Predicting the effective elastic properties of a composite material based on the elastic properties of the constituent materials is extremely difficult, even when the microstructure is known. However, there are cases where certain properties in constituents always carry over to a composite, regardless of the microstructure of the composite. We call such instances exact relations. The general theory of exact relations allows us to find all of these instances in a wide variety of contexts including elasticity, conductivity, and piezoelectricity. We combine this theory with ideas from representation theory to find all exact relations for fiber-reinforced polycrystalline composites. We further extend these ideas to the concept of links. When two composites have the same microstructure but different constituent materials, their effective tensors may be related. We use the theory of exact relations to find such relations, which we call links. In this work we describe a special set of links between elasticity tensors of fiber-reinforced polycrystalline composites. These links allow us to generalize certain results from specific examples to generate new information about this widely-used class of composites. In particular, we apply the link to obtain information about composites made from two transversely isotropic materials and polycrystals made from one orthotropic material. / Mathematics

Compared to materials with a straight geometry, materials with a corrugated architecture have shown potential to improve ductility without sacrificing strength due to the unbending of the corrugation during loading. The purpose of this research was to study the effect of geometric and material parameters on the stress-strain response of materials with a corrugated geometry and understand what controls the unbending process and under what conditions improved ductility was achievable. This involved studying isolated corrugations and corrugation reinforced composites under tensile and transverse compressive loading by performing parametric studies using Finite Element Modeling (FEM) simulations. These simulations showed that improvements in ductility are directly related to the degree of corrugation present and can be attributed to an initial bending dominated process. The unbending of the corrugation leads to an evolving geometry which causes the material to strengthen and ultimately delays necking. For corrugated composites, it was found that there is significant interplay between the properties of the components and the geometry of the corrugation. To obtain a benefit in ductility through corrugation, the matrix must have sufficiently high work hardening to accommodate the unbending corrugation without itself necking, but also have sufficiently low flow stress relative to the reinforcement yield strength to prevent the corrugation from stretching instead of unbending. Also, if the boost in work hardening from unbending occurs too early, no gain in ductility is achieved. In addition to these findings, tools for predicting the strength and ductility of these materials were developed, including an analytical model for the isolated corrugations and a series of benefit maps and surfaces for the corrugated composites. These tools proved to be fairly effective. Finally, the FEM findings were compared to experimental stress-strain curves and strain maps for validation and showed relatively good qualitative agreement. / Thesis / Doctor of Philosophy (PhD) / It is uncommon to find a material that possesses both high strength as well as the ability to elongate a lot without failing. One way to achieve this combination of properties is to use a wavy or corrugated structure that provides increased elongation when loaded due to the straightening of the corrugation. The purpose of this thesis was to study how materials which possess a wavy or corrugated geometry behave when they are subjected to a stretching load. This research utilized computer simulations and simple experimental testing to evaluate both isolated corrugations and corrugations embedded in another material. It was found that the amount of improvement in elongation is dependent on the initial amount of waviness. Also, whether a material shows improved elongation depends on whether the corrugation is able to unbend, which in turn depends on the corrugation geometry and the relative mechanical properties of the two materials.

Our research features diffusion in elastically deformable solids with complex microstructure. A prominent example are electrodes of Li-ion batteries which are typically a porous compound consisting of a binder, conductive particles, and active particles, filled with an electrolyte. The charge and discharge processes are complex multi-physics problems. Based on the used materials, they may include chemical reactions, electrochemically driven diffusion, separation into lithium poor and lithium rich regions in the active particles, or swelling phenomena [1]. Here, we consider a simplified version of this problem restricting ourselves to diffusion in an elastic matrix-particle composite. In the matrix, the transport of the mobile species is described using a Fickian-type flux driven by the gradient of the chemical potential. In the particles, the mobile species tends to accumulate and build separate regions of equal concentration – either high or low. This behavior is modeled using the Cahn-Hilliard equation.

No description available.

yes / The results of testing two simply and three continuously supported concrete beams reinforced with glass fiber-reinforced polymer (GFRP) bars are presented. The amount of GFRP reinforcement was the main parameter investigated. Over and under GFRP reinforcements were applied for the simply supported concrete beams. Three different GFRP reinforcement combinations of over and under reinforcement ratios were used for the top and bottom layers of the continuous concrete beams tested. A concrete continuous beam reinforced with steel bars was also tested for comparison purposes. The experimental results revealed that over-reinforcing the bottom layer of either the simply or continuously supported GFRP beams is a key factor in controlling the width and propagation of cracks, enhancing the load capacity, and reducing the deflection of such beams. Comparisons between experimental results and those obtained from simplified methods proposed by the ACI 440 Committee show that ACI 440.1R-06 equations can reasonably predict the load capacity and deflection of the simply and continuously supported GFRP reinforced concrete beams tested.

