This dissertation concerns failure modelling with material imperfections and element erosion in finite element analyses. The aim has been to improve the element erosion technique, which is simple to use and implement and also computationally inexpensive. The first part of the dissertation serves as an introduction to the topic and as a summary of the methodologies presented in the following part. The second part consists of seven appended papers. In paper A the standard element erosion technique is used for projectile penetration. In papers B and C a methodology that accounts for size effects is developed and applied to crack initiation in armour steel and tungsten carbide. A methodology to better predict the stress state at crack tips with coarse meshes is presented and applied to armour steel in paper D. Papers E and F concern the development of selective mass scaling which allows for larger time steps in explicit methods. Finally, in paper G the previously presented methodologies are used in combination and validated against experimental results on tungsten carbide. The computations show good agreement with the experimental results on failure initiation for both materials, while the computational results on the propagation of cracks show better agreement for the armour steel than for the tungsten carbide. / On the day of the public defence of the doctoral thesis, the status of articles I, III and IV was Accepted and article VII was Submitted.

Steel pipelines are widely used in offshore oil/gas facilities. To achieve economically feasible designs, regulatory codes permit utilization of the pipelines well past their elastic response limit. This requires thorough integrity check of the pipeline subject to large scale yielding (LSY). Engineering criticality assessments (ECA) are used to justify the integrity of a cracked pipeline against fracture failure. The currently used ECA crack driving force equation was developed for load-controlled components subject to very limited crack-tip plasticity. Moreover, fracture toughness data are extracted from deeply-cracked laboratory specimens that produce the lowest margin of toughness values. Therefore, the current framework can be overly conservative (or include non-uniform inaccuracies) for ECA of modern pipelines that undergo LSY and ductile crack growth prior to failure. The two main goals of this thesis are: (i) Development of an alternative crack driving force estimation scheme, (ii) Justification of the use of use of shallow-cracked single edge notch tensile (SENT) specimens for the ECA. Strain concentration in concrete coated pipelines, and effect of Lüders plateau on the fracture response are also investigated. A new reference strain J-estimation scheme is proposed and calibrated to 300 nonlinear parametric FE models, which takes advantage of the linear evolution of the J with LSY bending strains. The scheme is hence strain-based and needless of limit load solutions, providing additional accuracy and robustness. The near-tip stress and strain fields of cracked pipelines were also investigated and compared to those obtained from a K-T type formulation. It is shown that the J-Q constraint theory can satisfactorily characterize these fields up to extreme plastic bending levels. Similar J-Q trajectories were also observed in the SENT and pipeline models. Subsequently, FE models utilizing a voided plasticity material were used to parametrically investigate ductile crack growth and subsequent failure of pipelines subject to a biaxial stress state. Plastic strain and stress triaxiality fields ahead of the propagating crack, along with R-curves, were compared among SENT and pipeline models. It is concluded that the SENT specimen could be a viable option for ECA of such pipes based on the observed crack tip constraint similarity.

The high stiffness to weight ratio and fatigue resistance make carbon fibre composites suitable for both military and large civil aircraft. The limited ability of current numerical methods to capture the complex growth of damage in laminated composites leads to a conservative design approach applied in today??s composite aircraft structures. The aim of the presented research was to develop an improved methodology for the failure prediction of laminated composites containing delaminations located between arbitrary layers in the laminate, and to extend the investigations to composite structures subjected to barely visible impact damage (BVID). The advantages of fracture mechanics-based methodologies to predict interlaminar failure in composite structures were identified, from which the crack tip element (CTE) approach and the virtual crack closure technique (VCCT) were selected for assessment. Extensive validation of these fracture mechanics methods is presented on a number of composite structures ranging from coupons to large stiffened panels. It was shown that the VCCT was relatively insensitive to the crack front mesh size, whilst predictions using the CTE methodology were significantly influenced by the element size. Based on the obtained results modelling guidelines for the VCCT and CTE were established. Significant contribution of this research to the field of the analysis of composite structures was the development of a novel test method for the evaluation of embedded single and multi-level delaminations. The test procedure of the single delamination specimen was proposed as an analogous test to conventional compression experiments. The transverse test overcame the inherent problems of in-plane compression testing and produced less scatter of experimental measurements. Quantitative analysis of numerical results employing the validated finite element modelling approaches showed that the failure load and location were in agreement with experiments. Furthermore, new modelling techniques for composite structures containing BVID proposed in this research produced good correlation with test data from the compression after impact (CAI) test. The study of BVID provided a significant contribution toward the knowledge of the applicability of implicit FE solvers to predict failure of CAI specimens as well as the criticality of centrally impacted specimens.

