimization are to maximize the biaxial buckling load (design objective) and to minimize the dynamic response to external disturbances (control objective) subject to a constraint on the expenditure of control energy. The design∕control problem is formulated as a multiobjective optimization problem by employing a performance index that combines the design and control objectives in a weighted sum. Numerical results are given for a laminate made of an advanced composite material. Comparisons of controlled and uncontrolled laminates as well as optimally designed and nonoptimal laminates indicate the benefits of treating the design and control problems in unified formulation. The implications of solving these two problems are discussed. The values of optimal design and control variables are given for a number of problem parameters.     

Application of the Analytical Strip Method to Antisymmetric Laminates

The analytical strip method is presented in this paper for the analysis of the bending-extension coupling problem of antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being simply supported, clamped, or free. The laminate can be subjected to any combination of concentrated, uniform, line, and patch loads. This method overcomes the limitations of other analytical methods (e.g., Navier’s and Levy’s) and provides an alternative to numerical, seminumerical, and approximate methods for rectangular plates with two parallel edges simply supported. The results obtained from this method compare very well with the ones derived using the finite-element program ANSYS and, where applicable, the existing classical laminated plate theory.     

Thermal residual stresses in functionally graded and layered 6061 Al/SiC materials

The thermal residual stresses that develop in spray atomized and codeposited functionally graded and layered 6061 Al/SiC metal-matrix composites (MMCs) during cooling from the codeposition temperature to ambient temperature were studied using thermo-elastoplastic finite element analysis. In an effort to investigate the effect of layered and graded structures on the residual stress distribution, the composites with homogeneous distribution of SiC particulates were also analyzed. The effect of SiC volume fraction in the SiC-rich layers and the effect of SiC-rich layer thickness on the residual stresses were investigated. Based on the present study, it was found that the residual stress distribution is very distinct for the aluminum and the SiC-rich layers in the layered materials. As the volume fraction of SiC increases in the SiC-rich layer, the magnitude of residual stresses also increases. The radial stress was found to be tensile in the aluminum layers and compressive in the SiC-rich layers. It was also found that, as the thickness of the SiC-rich layer increases, the magnitude of radial stress in the aluminum layers increases, and that in the SiC-rich layers decreases. In the graded material, the lower region of each layer exhibits tensile radial stress, and the upper region of each layer shows compressive radial stress in order to maintain continuity between layers during cooldown. In general, the layered and the graded materials have greater residual stresses and more complicated stress distribution, as compared with those in the composite materials with homogeneous distribution of SiC particulates.     

Discussion of Theoretical Methods to Predict Scale Thickness in Hot Rolling of Steel Strips

Oxidation of iron during hot rolling is inevitable and scale layers are formed on the strip. There are different rate laws of oxidation of iron to predict the scale thickness, in which parabolic rate law and mixed rate law are usually used in hot rolling of strips. As the strip passes through the roll gap, the scale layer can plastically be deformed. Due to limited plasticity of the oxide, cracks through the scale layer can be formed in every roll gap. They open and form new free metallic surfaces which are then oxidized in the interstand. By means of numerical simulations different rate laws of oxidation are compared and the scale deformation with different cases is taken into account. Sensitivity of some rolling parameters to prediction of the scale thickness is discussed in the present paper. Numerical results show that the parabolic rate law overestimates the scale thickness as compared with the mixed rate law and the mixed rate law is not sensitive to the deformation extent of scale.     

Micromechanical Modeling of Filament Wound Cement-Based Composites

A theoretical model to predict the response of laminated cement-based composites is developed. The micromechanical model simulates the mechanical response of a multilayer cement-based composite laminate under uniaxial, biaxial, and flexural loading modes. Tsai-Wu Criterion is used for each lamina and the stacking sequence is utilized to obtain the overall stiffness matrix. The effect of distributed cracking on the stiffness degradation of the cross ply layers under tensile loading is measured using a scalar damage parameter that is empirically related to the apparent strain. The model is calibrated by predicting the load versus deformation response of unidirectional, cross ply, and angle ply laminates under tensile and flexural loading. Results are then compared to the experimental results cross ply and angle composites with various stacking sequences.     

