Progressive failure analysis of laminated composite with hole under flexural loading

Abstract

Understanding the progressive failure of laminated composite plays an important role in the structural integrity analysis of a structure. Continuum damage mechanics-based approach is one of the powerful tools to analyze the failure of laminated composite structures. The present paper investigates the damage evolution and progression in laminated composites with a hole under flexural loading. The presence of high-stress concentrations along with the free edge stresses at the vicinity of the hole in laminated composite leads to complex failure mechanisms. The influence of the change in thickness and lamina configuration on the strength characteristics is presented.     

复合材料非对称正交薄层板的固化变形

利用Rayleigh-Ritz 法研究了复合材料非对称正交薄层板的固化变形。建立了考虑几何非线性的固化变形分析模型, 预报了其固化后的变形形状及变形量。利用热压釜工艺进行了实验研究。实验发现, 方板边缘发生了较大的向内卷曲变形, 板边缘附近理论预报值与实验结果差别较大, 在距板边缘一定距离内理论预报值和实验结果吻合较好, 矩形板实验结果与理论预报值吻合良好。      

复合材料层合板固化压实过程有限元数值模拟及影响因素分析

根据有效应力准则和达西定律建立了描述复合材料固化压实过程层合板压缩和树脂流动的二维有限元方程, 节点自由度为位移和树脂压力, 采用向后差分方法直接耦合积分求解以提高收敛速度。数值计算结果表明: 随着层合板厚度的增加, 厚度压缩率减小, 固化压实所需时间增加, 树脂在厚度方向的不均匀性逐渐增加。对于厚度较大的层合板, 采用提高固化压力和双面吸胶两种工艺对比情况说明, 后者可以显著提高压实程度并得到相对均匀的树脂含量分布。      

Large deflection initial failure analysis of angle-ply laminated plates

A large deflection initial failure analysis of square angle-ply laminated plates subjected to uniform pressure loading is described. Approximate numerical solutions of the Mindlin laminated plate equations are derived using finite differences in conjunction with the Dynamic Relaxation (DR) technique. The solutions are scaled to satisfy the Tsai-Hill lamina failure criterion. The effects of plate slenderness, in-plane edge restraint and lay-up on the initial failure pressure and associated plate centre deflection are quantified for ±45° laminated plates with simply supported and clamped edges. It is shown, particularly for thin plates, that in-plane edge restraint increases the initial failure pressure substantially, though changing the plate edge conditions from simply supported to clamped does not always increase the initial failure pressure.     

Stress and failure analysis of laminated composites based on layerwise B-spline finite strip method

A layerwise B_k,k−1-spline finite strip method is developed for stress and failure analysis in fibre reinforced composite laminates. The composite laminates are divided into a number of numerical layers in the thickness direction. A linear variation of in-plane displacements are assumed across the thickness of each numerical layer to represent the sectional warping which can have significant effects on through thickness shear stresses. The development of B_k,k−1-spline finite strip method is presented. Material failure criteria and material degradation models for progressive failure are discussed and integrated in a progressive failure analysis for composite laminates. Numerical applications include a progressive failure analysis example are presented to verify the layerwise B-spline finite strip method developed for stress and failure analysis in composite laminates. Whenever possible the present predictions are compared with the existing analytical and numerical results.     

Three-dimensional stress and progressive failure analysis of ultra thick laminates and experimental validation

Test methods and analysis capabilities for fibre reinforced composites are generally limited to thin laminates. However, extending the range of application of composite materials to thick laminates is essential for a multitude of possible composite structures. This paper presents an adapted three-point bending test for a new quasi isotropic stacking sequence for non crimped fabrics for the application in ultra thick laminates (UTL). In addition, numerical simulation capabilities for thick laminates using a multiscale analysis are shown. The three-point bending test setup is developed to examine the failure behaviour of 30–60 mm thick coupons.     

Stationary thermoelastic analysis of thick cross-ply laminated cylinders and cylindrical panels

Summary This paper deals with the three-dimensional stationary thermoelastic behaviour of cross-ply laminated cylindrial shells and panels having simply supported edges. The analysis is based on a very rapidly converging successive approximation approach which has already been applied, successfully, in connection with three-dimensional static and dynamic analyses of orthotropic homogeneous and crossply laminated cylinders and cylindrical panels. Here, an extension of that approach is used that takes into consideration the implications of the heat conduction equation. The mathematical formulation is suitable for the study of thermoelastic behaviour of shells and panels subjected to any type of stationary thermal conditions on their lateral boundaries. This is achieved by suitably expanding the lateral surface boundary conditions in the form of appropriate Fourier-series. For simplicity, however, all numerial results presented and discussed throughout paper are dealing with a single harmonic of such Fourier-series expansions.     