The crack-tip displacement concept has been applied to austenitic steels at 25°C and in the temperature range 400-800°C. The measurement of a maximum load crack-tip displacement in a notch bend test, provided a good indication of fracture-toughness since it included a portion of slot: crack-growth. The ability of these alloys to tolerate slow crack-growth, and even to arrest cracks without becoming unstable, is of considerable engineering importance since many service failures originate at stress concentrations produced by welding of poor design. Slow crack-growth was intermittent and highly dependent upon microstructural irregularities in the immediate vicinity of the crack-tip. The stress concentration at the crack-tip could be relieved (and the fracture-toughness improved) by localized plastic deformation. The degree of stress relief depended upon the locality and proximity of the various microstructural features as determined by the alloy manufacturing process. The temperature sensitivity of the bond strengths of the various interfaces particularly in cast alloys, had a marked-effect on fracture-toughness. This may have been the result of segregation of trace elements e.g. lead to the interface. Above the equicohesive temperature, the greatest contribution to fracture-toughness was associated with the presence of large amounts of second phase particles in the boundaries. In many cases, and particularly cast alloys, more than one crack formed at the notch root. Only one of these cracks propagated to failure. Heterogeneous cracking of this kind (itself an indication of fracture-toughness), lead to difficulties in correlating an initiation C. O. D. with the macroscopic plastic properties of the material. Similar correlations were however possible with the maximum load crack opening displacement.

An understanding of crack tip fields and fracture mechanisms in single crystals can help in developing better polycrystalline alloys and manufacturing processes. To this end, the effects of loading rate, material inertia and strain rate sensitivity on crack tip fields and their influence on fracture mechanisms in FCC single crystals are examined in this work by performing finite element analysis. It is shown that, in the absence of inertial effects, high loading rates elevate the stresses ahead of a crack tip and decrease the plastic strains in rate dependent single crystals. Also, it is found that the quasi-static near-tip stress field can be adequately characterized by the energy release rate J and a constraint parameter Q. Similar two-parameter characterization is possible even under dynamic loading. It is observed that if a suitable reference solution is used, the role of inertia manifests as a loss of constraint with increasing loading rate irrespective of strain rate sensitivity and lattice orientation. Thus, at very high loading rates, inertial effects oppose the role of rate sensitivity and cause a decrease in stresses near the tip. The relative influence of these two factors depends on rate sensitivity index. For a mildly rate dependent single crystal, the predicted cleavage fracture toughness remains constant up to a certain loading rate and thereafter increases sharply. On the other hand, for a strongly rate dependent single crystal, fracture toughness drops initially up to a certain loading rate beyond which it increases marginally. The loss of crack tip constraint is found to retard the ductile fracture mechanisms of void growth and coalescence. However, this is dependent on lattice orientation. In-situ experimental observation of void growth near a notch tip also shows strong orientation dependence. In addition, 3D finite element results indicate though-thickness dependence of equivalent plastic slip and hydrostatic stress leading to variations in void growth along the thickness direction of the specimens. The predicted load-displacement curves, lattice rotation, slip traces and void growth using finite element analysis are found to be in good agreement with the experimental observations. Thus, the present study has provided an understanding of the role of several factors such as constraint level, rate sensitivity, material inertia, lattice orientation and 3D effects on the mechanics of fracture of ductile single crystals.

