Computational prediction of the influence of crosslink distribution on the thermo-mechanical properties of epoxies

Experimental studies on epoxies report that the microstructure consists of highly crosslinked localized regions connected with a dispersed phase of low crosslink density. The various thermo-mechanical properties of epoxies might be affected by the crosslink distribution. But as experiments cannot report the exact number of crosslinked covalent bonds present in the structure, molecular dynamics is thus being used in this work to determine the influence of crosslink distribution on thermo-mechanical properties. Molecular dynamics and molecular mechanics simulations are used to establish wellequilibrated molecular models of EPON 862-DETDA epoxy system with a range of crosslink densities and various crosslink distributions. Crosslink distributions are being varied by forming differently crosslinked localized clusters and then by forming different number of crosslinks interconnecting the clusters. Simulations are subsequently used to predict the volume shrinkage, thermal expansion coefficients, and elastic properties of each of the crosslinked systems. The results indicate that elastic properties increase with increasing levels of overall crosslink density and the thermal expansion coefficient decreases with overall crosslink density, both above and below the glass transition temperature. Elastic moduli and coefficients of linear thermal expansion values were found to be different for systems with same overall crosslink density but having different crosslink distributions, thus indicating an effect of the epoxy nanostructure on physical properties. The values of thermo-mechanical properties for all the crosslinked systems are within the range of values reported in literature.

Molecular modeling of EPON 862-DETDA polymer

EPON 862 is an epoxy resin which is cured with the hardening agent DETDA to form a crosslinked epoxy polymer and is used as a component in modern aircraft structures. These crosslinked polymers are often exposed to prolonged periods of temperatures below glass transition range which cause physical aging to occur. Because physical aging can compromise the performance of epoxies and their composites and because experimental techniques cannot provide all of the necessary physical insight that is needed to fully understand physical aging, efficient computational approaches to predict the effects of physical aging on thermo-mechanical properties are needed. In this study, Molecular Dynamics and Molecular Minimization simulations are being used to establish well-equilibrated, validated molecular models of the EPON 862-DETDA epoxy system with a range of crosslink densities using a united-atom force field. These simulations are subsequently used to predict the glass transition temperature, thermal expansion coefficients, and elastic properties of each of the crosslinked systems for validation of the modeling techniques. The results indicate that glass transition temperature and elastic properties increase with increasing levels of crosslink density and the thermal expansion coefficient decreases with crosslink density, both above and below the glass transition temperature. The results also indicate that there may be an upper limit to crosslink density that can be realistically achieved in epoxy systems. After evaluation of the thermo-mechanical properties, a method is developed to efficiently establish molecular models of epoxy resins that represent the corresponding real molecular structure at specific aging times. Although this approach does not model the physical aging process, it is useful in establishing a molecular model that resembles the physically-aged state for further use in predicting thermo-mechanical properties as a function of aging time. An equation has been predicted based on the results which directly correlate aging time to aged volume of the molecular model. This equation can be helpful for modelers who want to study properties of epoxy resins at different levels of aging but have little information about volume shrinkage occurring during physical aging.

Shear band evolution in Zr/Hf-based bulk metallic glasses under static and dynamic indentations

