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The concept of the Forming Limit Diagram (FLD) has proved to be useful for representing conditions for the onset of sheet necking, and is now a standard tool for characterizing materials in terms of their overall forming behavior. In this study, the M-K approach, in conjunction with Gurson model, is used to calculate FLDs. The influences of mechanical properties, including strain hardening, strain rate sensitivity, as well as the void nucleation, growth and coalescence, on the FLDs are examined. Most sheet metals undergo multiple deformation modes (strain paths) when being formed into complex manufacturing parts. When the strain path is changed in the deformation processing of metal, it's work-hardening and flow strength differs from the monotonic deformation characteristics. As a consequence, sheet metal formability is very sensitive to strain path changes. In this study, the hardening behavior and damage evolution under non-proportional loading paths are investigated. The effect of strain path change on FLDs is studied in detail. FLDs are conventionally constructed in strain space and are very sensitive to strain path changes. Alternatively, many researchers represented formability based on the state of stress rather than the state of strain. They constructed a Forming Limit Stress Diagram (FLSD) by plotting the calculated principal stresses at necking. It was concluded that FLSDs were almost path-independent. In this work, the FLSD has been constructed under non-proportional loading conditions to assess its path dependency when damage effect is included. / Thesis / Master of Applied Science (MASc)

Over the past decade, environmental concerns and safety regulation have led to increasing demand for vehicles with higher passenger safety and fuel economy. This has spurred intensive research on advanced high strength steels (AHSS). The quench and partitioning (Q&P) heat treatment is a novel approach that has led to development of one group of third generation AHSS alloys. In recent years most of the studies on the Q&P process were dedicated to the effect of the heat treatment parameters on microstructural evolution and mechanical properties. However, micromechanical deformation behavior of constituent phases and damage evolution in Q&P steels are not fully understood. In this study, damage micromechanisms in a commercial QP980 were investigated with the aid of in-situ tensile tests under a scanning electron microscope (SEM) followed by local strain mapping using microscopic digital image correlation (µ-DIC) analysis so as to quantify the microstructural deformation of constituent phases. Nano-hardness measurements were conducted to correlate the amount of plastic deformation of each phases to its strength. Ex-situ tensile tests coupled with electron back scattered diffraction (EBSD) and X-ray diffraction (XRD) were conducted to study the influence of transformation induced plasticity (TRIP) of the retained austenite phase on microstructural damage and deformation. It was found that average local true strain in ferrite was approximately two times and three times greater than that of martensite and blocky retained austenite respectively, which was with the good agreement with nano-hardness measurements showing that retained austenite blocks was three times and two times harder than martensite and ferrite respectively. Damage in both ferrite and martensite starts at the same total strain; however, damage growth is faster in martensite leading to the formation of large cavities. The average local true strain ratio of ferrite to martensite decreases after total true strains higher than 0.1 and the reduction is more pronounced in regions with higher martensite volume fraction. EBSD results showed that at total true strain of 0.07 some of the retained austenite blocks located at the ferrite and martensite interfaces were almost fully transformed to martensite. According to XRD results at the point of necking 57% of retained austenite transformed to martensite. There is evidence of brittle cracking of large blocky retained austenite in regions with strain localization starting at relatively low strains but appear to have little impact on the final failure process. The good deformation ability of QP980 is attributed primarily to co-deformation of ferrite and martensite and secondarily to the TRIP effect. / Thesis / Master of Applied Science (MASc)

