Failure analysis of fiber-reinforced composite laminates subjected to biaxial loads

A nonlinear constitutive model for a single lamina is proposed for the failure analysis of composite laminates. In the material model, both fiber and matrix are assumed to behave as elastic-plastic and the in-plane shear is assumed to behave nonlinearly with a variable shear parameter. The damage onset for individual lamina is detected by a mixed failure criterion, composed of the Tsai-Wu criterion and the maximum stress criterion. After damage takes place within the lamina, the fiber and in-plane shear are assumed to exhibit brittle behavior, and the matrix is assumed to exhibit degrading behavior. The proposed nonlinear constitutive model is tested against experimental data and good agreement is obtained. Then, numerical analyses are carried out to study the failure behavior of symmetric angle-ply composite laminates and symmetric cross-ply composite laminates subjected to biaxial loads. Finally, the conclusions obtained from the numerical analysis are given.     

Postbuckling strengths of composite laminate with various shaped cutouts under in-plane shear

The aim of present investigation is to study the buckling and postbuckling response and strengths under positive and negative in-plane shear loads of simply-supported composite laminate with various shaped cutouts (i.e., circular, square, diamond, elliptical-vertical and elliptical-horizontal) of various sizes using finite-element method. The FEM formulation is based on the first order shear deformation theory which incorporates geometric nonlinearity using von Karman’s assumptions. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. The effect of cutout shape, size and direction of shear load on buckling and postbuckling responses, failure loads and failure characteristics of quasi-isotropic [i.e., (+45/−45/0/90)_2s] laminate has been discussed. In addition, the effect of composite lay-up [i.e., (+45/−45/0/90)_2s, (45/−45)_4s and (0/90)_4s] has also been reported. It is observed that the cutout shape has considerable effect on the buckling and postbucking behaviour of the quasi-isotropic laminate with large size cutout. It is also observed that the direction of shear load and composite lay-up have substantial influence on strength and failure characteristics of the laminate.     

Examination of the failure of sandwich beams with core junctions subjected to in-plane tensile loading

The paper concerns local effects occurring in the vicinity of junctions between different cores in sandwich beams subjected to tensile in-plane loading. It is known from analytical and numerical modelling that these effects display themselves by an increase of the bending stresses in the faces as well as the core shear and transverse normal stresses at the junction. The local effects have been studied experimentally to assess the influence on the failure behaviour both under quasi-static and fatigue loading conditions. Typical sandwich beam configurations with aluminium and glass-fibre reinforced plastic (GFRP) face sheets and core junctions between polymer foams of different densities and rigid plywood or aluminium were investigated. Depending on the material configuration of the sandwich beam, premature failure accumulating at the core junction was observed for quasi-static and/or fatigue loading conditions. Using Aluminium face sheets, quasi-static loading caused failure at the core junction, whereas no significance of the junction was observed for fatigue loading. Using GFRP faces, a shift of the failure mode from premature core failure in quasi-static tests to face failure at the core junction in fatigue tests was observed. In addition to the failure tests, the sandwich configurations have been analysed using finite element modelling (FEM) to elaborate on the experimental results with respect to failure prediction. Both linear modelling and nonlinear modelling including nonlinear material behaviour (plasticity) was used. Comparing the results from finite element modelling with the failure behaviour observed in the quasi-static tests, it was found that a combination of linear finite element modelling and a point stress criterion to evaluate the stresses at the core junction can be used for brittle core material constituents. However, this is generally not sufficient to predict the failure modes and failure loads properly. Using nonlinear material properties in the modelling and a point strain criterion improves the failure prediction especially for ductile materials, but this has to be examined further along with other failure criteria.     

Evaluation of in-plane ply shear properties from unidirectional plate torsion tests

Torsion tests were conducted on unidirectional carbon/epoxy laminated plates. Preliminary finite element analyses showed that the specimen geometry selected avoided pronounced geometric non-linearity and ensured that a significant volume of material would be under a high fraction of the maximum shear stress. Furthermore, the clear prevalence of in-plane shear stresses allowed the development of a simplified data analysis model. Calculated shear-stress strain curves were consistent with the results of tensile tests on angle-ply coupons, despite lower failure stresses that may have been caused by surface defects or by spurious transverse tensile stresses. Nevertheless, the unidirectional plate torsion test is worthy of further research, given the structural relevance of torsional loads and the problems of in-plane shear tests methods.     

