The discovery of carbon nanotubes in 1990s popularized a new area of research in materials science called Nanoscience. In the following decades, several carbon based nanoparticles were discovered or engineered and with the discovery of Graphene nanoplatelets (GNP) in 2010, carbon based nanoparticles were propelled as the most promising class of nanoparticles. High mechanical strength and stiffness, excellent electrical and thermal conductivity, and high strength to weight ratios are some of the unique abilities of CNTs and GNPs which allow their use in a wide array of applications from aerospace materials to electronic devices. In the current work presented herein, CNTs and GNPs are added to polymeric materials to create a nanocomposite material. The effects of this nanoparticle addition (a.k.a reinforcement) on the mechanical properties of the nanocomposite polymer materials are studied. Specifically, efforts are focused on studying fracture toughness, a material property that describes the material's ability to resist crack growth. Relative to the conventional metals used in structures, epoxy-based composites have poor fracture toughness. This has long been a weak link when using epoxy composites for structural applications and therefore several efforts are being made to improve their fracture toughness. In the first, second and third chapters, the enhancement of fracture toughness brought about by the addition of carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs) was investigated. CNT-Epoxy and GNP-Epoxy Compact Tension (CT) samples were fabricated with 0.1% and 0.5% nanofiller weight concentrations. The potential synergistic effects of dual nanofiller reinforcements were also explored using CNT/GNP-Epoxy CT samples at a 1:3, 3:1 and 1:1 ratio of CNT:GNP. Displacement controlled CT tests were conducted according to ASTM D5045 test procedure and the critical stress intensity factor, $K_{IC}$, and the critical fracture energy, $G_{IC}$, were calculated for all the material systems. Significant enhancements relative to neat epoxy were observed in reinforced epoxies. Fracture surfaces were analyzed via scanning electron microscopy. Instances of CNT pullouts on the fracture surface were observed, indicating the occurrence of crack bridging. Furthermore, increased surface roughness, an indicator of crack deflection, was observed along with some crack bifurcations in the GNP-Epoxy samples. In the fourth chapter of Part I, the influence of pre-crack characteristics on the Mode-I fracture toughness of epoxy is investigated. Pre-crack characteristics such as pre-crack length, crack front shape, crack thickness and crack plane profile are evaluated and their influence on the peak load, fracture displacement, and the critical stress intensity factor, $K_{IC}$ is studied. A new method of razor blade tapping was used, which utilized a guillotine-style razor tapping device to initiate the pre-crack and through-thickness compression to arrest it. A new approach of quantitatively characterizing the crack front shape using a two-parameter function is introduced. Surface features present on the pre-crack surface are classified and their effects on the post crack initiation behavior of the sample are analyzed. This study aims to identify and increase the understanding of the various factors that cause variation in the fracture toughness data of polymeric materials, thus leading to more informed engineering design decisions and evaluations. Chapters six and seven of Part II investigate the SHM capabilities of dispersed MWCNTs in mock, inert, and active energetics. In these experimental investigations, the strain and damage sensing abilities of multi-walled carbon nanotube (MWCNT) networks embedded in the binder phase of polymer bonded energetics (PBEs) are evaluated. PBEs are a special class of particulate composite materials that consist of energetic crystals bound by a polymer matrix, wherein the polymer matrix serves to diminish the sensitivity of the energetic phase to accidental mechanical stimuli. The structural health monitoring (SHM) approach presented in this work exploits the piezoresistive properties of the distributed MWCNT networks. Major challenges faced during such implementation include the low binder concentrations of PBEs, presence of conductive/non-conductive particulate phases, high degree of heterogeneity in the PBE microstructure, and achieving the optimal MWCNT dispersion. In chapter seven, Ammonium Perchlorate (AP) crystals as the oxidizer, Aluminum grains as the metallic fuel, and Polydimethylsiloxane (PDMS) as the binder are used as the constituents for fabricating PBEs. To study the effect of each constituent on the MWCNT network's SHM abilities, various materials systems are comprehensively studied: MWCNT/PDMS (nBinder) materials are first evaluated to study the binder's electromechanical response, followed by AP/MWCNT/PDMS (inert nPBE) to assess the impact of AP addition, and finally, AP/AL/MWCNT/PDMS (active nPBE-AL) to evaluate the impact of adding conductive aluminum grains. Compression samples (ASTM D695) were fabricated and subjected to monotonic compression. Electrical resistance is recorded in conjunction with the mechanical test via an LCR meter. Gauge factors relating the change in normalized resistance to applied strain are calculated to quantify the electromechanical response. MWCNT dispersions, and mechanical failure modes are analyzed via scanning electron microscopy (SEM) imaging of the fracture surfaces. Correlations between the electrical behavior in response to the mechanical behavior are presented, and possible mechanisms that influence the electromechanical behavior are discussed. The results presented herein demonstrate the successful ability of MWCNT networks as structural health monitoring sensors capable of real-time strain and damage assessment of polymer bonded energetics. / Doctor of Philosophy / The discovery of carbon nanotubes in 1990s popularized a new area of research in materials science called Nanoscience. Carbon nanotubes (CNTs) are one of several forms of Carbon, meaning a differently structured carbon molecule in the same physical state similar to diamonds, graphite, and coal. In the following decades, several carbon based nanoparticles were discovered or engineered and with the discovery of Graphene (GNP) in 2010, carbon based nanoparticles were propelled as the most promising class of nanoparticles. High mechanical strength and stiffness, excellent electrical and thermal conductivity, and high strength to weight ratios are some of the unique abilities of CNTs and GNPs which allow their use in a wide array of applications from aerospace materials to electronic devices. In the current work presented herein, CNTs and GNPs are added to polymeric materials to create a nanocomposite material, where the term "composite" refers to a material prepared with two or more constituent materials. The effects of this nanoparticle addition (a.k.a reinforcement) on the mechanical properties of the nanocomposite polymer materials are studied. Specifically, efforts are focused on studying fracture toughness, a material property that describes the material's ability to resist crack growth. Fracture toughness is a critical material property often associated with material and structural failures, and as such it is very important for safe and reliable engineering design of structures, components, and materials. Moving from a single function (i.e. mechanical enhancement) to a more multi-functional role, taking advantage of the excellent electrical and mechanical abilities of CNTs, a structural health monitoring system is developed for use in polymer bonded energetics (eg. solid rocket propellants). When a material undergoes mechanical deformation or damage, the measured electrical properties of the material undergo some change as well. Using sensor networks built with multiple CNTs dispersed within a polymeric material, a whole structure can be made into an effective sensor where by simply monitoring the electrical properties, the extent of material deformation and damage can be known. Such a system is geared towards providing early warning of impending catastrophic material failures thus directly improving the safety during material handling and operations.