Conventional methods of imparting toughness to ordinarily brittle thermosetting resins involve the incorporation of a second, discreet phase. Traditionally, this phase has been either a functionalized butadiene-acrylonitrile based elastomer or an unreactive thermoplastic. This dissertation describes the preparation, characterization, and evaluation of new functionalized polysiloxane elastomer and thermoplastic modifiers and their morphological implications to the toughening and physical behavior of, principally, epoxy thermosetting systems. Secondary amine-terminated poly(dimethyl-co-diphenyl siloxane) oligomers were found to be comparable tougheners to acrylonitrile-butadiene rubbers for a bisphenol-A based epoxy resin. The system that imparted the highest toughness was comprised of statistically placed 40% diphenyl and 60% dimethylsiloxane units with Mn̅ of 5000 g/mole loaded at 15% w/w. This composition resulted in a discreet second phase consisting of l μm spherical particles which were evenly dispersed throughout the cured epoxy matrix. Amine-terminated poly(arylene ether ketone) and poly(arylene ether sulfone) thermoplastics were reacted into an EPON 828/4,4'·DDS system. However, the polyketones proved to be ineffective toughening agents due to an incompatibility resulting in macroscopic phase separation. In contrast, the functionalized polysulfones were shown to be effective toughening agents, with the resultant morphology primarily a function of percent incorporation. At ~15% w/w, the polysulfone separated as l-2μm discreet particles while a 30% loading level resulted in a bicontinuous “honeycomb” morphology. The amine endgroups were shown to be necessary in controlling morphology and maximizing toughness. The polysulfone oligomers were also incorporated into a graphite fiber reinforced epoxy composite. Although improved mechanical properties were achieved, the toughness values were not as high as predicted by the neat resin evaluation. The morphology was less definable due to the complex nature and dimensions of the carbon fiber/matrix interactions. Finally, melt processing experiments indicated that amine-terminated polysulfones may act as effective processing aids for brittle bismaleimide systems, by reacting with the BMI, possibly via a Michael addition. This results in a chain extension and higher molecular weight without premature gelation occurring. / Ph. D.

Modern durability and damage tolerance predictions for composite material systems rely on accurate estimates of the local stress and material states for each of the constituents, as well as the manner in which the constituents interact. In this work, an number of approaches to estimating the stress states and interactions are developed. First, an elasticity solution is presented for the problem of a penny-shaped crack in an N-phase composite material system opened by a prescribed normal pressure. The stress state around such a crack is then used to estimate the stress concentrations due to adjacent fiber fractures in a composite materials. The resulting stress concentrations are then used to estimate the tensile strength of the composite. The predicted results are compared with experimental values. In addition, a cumulative damage model for fatigue is presented. Modifications to the model are made to include the effects of variable amplitude loading. These modifications are based upon the use of remaining strength as a damage metric and the definition of an equivalent generalized time. The model is initially validated using results from the literature. Also, experimental data from APC-2 laminates and IM7/K3B laminates are used in the model. The use of such data for notched laminates requires the use of an effective hole size, which is calculated based upon strain distribution measurements. Measured remaining strengths after fatigue loading are compared with the predicted values for specimens fatigued at room temperature and 350°F (177°C). / Ph. D.

The response of elliptical composite cylindrical shells under torsion is studied. The torsional condition is developed by rotating one end of the cylinder relative to the other. Prebuckling, buckling, and postbuckling responses are examined, and material failure is considered. Four elliptical cross sections, defined by their aspect ratio, the ratio of minor to major radii, are considered: 1.00 (circular), 0.85, 0.70, and 0.55. Two overall cylinder sizes are studied; a small size with a radius and length for the circular cylinder of 4.28 in. and 12.85 in., respectively, and a large size with radii and lengths five times larger, and thicknesses two times larger than the small cylinders. The radii of the elliptical cylinders are determined so the circumference is the same for all cylinders of a given size. For each elliptical cylinder, two lengths are considered. One length is equal to the length of the circular cylinder, and the other length has a sensitivity of the buckling twist to changes in the length-to-radius ratio the same as the circular cylinder. A quasi-isotropic lamination sequence of a medium-modulus graphite-epoxy composite material is assumed. The STAGS finite element code is used to obtain numerical results. The geometrically-nonlinear static and transient, eigenvalue, and progressive failure analysis options in the code are employed. Generally, the buckling twist and resulting torque decrease with decreasing aspect ratio. Due to material anisotropy, the buckling values are generally smaller for a negative twist than a positive twist. Relative to the buckling torque, cylinders with aspect ratios of 1.00 and 0.85 show little or no increase in capacity in the postbuckling range, while cylinders with aspect ratios of 0.70 and 0.55 show an increase. Postbuckling shapes are characterized by wave-like deformations, with ridges and valleys forming a helical pattern due to the nature of loading. The amplitudes of the deformations are dependent on cross-sectional geometry. Some elliptical cylinders develop wave-like deformations prior to buckling. Instabilities in the postbuckling range result in shape changes and loss of torque capacity. Material failure occurs on ridges and in valleys. Cylinder size and cross-sectional geometry influence the initiation and progression of failure. / Ph. D.