Bulk metallic glasses (BMGs) exhibit superior mechanical properties as compared with other conventional materials and have been proposed for numerous engineering and technological applications. Zr/Hf-based BMGs or tungsten reinforced BMG composites are considered as a potential replacement for depleted uranium armor-piercing projectiles because of their ability to form localized shear bands during impact, which has been known to be the dominant plastic deformation mechanism in BMGs. However, in conventional tensile, compressive and bending tests, limited ductility has been observed because of fracture initiation immediately following the shear band formation. To fully investigate shear band characteristics, indentation tests that can confine the deformation in a limited region have been pursued. In this thesis, a detailed investigation of thermal stability and mechanical deformation behavior of Zr/Hf-based BMGs is conducted. First, systematic studies had been implemented to understand the influence of relative compositions of Zr and Hf on thermal stability and mechanical property evolution. Second, shear band evolution under indentations were investigated experimentally and theoretically. Three kinds of indentation studies were conducted on BMGs in the current study. (a) Nano-indentation to determine the mechanical properties as a function of Hf/Zr content. (b) Static Vickers indentation on bonded split specimens to investigate the shear band evolution characteristics beneath the indention. (c) Dynamic Vickers indentation on bonded split specimens to investigate the influence of strain rate. It was found in the present work that gradually replacing Zr by Hf remarkably increases the density and improves the mechanical properties. However, a slight decrease in glass forming ability with increasing Hf content has also been identified through thermodynamic analysis although all the materials in the current study were still found to be amorphous. Many indentation studies have revealed only a few shear bands surrounding the indent on the top surface of the specimen. This small number of shear bands cannot account for the large plastic deformation beneath the indentations. Therefore, a bonded interface technique has been used to observe the slip-steps due to shear band evolution. Vickers indentations were performed along the interface of the bonded split specimen at increasing loads. At small indentation loads, the plastic deformation was primarily accommodated by semi-circular primary shear bands surrounding the indentation. At higher loads, secondary and tertiary shear bands were formed inside this plastic zone. A modified expanding cavity model was then used to predict the plastic zone size characterized by the shear bands and to identify the stress components responsible for the evolution of the various types of shear bands. The applicability of various hardness—yield-strength ( H −σγ ) relationships currently available in the literature for bulk metallic glasses (BMGs) is also investigated. Experimental data generated on ZrHf-based BMGs in the current study and those available elsewhere on other BMG compositions were used to validate the models. A modified expanding-cavity model, employed in earlier work, was extended to propose a new H −σγ relationship. Unlike previous models, the proposed model takes into account not only the indenter geometry and the material properties, but also the pressure sensitivity index of the BMGs. The influence of various model parameters is systematically analyzed. It is shown that there is a good correlation between the model predictions and the experimental data for a wide range of BMG compositions. Under dynamic Vickers indentation, a decrease in indentation hardness at high loading rate was observed compared to static indentation hardness. It was observed that at equivalent loads, dynamic indentations produced more severe deformation features on the loading surface than static indentations. Different from static indentation, two sets of widely spaced semi-circular shear bands with two different curvatures were observed. The observed shear band pattern and the strain rate softening in indentation hardness were rationalized based on the variations in the normal stress on the slip plane, the strain rate of shear and the temperature rise associated with the indentation deformation. Finally, a coupled thermo-mechanical model is proposed that utilizes a momentum diffusion mechanism for the growth and evolution of the final spacing of shear bands. The influence of strain rate, confinement pressure and critical shear displacement on the shear band spacing, temperature rise within the shear band, and the associated variation in flow stress have been captured and analyzed. Consistent with the known pressure sensitive behavior of BMGs, the current model clearly captures the influence of the normal stress in the formation of shear bands. The normal stress not only reduces the time to reach critical shear displacement but also causes a significant temperature rise during the shear band formation. Based on this observation, the variation of shear band spacing in a typical dynamic indentation test has been rationalized. The temperature rise within a shear band can be in excess of 2000K at high strain rate and high confinement pressure conditions. The associated drop in viscosity and flow stress may explain the observed decrease in fracture strength and indentation hardness. The above investigations provide valuable insight into the deformation behavior of BMGs under static and dynamic loading conditions. The shear band patterns observed in the above indentation studies can be helpful to understand and model the deformation features under complex loading scenarios such as the interaction of a penetrator with armor. Future work encompasses (1) extending and modifying the coupled thermo-mechanical model to account for the temperature rise in quasistatic deformation; and (2) expanding this model to account for the microstructural variation-crystallization and free volume migration associated with the deformation.

Use of manual adaptive remeshing in the mechanical modeling of an intraneural ganglion cyst

Intraneural Ganglion Cysts expand within in a nerve, causing neurological deficits in afflicted patients. Modeling the propagation of these cysts, originating in the articular branch and then expanding radially outward, will help prove articular theory, and ultimately allow for more purposeful treatment of this condition. In Finite Element Analysis, traditional Lagrangian meshing methods fail to model the excessive deformation that occurs in the propagation of these cysts. This report explores the method of manual adaptive remeshing as a method to allow for the use of Lagrangian meshing, while circumventing the severe mesh distortions typical of using a Lagrangian mesh with a large deformation. Manual adaptive remeshing is the process of remeshing a deformed meshed part and then reapplying loads in order to achieve a larger deformation than a single mesh can achieve without excessive distortion. The methods of manual adaptive remeshing described in this Master’s Report are sufficient in modeling large deformations.