Failure mechanisms of laminated carbon-carbon composites—II. Under shear loads

Failure mechanisms under both interlaminar and in-plane shear loading are determined for two-dimensional carbon-carbon composites by using a direct shear set-up. This set-up is applicable for both types of shear loading, “as manufactured” laminate thickness can be tested without the need to make long samples by gluing different pieces together. A detailed finite element analysis, which considers the microstructure of the composite shows that for woven laminates, the initial crimp angle morphology does not allow the composite to deform in a state of simple shear. In fact, normal tensile and compressive stresses of almost twice the magnitude of the peak shear stress are produced in the vicinity of the crimped bundles. Consistent with these predictions, we observed the shear fault following the crimp boundaries in 0°/90° and quasi-isotropic laminates. Therefore, experimental techniques which can secure a state of pure shear stress in aligned, unkinked, uniaxial fiber composites cannot do so in woven laminated composites.     

硬质合金金刚石涂层的残余应力分析

采用有限元方法分析硬质合金金刚石涂层的热残余应力,采用轴对称二维几何模型和自由边界条件,考虑了涂层厚度及不同基体对应力场的影响。分析表明,在多晶金刚石涂层中存在压应力,在基体中出现了拉应力,这种应力结构分布对材料性能的影响是有利的。在明锐界面出现了大的剪切应力(415MPa),应力奇异场出现在明锐界面靠近自由边界处。涂层压应力随基体中钴含量的增加而增加,随涂层厚度的增加而减小。因此可以借助这两个因素来适当控制和调节材料中的应力场以得到性能优良的产品。     

Delamination Analysis for Laminated Composites. II: Numerical Verification

A validation of the delamination analysis models developed in a companion paper is provided through comparisons of predictions with finite‐element and elasticity solutions. The models are applied to the analysis of composite compression specimens reinforced with end tabs. An elasticity solution for the gage section of the specimens is developed. A comparison of the characteristic roots shows that the predictions of the models include the material and geometric parameters that control the behavior, and the roots corresponding to the basic stretching and bending modes are accurately predicted. The stress distribution at the interface between tabs and specimen is in good agreement with a finite‐element simulation. The interlaminar shear and peel stresses show an exponential increase with a maximum intensity at the free edges of the tabs. The behavior of previously tested specimens is explained; and practical guidelines for specimen design are provided to avoid unwanted extraneous modes of failure. The influence of the deformation modes associated with each model is investigated. An assessment of the accuracy and level of complexity is presented.     

Residual stresses and cracking in brittle solids bonded with a thin ductile layer

Residual stresses that exist between two brittle materials bonded by a thin ductile layer are calculated. In particular, the stresses at and near the interface are examined as well as the plastic zone profile. The stress intensity factors associated with interface cracks are then computed and used to address problems of cracking and bond strength. The analysis reveals the relative influence of thermal expansion mismatch, yield strength, bond thickness and interface fracture resistance.     

Moving Least-Squares Differential Quadrature Method for Free Vibration of Antisymmetric Laminates

In this paper, the moving least-squares differential quadrature (MLSDQ) method is employed for free vibration of thick antisymmetric laminates based on the first-order shear deformation theory. The generalized displacements of the laminates are independently approximated with the centered moving least-squares (MLS) technique within each domain of influence. The MLS nodal shape functions and their partial derivatives are computed quickly through back-substitutions after only one LU decomposition. Subsequently, the weighting coefficients in the MLSDQ discretization are determined with the nodal partial derivatives of the MLS shape functions. The MLSDQ method combines the merits of both the differential quadrature and meshless methods which can be conveniently applied to complex domains and irregular discretizations without loss of implementation efficiency and numerical accuracy. The natural frequencies of the laminates with various edge conditions, ply angles, and shapes are calculated and compared with the existing solutions to study the numerical accuracy and stability of the MLSDQ method. Effects of support size, order of completeness of basis functions, and node irregularity on the numerical accuracy are investigated in detail.     

