This investigation is focused on the consideration of structural uncertainties in nearly-straight pipes conveying fluid and on the effects of these uncertainties on the dynamic response and stability of those pipes. Of interest more specifically are the structural uncertainties which affect directly the fluid flow and its feedback on the structural response, e.g., uncertainties on/variations of the inner cross-section and curvature of the pipe. Owing to the complexity of introducing such uncertainties directly in finite element models, it is desired to proceed directly at the level of modal models by randomizing simultaneously the appropriate mass, stiffness, and damping matrices. The maximum entropy framework is adopted to carry out the stochastic modeling of these matrices with appropriate symmetry constraints guaranteeing that the nature, e.g., divergence or flutter, of the bifurcation is preserved when introducing uncertainty.

To support the formulation of this stochastic ROM, a series of finite element computations are first carried out for pipes with straight centerline but inner radius varying randomly along the pipe. The results of this numerical discovery effort demonstrate that the dominant effects originate from the variations of the exit flow speed, induced by the change in inner cross-section at the pipe end, with the uncertainty on the cross-section at other locations playing a secondary role. Relying on these observations, the stochastic reduced order model is constructed to model separately the uncertainty in inner cross-section at the pipe end and at other locations. Then, the fluid related mass, damping, and stiffness matrices of this stochastic reduced order model (ROM) are all determined from a single random matrix and a random variable. The predictions from this stochastic ROM are found to closely match the corresponding results obtained with the randomized finite element model. It is finally demonstrated that this stochastic ROM can easily be extended to account for the small effects due to uncertainty in pipe curvature.

Hydrodynamic phenomena such as the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities can be described by exponential/linear growth of surface perturbations at a bimaterial interface when subjected to constant/impulsive acceleration. A challenge in designing systems to mitigate or exploit these effects is the lack of accurate material models at large dynamic strain rates and pressures. In particular, little stress-strain constitutive information at large strain rates and pressures is available for transient material phases formed at high pressures, and the continuum effect the phase transformation process has on the instability evolution. In this work, a phase-aware isotropic strength model is developed and partially validated with a novel RM-based instability experiment in addition to existing data from the literature. With the validated material model additional simulations are performed to provide insight into to the role that robust material constitutive behavior (e.g., pressure, temperature, rate dependence) has on RM instability and how RM instability experiments can be used to characterize and validated expected material behavior. For phase aware materials, particularly iron in this work, the simulations predict a strong dependence on the Atwood number that single phase materials do not have. At Atwood numbers close to unity, and pressures in the high pressure stability region, the high pressure phase dominates the RM evolution. However, at Atwood numbers close to negative one, the RM evolution is only weakly affected by the high-pressure phase even for shocks well above the phase transformation threshold. In addition to RM evolution this work looks at the closely related shock front perturbation evolution. Existing analytical models for isentropic processes in gases and liquids are modified for metal equation of states and plastic behavior for the first time. It is found that the presence of a volume collapsing phase transformation with increased pressure causes shock front perturbations to decay sooner, while plastic strength has the opposite effect which is significantly different from the effect viscosity has. These results suggest additional experimental setups to validate material models, or relevant material parameters that can be optimized for system design objectives, e.g., minimize feed through perturbations in inertial confinement fusion capsules.

The Very High Temperature Reactor (VHTR) is one of six conceptual designs proposed for Generation IV nuclear reactors. Alloy 617, a solid solution strengthened Ni-base superalloy, is currently the primary candidate material for the tubing of the Intermediate Heat Exchanger (IHX) in the VHTR design. Steady-state operation of the nuclear power plant at elevated temperatures leads to creep deformation, whereas loading transients including startup and shutdown generate fatigue. A detailed understanding of the creep-fatigue interaction in Alloy 617 is necessary before it can be considered as a material for nuclear construction in ASME Boiler and Pressure Vessel Code. Current design codes for components undergoing creep-fatigue interaction at elevated temperatures require creep-fatigue testing data covering the entire range from fatigue-dominant to creep-dominant loading. Classical strain-controlled tests, which produce stress relaxation during the hold period, show a saturation in cycle life with increasing hold periods due to the rapid stress-relaxation of Alloy 617 at high temperatures. Therefore, applying longer hold time in these tests cannot generate creep-dominated failure. In this study, uniaxial isothermal creep-fatigue tests with non-traditional loading waveforms were designed and performed at 850 and 950°C, with an objective of generating test data in the creep-dominant regime. The new loading waveforms are hybrid strain-controlled and force-controlled testing which avoid stress relaxation during the creep hold. The experimental data showed varying proportions of creep and fatigue damage, and provided evidence for the inadequacy of the widely-used time fraction rule for estimating creep damage under creep-fatigue conditions. Micro-scale damage features in failed test specimens, such as fatigue cracks and creep voids, were quantified using a Scanning Electron Microscope (SEM) to find a correlation between creep and fatigue damage. Quantitative statistical imaging analysis showed that the microstructural damage features (cracks and voids) are correlated with a new mechanical driving force parameter. The results from this image-based damage analysis were used to develop a phenomenological life-prediction methodology called the effective time fraction approach. Finally, the constitutive creep-fatigue response of the material at 950°C was modeled using a unified viscoplastic model coupled with a damage accumulation model. The simulation results were used to validate an energy-based constitutive life-prediction model, as a mechanistic model for potential component and structure level creep-fatigue analysis.