Experimental results on gravity driven fully condensing flows in vertical tubes, their agreement with theory, and their differences with shear driven flows' boundary-condition sensitivities

This doctoral thesis presents the experimental results along with a suitable synthesis with computational/theoretical results towards development of a reliable heat transfer correlation for a specific annular condensation flow regime inside a vertical tube. For fully condensing flows of pure vapor (FC-72) inside a vertical cylindrical tube of 6.6 mm diameter and 0.7 m length, the experimental measurements are shown to yield values of average heat transfer co-efficient, and approximate length of full condensation. The experimental conditions cover: mass flux G over a range of 2.9 kg/m2-s ≤ G ≤ 87.7 kg/m2-s, temperature difference ∆T (saturation temperature at the inlet pressure minus the mean condensing surface temperature) of 5 ºC to 45 ºC, and cases for which the length of full condensation xFC is in the range of 0 < xFC < 0.7 m. The range of flow conditions over which there is good agreement (within 15%) with the theory and its modeling assumptions has been identified. Additionally, the ranges of flow conditions for which there are significant discrepancies (between 15 -30% and greater than 30%) with theory have also been identified. The paper also refers to a brief set of key experimental results with regard to sensitivity of the flow to time-varying or quasi-steady (i.e. steady in the mean) impositions of pressure at both the inlet and the outlet. The experimental results support the updated theoretical/computational results that gravity dominated condensing flows do not allow such elliptic impositions.

Mechanical modeling of Intraneural Ganglion Cyst

Intraneural Ganglion Cyst is a 200 year old mystery related to nerve injury which is yet to be solved. Current treatments for the above problem are relatively simple procedures related to removal of cystic contents from the nerve. However, these treatments may result into neuropathic pain and recurrence of the cyst. The articular theory proposed by Spinner et al., (Spinner et al. 2003) takes into consideration the neurological deficit in Common Peroneal Nerve (CPN) branch of the sciatic nerve and affirms that in addition to the above treatments, ligation of articular branch results into foolproof eradication of the deficit. Mechanical Modeling of the Affected Nerve Cross Section will reinforce the articular theory (Spinner et al. 2003). As the cyst propagates, it compresses the neighboring fascicles and the nerve cross section appears like a signet ring. Hence, in order to mechanically model the affected nerve cross section; computational methods capable of modeling excessively large deformations are required. Traditional FEM produces distorted elements while modeling such deformations, resulting into inaccuracies and premature termination of the analysis. The methods described in this Master’s Thesis are effective enough to be able to simulate such deformations. The results obtained from the model adequately resemble the MRI image obtained at the same location and shows an appearance of a signet ring. This Master’s Thesis describes the neurological deficit in brief followed by detail explanation of the advanced computational methods used to simulate this problem. Finally, qualitative results show the resemblance of mechanical model to MRI images of the Nerve Cross Section at the same location validating the capability of these methods to study this neurological deficit.

Predicting the Mechanical Properties of Carbon-Based Materials Using Molecular Dynamics

