First-ply Failure Load Research Articles

Probabilistic Failure Analysis of Transversely Loaded Laminated Composite Plates Using First-Order Second Moment Method

A method for the probabilistic failure analysis of laminated composite plates with random system parameters subject to transverse loads is presented. System parameters such as material properties, plate thickness, and lamina strengths of a laminated composite plate are treated as baseline random variables. The statistics of the baseline random variables obtained from experiments are used in a stochastic finite-element analysis for computing the statistical moments of stresses in the laminated composite plate. An appropriate failure criterion from which the statistical moments of first-ply failure load are derived via a first-order second moment method is used to construct the limit state equation of the plate in the probabilistic failure analysis. The reliability of the laminated plate is then computed using an assumed probability distribution function of the first-ply failure load. The feasibility and accuracy of the present method are validated by the experimental data of centrally loaded laminated composite plates with different layups. The suitability of several commonly used failure criteria for reliability analysis of laminated composite plates is also investigated by means of several examples.

Reliability predictions of laminated composite plates with random system parameters

Reliability predictions of laminated composite plates with random system parameters subjected to transverse loads are performed using different methods. System parameters such as material properties, layer thicknesses, and lamina strengths of a laminated composite plate are treated as base-line random variables and an appropriate failure criterion is used to construct the limit state equation of the plate in the reliability analysis. Based on the statistics of the base-line random variables obtained from experiments, different methods, namely, Monte Carlo method, β method, and first-order second moment method, are used to calculate the reliability of the laminated composite plates. In the first-order second moment method, the stochastic finite element method is used to derive for the statistics of the first-ply failure load of the laminated composite plates from those of the base-line random variables. The reliability of the laminated plate is then computed using the theoretically determined statistics together with an assumed probability distribution function of the first-ply failure load. The feasibility and accuracy of the different methods are studied by means of the experimental data of centrally loaded laminated composite plates with different lay-ups. The suitability of several commonly used failure criteria for reliability analysis of laminated composite plates is also investigated by means of several examples.

Postbuckling response and failure of symmetric laminates under in-plane shear

This paper summarizes a study aimed at understanding the postbuckling behaviour and progressive failure of thin, simply supported symmetric rectangular laminates with various possible in-plane boundary conditions and under the action of in-plane shear loads. First-order shear deformation theory and geometric non-linearity, in the von-Karman sense, is used with a finite-element procedure. The 3D Tsai–Hill criterion is used to predict failure of lamina and the maximum stress criterion is used to predict the onset of delamination at the interface of two adjacent layers. The effect of in-plane boundary conditions, plate lay-ups, plate aspect ratio, fiber orientations and lamina material properties on the load deflection response, buckling load, first-ply failure load, ultimate load and the maximum transverse displacement associated with failure loads is presented.

Evaluation of buckling and first-ply failure probabilities of composite laminates

A procedure for failure probability evaluation of composite laminates subjected to inplane loads is proposed. The material properties, fiber angles and layer thicknesses of the laminates are treated as random variables in the reliability analysis. The statistics of first-ply failure loads and buckling strengths of the laminates are determined via the stochastic finite element method. The failure probabilities of the laminates which are susceptible to buckling and first-ply failure are computed using the statistics obtained in the stochastic finite element analysis. The feasibility and accuracy of the present approach are validated using the results obtained via the Monte-Carlo method. A number of examples of reliability analysis of composite laminates subject to in-plane loads are given to illustrate the applications of the procedure.

First-ply flexural failure analysis of symmetric cross-ply laminates by the postprocess method

First-ply flexural failure analysis for symmetric cross-ply laminates has been analyzed by the postprocess method. The results are compared with those of the exact and first-order shear deformation theory. Failure loads are computed for transverse sinusoidally distributed loads and transverse uniformly distributed loads applied at the top surface of the laminates. Analysis for various thickness ratios and number of layers is carried out. The layup configuration is confined to symmetric cross-ply laminates. Various failure criteria are used for the estimation of failure loads. Under Tsai-Hill's, Hoffman, Tsai-Wu's and independent maximum strain criteria, the postprocess method predicts the accurate first-ply failure loads. Furthermore, independent of thickness ratios, the postprocess method can be applied for the efficient prediction of failure loads.

