Post-buckling and delamination propagation behavior of composite laminates with embedded delamination

Delamination occurred due to poor manufacturing process or in-service actions significantly affects the mechanical and failure behavior of laminated composite structures. In this study, the buckling and post-buckling delamination behavior of laminated composite with an embedded initial delamination under in-plane compression was studied experimentally and numerically. First, compression tests for laminated composite specimens with embeded initial delamination were performed and the buckling and delamination responses were obtained. Then the experimental test was numerically simulated using finite element methods with the progressive failure accounted for by using cohesive zone modeling. The load-displacement curve, strain behavior and delamination shapes of experimental specimens obtained from load cells, strain gages installed at different locations, and C scan images, respectively, were compared with the FEM results, and good agreements were attained. The effect of the buckling modes, laminate stacking sequence and shape of initial delamination on the buckling load and propagation behavior was studied by considering different ply stacking and shapes of initial delaminations. It was found that the buckling mode determined the growth direction of the delamination propagation, and the stacking sequence influenced the extent of the propagation area, while the orientation of the delamination affected the buckling loads.     

Buckling analysis of FGM plates under uniform,linear and non-linear in-plane loading

The paper investigates the buckling responses of functionally graded material (FGM) plate subjected to uniform, linear, and non-linear in-plane loads. New nonlinear in-plane load models are proposed based on trigonometric and exponential function. Non-dimensional critical buckling loads are evaluated using non-polynomial based higher order shear deformation theory. Navier’s method, which assures minimum numerical error, is employed to get an accurate explicit solution. The equilibrium conditions are determined utilizing the principle of virtual displacements and material property are graded in the thickness direction using simple Voigt model or exponential law. The present formulation is accurate and efficient in analyzing the behavior of thin, thick and moderately thick FGM plate for buckling analysis. It is found that with the help of displacement-buckling load curve, critical buckling load can be derived and maximum displacement due to the instability of inplane load can be obtained. Also, the randomness in the values of transverse displacement due to inplane load increases as the extent of uniformity of the load on the plate is disturbed. Furthermore, the parametric varying studies are performed to analyse the effect of span-to-thickness ratio, volume fraction exponent, aspect ratio, the shape parameter for non-uniform inplane load, and non-dimensional load parameter on the non-dimensional deflections, stresses, and critical buckling load for FGM plates.

     

Effect of fiber orientation on interfacial fracture toughness for adhesively bonded composite plates

In this study, interfacial fracture toughness was investigated experimentally and numerically in laminated composite plates with different fiber reinforcement angles bonded with adhesive. The composite plates are four-layered and the layer sequence is [0º/θ]_s. DCB test was applied to composite plates reinforced with epoxy resin matrix and unidirectional carbon fiber. The experimental sample model for the DCB test was made using the ANSYS finite element package program. In the numerical study, four layered composites were prepared in three dimensions. Under critical displacement value; mode I fracture toughness at the crack tip was calculated using VCC (virtual crack closure) technique. Numerical values consistent with experimental results have presented in graphical forms. At 60o and 75° the greatest fracture toughness was obtained. In addition, numerical results have shown that fiber orientation prevents the uniform distribution of stress on the interface crack tip and causes stress accumulation, especially at the edge of the plate.

     

Thermal buckling behavior of laminated composite plates: a finite-element study

In this paper, the thermal buckling behavior of composite laminated plates under a uniform temperature distribution is studied. A finite element of four nodes and 32 degrees of freedom (DOF), previously developed for the bending and mechanical buckling of laminated composite plates, is extended to investigate the thermal buckling behavior of laminated composite plates. Based upon the classical plate theory, the present finite element is a combination of a linear isoparametric membrane element and a high precision rectangular Hermitian element. The numerical implementation of the present finite element allowed the comparison of the numerical obtained results with results obtained from the literature: 1) with element of the same order, 2) the first order shear deformation theory, 3) the high order shear deformation theory and 4) the three-dimensional solution. It was found that the obtained results were very close to the reference results and the proposed element offers a good convergence speed. Furthermore, a parametrical study was also conducted to investigate the effect of the anisotropy of composite materials on the critical buckling temperature of laminated plates. The study showed that: 1) the critical buckling temperature generally decreases with the increasing of the modulus ratio E _L/E _T and thermal expansion ratio α _T/α _L, and 2) the boundary conditions and the orientation angles significantly affect the critical buckling temperature of laminated plates.     