The integrity of nearly all engineering structures are threatened by the presence of cracks. Structural failure occurs if a crack larger than a critical size exists. Although most well designed structures initially contain no critical cracks, subcritical cracks can grow to failure under fatigue loading, called fatigue crack growth (FCG). Because it is impossible or impractical to prevent subcritical crack growth in most applications, a damage tolerant design philosophy was developed for crack sensitive structures. Design engineers have taken advantage of the FCG threshold concept to design for long fatigue lives. FCG threshold (DKth) is a value of DK (crack-tip loading), below which no significant FCG occurs. Cracks are tolerated if DK is less than DKth. However, FCG threshold is not constant. Many variables influence DKth including microstructure, environment, and load ratio. The current research focuses on load ratio effects on DKth and threshold FCG. Two categories of load ratio effects are studied here: extrinsic and intrinsic. Extrinsic load ratio effects operate in the crack wake and include fatigue crack closure mechanisms. Intrinsic load ratio effects operate in the crack-tip process zone and include microcracking and void production. To gain a better understanding of threshold FCG load ratio effects (1) a fatigue crack closure model is developed to consider the most likely closure mechanisms at threshold, simultaneously, and (2) intrinsic load ratio mechanisms are identified and modeled. An analytical fatigue crack closure model is developed that includes the three closure mechanisms considered most important at threshold (PICC, RICC, and OICC). Crack meandering and a limited amount of mixed-mode loading are also considered. The rough crack geometry, approximated as a two-dimensional sawtooth wave, results in a mixed-mode crack-tip stress state. Dislocation and continuum mechanics concepts are used to determine mixed-mode crack face displacements. Plasticity induced crack closure is included by modifying an existing analytical model, and an oxide layer in the crack mouth is modeled as a uniform layer. Finite element results were used to verify the analytical solutions for crack-tip stress intensity factor and crack face displacements. These results indicate that closure for rough cracks can occur at two locations: (1) at the crack-tip, and (2) at the asperity nearest the crack-tip. Both tip contact and asperity contact must be considered for rough cracks. Tip contact is more likely for high Kmax levels, thick oxide layers, and shallow asperity angles, a. Model results indicate that closure mechanisms combine in a synergistic manner. That is, when multiple closure mechanisms are active, the total closure level is greater than the sum of individual mechanisms acting alone. To better understand fatigue crack closure where multiple closure mechanisms are active (i.e. FCG threshold), these interactions must be considered. Model results are well supported by experimental data over a wide range of DK, including FCG threshold. Closure-free load ratio effects were studied for aluminum alloys 2024, 7050, and 8009. Alloys 7050 and 8009 were selected because load ratio effects at FCG threshold are not entirely explained by fatigue crack closure. It is believed that closure-free load ratio mechanisms occur in these alloys. Aluminum alloy 2024 was selected for study because it is relatively well behaved, meandering most load ratio effects are explained by fatigue crack closure. A series of constant Kmax threshold tests on aluminum alloys were conducted to eliminate fatigue crack closure at threshold. Even in the absence of fatigue crack closure load ratio (Kmax) effects persist, and are correlated with increased crack-tip damage (i.e. voids) seen on the fatigue crack surfaces. Accelerated FCG was observed during constant Kmax threshold testing of 8009 aluminum. A distinct transition is seen the FCG data and is correlated with a dramatic increase in void production seen along the crack faces. Void production in 8009 aluminum is limited to the specimen interior (plane-strain conditions), promoting crack tunneling. At higher values of Kmax (+_ 22.0 MPaà m), where plane-stress conditions dominate, a transition to slant cracking occurs at threshold. The transition to slant cracking produces an apparent increase in FCG rate with decreasing DK. This unstable threshold behavior is related to constraint conditions. Finally, a model is developed to predict the accelerated FCG rates, at higher Kmax levels, in terms of crack-tip damage. The effect of humidity (in laboratory air) on threshold FCG was studied to ensure that environmental effects at threshold were separated from load ratio effects. Although changes in humidity were shown to strongly affect threshold FCG rates, this influence was small for ambient humidity levels (relative humidity between 30% and 70%). Transient FCG behavior, following an abrupt change in humidity level, indicated environmental damage accumulated in the crack-tip monotonic plastic zone. Previous research implies that hydrogen (a component of water vapor) is the likely cause of this environmental damage. Analysis suggests that bulk diffusion is not a likely hydrogen transport mechanism in the crack-tip monotonic plastic zone. Rather, dislocation-assisted diffusion is presented as the likely hydrogen transport mechanism. Finally, the (extrinsic) fatigue crack closure model and the (intrinsic) crack-tip damage model are put in the context of a comprehensive threshold model. The ultimate goal of the comprehensive threshold model is to predict fatigue lives of cyclically loaded engineering components from (small) crack nucleation, through FCG, and including failure. The models developed in this dissertation provide a basis for a more complete evaluation of threshold FCG and fatigue life prediction. The research described in this dissertation was performed at NASA-Langley Research Center in Hampton, Virginia. Funding was provided through the NASA GSRP program (Graduate Student Researcher Program, grant number NGT-1-52174). / Ph. D.