In this thesis a study is made of the damage layer (as defined by its solubility in a HF-H2o2, or concentrated HF solution) produced by ion bombardment of Si. This thesis is concerned with not only the layer but also its usefulness in the study of radiation damage itself. The layer is examined with respect to the adverse effects it has upon the anodic oxidation and stripping technique, to the dose of incident ions required to produce it (ie the threshold dose), and to its relationship to the amorphous layer which has been observed with ion bombardment of Si. Annealing of the damage has been approached from two points of view. First the temperature dependence of the threshold dose is used to obtain information about the annealing of the damage that occurs between the formation of a discrete damage zone and the formation of a layer. Secondly using gas release of the radioactive Kr85 the annealing of the fully formed amorphous damage layer is followed. The solubility of the damage layer in a HF-H2o2 solution is shown to be a very useful tool in the study of radiation damage. Firstly it provides a convenient means of obtaining the mean range of the damage distribution as a function of incident ion energy. Secondly it is used to obtain the threshold dose for the formation of the damage layer, and thirdly it is used in the gas release experiments to give more detailed information about the Kr85 motion. / Thesis / Master of Science (MS)

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With the traditional fracture mechanics approaches, an initial crack and self-similar progression of cracks are assumed. In this treatise, theoretical and numerical tools are developed to mathematically describe non-self-similar progression of cracks without specifying an initial crack. A cohesive-decohesive zone model, similar to the cohesive zone model known in fracture mechanics as Dugdale-Barenblatt model, is adopted to represent the degradation of the material ahead of the crack tip. This model unifies strength-based crack initiation and fracture based crack progression. The cohesive-decohesive zone model is implemented with an interfacial surface material that consists of an upper and lower surface connected by a continuous distribution of normal and tangential nonlinear elastic springs that act to resist either Mode I opening, Mode II sliding, Mode III sliding, or mixed mode. The initiation of fracture is determined by the interfacial strength and the progression of fracture is determined by the critical energy release rate. The material between two adjacent laminae of a laminated composite structure or the material between the adherend and the adhesive is idealized with an interfacial surface material to predict interfacial fracture. The interfacial surface material is positioned within the bulk material to predict discrete cohesive cracks. The proper work-conjugacy relations between the stress and deformation measures are identified for the interfacial surface theory. In the principle of virtual work, the interfacial cohesive-decohesive tractions are conjugate to the displacement jumps across the upper and lower surfaces. A finite deformation kinematics theory is developed for the description of the upper and lower surface such that the deformation measures are invariant with respect to superposed rigid body translation and rotation. Various mechanical softening constitutive laws thermodynamically consistent with damage mechanics are postulated that relate the interfacial tractions to the displacement jump. An exponential function is used for the constitutive law such that it satisfies a multi-axial stress criterion for the onset of delamination, and satisfies a mixed mode fracture criterion for the progression of delamination. A damage parameter is included to prevent the restoration of the previous cohesive state between the interfacial surfaces. In addition, interfacial constitutive laws are developed to describe the contact-friction behavior. Interface elements applicable to two dimensional and three dimensional analyses are formulated for the analyses of contact, friction, and delamination problems. The consistent form of the interface element internal force vector and the tangent stiffness matrix are considered in the formulation. We investigate computational issues related to interfacial interpenetration, mesh sensitivity, the number of integrations points and the integration scheme, mathematical form of the softening constitutive law, and the convergence characteristics of the nonlinear solution procedure when cohesive-decohesive constitutive laws are used. To demonstrate the predictive capability of the interface finite element formulation, steadystate crack growth is simulated for quasi-static loading of various fracture test configurations loaded under Mode I, Mode II, Mode III, and mixed-mode loading. The finite element results are in agreement with the analytical results available in the literature and those developed in this work. A progressive failure methodology is developed and demonstrated to simulate the initiation and material degradation of a laminated panel due to intralaminar and interlaminar failures. Initiation of intralaminar failure can be by a matrix-cracking mode, a fiber-matrix shear mode, and a fiber failure mode. Subsequent material degradation is modeled using damage parameters for each mode to selectively reduce lamina material properties. The interlaminar failure mechanism such as delamination is simulated by positioning interface elements between adjacent sublaminates. The methodology is validated with respect to experimental data available in the literature on the response and failure of quasi-isotropic panels with centrally located circular cutouts. Very good agreement between the progressive failure analysis and the experiments is achieved if the failure analyses includes the interaction of intralaminar and interlaminar failures in the postbuckling response of the panels. In addition, ideas concerning the implementation of a fatigue model incorporated with a cohesive zone model are discussed. / Ph. D.