The development of innovative carbon-based materials can be greatly facilitated by molecular modeling techniques. Although molecular modeling has been used extensively to predict elastic properties of materials, modeling of more complex phenomenon such as fracture has only recently been possible with the development of new force fields such as ReaxFF, which is used in this work. It is not fully understood what molecular modeling parameters such as thermostat type, thermostat coupling, time step, system size, and strain rate are required for accurate modeling of fracture. Selection of modeling parameters to model fracture can be difficult and non-intuitive compared to modeling elastic properties using traditional force fields, and the errors generated by incorrect parameters may be non-obvious. These molecular modeling parameters are systematically investigated and their effects on the fracture of well-known carbon materials are analyzed. It is determined that for coupling coefficients of 250 fs and greater do not result in substantial differences in the stress-strain response of the materials using any thermostat type. A time step of 0.5 fs of smaller is required for accurate results. Strain rates greater than 2.2 ns-1 are sufficient to obtain repeatable results with slower strain rates for the materials studied. The results of this study indicate that further refinement of the Chenoweth parameter set is required to accurately predict the mechanical response of carbon-based systems. The ReaxFF has been used extensively to model systems in which bond breaking and formation occur. In particular ReaxFF has been used to model reactions of small molecules. Some elastic and fracture properties have been successfully modeled using ReaxFF in materials such as silicon and some metals. However, it is not clear if current parameterizations for ReaxFF are able to accurately reproduce the elastic and fracture properties of carbon materials. The stress-strain response of a new ReaxFF parameterization is compared to the previous parameterization and density functional theory results for well-known carbon materials. The new ReaxFF parameterization makes xv substantial improvements to the predicted mechanical response of carbon materials, and is found to be suitable for modeling the mechanical response of carbon materials. Finally, a new material composed of carbon nanotubes within an amorphous carbon (AC) matrix is modeled using the ReaxFF. Various parameters that may be experimentally controlled are investigated such as nanotube bundling, comparing multi-walled nanotube with single-walled nanotubes, and degree of functionalization of the nanotubes. Elastic and fracture properties are investigated for the composite systems and compared to results of pure-nanotube and pure-AC models. It is found that the arrangement of the nanotubes and degree of crosslinking may substantially affect the properties of the systems, particularly in the transverse directions.

Influence of Mechanical and Thermal Boundary Conditions on Stabilizing/Destabilizing Mechanisms in Evaporating Liquid Films

Liquid films, evaporating or non-evaporating, are ubiquitous in nature and technology. The dynamics of evaporating liquid films is a study applicable in several industries such as water recovery, heat exchangers, crystal growth, drug design etc. The theory describing the dynamics of liquid films crosses several fields such as engineering, mathematics, material science, biophysics and volcanology to name a few. Interfacial instabilities typically manifest by the undulation of an interface from a presumed flat state or by the onset of a secondary flow state from a primary quiescent state or both. To study the instabilities affecting liquid films, an evaporating/non-evaporating Newtonian liquid film is subject to a perturbation. Numerical analysis is conducted on configurations of such liquid films being heated on solid surfaces in order to examine the various stabilizing and destabilizing mechanisms that can cause the formation of different convective structures. These convective structures have implications towards heat transfer that occurs via this process. Certain aspects of this research topic have not received attention, as will be obvious from the literature review. Static, horizontal liquid films on solid surfaces are examined for their resistance to long wave type instabilities via linear stability analysis, method of normal modes and finite difference methods. The spatiotemporal evolution equation, available in literature, describing the time evolution of a liquid film heated on a solid surface, is utilized to analyze various stabilizing/destabilizing mechanisms affecting evaporating and non-evaporating liquid films. The impact of these mechanisms on the film stability and structure for both buoyant and non-buoyant films will be examined by the variation of mechanical and thermal boundary conditions. Films evaporating in zero gravity are studied using the evolution equation. It is found that films that are stable to long wave type instabilities in terrestrial gravity are prone to destabilization via long wave instabilities in zero gravity.

DENSITY OF AMORPHOUS CARBON BY USING DENSITY FUNCTIONAL THEORY

Amorphous carbon has been investigated for a long time. Since it has the random orientation of carbon atoms, its density depends on the position of each carbon atom. It is important to know the density of amorphous carbon to use it for modeling advance carbon materials in the future. Two methods were used to create the initial structures of amorphous carbon. One is the random placement method by randomly locating 100 carbon atoms in a cubic lattice. Another method is the liquid-quench method by using reactive force field (ReaxFF) to rapidly decrease the system of 100 carbon atoms from the melting temperature. Density functional theory (DFT) was used to refine the position of each carbon atom and the dimensions of the boundaries to minimize the ground energy of the structure. The average densities of amorphous carbon structures created by the random placement method and the liquid-quench method are 2.59 and 2.44 g/cm3, respectively. Both densities have a good agreement with previous works. In addition, the final structure of amorphous carbon generated by the liquid-quench method has lower energy.