Reliability analysis of nonlinear laminated composite plate structures

A procedure for the reliability analysis of laminated composite plate structures subjected to large deflections under random static loads is presented. The nonlinear analysis of laminated composite plate structures is achieved via a corotational total Lagrangian finite element formulation which is based on the von Karman assumption and first order shear deformation theory. This formulation is applicable for the nonlinear analysis of plate structures with large rotations but moderate deformation and thus accurate enough to predict the behavior of the structures at the point of failure. The reliability assessment of laminated composite plate structures with random strength subjected to random loads is approached by the determination of limit state surfaces in load space. The limit space surfaces are obtained by performing a series of first ply failure analyses following different load paths in load space using the proposed nonlinear structural analysis technique and an appropriate failure criterion. A numerical technique is then proposed to evaluate the reliability of the plate structures. Examples of the reliability analyses of laminated plates with different layer orientations subject to random loads are given for illustration.     

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.     

Mechanical behaviors of carbon fiber composite sandwich columns with three dimensional honeycomb cores under in-plane compression

Mechanical properties and failure modes of carbon fiber composite egg and pyramidal honeycombs cores under in plane compression were studied in the present paper. An interlocking method was developed for both kinds of three-dimensional honeycombs. Euler or core shear macro-buckling, face wrinkling, face inter-cell buckling, core member crushing and face sheet crushing were considered and theoretical relationships for predicting the failure load associated with each mode were presented. Failure mechanism maps were constructed to predict the failure of these composite sandwich panels subjected to in-plane compression. The response of the sandwich panels under axial compression was measured up to failure. The measured peak loads obtained in the experiments showed a good agreement with the analytical predictions. The finite element method was used to investigate the Euler buckling of sandwich beams made with two different honeycomb cores and the comparisons between two kinds of honeycomb cores were conducted.     

Optimization of laminated composites considering different failure criteria

The purpose of the present work is to analyse how different the optimal structures are when different first ply failure criterion are considered in the optimization of laminated composites. Two problems are solved: the minimum weight and the minimum material cost of laminated plates subjected to in-plane loads. The failure criterion is taken into account by means of constraints introduced in the optimization problem. Three different failure criteria are tested independently: maximum stress, Tsai–Wu and the Puck failure criterion (PFC). Emphasis is given to the PFC as it appears to agree better with practical observations. The design variables are the ply orientations, the number of layers and the layer material, and the optimization problem is solved by a genetic algorithm (GA). The results show that optimal structures highly differ when different failure criterion are considered and that none of the failure criteria is always the most or the least conservative when different load conditions are applied.     

Stability and failure of composite laminates with various shaped cutouts under combined in-plane loads

The objective of this paper is to study stability and failure of a composite laminate with a centrally placed cutout of various shapes (i.e., circular, square, diamond, elliptical-vertical and elliptical-horizontal) under combined action of uni-axial compression and in-plane shear loads. The FEM formulation based on the first order shear deformation theory and von Karman’s assumptions has been utilized. Newton–Raphson method is used to solve nonlinear algebraic equations. Failure of a lamina is predicted by the 3-D Tsai–Hill criterion whereas the onset of delamination is predicted by the interlaminar failure criterion. The effects of cutout shape, direction of shear load and composite lay-up on buckling and postbuckling responses, failure loads and failure characteristics of the laminate has been discussed. An efficient utilization of material strength is observed in the case of laminate with circular cutout as compared to the laminate with other shaped cutouts. In addition, it is also concluded that although the buckling strength of the (0/90)_4s laminate is lower than that of the (+45/?45/0/90)_2s and (45/?45)_4s laminates, but its strength is increased in the advanced stage of postbuckling deformation.     

A methodology to design fibre reinforced laminated composite structures for maximum strength

A procedure to select the optimal fibre orientations and determine the maximum load carrying capacity of symmetrically laminated fibre reinforced composite structures is described. Cylindrical shells subject to combinations of torque and in-plane forces are used to illustrate the methodology and are optimally designed for maximum strength. Torque tubes are generally used as control mechanisms, for example, in the tail fins of aircraft. The finite element method, based on Mindlin plate and shell theory, is used in this application in conjunction with an optimisation routine in order to obtain the optimal designs. The methodology consists of two stages; the objective of the first is to maximise the strength of the cylindrical shells by determining the fibre orientations optimally while the objective of the second stage is to maximise the in-plane compression loading subject to a failure criterion. The effect of different shell aspect ratios, wall thickness, layer numbers and boundary conditions on the results is investigated.     