复合材料螺接力学行为精细化有限元分析方法

针对航空用纤维增强树脂基复合材料螺栓连接的力学行为研究难题,采用有限元软件二次开发的方法,提出了涵盖层合板高效建模、扭矩与预紧力关系、钉孔配合间隙与滑移过渡段、渐进损伤判断与性能退化等方面的精细化有限元分析模型。提出了基于应变等效原理的紧固件预紧力-扭矩试验测试方法,降低了紧固件预紧力-扭矩转换精度对数值模拟精度的影响。提出了基于修改螺栓头与层合板接触平面摩擦因数的方法以实现对含钉孔配合间隙的复合材料螺接接头的力-位移响应在滑移过渡段的较好模拟。复合材料单搭接螺接接头单剪试验和有限元预测的力-位移曲线对比结果显示极限载荷最大预测误差为17.2%,证明了所提方法能有效地预测复合材料单钉/多钉螺接结构的力学性能演变规律,且所提方法提高了预测结果与试验结果的匹配度,提升了有限元分析的效率,为航空先进复合材料连接结构的力学行为分析奠定了建模技术基础。     

复合材料加筋板在剪切载荷下的屈曲特性研究

通过对复合材料薄壁加筋板结构进行剪切载荷下的屈曲试验研究,得到结构的屈曲模态、屈曲失稳载荷以及破坏形式,并通过有限元方法对结构的屈曲进行数值分析,分析得到的复合材料薄壁加筋板结构的屈曲模态和试验结果一致,屈曲载荷与试验结果吻合较好.试验还发现复合材料薄壁加筋板结构有较高的后屈曲承载能力,后屈曲过程中由于桁条脱胶会造成屈曲模态的变化.还分析了筋条的连续性对屈曲载荷的影响.     

Analytical models of composite material drilling

Drilling of composite material structures is widely used for aeronautical assemblies. When drilling, damage to the composite laminate is directly related to the cutter geometry and the cutting conditions. Delamination of the composite materials at the hole exit as directly related to the axial force (F _Z) of the cutter is considered to be the major such defect. To address this issue, an orthotropic analytical model is developed in order to calculate the critical force of delamination during drilling and a number of hypotheses for loading are proposed. This critical axial load is related to the delamination conditions (propagation of cracks in the last layers) and the mechanical characteristics of the composite material machined. A numerical model is also drawn up to allow for numerical validation of the analytical approach. A comparison between these analytical and numerical modellings and experimental results from quasi-static punch tests led to the choice of the loading hypothesis closest to the experimental conditions. The selection of corresponding load permits to model the drilling critical thrust force on delamination and then to optimise the cutting conditions. The dimensions and geometrical shape of the cutter are of considerable importance when it comes to choosing this load. The present article focuses on the case of the twist drill, which is commonly used to drill thick plates. However, this work can be adapted to different cutter geometries.     

Dynamic relaxation method for nonlinear buckling analysis of moderately thick FG cylindrical panels with various boundary conditions

Using new approach proposed by Dynamic relaxation (DR) method, buckling analysis of moderately thick Functionally graded (FG) cylindrical panels subjected to axial compression is investigated for various boundary conditions. The mechanical properties of FG panel are assumed to vary continuously along the thickness direction by the simple rule of mixture and Mori-Tanaka model. The incremental form of nonlinear formulations are derived based on First-order shear deformation theory (FSDT) and large deflection von Karman equations. The DR method combined with the finite difference discretization technique is employed to solve the incremental form of equilibrium equations. The critical mechanical buckling load is determined based on compressive load-displacement curve by adding the incremental displacements in each load step to the displacements obtained from the previous ones. A detailed parametric study is carried out to investigate the influences of the boundary conditions, rule of mixture, grading index, radius-to-thickness ratio, length-to-radius ratio and panel angle on the mechanical buckling load. The results reveal that with increase of grading index the effect of radius-to-thickness ratio on the buckling load decreases. It is also observed that effect of distribution rules on the buckling load is dependent to the type of boundary conditions.