Buckling analysis of cross-ply laminated conical panels using GDQ method

The buckling analysis of cross-ply laminated conical shell panels with simply supported boundary conditions at all edges and subjected to axial compression is studied. The conical shell panel is a very interesting problem as it can be considered as the general case for conical shells when the subtended angle is set to 2π and also cylindrical panels and shells when the semi-vertex angle is equal to zero. Equations were derived using classical shell theory of Donnell type and solved using generalized differential quadrature method. The results are compared and validated with the known results in the literature. The effects of subtended angle, semi-vertex angle, length, thickness and radius of the panel on the buckling load and mode are investigated.     

New analytical method for electric current and multiple delamination cracks for thin CFRP cross-ply laminates using equivalent electric conductance

Carbon fiber reinforced polymer (CFRP) composites have low inter-lamina strength. One of the monitoring technologies is a self-sensing method that uses the electrical resistance change of a CFRP structure for detecting damage. The electric current distribution is vital information for the self-sensing method when optimizing the arrangement of probes to measure electric potential changes. We have developed a new orthotropic electric potential function analysis approach using affine transformation for unidirectional CFRP. In this study, the orthotropic electric potential function analysis method is improved to calculate the electric current of a thin cross-ply CFRP. Two types of stacking sequences for the beam-type cross-ply laminates were calculated to confirm the effectiveness of the improved method. The electrical voltage changes caused by multiple delamination cracks of a cross-ply laminate are new outcomes of this study. The analytical results were compared with computed results using the finite difference method. Consequently, the new equivalent electric conductance method proved to be effective for calculations of the electric current density of a cross-ply CFRP laminate. Furthermore, the new method for calculating the electric potential difference changes caused by multiple delamination cracks using orthotropic distributed doublet analysis, with the equivalent electric conductance, has also proved to be effective.     

Stochastic progressive failure analysis of laminated composite plates using Puck's failure criteria

The present work deals with second-order statistics of the progressive failure response of laminated composite plates subjected to in-plane uniaxial and bi-axial loadings with random system properties. A stochastic finite element method based on higher-order shear deformation theory combined with first- and second-order perturbation technique is used for solution of random progressive failure equation. A Puck failure criterion is used for the evaluation of first ply and last-ply failure load. The results obtained using the present solution approach are validated with the results available in the literature and Monte Carlo simulation.     

On the stress analysis of cross-ply laminated plates and shallow shell panels

This paper extends the applicability of a new stress analysis method (Soldatos KP, Watson PA. Acta Mech 1997;123:163–186) towards the accurate prediction of stresses within cross-ply laminated doubly curved shell segments having a rectangular plan-form. The method is based on the successful incorporation of three-dimensional elasticity information for stress distributions into a two-dimensional five-degrees-of-freedom shallow shell theory. This successful matching is achieved by means of a set of two shape functions, which are incorporated within the two-dimensional shell model whereas their form depends on the particular problem considered. In the present case, two different sets of shape functions are developed and tested, one of which is more accurate than the other is, the later being however simpler than the former.     

Stress analysis of axisymmetric shear deformable cross-ply laminated circular cylindrical shells

A generalized mixed theory for bending analysis of axisymmetric shear deformable laminated circular cylindrical shells is presented. The classical, first-order and higher-order shell theories have been used in the analysis. The Maupertuis–Lagrange (M–L) mixed variational formula is utilized to formulate the governing equations of circular cylindrical shells laminated by orthotropic layers. Analytical solutions are presented for symmetric and antisymmetric laminated circular cylindrical shells under sinusoidal loads and subjected to arbitrary boundary conditions. Numerical results of the higher-order theory for deflections and stresses of cross-ply laminated circular cylindrical shells are compared with those obtained by means of the classical and first-order shell theories. The effects, due to shear deformation, lamination schemes, loadings ratio, boundary conditions and orthotropy ratio on the deflections and stresses are investigated.     