Analysis of Water Waves Passing Over a Submerged Rectangular Dike

The analytic solutions of inviscid and viscous water waves passing over a submerged rectangular dike are investigated. Owing to the fact that the orthogonality of eigenfunctions is invalid for viscous wave problem, two newly developed orthogonal inner products are applied to reduce the mathematical difficulty of viscous wave problem. Both inviscid and viscous water wave solutions are obtained under the assumption of linear water wave without separation. It shows that two solutions have no significant kinematic difference but the viscous contribution of dynamic effect is not negligible. Beside giving a better theoretical approach, which reduces the error of the conventional minimal squares method, the result of the present analytical solution can be used to quantitatively evaluate the correctness of experiments and also provides helpful information such as near wall boundary layer thickness and oscillating free surface for computational use.     

The Influence of the Thickness and Areal Density on the Mechanical Properties of Carbon Fibre Reinforced Aluminium Laminates (CARAL)

A novel composite material consisting of a laminate of several thin aluminium sheets bonded with layers of carbon fibre mat/epoxy resin. Carbon fibre reinforced aluminium laminates (CARAL) offer specific advantageous properties such as better strength, fatigue, impact, corrosion resistance, fire resistance and weight savings. CARAL is a kind of fibre metal laminate system. In the present work, CARAL was prepared and experimental tests were conducted to evaluate the influence of the thickness and areal density on the mechanical properties of CARAL. Mechanical properties such as, the tensile strength and flexural strength of the laminates were increased with the increase in thickness and areal density. CARAL with four aluminium layers and three carbon fibre mat layers have superior strength than the laminates with lesser number of layers due to thickness of laminates and areal density.     

Estimation of Maximum Liquid Depth in Layered Drainage Blankets over Landfill Barriers

Based on an extended form of the Dupuit assumption, this technical note proposes a computational solution for calculating the maximum liquid depth (Dmax) in layered porous media (e.g., geosynthetic and/or soil drainage blankets of landfills) under free discharge condition. The liquid profile and the location of Dmax for either homogeneous media or layered media can be provided from the approach presented in this technical note. In comparison with the results obtained by application of other methods, the presented approach is verified. Most approaches other than the presented method may lead to considerable error, especially when applied to the drainage system, which consists of a drainage geocomposite overlain by a sand layer with low hydraulic conductivity. The variations of Dmax in two-layered drainage media with varying geometrical parameters and varying hydraulic properties are studied by a parametric analysis. The results demonstrate for a medium consisting of two sand layers, if the hydraulic conductivity of the upper layer is smaller than that of the lower layer and the maximum liquid thickness above the barrier exceeds the thickness of the lower layer, Dmax is very sensitive to the hydraulic conductivity of the upper layer. For a medium consisting of a drainage geocomposite overlain by a sand layer, Dmax is significantly influenced by inflow rate, transmissivity of the geocomposite, and the hydraulic conductivity of the sand when they are not extraordinarily low, and Dmax is much more sensitive to the slope of the drainage layer compared with the system consisting of two sand layers. It is of great advantage to increase the inclination when geocomposites are applied as drainage material.     

Analysis of Hybrid Laminated Composite Plates

Hybrid laminated composite plates are analyzed using a nine‐noded isoparametric plate finite element based on Mindlin's theory. The shear flexibility is included in the finite element modeling. Shear flexibility is of importance, especially when different materials are used in the laminate design. Hybrid laminates consisting of graphite∕epoxy and kevlar∕epoxy plies are considered for illustration. The study indicates that hybrid laminates provide stiffnesses that are intermediate to the values obtained for single‐material laminates. The minimum deflection is achieved at different fiber orientation for thick plates compared to thin plates. The deflection behavior of hybrid laminates seems to be less affected by outer‐ply stiffness in the case of thick plates. Thick plates show less variation in the first natural frequency with fiber orientation but hybridization changes the natural frequency considerably. The first natural frequency of the hybrid laminate can be made higher than the stiffer single‐material laminate.