As a new concept for morphing structures, the use of piezoelectric actuators to effect snap-through behavior of simple unsymmetric cross-ply composite laminates is examined. Many unsymmetric laminates have more than one stable room-temperature shape and can be snapped through from one stable shape to another. In this new concept for morphing structures, one or more piezoelectric actuators are bonded to unsymmetric laminates, and are then used to snap the laminate from one shape to another. The actuator would be used to change shape, but would not be required to maintain the shape. Using the Rayleigh-Ritz technique, several models are developed to predict the interaction between the base laminate and the actuator. In particular, the voltage (applied to the actuator) needed to snap the laminate is predicted. The NASA-LaRC Macro-Fiber Composite&174; (MFC&174;) actuator is chosen as the actuator of choice for this work. A laminate is manufactured, an actuator is bonded to the laminate, and experiments are performed. Since the agreement between the initial models and experimental results was not good, the models were revised. Good agreement between the predictions of the revised model and experiment is reached. Suggestions for future research directions are presented. / Ph. D.

Thermophysical characterization of anisotropic composite materials is extremely important in the control of today fabrication processes and in the prediction of structure failure due to thermal stresses. Accuracy in the estimation of the thermal properties can be improved if the experiments are designed carefully. However, on one hand, the typically used parametric study for the design optimization is tedious and time intensive. On the other hand, commonly used gradient-based estimation methods show instabilities resulting in nonconvergence when used with models that contain correlated or nearly correlated parameters. The objectives of this research were to develop systematic and reliable methodologies for both Experimental Design Optimization (EDO) used for the determination of thermal properties, and Simultaneous Parameter Estimation (SPE). Because of their advantageous features, Genetic Algorithms (GAs) were investigated for use as a strategy for both EDO and SPE. The EDO and SPE approaches used involved the maximization of an optimality criterion associated with the sensitivity matrix of the unknown parameters, and the minimization of the ordinary least squares error, respectively. Two versions of a general-purpose genetic-based program were developed: one is designed for the analysis of any EDO / SPE problems for which a mathematical model can be provided, while the other incorporates a control-volume finite difference scheme allowing for the practical analysis of complex problems. The former version was used to illustrate the genetic performance on the optimization of a difficult mathematical test function. Two test cases previously solved in the literature were first analyzed to demonstrate and assess the GA-based {EDO/SPE} methodology. These problems included the optimization of one and two dimensional designs for the estimation at ambient temperature of two and three thermal properties, respectively (effective thermal conductivity parallel and perpendicular to the fibers plane and effective volumetric heat capacity), of anisotropic carbon/epoxy composite materials. The two dimensional case was further investigated to evaluate the effects of the optimality criterion used for the experimental design on the accuracy of the estimated properties. The general-purpose GA-based program was then successively applied to three advanced studies involving the thermal characterization of carbon/epoxy anisotropic composites. These studies included the SPE of successively three, seven and nine thermophysical parameters, with for the latter case, a two dimensional EDO with seven experimental key parameters. In two of the three studies, the parameters were defined to represent the dependence of the thermal properties with temperature. Finally, the kinetic characterization of the curing of three thermosetting materials (an epoxy, a polyester and a rubber compound) was accomplished resulting in the SPE of six kinetic parameters. Overall, the GA method was found to perform extremely well despite the high degree of correlation and low sensitivity of many parameters in all cases studied. This work therefore validates the use of GAs for the thermophysical characterization of anisotropic composite materials. The significance in using such algorithms is not only the solution to ill-conditioned problems but also, a drastically cost savings in both experimental and time expenses as they allow for the EDO and SPE of several parameters at once. / Ph. D.