     

层合板多钉机械连接载荷分配三维有限元分析

用三维有限元方法对层合板单排四钉机械连接钉载分配进行了分析。计算了复材板与钢板、铝板双搭接时的载荷分布。结果表明,在最大承载孔上理论值与试验值误差不大于１６％。各孔的载荷分配主要取决于连接板的刚度,与孔径关系不大。     

切向加载下螺栓连接复合板的失效分析*

极限载荷和孔周应力是导致螺栓连接复合板失效的主要因素。基于Hashin失效准则和有限元模型建立螺栓连接复合板的渐进损伤有限元模型,通过位移载荷响应讨论预紧力、界面摩擦因数和孔隙变化对极限载荷的影响,分析不同铺层角下孔周应力分布规律。结果表明：随预紧力增大,螺栓连接复合板极限载荷先增大后减小,随摩擦因数增大,螺栓连接复合板极限载荷逐渐增大;不同孔隙下准线性阶段位移载荷响应基本一致,孔隙对极限载荷的影响主要体现在滑移阶段及剪切变形阶段;孔隙增大会减小螺栓与螺孔间的有效接触面积,影响螺栓连接的压力分布和强度;纤维铺层方向与应力分量同向时可有效减少外载荷导致的该方向应力分量的变化,且主应力分量皆在承压区域达到其最小值;应力分量方向与纤维铺层方向相同且该方向无外载荷作用时,应力分量随着角度从承压区到非承压区递增变化。     

Stability behaviour of arbitrarily laminated composite plates with free and elastically restrained unloaded edges

In this paper, the initial buckling loads and the corresponding buckling modes of symmetric rectangular laminated plates are investigated. The considered laminates are supposed to have a uniform thickness, are subjected to a linearly distributed inplane compressive normal load and are simply supported at the two loaded edges with one free unloaded plate edge and with one simply supported unloaded edge where elastic rotational restraints are considered. Unlike in many other investigations, the composite laminates presently under consideration may have arbitrary yet symmetric lamination schemes with bending–torsion coupling. The initial buckling loads of such plates are calculated using the RITZ-method for which some especially adjusted displacement shape functions are employed. Since a series expansion of the buckling shape is performed in the load direction only while in the perpendicular direction one single displacement function can be shown to be sufficient, the present approach is numerically very efficient when compared to approaches in which a series representation is chosen with respect to both inplane directions. Comparison with reference results and with finite element computations leads to an excellent agreement. Some new findings on the general stability behaviour of this class of laminated plates are presented as a closure.     

Evaluation of failure criteria for composite plate under high-velocity impact

Numerical simulations of bird-striking composite plates were conducted by using smoothed particle hydrodynamics and finite element method to evaluate the failure criteria. The damage prediction capability of four composite failure models (MAT22, MAT54, MAT55, and MAT58) with Shell and TShell element formulations was evaluated by using the finite element software LS-DYNA, and the numerical results were compared with the experimental results. Results show that the damage distributions of different composite material models differ significantly under high-velocity impact conditions. The time histories of the impact force and the kinetic energy of bird are similar for the four models. This condition can be attributed to the fact that the materials’ strength and elastic parameters are the same between the different models. The damage characteristics of MAT55 and MAT22 with TShell elements are poorly related to the experimental results. MAT58 with Shell and TShell element formulations shows good agreement with the experiments, and the TShell element can better avoid the boundary effect during the impact process.

     

The compressive behavior of CFRP laminates with delamination of different shapes using numerical and experimental approaches

Composite laminates often produce delamination due to a series of factors during the manufacture and service process. In order to research the effect of containing oblique elliptical and circular initial delamination damage on the compressive strength of composite laminates, numerical and experimental methods are used in this paper. Finite element models (FEMs) and the progressive damage subroutine USDFLD are developed to predict the damage initiation and extension behavior of the intralaminar of the laminate. Interlaminar damage is predicted based on cohesive zone models (CZM). At the same time, four compression tests containing different initial delamination damage are performed. The results show that experimental measurements of compression tests concur with the numerical predictions and validate the FEMs. The strength and stiffness of the specimens gradually decrease with the increase of the initial delamination area. It reveals that, for the compression process, the delamination damage extends from the edge of the initial damage to the surroundings. The bearing capacity of the composite laminates is mainly determined by the material properties of the fibers and matrix, rather than the initial delamination.

