Larry Lessard

Damage Tolerance of Laminated Composites Containing an Open Hole and Subjected to Compressive Loadings: Part II—Experiment

An analytical investigation was performed to study the damage in laminated composites containing an open hole and subjected to compressive loading. A progressive damage model was developed during the investigation to predict the extent and the failure modes of the internal damage in the laminates as a function of the applied load and to simulate the in-plane response of the laminates from initial loading to final collapse. The model consists of a stress analysis and a failure analysis. Stresses and strains inside the laminates were calculated by a nonlinear finite element analysis which is based on finite deformation theory with consideration of material and geometric nonlinearities. The types and extent of damage in the material were predicted by a failure analysis which includes a set of proposed failure criteria and material degradation models. Numerical results from the model were compared with the data which were obtained during the investigation and are presented in a companion paper [1]. Good agreements were found between the predictions and the test results. A computer code was developed based on the model which can be used as a tool for sizing and designing composite plates containing holes and subjected to compression.

Progressive Fatigue Damage Modeling of Composite Materials, Part I: Modeling

In this research a modeling technique for simulating the fatigue behaviour of laminated composite materials, with or without stress concentrations, called progressive fatigue damage modeling, is established. The model is capable of simulating the residual stiffness, residual strength and fatigue life of composite laminates with arbitrary geometry and stacking sequence under complicated fatigue loading conditions. The model is an integration of three major components: stress analysis, failure analysis, and material property degradation rules. A three-dimensional, nonlinear, finite element technique is developed for the stress analysis. By using a large number of elements near the edge of the stress concentration and at layer interfaces, the edge effect has been accounted for. Each element is considered to be an orthotropic material under multiaxial state of stress. Using the three-dimensional state of stress within each element, different failure modes of a unidirectional ply under multiaxial states of stress are detected by a set of fatigue failure criteria. An analytical technique, called the generalized residual material property degradation technique, is established to degrade the material properties of elements. This analytical technique is not restricted to the application of failure criteria to limited applied stress ratios. Based on the model, a computer code is developed that simulates cycle-by-cycle behaviour of composite laminates under fatigue loading.

Two-dimensional modeling of composite pinned-joint failure

The modeling of damage in a laminated composite pinned-joint presents many difficulties because of the inherent complexity of the failure process. The joint area is a region with stress concentrations thus a complicated stress state exists. In order to model progressive damage from initial to final failure, finite element methods are used rather than closed form stress analyses. Two approaches for the finite element technique can be used: a simple two-dimensional linear model or one that has been enhanced with non-linear assumptions. Adding non-linear material behaviour and large deformation theory are two improvements that can be made to a linear finite element model. Failure analysis must be a logical combination of suitable failure criteria and appropriate material property degradation rules. It is understood that a three-dimensional analysis may now be a better alternative, but the goal here is to fly understand the limits of two-dimensional modeling for solving the composite pinned-joint problem.

Progressive fatigue damage modeling of composite materials, Part II : Material characterization and model verification

To validate the fatigue progressive damage model, developed in the first part of this paper, an experimental program was conducted using graphite/epoxy AS4/3501-6 material. As the input for the model, the material properties (residual stiffness, residual strength and fatigue life) of unidirectional AS4/3501-6 graphite/epoxy material are fully characterized under tension and compression, for fiber and matrix directions, and under in-plane and out-of-plane shear in static and fatigue loading conditions. An extensive experimental program, by using standard experimental techniques, is performed for this purpose. Some of the existing standard testing methods are necessarily modified and improved. To evaluate the progressive fatigue damage model, fatigue behaviour of pin/bolt-loaded composite laminates is simulated as a complicated example. The model is validated by conducting an experimental program on pin/bolt-loaded composite laminates and by comparison with experimental results from other authors. Different capabilities of the model are examined by conducting different types of experiments. The comparison between the analytical results and the experiments shows the successful simulation capability of the model.

Multiaxial fatigue behaviour of unidirectional plies based on uniaxial fatigue experiments — I. Modelling

The fatigue behaviour of a unidirectional composite lamina is examined from theoretical and experimental viewpoints. The goal is to establish a technique to use experimental data from a unidirectional ply under uniaxial fatigue to simulate the behaviour of that ply in multiaxial fatigue loading. Traditional polynomial failure criteria for fatigue are of limited use because fatigue strength is a function of number of cycles and applied fatigue stress ratio. In practice, a problem such as a fatigue-loaded complex composite structure containing stress concentrations, is subjected to varying stress ratios at different points, especially if material or geometric nonlinearities are involved. However, fatigue testing under a wide range of stress ratios is time consuming and expensive. Therefore it is important to establish a technique to consider fatigue damage due to arbitrary stress ratio without having to perform excessive amounts of testing. Here the theoretical basis of a new model, called the generalized residual material property degradation model is explained in detail.

