The present work is a study of the matrix cracking behaviour of composite laminates which contain plies oriented at an angle to the loading axis. Incremental tensile tests were conducted on a set of glass-epoxy laminates having the [0/θ][formula omitted] geometry where θ takes the values of 45°, 60°, 75° and 90°. At each load increment, the stiffness reduction was measured and the cracking sequence was photographed. A novel technique using image analysis was used to measure the crack length and digitize the crack pattern in each photograph. The results were analysed in two ways - deterministically (using fracture mechanics) and statistically. In the first instance, the relationship between stiffness loss and crack length was used to calculate the strain energy release rate, G from a compliance expression. It was found that the overall stiffness loss for a given crack length increased with increasing θ. As G can also be viewed as the resistance to cracking, the calculated values were used to plot matrix cracking resistance curves (R-curves) for each lay-up. The R-curves showed that the overall resistance to cracking increased with increasing orientation angle, θ. For the [0/45][formula omitted] laminate, where cracking is driven by the highest proportion of G₁₁ component, the least increase in resistance was observed. The differences in crack resistance in these lay-ups could be explained with results from the statistical analysis. A statistical analysis of the changes in distribution of crack length and number indicated that most of cracks in the [0/90][formula omitted] were short even at high loads. In addition, a calculation of the incremental growth with each incremental load showed that the amount of growth in that lay-up was limited. This implied that the process of crack initiation continually dominated crack propagation even late in the loading sequence. The opposite behaviour is seen as θ decreases. In the [0/45][formula omitted], [0/60][formula omitted], and [0/75][formula omitted] lay-ups, the additional Mode II shear loading appeared to have assisted significantly the coalescence and growth of cracks. Hence, the overall crack resistance decreased as the proportion of the GH component increased. Cracking in the off-axis plies is not uniform. In the [0/45][formula omitted], [0/60][formula omitted] and [0/75][formula omitted] laminates, cracking begins in distinct bands and are referred to as shear bands since they occur due to the presence of the Mode II shear loading. This phenomenon, however, has little effect on the stiffness. Although cracking is not uniform, the cracks tend to space themselves to within two ply thickness apart as crack density increases. In the shear band areas, the crack spacing can approach one ply thickness. It was also observed that crack tips stop growing either when they are two ply thickness apart or when they approach a stronger area in the laminate. Generally, the resistance to cracking is not affected when the crack density is low. However, as cracks begin to interact when they are spaced to within two ply thickness, the resistance increases dramatically. / Applied Science, Faculty of / Materials Engineering, Department of / Graduate

The problem of determining whether a crack impinging on an interface will penetrate into the substrate or deflect along the interface is vital to the effective design of layered and composite material systems. Of particular interest is the transition between crack propagation by penetration through an interface and deflection along an interface. There has been a great deal of work done on this problem to determine what parameters and formulations are necessary to accurately determine under what conditions penetration-deflection transition will occur. Previous work has studied this problem using stress-based, energy-based, and combined stress-energy-based approaches. Most recently, a combined stress-energy-based approach was implemented via a cohesive-zone formulation; this work showed the conceptual basis and correctness of the cohesive-zone approach, however only presented limited investigation into the behavior penetration-deflection transition. Work presented here expands this investigation on transition, exposing trends and behavior that emerge as certain dimensionless groups are varied. Principles of linear elastic fracture mechanics and, as in previous work, cohesive-theory are applied to a bi-material system in tension through the use of the commercial finite element analysis package ABAQUS. Dimensionless groups, including strength ratios, toughness ratios, fracture-length scales, and substrate toughness scales are varied systematically to show resulting system behavior in a generalized fashion. In using the cohesive-zone method, aspects of previous stress-based and energy-based formulations are reproduced. It is also shown where these formulations cease to be valid, revealing unique and previously undetected transitional interface fracture behavior. The results presented here will prove valuable in interface design as the described generalized trends can be used as references in the design of new layered and composite systems. / Graduation date: 2013

A numerical method is developed to determine the dynamic behavior of delamination and transverse cracks in multilayered plates. The plate is subjected to a time dependent antiplane shear stress field which is acting on the plate surfaces. The interaction of waves diffracted at the crack tip with those reflected at the plate boundaries and transmitted at the material interface makes the problem very complicated, so analytical study of this problem cannot be carried out with our present state of knowledge; hence the problem is solved numerically. The finite element equations are obtained by variational calculus applied in the frequency domain. Thus time intregration schemes are avoided, but time dependent response can still be obtained after inverting the frequency dependent response spectra numerically by Fast Fourier Transform (FFT) routine. Another advantage of the frequency domain analysis is that the resonance frequency can be easily detected from the sharp peaks of the response spectra. The numerical difficulty associated with the singular behavior of the stress field near the crack tip has been avoided by using quarter point elements. The numerical results obtained from this investigation are compared with analytical results to verify the accuracy of the method.

No description available.

The problem examined is an infinite anisotropic layer with a through crack at arbitrary orientation, subjected to uniform in-plane remote loading. The purpose of this study is to gain a better understanding of several theoretical models for predicting the direction of crack propagation and the level of load causing crack extension, and to present a new model for predicting the critical load. The discussed models are particularly examined in detail with regard to the physical parameters affecting the results. Comparison is made with available experimental results. It is shown that the normal stress ratio theory provides good agreement with experimental crack growth direction, independent of physical parameters, and that the newly proposed traction ratio theory predicts well the critical load causing crack extension. / M.S.

