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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

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The dynamic response of subsurface cracks in fiber reinforced composites is analytically studied. The response of layered half-space and three-layered plate with two interface cracks excited by a plane SH-wave and line load respectively are studied by formulating the problem as integral equations in the frequency domain. The governing equations along with boundary, regularity and continuity conditions across the interface are reduced to a coupled set of singular integral equations by using Betti's reciprocal theorem along with the Green's functions. In addition, the transient response of an orthotropic half-space with a subsurface crack subjected to inplane line load at an arbitrary angle is analyzed. Two new Green's functions for the uncracked medium are developed and used along with the representation theorem to derive the scattered field. Satisfaction of the traction free condition at the crack surfaces gives rise to a system of singular integral equations. Singular integrals involved in the analysis are computed numerically by removing the poles. Part of the integrals containing the poles are then obtained analytically by using residue theorem. The solution of singular integral equations are obtained by expanding the unknown crack opening displacements (COD) in terms of a complete set of Chebychev polynomials. The problem is first solved in the frequency domain, the time histories are then obtained numerically by inverting the spectra via Fast Fourier Transform (FFT) routine. Numerical results are presented for isotropic and anisotropic materials for several different crack geometries. The results show significant influence of crack geometries and material properties on the COD and surface response of composites.

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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.