     

汽车半轴套管失效载荷数值模拟

本文对我国生产的一种汽车半轴套管进行了大位移、大应变弹塑性有限元模拟,求得了加载点的栽荷-位移曲线、最大应力点的弹塑性应变-载荷曲线、危险截面的弹塑性应力-载荷曲线、危险截面达到全面屈服时的失效载荷等,为汽车半轴套管的强度评价及疲劳寿命估算提供了有关数据.     

Theory and comparison of the effect of composite and shape memory alloy stiffeners on stability of composite shells and plates

The effects of composite and shape memory alloy stiffeners on stability of composite cylindrical shells and rectangular plates subjected to a compressive load are compared. The governing equations for reinforced cylindrical shells are developed based on the Love first approximation theory and smeared stiffeners technique. It is shown that composite stiffeners are more efficient in cylindrical shells, while shape memory alloy stiffeners may be preferable in plates or in long shallow shells. It is also proven that shape memory alloy stiffeners increase the upper and lower buckling loads, i.e. the linear buckling load and the minimum postbuckling load-carrying capacity of cylindrical shells modeled as single-degree-of-freedom systems by the same amount.     

Thermomechanical buckling of laminated composite and sandwich plates using global–local higher order theory

In this paper, a global–local higher order theory has been used to study buckling response of the laminated composite and sandwich plates subjected to thermal/mechanical compressive loads. The present global–local theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces, and the number of unknowns is independent of the layer numbers of the laminate. Based on this higher-order theory, a refined three-noded triangular element satisfying C¹ weak-continuity conditions has been also proposed. The present theory not only predicts accurately the buckling response of general laminated composite plates but also calculates the critical buckling loads of the soft-core sandwich plates. However, numerical results show that the global higher-order theories as well as first order theories encounter some difficulties and overestimate the critical buckling loads for the sandwich plates with a soft core.     

铝合金及复合材料板开孔损伤分析

分析计算了中心开孔损伤对铝合金板和不同铺层方式的复合材料板承载能力的影响。结果表明：在开孔尺寸一定的情况下，随着板宽的增大，开孔损伤板的应力集中因数减小；随着材料各向异性程度的提高，开孔损伤对板件的应力集中因数和承载能力的影响增大。这一结果在试验中得到证实。     

Buckling analysis of circular and annular composite plates reinforced with carbon nanotubes using FEM

The critical compressive load in the buckling of circular and annular composite plates reinforced with carbon nanotubes (CNTs) is calculated using finite element method. The developed model is based on the third-order shear deformation theory for moderately thick laminated plates. Effects of CNTs orientation angles and thickness-to-inner radius ratio on the buckling of composite plates are discussed. The results are compared with those obtained by analytical method based on classical plate theory. The finite element method shows lower values for critical buckling load because of the elimination of shear strain in the classical plate theory.     

Linear and nonlinear buckling analysis of a locally stretched plate

Uniformly stretched thin plates do not buckle unless they are in special boundary conditions. However, buckling commonly occurs around discontinuities, such as cracks, cuts, narrow slits, holes, and different openings, of such plates. This study aims to show that buckling can also occur in thin plates that contain no defect or singularity when the stretching is local. This specific stability problem is analyzed with the finite element method. A brief literature review on stretched plates is presented. Linear and nonlinear buckling stress analyses are conducted for a partially stretched rectangular plate, and various load cases are considered to investigate the influence of the partial loading expanse on the critical tensile buckling load. Results are summarized in iso-stress areas, tables and graphs. Local stretching on one end of the plate induces buckling in the thin plate even without geometrical imperfection.     

Application of Trefftz theory in thin-plate buckling with in-plane pre-buckling deformations

The paper presents the application of Trefftz initial stress theory in determining the elastic buckling load of rectangular thin plates under in-plane stress resultants, with allowance for in-plane pre-buckling deformations. Exact buckling solutions for simply supported plates are obtained and compared with earlier results furnished by Ziegler (1983, Ing.-Arch.53, 61 [1]). Although somewhat different, due to the use of different theories, both sets of results show that the buckling loads may be reduced when pre-buckling deformations are accounted for. This observation is contrary to that for column buckling where it has been shown that the allowance for pre-buckling shortening results in a higher buckling load. This reduction in plate-buckling load is significant especially for plates with large thickness-to-span ratios and subject to a combination of tensile and compressive in-plane stress resultants that increase pre-buckling deformations.