The power plant and aerospace industries have been facing a huge loss, due to structural failure. The structural failure occurs due to the presence of the crack in it. Hence, it becomes necessary to monitor the structural health under operating condition. Most of the techniques, for structural health monitoring are used for a specific purpose. Some of these techniques require structure dismantling, which is very much expensive and time consuming. So the vibration based structural health monitoring is advantageous, compared to other techniques. Most of the vibration based Structural Health Monitoring (SHM) approaches, use linear vibration theory. But, these linear vibration based procedures, have inherently low sensitivity to crack. Since crack introduces nonlinearities in the system, their merits in damage detection need to be investigated for SHM. In this thesis, the problem is focused on studying nonlinear dynamics of cracked structures for Structural Health Monitoring. For this, simulations and experiments are performed. The new procedure for the simulation is developed using Matlab-Simulink. It uses the numerical approximation for dynamic compliance operators and a nonlinear model of cracks contact faces interaction to study the dynamic behaviour of the cracked bar. Furthermore, the finite element model of the cracked cantilever bar with crack- tip plasticity is developed and the dynamic behaviour of the elasto-plastic bar is studied. Additionally, numerous experiments are performed to study the dynamics of cantilever bar with the fatigue crack in it. The results from Matlab-Simulink simulation shows the distribution of higher harmonics generated along the bar length, as a function of distance from the crack. In finite element simulation, comparison is made between the resonance frequency of cracked cantilever bar with and without crack-tip plasticity. It is found that, there is decrease in resonance frequency of the cracked bar with cracked tip plasticity, when compared with the resonance frequency of cracked bar without crack-tip plasticity. This reduction in resonance frequency is due to the crack-induced plasticity near the crack tip which affects the overall stiffness of bar. In experiments, the response is measured at four different points on the cracked cantilever bar at a given resonant frequency of excitation at lower and higher vibration amplitude. For lower vibration amplitude, it is found that the response obtained near the vicinity of the crack shows the presence of higher harmonics of resonant frequency, which disappears in the response obtained far away from the crack. For higher vibration amplitude, it is found that the response obtained near the vicinity of the crack shows the presence of higher harmonics along with the low frequency component. This low frequency component causes modulation, which leads to the generation of side band frequencies near the resonant frequency. The occurrence of low frequency component and side band frequencies is due to the vibro-impact behaviour of crack. The amplitude of these side band frequencies and higher harmonics are reduced in the response obtained far away from the crack. This indicates that crack-induced nonlinearity has a localized effect on the dynamics of bar. It is also observed that the magnitude of low frequency component is proportional to the magnitude of resonant frequency of excitation. This indicates that crack behaves like a signal modulator, detector of low frequency component and amplifier as the magnitude of low frequency component is proportional to the magnitude of resonant frequency excitation. From the Matlab-Simulink simulation and experimental results, it is concluded that crackinduced nonlinearity affects the dynamic behaviour of the cracked bar significantly, which will be effective in structural health monitoring. Keywords: vibro-impact, crack, dynamic compliance, harmonics, modulator, detector, amplifier, crack-tip plasticity, resonance frequency, structural health monitoring.