Vibration of non-ideal simply supported laminated plate on an elastic foundation subjected to in-plane stresses

In this paper, the effect of non-ideal boundary conditions and initial stresses on the vibration of laminated plates on Pasternak foundation is studied. The plate has simply supported boundary conditions and is assumed that one of the edges of the plate allows a small non-zero deflection and moment. The initial stresses are due to in-plane loads. The vibration problem is solved analytically using the Lindstedt–Poincare perturbation technique. So the frequencies and mode shapes of the plate with non-ideal boundary condition is extracted by considering the Pasternak foundation and in-plane stresses. The results of finite element simulation, using ANSYS software, are presented and compared with the analytical solution. The effect of various parameters like stiffness of foundation, boundary conditions and in-plane stresses on the vibration of the plate is discussed. Dependency of non-ideal boundary conditions on the aspect ratio of the plate for changing the frequencies of vibrations is presented. The relation between the shear modulus of elastic foundation and the frequencies of the plate is investigated.     

Hygrothermal effects on the buckling of laminated composite plates

The effects of moisture and temperature on the static instability of laminated composite plates are investigated. The analysis is carried out by the finite element method using a quadratic isoparametric element which takes transverse shear deformation into account. The conventional finite element formulation is modified to include hygrothermal effects. The stiffness matrix, geometric stiffness matrix due to residual stresses, geometric stiffness matrix due to applied in-plane loads and load vector of the element are derived based upon the principle of minimum potential energy. The analysis accounts for reduced lamina material properties at elevated moisture concentrations and temperatures. Critical loads are obtained for symmetric and anti-symmetric laminates with simply-supported and clamped boundary conditions at different moisture concentrations and temperatures. Their dependence on moisture and temperature is studied. The effects of aspect ratio and side-to-thickness ratio on the critical loads are also considered. Mode shapes are verified in a few cases for anti-symmetric cross-ply laminate.     

Effect of in-plane boundary restraints on optimal design of skew laminates under buckling loads

Symmetrically laminated cross-ply and angle-ply skew plates subject to uniaxial buckling loads and various combinations of in-plane boundary restraints are studied using a shear deformable theory. For this purpose a finite element code is developed and applied to a couple of verification problems. The formulation of the parabolic iso-parametric plate element is briefly given and numerical results obtained for the verification problems related to stability analysis and stress diffusion are presented. The effect of in-plane restraints on the non-uniform distribution of in-plane stresses is studied by means of contour graphs. Next the buckling loads are maximized with respect to layer thicknesses in the case of cross-ply laminates and with respect to fiber orientations in the case of angle-ply laminates. The optimization results show that the exclusion of the in-plane restraints, which arise in several engineering applications, may lead to errors in the stability analysis and consequently in the design of laminated plates against buckling.     

点支撑预应力中厚矩形板的横向振动

基于Reissner-Mindlin一阶剪切变形板理论,讨论在预加面内机械荷载或温度场作用下,点支撑中厚矩形板的横向振动。温度场假定沿板表面为均布,沿板厚方向为线性分布的。利用考虑剪切变形影响的Timoshenko梁函数,采用Rayleigh-Ritz法给出不同边界条件下点支撑中厚板的自振频率。结果表明,温度升高与预加面内压力将使板的自振频率下降,支撑点位置的变化、边界约束条件和横向剪切变形效应都对板的自振频率有显著影响。     

A size-dependent third-order shear deformable plate model incorporating strain gradient effects for mechanical analysis of functionally graded circular/annular microplates

In this paper, we develop a novel size-dependent plate model for the axisymmetric bending, buckling and free vibration analysis of functionally graded circular/annular microplates based on the strain gradient elasticity theory. The displacement field is chosen by using a refined third-order shear deformation theory which assumes that the in-plane and transverse displacements are partitioned into bending and shear components and satisfies the zero traction boundary conditions on the top and bottom surfaces of the microplate. Besides, the present model contains three material length scale parameters to capture the size effect. The material properties of the microplate are assumed to vary in the thickness direction and estimated through the classical rule of mixture. By using Hamilton's principle, the equations of motion and boundary conditions are obtained. Afterward, the differential quadrature method is adopted to discretise the governing differential equations along with various types of edge supports and therefore the deflection, critical buckling load and natural frequency can be determined. Convergence and comparison studies are carried out to establish the reliability and accuracy of the numerical results. Finally, a parametric study is conducted to investigate the influences of material length scale parameters, gradient index, thickness-to-outer radius ratio, outer-to-inner radius ratio and boundary conditions on the mechanical characteristics of the microplate.     