This investigation develops small-size reduced order models (ROMs) that provide an accurate prediction of the response of only part of a structure, referred to as component-centric ROMs. Four strategies to construct such ROMs are presented, the first two of which are based on the Craig-Bampton Method and start with a set of modes for the component of interest (the β component). The response in the rest of the structure (the α component) induced by these modes is then determined and optimally represented by applying a Proper Orthogonal Decomposition strategy using Singular Value Decomposition. These first two methods are effectively basis reductions techniques of the CB basis. An approach based on the “Global - Local” Method generates the “global” modes by “averaging” the mass property over α and β comp., respectively (to extract a “coarse” model of α and β) and the “local” modes orthogonal to the “global” modes to add back necessary “information” for β. The last approach adopts as basis for the entire structure its linear modes which are dominant in the β component response. Then, the contributions of other modes in this part of the structure are approximated in terms of those of the dominant modes with close natural frequencies and similar mode shapes in the β component. In this manner, the non-dominant modal contributions are “lumped” onto the dominant ones, to reduce the number of modes for a prescribed accuracy. The four approaches are critically assessed on the structural finite element model of a 9-bay panel with the modal lumping-based method leading to the smallest sized ROMs. Therefore, it is extended to the nonlinear geometric situation and first recast as a rotation of the modal basis to achieve unobservable modes. In the linear case, these modes completely disappear from the formulation owing to orthogonality. In the nonlinear case, however, the generalized coordinates of these modes are still present in the nonlinear terms of the observable modes. A closure-type algorithm is then proposed to eliminate the unobserved generalized coordinates. This approach, its accuracy and computational savings, was demonstrated on a simple beam model and the 9-bay panel model.

A method for modelling the interactions of dislocations with inclusions has been developed to analyse toughening mechanisms in alloys. This method is different from the superposition method in that infinite domain solutions and image stress fields are not superimposed. The method is based on the extended finite element method (XFEM) in which the dislocations are modelled according to the Volterra dislocation model. Interior discontinuities are introduced across dislocation glide planes using enrichment functions and the resulting boundary value problem is solved through the standard finite element variational approach. The level set method is used to describe the geometry of the dislocation glide planes without any explicit treatment of the interface geometry which provides a convenient and an appealing means for describing the dislocation. A method for estimating the Peach-Koehler force by the domain form of J-integral is considered. The convergence and accuracy of the method are studied for an edge dislocation interacting with a free surface where analytical solutions are available. The force converges to the exact solution at an optimal rate for linear finite elements. The applicability of the method to dislocation interactions with inclusions is illustrated with a system of Aluminium matrix containing Aluminium-copper precipitates. The effect of size, shape and orientation of the inclusions on an edge dislocation for a difference in stiffness and coefficient of thermal expansion of the inclusions and matrix is considered. The force on the dislocation due to a hard inclusion increased by 8% in approaching the sharp corners of a square inclusion than a circular inclusion of equal area. The dislocation experienced 24% more force in moving towards the edges of a square shaped inclusion than towards its centre. When the areas of the inclusions were halved, 30% less force was exerted on the dislocation. This method was used to analyse interfaces with mismatch strains. Introducing eigenstrains equal to 0.004 to the elastic mismatch increased the force by 15 times for a circular inclusion. The energy needed to move an edge dislocation through a domain filled with circular inclusions is 4% more than that needed for a domain with square shaped inclusions.

Finite element simulations modeling the hydrodynamic impact loads subjected to an elastomeric coating were performed to develop an understanding of the performance and failure mechanisms of protective coatings for cavitating environments.

In this work, two major accomplishments were achieved: 1) scaling laws were developed from hydrodynamic principles and numerical simulations to allow conversion of measured distributions of pressure peaks in a cavitating flow to distributions of microscopic impact loadings modeling individual bubble collapse events, and 2) a finite strain, thermo-mechanical material model for polyurea-based elastomers was developed using a logarithmic rate formulation and implemented into an explicit finite element code.

Combining the distribution of microscopic impact loads and finite element modeling, a semi-quantitative predictive framework is created to calculate the energy dissipation within the coating which can further the understanding of temperature induced coating failures.

The influence of coating thickness and elastomer rheology on the dissipation of impact energies experienced in cavitating flows has also been explored.

The logarithmic formulation has many desired features for the polyurea constitutive model, such as objectivity, integrability, and additive decomposition compatibility.

A review and discussion on the kinematics in large deformation, including a comparison between Lagrangian and Eulerian descriptions, are presented to explain the issues in building rate-dependent constitutive models in finite strains.

When comparing the logarithmic rate with other conventional rates in test examples, the logarithmic rate shows a better conservation of objectivity and integrability.

The modeling framework was validated by comparing predictions against temperatures measured within coatings subjected to a cavitating jet.

Both the experiments and models show that the temperatures generated, even under mild flow conditions, raise the coating temperature by a significant amount, suggesting that the failure of these coatings under more aggressive flows is thermally induced.