Understanding the mechanical behavior of composite materials requires extensive knowledge of fracture behavior as a crack approaches an interface between the bulk material and the reinforcement structure. Overall material toughness can be greatly influenced by the propensity of an impinging crack to propagate directly through the substrate or deflect along an interface boundary. As the basis for this thesis; the assertion that an impinging crack may encounter a reinforcement structure at various incident angles is explored. This requires the ability to predict crack penetration/ deflection behavior not only normal to the reinforcement, but at various incident angles. Previous work in the area of interface fracture mechanics has used a stress or energy based approach, with recent advances in the field of a combined cohesive-zone method. Work presented here investigates the interaction between strength and toughness when using the cohesive-zone method on the problem of an impinging crack not normally incident to the interface of a composite material. Computational mechanics methods using Abaqus and user-define cohesive elements will be applied to this angled incident crack problem. A circular model based on the displacement field equations for mode-I fracture loading is introduced and verified against well-established LEFM solutions. This circular model is used to study the effects of incident crack angle on the penetration vs. deflection behavior of an impinging crack at various angles of incidence. Additionally, the effects of angle on the load applied to the model at fracture are explored. Finally, a case study investigating how the interaction between strength and toughness found using the cohesive-zone method helps to explain some of the inconsistencies seen in the interface indentation fracture test procedure. / Graduation date: 2013

This thesis addresses the issues surrounding the application of the finite element method to analyse composite structure repairs with an emphasis on aircraft applications. A comprehensive literature survey has been carried out for this purpose and the results are presented. A preliminary study and a comparative study of different modelling approaches have been completed. These studies aim to explore and identify the problems in modelling repairso n simplec ompositep anelsw ith speciala ttention given to adhesivem odelling. Three modelling approaches have been considered: Siener's model which is an extension of the traditional plane strain 2D model used for adhesively bonded joints, Bait's model which is a promising new approach and a full 3D model. These studies have shown that these methods are complementary providing a different insight into bonded repairs. They have also highlighted the need for a new modelling approach which will provide an overall view of bonded repairs. Improved modelling approachesh ave been developedf or externallyb onded patch and flush repairs. These models enable the study of adhesive failure as well as composite adherendf ailures.T hesea pproachesh aveb eena ppliedt o real repairs and the predicted results compared to experimental data. Four case studies have been conducted: external bonded patch repairs to composite plates, a scarf joint for bonded repairs, a flat panel repaired with a scarfed patch and a repaired curved panel. These case studies have shown that bonded repairs to composite structures can be analyseds uccessfullyu sing PC-basedc ommercialf inite elementc odes.

This thesis addresses the issues surrounding the application of the finite element method to analyse composite structure repairs with an emphasis on aircraft applications. A comprehensive literature survey has been carried out for this purpose and the results are presented. A preliminary study and a comparative study of different modelling approaches have been completed. These studies aim to explore and identify the problems in modelling repairso n simplec ompositep anelsw ith speciala ttention given to adhesivem odelling. Three modelling approaches have been considered: Siener's model which is an extension of the traditional plane strain 2D model used for adhesively bonded joints, Bait's model which is a promising new approach and a full 3D model. These studies have shown that these methods are complementary providing a different insight into bonded repairs. They have also highlighted the need for a new modelling approach which will provide an overall view of bonded repairs. Improved modelling approachesh ave been developedf or externallyb onded patch and flush repairs. These models enable the study of adhesive failure as well as composite adherendf ailures.T hesea pproachesh aveb eena ppliedt o real repairs and the predicted results compared to experimental data. Four case studies have been conducted: external bonded patch repairs to composite plates, a scarf joint for bonded repairs, a flat panel repaired with a scarfed patch and a repaired curved panel. These case studies have shown that bonded repairs to composite structures can be analyseds uccessfullyu sing PC-basedc ommercialf inite elementc odes.

No description available.

Carbon Fiber / Epoxy Laminates are increasingly being used in the primary structure of aircraft. To make effective use these materials, it is necessary to consider the ability of a laminate to resist damage, as well as material strength and stiffness. A possible means for improving damage tolerance is the use of non-traditional composite laminates, in which the longitudinal 0 plies are replaced with 5 or 10 plies. The main objectives of this collaborative Georgia Tech / Boeing research was the characterization of these non-traditional laminates, and the determination of appropriate lamina-level analytical techniques that are capable of predicting the changes caused by the use of slightly off-axis longitudinal plies. A quasi-isotropic [45/90/-45/theta/45/90/-45/-theta]s and hard [45/theta/-45/theta/90/45]s lay-up, where theta =0,5 or 10, were tested in open hole tension, filled hole tension, open hole compression, single shear bearing, and unnotched tension. These coupon level tests illustrated the effects of lay-up, notch constraint, and load type on traditional and non-traditional laminates. Die penetrant enhanced in-situ radiography was performed to determine the extent of damage suppression. The use of non-traditional laminates was found to reduce longitudinal ply cracking and delamination, with significant effect on the stress distribution around the notch. The use of non-traditional laminates also resulted in a 15%-20% improvement in bearing strength of the traditional laminates. Several predictive techniques were implemented to evaluate their ability to predict the effect of slight changes in ply orientations. A progressive damage model was written to compare Tsai-Wu, Hashin, and Maximum Stress unnotched strength criterion. Additionally, several semi-empirical failure theories for notched strength prediction were compared with linear and bi-linear cohesive zone models to determine applicability to non-traditional laminates.