In this thesis, the application of composite materials for marine structures and specifically naval vessels has been explored by investigating its damage criticality. The use of composite materials for Mine Counter Measure Vessels (MCMVs) was desirable, especially for producing material characteristics, such as light weight, corrosion resistance, design flexibility due to its anisotropic nature and most importantly stealth capability. The T-Joint structure, as the primary connection between the hull and bulkhead forms the focus of this research. The aim of the research was to determine the methodology to predict the damage criticality of the T-Joint under a pull-off tensile loading using FE (Finite Element) based fracture mechanics theory. The outcome of the research was that the Finite Element (FE) simulations were used in conjunction with fracture mechanics theory to determine the failure mechanism of the T-Joint in the presence of disbonds in the critical loca tion. It enables certain pre-emptive strengthening mechanisms or other preventive solutions to be made since the T-Joint responses can be predicted precisely. This knowledge contributes to the damage tolerance design methodology for ship structures, particularly in the T-Joint design. The results comparison between the VCCT (Virtual Crack Closure Technique) analysis and the experiment results showed that the VCCT is a dependable analytical method to predict the T-Joint failure mechanisms. It was capable of accurately determining the crack initiation and final fracture load. The maximum difference between the VCCT analysis with the experiment results was approximately 25% for the T-Joint with a horizontal disbond. However, the application of the CTE (Crack Tip Element) method for the T-Joint displayed a huge discrepancy compared with the results (fracture toughness) obtained using the VCCT method, because the current T-Joint structure geometry did not meet the Classical Laminate Plate Theory (CLPT) criteria. The minimum fracture toughness difference for both analytical methods was approximately 50%. However, it also has been tested that when the T-Joint structure geometry satisfied the CLPT criteria, the maximum fracture toughness discrepancy between both analytical methods was only approximately 10%. It was later discovered from the Griffith energy principle that the fracture toughness differences between both analytical methods were due to the material compliance difference as both analytical methods used different T-Joint structures.

A two-parameter fracture criterion (TPFC) is used to correlate and predict failure loads on cracked configurations made of ductile materials. The current study was conducted to validate the use of the fracture criterion on more brittle materials, using elastic-plastic finite-element analyses with the critical crack-tip-opening angle (CTOA) failure criterion. Forman generated fracture data on middle-crack tension, M(T), specimens made of thin-sheet 7075-T6 aluminum alloy, which is a quasi-brittle material. The fracture data included a wide range of specimen widths (2w) ranging from 3 to 24 inches. A two-dimensional (2D) finite-element analysis code (ZIP2D) with a ''plane-strain core" option was used to model the fracture process. Fracture simulations were conducted on M(T), single-edge-crack tension, SE(T), and single-edge-crack bend, SE(B), specimens. The results supported the TPFC equation for net-section stresses less than the material proportional limit. However, some discrepancies were observed among the numerical results of the three specimen types. Thus, more research is needed to improve the transferability of the TPFC from the M(T) specimen to both the SE(T) and SE(B) specimens.

The objective of this thesis is to study the fracture behavior of bulk metallic glasses. For this purpose, detailed finite element investigation of the mode I and mixed mode (I and II) stationary crack tip fields under plane strain, small scale yielding conditions is carried out. An implicit backward Euler finite element implementation of the Anand and Su constitutive model [Anand, L. and Su, C., 2005, J. Mech. Phys. Solids 53, 1362] is used in the simulations. The effects of internal friction (μ), strain softening, Poisson's ratio (ν) and elastic mode mixity (Me) on the near-tip stress and deformation fields are examined. The results show that under mode I loading, a higher μ leads to a larger normalized plastic zone size and higher plastic strain level near the notch tip, but causes a substantial decrease in the opening stress. The brittle crack trajectories and shear band patterns around the notch are also simulated. An increase in ν reduces the extent of plastic zone and plastic strain levels in front of the notch tip. The results from mixed mode simulations show that increase in the mode II component of loading dramatically increases the maximum plastic zone extent, lowers the stresses and significantly enhances the plastic strain levels near the notch tip. Higher μ causes the peak magnitudes of tensile tangential stress to decrease. The implications of the above results on the fracture response of bulk metallic glasses are discussed. The possible variations of fracture toughness with mode mixity predicted by employing two simple fracture criteria are examined. Finally, mixed mode (I and II) fracture experiments on a Zr-based bulk metallic glass are performed. It is found that the fracture toughness increases with Me and Jc under mode I is higher than that under mode II loading by a factor of 4. The operative failure mechanism and fracture process zone size are discerned based on observations of incipient crack growth and fractographs. Lastly, a fracture criterion is proposed which predicts the experimentally observed variation of fracture toughness with mode mixity.