The models show that thin polyurea coatings synthesized with shorter molecular weight soft segments dissipate significantly less energy per impact and conduct heat more efficiently.

This work represents an important step toward understanding thermally induced failure in elastomers subjected to cavitating flows, which provides a foundation for design and optimization of coatings with enhanced erosion resistance.

ABSTRACT

A large fraction of the total energy consumption in the world comes from heating and cooling of buildings. Improving the energy efficiency of buildings to reduce the needs of seasonal heating and cooling is one of the major challenges in sustainable development. In general, the energy efficiency depends on the geometry and material of the buildings. To explore a framework for accurately assessing this dependence, detailed 3-D thermofluid simulations are performed by systematically sweeping the parameter space spanned by four parameters: the size of building, thickness and material of wall, and fractional size of window. The simulations incorporate realistic boundary conditions of diurnally-varying temperatures from observation, and the effect of fluid flow with explicit thermal convection inside the building. The outcome of the numerical simulations is synthesized into a simple map of an index of energy efficiency in the parameter space which can be used by stakeholders to quick look-up the energy efficiency of a proposed design of a building before its construction. Although this study only considers a special prototype of buildings, the framework developed in this work can potentially be used for a wide range of buildings and applications.

A previously developed small time scale fatigue crack growth model is improved, modified and extended with an emphasis on creating the simplest models that maintain the desired level of accuracy for a variety of materials. The model provides a means of estimating load sequence effects by continuously updating the crack opening stress every cycle, in a simplified manner. One of the significant phenomena of the crack opening stress under negative stress ratio is the residual tensile stress induced by the applied compressive stress. A modified coefficient is introduced to determine the extent to which residual stress impact the crack closure and is observed to vary for different materials. Several other literature models for crack closure under constant loading are also reviewed and compared with the proposed model. The modified model is then shown to predict several sets of published test results under constant loading for a variety of materials.

The crack opening stress is formalized as a function of the plastic zone sizes at the crack tip and the current crack length, which provided a means of approximation, accounting for both acceleration and retardation effects in a simplified manner. A sensitivity parameter is introduced to modify the enlarged plastic zone due to overload, to better fit the delay cycles with the test data and is observed to vary for different materials. Furthermore, the interaction effect induced by the combination of overload and underload sequence is modeled by depleting the compressive plastic zone due to an overload with the tensile plastic zone due to an underload. A qualitative analysis showed the simulation capacity of the small time scale model under different load types. A good agreement between prediction and test data for several irregular load types proved the applicability of the small time scale model under variable amplitude loading.

Cohesive zone model is one of the most widely used model for fracture analysis, but still remains open ended field for research. The earlier works using the cohesive zone model and Extended finite element analysis (XFEM) have been briefly introduced followed by an elaborate elucidation of the same concepts. Cohesive zone model in conjugation with XFEM is used for analysis in static condition in order to check its applicability in failure analysis. A real time setup of pipeline failure due to impingement is analyzed along with a detailed parametric study to understand the influence of the prominent design variable. After verifying its good applicability, a creep model is built for analysis where the cohesive zone model with XFEM is used for a time dependent creep loading. The challenge in this simulation was to achieve coupled behavior of cracks initiation and propagation along with creep loading. By using Design of Experiment, the results from numerical simulation were used to build an equation for life prediction for creep loading condition. The work was further extended to account for fatigue damage accumulation for high cycle fatigue loading in cohesive elements. A model was conceived to account for damage due to fatigue loading along within cohesive zone model for cohesive elements in ABAQUS simulation software. The model was verified by comparing numerical modelling of Double cantilever beam under high cycle fatigue loading and experiment results from literature. The model was also applied to a major industrial problem of blistering in Cured-In-Plane liner pipelines and a demonstration of its failure is shown. In conclusion, various models built on cohesive zone to address static and time dependent loading with real time scenarios and future scope of work in this field is discussed.

In this paper, at first, analytical formulation of J-integral for a non-local particle model (VCPM) using atomic scale finite element method is proposed for fracture analysis of 2D solids. A brief review of classical continuum-based J-integral and anon-local lattice particle method is given first. Following this, detailed derivation for the J-integral in discrete particle system is given using the energy equivalence and stress-tensor mapping between the continuum mechanics and lattice-particle system.With the help of atomistic finite element method, the J-integral is expressed as a summation of the corresponding terms in the particle system.

Secondly, a coupling algorithm between a non-local particle method (VCPM) and the classical finite element method (FEM) is discussed to gain the advantages of both methods for fracture analysis in large structures. In this algorithm, the discrete VCPM particle and the continuum FEM domains are solved within a unified theoretical framework. A transitional element technology is developed to smoothly link the 10-particles element with the traditional FEM elements to guaranty the continuity and consistency at the coupling interface. An explicit algorithm for static simulation is developed.

Finally, numerical examples are illustrated for the accuracy, convergence, and path-independence of the derived J-integral formulation. Discussions on the comparison with alternative estimation methods and potential application for fracture simulation are given. The accuracy and efficiency of the coupling algorithm are tested by several benchmark problems such as static crack simulation.