Reliability formulation for composite laminates subjected to first-ply failure

Methods formulated on the basis of the concept of first-ply failure and the structural reliability theory are presented for the reliability analysis of laminated composite plates. In the reliability formulation, an appropriate phenomenological failure criterion is used to establish the limit state equation of the laminated composite plates, and different numerical techniques are employed to evaluate the reliability of the plates. Experimental investigations of lamina strengths and first-ply failure loads of laminated composite plates were performed. Baseline probability distributions of lamina strength parameters constructed from the test data are used to study the reliability of the laminated plates. The accuracy of the proposed models in reliability assessment of the laminated plates are verified by the experimental results on first-ply failure load distributions.

Minimum weight design of laminated composite plates subject to strength constraint

The minimum weight design of laminated composite plates subject to strength and side constraints is studied via a constrained global optimization technique. The first-ply failure load that is treated as the strength of a laminated plate is determined by using a shear deformable finite element and one of the several commonly used phenomenological failure criteria. The optimal layer group parameters (fiber angles and thicknesses of layer groups) of the laminated composite plate are determined via the proposed constrained global optimization technique for attaining the global minimum weight of the plate and satisfying the imposed constraints. A number of examples of the minimum weight design of symmetrically laminated composite plates with various aspect ratios, different number of layer groups, and different boundary conditions are given to illustrate the applications of the present constrained global optimal design method. The effects of the failure criteria on the optimal design parameters are also investigated via the examples. Finally, experimental investigation of the capability of the present method in obtaining global optima is performed. Failure tests of a number of graphite/epoxy laminates designed by different methods are performed, and the superiority of the present method over the other methods is demonstrated via the test results.

Predictions of deflection and first-ply failure load of thin laminated composite plates via the finite element approach

A nonlinear finite element method, which is based on the von Karman-Mindlin plate theory and the principle of minimum total potential energy, is used to study the deformation and first-ply failure of thin laminated composite plates. The load displacement curves of a number of laminated composite plates are determined using the proposed finite element method. Stresses obtained fr'om the linear and nonlinear finite element analyses are used to determine, respectively, the linear and nonlinear first-ply failure loads of the laminated plates based on several phenomenological failure criteria. The accuracy of the finite element results is then verified by comparison with the available experimental data. It has been found that good agreement between the finite element and experimental load strain curves before first-ply failure is observed. If the reduction in plate stiffness induced by failure of plies is taken into account in the finite element model, close agreement between finite element and experimental load displacement curves from first-ply failure up to total failure may be obtained. Regarding the prediction of the first-ply failure load, it has been found that some of the phenomenological failure criteria may yield results of consistent accuracy for the laminated composite plates under consideration. Nevertheless, accurate prediction of the failure process after first-ply failure is still intractable. Hence, for reliability assurance further research on failure analysis of laminated composite plates subject to transverse loading is needed.

Nonlinear and First-Ply Failure Analyses of Laminated Composite Cross-Ply Plates

A method is presented to study the nonlinear behaviors and first-ply failure strengths of centrally loaded laminated composite plates with semi-clamped edges. The method which is developed from the von Karman-Mindlin plate theory and the Ritz method is used to construct the nonlinear load-deflection curves of the composite plates with or without considering the reduction in plate stiffness induced by ply failure and predict the first-ply failure loads of the plates based on various commonly used strength-of-material type failure criteria. Experiments on laminated composite plates loaded to failure are performed to construct the experimental load-displacement curves of the plates. During testing, the first-ply failure loads of the plates are identified using the acoustic emission technique. The experimental results are used to investigate the capabilities of the present method in predicting the nonlinear behaviors and first-ply failure loads of the laminated composite plates. It has been found that when compared with the experimental load-deflection curves the present method with the consideration of stiffness reduction can yield reasonable results on load-deflection curve and even for some cases the ultimate strength. As for the determination of first-ply failure load, the inconsistent results predicted by the adopted failure criteria indicate that the strength-of-material approach may be inappropriate for the first-ply failure analysis of laminated composite plates. Hence, more research on failure mechanism and, especially, the development of appropriate failure criteria for composite laminates is needed.