复合材料单向层合板损伤失效试验研究

对T300/BMP-316单向层合板静载及疲劳加载各主方向损伤失效进行了试验研究, 为建立该材料各主方向疲劳加载剩余刚度退化表达式及剩余强度退化表达式提供了依据。同时, 获得了该材料剪切非线性因子, 给出了面内剪切疲劳加载试验循环过程中剪切刚度计算公式, 使用渗透剂增强的X射线图像技术对试样静载及疲劳破坏损伤状态进行了无损检测, 并对损伤失效机理形式进行了分析探讨。试验表明, 层合板结构应力分析中考虑材料剪切应力-应变的非线性效应是非常必要的。      

The non-linear buckling analysis of cross-ply laminated orthotropic truncated conical shells

In this study, the non-linear buckling behavior of cross-ply laminated orthotropic truncated conical shells under axial load has been investigated. The basic relations of the cross-ply laminated orthotropic truncated conical shells are derived using the von Karman–Donnell-type of kinematic non-linearity. Then modified Donnell type non-linear stability and compatibility equations are obtained and are solved. Finally, the influences of the number and ordering of layers and the variations of the conical shell characteristics on the non-linear axial buckling load are investigated. Comparison with available results is satisfactorily good.     

Elastic characterization of laminated composites based on multiaxial tests

This paper presents a technique that continuously identifies the elastic moduli of laminated composites from multiaxial tests and its application to multiaxial identification. Unlike the conventional characterization where materials are characterized uniaxially, the technique identifies the elastic moduli by considering specimens on a continuum basis. The technique further controls the multiaxial testing machine by extracting quantities from the matrix used for identification and maximizing the quantities. Numerical examples first investigate the significance, robustness and efficiency of the proposed technique where its efficacy has been then confirmed via various quantifications. The proposed technique was finally applied to a realistic characterization problem, and its practicality has been demonstrated.     

Fabrication and modelling of the macro-mechanical properties of cross-ply laminated fibre-reinforced polymer composites using artificial neural network

The mechanical behaviour of fibre-reinforced polymer composites (FRPCs) is considered very complex due to many factors such as composition, material type, manufacturing process and end user applications. This article presents the mechanical properties and artificial neural network (ANN) modelling results of cross-ply laminated FRPCs. Twenty composite samples were fabricated by varying the number of layers of carbon fibre and glass fibre as reinforcement and polyphenylene sulphide and high-density polyethylene as matrix. Mechanical properties were measured in terms of flexural modulus, hardness, impact and transverse rupture strength. Multilayer feed-forward backpropagation ANN approach was used to predict the mechanical properties by using material type, composition and number of reinforcement and matrix layers as input variables. From 20 data patterns, 16 were used for network training and remaining 4 were used to test the models. Furthermore, trend analysis was also performed to understand the influence of inputs on developed models. It is evident from the ANN prediction results that there is good correlation between predicted and actual values within acceptable mean absolute error. The outcomes of this research will help to reduce cost and time by eliminating tedious composite property measurements and to fabricate tailored composites meeting application requirements.     

Flexural analysis of cross-ply laminated plates subjected to nonlinear thermal and mechanical loadings

The objective of this paper is to present an equivalent single-layer shear deformation theory for evaluation of displacements and stresses of cross-ply laminated plates subjected to uniformly distributed nonlinear thermo-mechanical load. A trigonometric shear deformation theory is used. The in-plane displacement field uses a sinusoidal function in terms of the thickness coordinate to include the shear deformation effect. The theory satisfies the shear stress free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of a shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Stresses and displacements for orthotropic, two-layer antisymmetric, and three-layer symmetric square cross-ply laminated plates subjected to uniformly distributed nonlinear thermo-mechanical load are obtained. Numerical results of the present theory for displacement and thermal stresses are compared with those of classical, first-order and higher-order shear deformation plate theories.     

A semi-analytical discretization method for the near-field analysis of unsymmetrically laminated multimaterial junctions

In the present contribution, the theoretical basics of a novel semi-analytical discretization procedure are described. The method relies on the discretization of the structural situation into an arbitrary number of sectorial elements in which adequate displacement formulations are postulated. Speaking in terms of a cylindrical coordinate system, the sectorial elements are supposed to be of infinite dimensions in the radial direction, hence the actual discretization takes place in the circumferential direction only. While linear shape functions are employed in each of the infinite sectorial elements in the circumferential direction, a set of unknown displacement functions is postulated in each of the resultant interfaces between the individual elements with respect to the radial coordinate. The principle of minimum elastic potential yields the governing Euler–Lagrange equations straightforwardly which allow for closed-form solutions for the unknown interface displacement functions. Since the method yields closed-form solutions for all state variables with respect to the radial coordinate and employs a discretization in the circumferential direction exclusively, we may actually speak of a semi-analytical methodology. Examples are presented for the near-field analysis of unsymmetrically laminated multimaterial notches. The presented semi-analytical method proves to be of high accuracy. Furthermore, while this novel discretization procedure clearly outperforms purely numerical analysis methods like FEM in terms of computational time and effort, it works with comparable accuracy which makes it very attractive for any practical application purpose with involved localization effects where reliable results need to be computed with low computational effort.