Effects of Boundary Conditions in Laminated Composite Plates Using Higher Order Shear Deformation Theory

This paper extends the applicability of a modified higher order shear deformation theory to accurately determine the in-plane and transverse shear stress distributions in an orthotropic laminated composite plate subjected to different boundary conditions. A simpler, two-dimensional, shear deformable, plate theory accompanied with an appropriate set of through-thickness variations, is used to accurately predict transverse shear stresses. A finite element code was developed based on a higher order shear deformation theory to study the effects of boundary conditions on the behavior of thin-to-thick anisotropic laminated composite plates. The code was verified against three dimensional elasticity results. The study also compared the stresses and deformation results of higher order theory with those obtained using commercial software such as LUSAS, ANSYS and ALGOR. The commercial software are heavily used by designers to design various components/products made of composites. Various combinations of fixed, clamped and simply supported boundary conditions were used to verify a large class of anticipated applications. Results obtained from software are in good agreement for some cases and significantly differ for others. It was found that LUSAS and ANSYS yield better results for transverse deflection and in-plane stresses. But for transverse shear stresses, it is highly dependent on boundary conditions.     

Unequal Faces Effect on Fracture of Composite Sandwich Beam with Flexible Core

Sandwich panel higher order theory (SPHOT) which estimates core compression and face stresses is used to predict damage modes of a sandwich beam with unequal faces. It is shown that sandwich panel classical theory (SPCT) which is based on investigating of behavior of the structure with considering core shear stress in simply supported boundary conditions and neglecting shear modulus of core can not predict the failure load in the case of unequal faces when core yielding is happened. Comparing the results obtained by SPHOT, SPCT and available experimental ones shows that the higher order theory is a suitable approach to predict failure loads in this case for different damage modes.     

Optimization of shear-deformable laminated plates under buckling and strength criteria

A shear deformable laminated theory is used to study the optimal design of rectangular plates under biaxial compressive loads. Such loads lead to plate failure by buckling or material failure which corresponds to the violation of the selected strength criterion. The minimum of the two loads (buckling load or material failure load) determines the critical failure load for a given set of problem parameters. At the optimum values of the ply angles, buckling or both failure criteria may be operational depending on the laminate thickness. The present study investigates the effect of laminate thickness on the optimal design and gives numerical results for symmetrically laminated angle-ply plates.     

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.     

Deformation and tearing of circular plates with varying support conditions under uniform impulsive loads

Transient dynamic finite element analysis of circular plates with varying support configurations under uniform single square wave form impulsive load has been carried out in FEA package ANSYS. Experimental results of Teeling-Smith and Nurick [The deformation and tearing of thin circular plates subjected to impulsive loads. Int J Impact Eng 1991;11(1):77–91] and Nurick et al. [Tearing of blast loaded plates with clamped boundary conditions. Int J Impact Eng 1996;18(7–8):803–27] for the onset of thinning and tearing at the boundary of clamped circular plates subjected to uniformly loaded air blasts have been used to compare and validate the numerical simulation and procedure. The Mode II failure with respect to clamped circular plates has been simulated using a rupture strain criteria. Mode III failure or plastic shear sliding, has been considered using a shear strain failure criteria as proposed by Wen and Jones for plates. A stiffness reduction scheme has been proposed to decide on the initiation and progression of tearing in conjunction with suitable failure model under Modes II and III. The evolution of deflections, plastic zones, rupture zones and failure modes under the blast loading conditions are found to match well with the experimental results. The validated numerical model has further been used to study the effect of plate thickness on the deformation and tearing response of the circular plates subjected to impulsive loads. The deformation, tearing and shock absorption response of clamped circular plates under uniform impulsive loads with ring support of varying edge configurations at the boundary have also been numerically studied. Further, the response of circular plate–tube combination with varying boundary support configurations has been studied. The plate has been considered at the mid-span of the tube of length equal to the plate diameter with the ends of the tube modelled as clamped. The numerical model has been used to study the effect of tube thickness variations on the deformation and tearing response of the circular plate under shock loads. The response of tube–plate combinations under uniform impulsive loads with ring support at the plate–tube junction have also been numerically studied.