First-ply failure analysis of laminated composite plates based on the layerwise linear displacement theory

A finite element formulated on the basis of the layerwise linear displacement theory is used to study the first-ply failure of moderately thick laminated composite plates. In the finite element formulation, a laminated composite element is divided into a number of mathematical layer groups and displacements are assumed to vary linearly in each layer group which contains eight nodal points. The accuracy of the finite element in predicting displacements and stresses has been verified by comparing results with experimental data and previously obtained analytical results. The finite element is used to determine the first-ply failure loads of a number of laminated composite plates on the basis of several phenomenological failure criteria. The capabilities of the failure criteria in predicting first-ply failure loads are investigated by comparing the finite element first-ply failure loads with the experimental ones. It has been found that the failure criteria can yield reasonably good results for the cases considered.

Linear and non-linear failure analysis of composite laminates with transverse shear

A finite element computational procedure has been developed to find linear and non-linear (von Kármán) first-ply failure loads of composite laminates subjected to in-plane and transverse loads. The finite element model is based on first-order shear deformation theory and several phenomenological failure criteria. Linear and non-linear first-ply failure loads are computed for a uniformly distributed transverse load, a concentrated transverse load acting at the centre of the plate, and a uniformly distributed in-plane edge load for simply supported and clamped boundary conditions. It is found that the failure loads predicted by various failure criteria differ from one another by a maximum of 35% in the case of linearloads and 50% in the case on non-linear loads; the failure locations differ from each other in a random way. Furthermore, it is demonstrated that the difference between the linear and non-linear failure loads is large in the case of transversely loaded simply supported laminates and thin plates. The difference is found to be quite small in the case of in-plane (tensile) loading and thick laminates.

Theoretical investigation into the effect of the winding angle of the fibres on the strength of filament wound GRP pipes subjected to combined external pressure and axial compression

Finite element analysis has been carried on composite pipes of length-to-internal diameter ratio of 5 and internal diameter-to-thickness ratio of 20 to assess their strength when subjected to a combination of external pressure and axial compression. The effect of the winding angle of the fibre reinforcements on the buckling and first-ply failure loads of the pipes have been examined. It is shown that the optimum winding angle of the fibres varies according to the ratio of hoop-to-axial membrane stresses in the pipes. In the case of hydrostatic external pressure loading of the pipes, the optimum angle is close to 80° instead of 55° reported elsewhere for internal pressure loading.

Experimental/analytical characterization of composite tubes under combined loading

The paper outlines the results of an investigation to characterize the response of P75/934 graphite/epoxy tubes with a stacking sequence of [15/0/±10/0/−15] s under pure torsion and combined axial/torsion loading. The experimentally observed nonlinear response and path-dependent failure are discussed in terms of material nonlinearities at the ply level and first-ply failure loads with the help of an analytical model.

Failure analysis of laminated composites by using iterative three-dimensional finite element method

In this paper, a failure analysis of laminated composites is accomplished by using an iterative three-dimensional finite element method. Based on Tsai-Wu failure theory, we first propose three different modes of failure, namely, fiber breakage, matrix cracking and delamination. The first-ply failure load is then evaluated. As the applied load exceeds the first-ply failure load, localized structural failure occurs and the global structural stiffness should change. We modify the global stiffness matrix by taking nonlinearity due to partial failures within a laminate into consideration. The first-ply failure load is analyzed by using an iterative mixed field in solving the linear part of the finite element equations. The progressive failure problem is solved numerically by using Newton-Raphson iterative schemes for the solution of nonlinear finite element equations. Numerical examples include a three-layered cross-ply (0/90/0) E-glass-epoxy and an angle-ply four-layer Thornel 300 graphite-934 resin epoxy laminates under uniaxial tension in both cases. First-ply failure loads as well as the final loads are evaluated. Good correlation between analytical results and experimental data are observed. Numerical results also include the investigation of composite specimens with a centered hole, under uniaxial tension. First-ply failure loads and final failure loads are obtained by using the finite element program. Excellent correlation with the experimental data is observed.

Reliability Analysis Of Composite Laminates Sub- Ject To Buckling And First-ply Failure

A procedure for relability assessment of composite laminates subjected to inplane loads is proposed. The material properties, fiber angles and layer thicknesses of the laminates are treated as random variables in the reliability analysis. The statistics of first-ply failure loads and buckling strengths of the laminates are determined via the stochastic finite element method. The reliabilities of the laminates which are susceptible to buckling and first-ply failure are computed using the statistics obtained in the stochastic finite element analysis. The feasibility and accuracy of the present approach are validated using the results obtained via the Monte Carlo method. A number of examples of reliability analysis of composite laminates subject to in-plane loads are given to illustrate the applications of the procedure.