A time-domain model-based crack diagnostic methodology using vibration data is presented. Most of the damage detection methods proposed to date are based on modal parameters and are limited by the loss of information caused by data reduction and by the implicit assumption of linearity. The use of time domain information permits the direct inclusion of the nonlinear behavior due to crack opening-closure cycles. In addition, very little information is lost, since no signal processing or parameter identification steps are involved. The proposed method is based on a continuous model for the transverse vibrations of beams consisting of partial differential equations of motion with varying coefficients to account for the presence of damage. In order to provide accurate representation of the structure's behavior over a broader frequency range, a new continuous cracked beam model including shear effects and rotatory inertia is developed using the Hu-Washizu-Barr variational method. The resulting equations of motion are discretized by a Galerkin method using local B-splines as test functions. The crack is assumed to be either fully open or fully closed, resulting in a bilinear system. The simultaneous identification of crack location and depth is performed by minimizing the norm of the differences between the numerical and experimental time responses to multiple excitations. Impact, low frequency sinusoidal and Schroeder--phased multisine inputs are investigated as potential excitation methods. The cost function to be minimized presents several local minima that are shown to be related to the length of the response records. A genetic algorithm is used to overcome the multimodal nature of the objective function. The methodology is validated through simulated identifications of several damage scenarios. The importance of the inclusion of the nonlinear behavior is addressed, and the effects of model uncertainties and measurement noise are quantified in terms of minimum identifiable crack size. / Ph. D.

The overall objective of this thesis is to develop, validate and assess a probabilistic collision damage model to support ongoing work by the Society of Naval Architecture and Marine Engineering (SNAME) Ad Hoc Panel #6 and IMO working groups. It is generally agreed that structural design has a major influence on tanker oil outflow and damaged stability in grounding and collision, but crashworthiness is not considered in present regulations. The proposed methodology provides a practical means of considering structural design in a regulatory framework, and when implemented would improve the safety and environmental performance of ships. This thesis continues the development and applies a Simplified Collision Model (SIMCOL) to calculate damage extent (transverse, vertical and longitudinal) and oil outflow in ship collisions. The primary contribution of this thesis is the development and validation of a theory for the determination of energy absorbed in longitudinal extent of damage, and the implementation of the theory within SIMCOL. SIMCOL is sufficiently fast to be applied to thousands of collision cases as is required for a probabilistic analysis. The following specific tasks were completed using SIMCOL in support of this project: Completed the development of SIMCOL Version 3.0 including: 1) Deformable Bow sub model 2) Implementation and validation of theory for the determination of energy absorbed in longitudinal extent of damage. • Developed the capability to model collision events using LSDYNA. • Validated Virginia Tech LSDYNA ship collision modeling procedure. • Validated SIMCOL using real collision data, and probabilistic collision data for penetrating collisions. / Ph. D.