Multiaxial fatigue behaviour of unidirectional plies based on uniaxial fatigue experiments. II. Experimental evaluation

To validate the generalized residual material property degradation model, developed in the first part of this paper, an experimental program was conducted using graphite/epoxy AS4/3501-6 material. The main advantage of the model is that it can simulate the fatigue behaviour of a unidirectional ply under multiaxial state of stress and arbitrary stress ratio by using the results of uniaxial fatigue experiments. The fatigue behaviour of the unidirectional ply under combined tensile matrix stress and in-plane shear stress (biaxial conditions) is considered. To prepare input for the model the material must be fully characterized in the matrix direction and in-plane shear condition under static and fatigue loading. For this purpose the static strength, residual strength and fatigue life of the material in the transverse direction and under in-plane shear conditions are measured. The results obtained by these series of experiments are used as input data for the model and the behaviour of a 30° off-axis specimen under uniaxial fatigue load, which in fact is a unidirectional ply under biaxial stress conditions, is simulated by the model. To evaluate the results calculated by the model, a series of uniaxial tension-tension fatigue tests are performed on unidirectional 30° off-axis laminates. A comparison between S-N curves (curve fitted mathematically and simulated by the model) shows the one simulated by the model slightly overestimates the fatigue life of the 30° off-axis specimen. However, the S-N curve simulated by the model is located reasonably inside the range of experimental scatter. It should be noted that the model proposed in this study is a deterministic model and further research is needed to couple a probabilistic for a more realistic simulation.

Fatique and damage-tolerance analysis of composite laminates: Stiffness loss, damage-modelling, and life prediction

Abstract The prediction of fatigue life and evaluation of progressive damage for general composite laminates are studied analytically. From theories of damage tolerance, residual-modulus degradation, and residual-strength d degradation, a simple and approximate approach is proposed for the prediction of progressive stiffness loss, matrix-crack density, and delamination area in terms of tension-tension fatigue load and number of cycles for general laminates containing 0° plies. The proposed approach provides four choices for predicting tension-tension allowable fatigue life and for assessing fail-safety for structures made of composite laminates, namely, a residual-modulus criterion, a matrix-cracking criterion, a delamination-size criterion, and a residual-strength criterion. The approximate analytical relationship between S-N curves for general laminates containing 0° plies and for a unidirectional 0°-ply laminate is proposed. Three glass/epoxy laminates of [0/90] s , [±45/0/90] s , and [0/±45] s lay-ups, and one [0/90±45] s T300/5208 graphite/epoxy laminate under tension-tension fatigue are used to illustrate and verify the proposed approach. The analytical results are in good agreement with experimental data.

Effects of material nonlinearity on the three-dimensional stress state of pin-loaded composite laminates

A three-dimensional nonlinear finite element code is established to analyze the effects of material nonlinearity on the state of stress and failure prediction near the stress concentrations of a pin-loaded laminated composite plate. Theoretically, stress singularities may occur at the interface between two layers of different ply orientation on the free edges. High magnitudes of stresses at the free edge of the ply interface are responsible for failure initiation at those locations. Therefore the state of stress near the edge of the hole and at the ply interface between two different layers is important and has been studied in detail. An existing nonlinear material model, for in-plane behaviour, has been modified to be applicable for three-dimensional cases. Nonlinear shear stress-strain behaviour of a unidirectional ply, in the x-y and z-x planes, is the source of nonlinearity. Three different configurations, namely, cross-ply [04/904] s , and [904/04] s and an angle-ply [+454/-454] s , were considered. A failure analysis, using stress based failure criteria, is performed to predict the failure initiation load of different configurations. The effect of material nonlinearity on the predicted failure initiation load is studied. The results of prediction of failure initiation load by considering the material nonlinearity is in excellent agreement with experimental results. The results obtained from failure analysis emphasize that considering the material nonlinearity, especially for highly shear induced cases like [+454/−454] s is important in failure analysis of composite laminates using stress based failure criteria.

Three-dimensional stress analysis of free-edge effects in a simple composite cross-ply laminate

Abstract A new model has been developed to analyze the free-edge effect in a symmetric cross-ply laminate. This new technique involves a three-dimensional finite element analysis that divulges the stress field at the free edge of a simple composite plate of finite dimensions. Three-dimensional 20-node quadratic brick elements were used to simulate the composite laminate. The cross-ply laminate is subjected to uniaxial tensile strain. The advantages of the “Slice Model Setup” are demonstrated in terms of computer time and memory. The slice model has been developed to simulate the actual case, and anticipated stress singularities have therefore not been induced artificially by using singular elements. The state of stress is determined and the results are favorably compared to the results of others found in the literature. The effect of thickness and width of a simple composite plate on the magnitude of stress at the free edge is also investigated. The purpose of the slice model is to create a reasonable finite element model whose state of stress can undergo failure analysis and whose elements can permit the use of property degradation techniques.

Shear buckling of a composite drive shaft under torsion

Abstract In this research the torsional stability of a composite drive shaft torsion is studied. Composite materials are considered as the suitable choice for manufacturing long drive shafts. The applications of this kind of drive shafts are developed in various products such as cars, helicopters, cooling towers, etc. From the design point of view, local and global torsional instability of drive shafts limits the capability for them to transfer torque. After reviewing the closed form solution methods to calculate the buckling torque of composite drive shafts, a finite element analysis is performed to study their behavior. Furthermore, to evaluate the results obtained by the finite element method, a comparison with experimental and analytical results is presented. A case study of the effects of boundary conditions, fiber orientation and stacking sequence on the mechanical behavior of composite drive shafts is also performed. Finally, the reduction of the torsional natural frequency of a composite drive shaft due to an increase of applied torque is studied.