The requirements for the next generation of nuclear reactors call for more radiation tolerant materials. One such material, nanostructured ferritic alloys (NFA) are a candidate material for use in cladding. The radiation tolerance of NFAs comes from the high number density of small oxide nanofeatures composed of Y, Ti, and O. These oxide nanofeatures or nano-oxides act as alternative nucleation sites for bubbles of transmutation He, thus preventing the accumulation of He atoms at the grain boundaries which would embrittle the metal. To further study the material, a mean-field rate theory model (MF-RTM) was created to simulate the radiation-induced segregation (RIS) of the alloy components Y, Ti, and O to the grain boundaries. Later, a kinetic Monte Carlo model (KMC) was made that replicated the results from the rate theory for the radiation induced segregation. Then the KMC model was modified to study the nano-oxide behavior in a range of different behaviors; the nano-oxide precipitation kinetics during heat treatment, resistance to dissolution under irradiation regimes similar to reactor conditions, and ability to trap He bubbles on the nano-oxide surfaces rather than the grain boundary. This KMC model is more complex than others as it includes 5 different atomic species (Fe, Y, Ti, O, and He) which migrate through three different mechanisms. Findings from the precipitation heat treatments were able to replicate the size, number density, and composition of nano-oxides from experiments and determined vacancy trapping at oxide interfaces was a significant for the NFA's coarsening resistance as opposed to interference from dislocations. In the irradiation simulations, the resistance of the nano-oxides to dissolution was confirmed and found the excess vacancy population plays an important role in healing the nano-oxides. He bubbles formed in the KMC simulations were found to preferentially form at the oxide interfaces, particularly the <111> interface, rather than the grain boundary and the characteristics of the He bubbles match expectations from literature. In the development of the KMC model, new insights into steady-state detection concepts were also found. A new type of steady-state detection (SSD) algorithm is described. Additionally, a method of forecasting the number of data points needed to make an accurate determination of steady-state, a 'predicting the pre-requisite to steady state detection' (ppSSD), is explored. / Doctor of Philosophy / Nuclear reactors need more radiation tolerant materials in the future, such as nanostructured ferritic alloys (NFA), used for nuclear fuel rod cladding, whose large amount of nanometer sized oxide particles contribute substantially to the radiation resistance of the metal overall. A mean-field rate theory method(MF-RTM) and a Kinetic Monte Carlo (KMC) computer model were made to study radiation induced segregation in the material. A more complex 5 element (Fe, Y, Ti, O, and He) KMC code was later developed to study the influence of the oxides at high temperatures and dose rates to gain insight into the causes the oxides remarkable thermal stability and resistance to irradiation. At all stages, the KMC model was able to replicate material behavior under high temperature heat treatment and irradiation. The model was used to simulate the formation of these oxides under different temperatures during their initial processing to gain more knowledge on how the oxide characteristics (size and number density) are influenced by temperature so we can tailor the processing method to achieve an ideal distribution of oxides in the material. Additionally, a mechanism for the oxides resistance to high temperature coarsening unrelated to the expected one caused by dislocations. The irradiation resistance of oxides to dissolution from irradiation was also investigated. While experimental measurements give a before and after picture of a material that underwent irradiation, the KMC can show the time evolution of the oxide size with increasing irradiation damage so the mechanisms behind the radiation resistance can be understood. The oxides remained stable at all temperatures and dose rates. Excess vacancies were found to play an important role in stabilizing the oxides against radiation damage. The KMC model also confirmed the ability of the oxides to trap transmutation He at the interfaces rather than the grain boundary and observed the process of He bubble nucleation. The He bubble form at the <111> oxide interface and they possess similar characteristics of He bubbles expected from literature. Additionally, a novel steady-state detection (SSD) algorithm was developed that can be used for long-term simulations and a method to determine how many data points the algorithm needs to accurately detect steady state is described here.

The results of this investigation indicate: 1. The deterioration rate in the lateral direction of the uniaxially prestressed members subjected to the deep-seated type of freeze-thaw damage increased as the level of the compressive stress field increased. 2. Under all levels of uniaxial compression, cracks formed parallel to the direction of the applied stress field and in any plane parallel to this direction when the members were subjected to freeze-thaw damage. 3. The cracks are assumed to start at the boundary of a capillary within the aggregate and propagate through the aggregate to the aggegate- mortar interface. 4. Due to previous investigations, bond and mortar cracks are assumed to exist in the concrete. These cracks increase for increasing stress levels. 5. For the prestressed direction of any uniaxially prestressed member, there was a certain prestress level for which the change in length due to internal freeze-thaw damage equaled the change in length due to the applied prestressing force plus any longitudinal creep effects. This resulted in a total zero change in length. This zero change in length condition is called the "stress equilibrum condition" and the level of prestress which causes this condition is called the "prestress stability level." However, this condition can only last a short while before equilibrium is destroyed, since freeze-thaw daamage and and creep are continuously changing. / Master of Science