Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 195-198). Also available on the Internet.

Notched unidirectional graphite/epoxy tubes with fiber orientations of 2.5°, 15°, 45°, and 87.5° were failed in tension, compression, torsion, and combined compression-torsion loading. The stress field around the slot-like notches, aligned with the tube axis, was determined using an infinite flat plate elasticity solution with an elliptical hole. The normal stress ratio theory was used to predict crack location, crack direction, and failure stress. The experimental failure modes of the tubes were determined using scanning electron microscopy and related to the stress field in the vicinity of the notch. The results showed that independent of loading the cracks usually initiated at the discontinuity of the notch where the semi-circular end intersects the straight sides and then grew along the fiber direction either at the fiber/matrix interface or within the matrix. The normal stress ratio theory correctly predicted the direction of crack growth but not the location of crack initiation since the model did not account for the notch discontinuity. The prediction of far-field failure stresses exhibited only limited agreement with the experimental results. When there was agreement, the predicted far-field failure stresses were dependent on the elliptical semi-axis ratio used to model the notch. The material principal stresses at the location of maximum normal stress ratio were correlated with the failure mode of the unidirectional tubes. Matrix failure tended to occur when the material principal shear stress and transverse stress (perpendicular to the fibers) were nearly equal in magnitude, while fiber/matrix interface failure was predominant when the stresses differed by a factor of 2.0 or more. In addition, several notched angle-ply ± 87.5° tubes were failed in torsion. The normal stress ratio theory was applied to these tubes and correctly predicted that fiber breakage would occur. The predicted crack initiation stress agreed poorly with experimental results and the location of the crack was influenced by the notch discontinuity not included in the model. The direction of crack growth and the failure morphology of the angle-ply tubes were dependent on the direction of torsion applied to the tubes. / Ph. D.

The local buckling, postbuckling, and crippling (failure) of channel, zee, and I- and J-section stiffeners made of AS4/3502 graphite-epoxy unidirectional tape are studied by experiment and analysis. Thirty-six specimens were loaded in axial compression as intermediate length columns. Examination of the experimental results indicates the existence of a number of damage initiation modes, all of which involve either delamination in some part of the specimen or local material strength failure in a comer of the specimen. The ratio of the flange width to thickness has a strong influence on the buckling stress and damage initiation mode. The inner corner radius strongly affects the buckling and crippling stresses for the I- and J-section specimens. Comparison of the numerical results from a computer code for shell analysis (STAGS) with experimental data shows good correlation prior to buckling and at the buckling load, but diminished agreement in the postbuckling region. This lack of postbuckling correlation is attributed to the neglecting of transverse shearing deformations in the structural theory, inaccuracies in the modeling of in-plane boundary conditions, and damage initiation in the experimental specimens. A plane stress failure analysis for five of the specimens shows the compressive fiber mode criterion of Hashin correlates reasonably well with the first detectable damage event. Equilibrium is used to develop interlaminar stress equations for classical laminated plate theory that require high order derivatives of the displacements. Derivatives computed from discrete displacement data using the Discrete Fourier Transform are inaccurate due to the Gibbs phenomenon. / Master of Science

This paper summarizes research on the structural perfomance of wood elements and assemblies exposed to fire and reviews methodologies available to predict performance. This reasecrh provides a wealth of information on topics such as how fast a flame spreads across the surface of wood, how much smoke is produced during combustion and at what rate does wood char and at what heat release rate.

The safety of engineering structures depends heavily on the presence of cracks, which may propagate and lead eventually to structural failure. This dissertation aims to advance the computational modeling of fracture, within the context of linear elastic fracture mechanics (LEFM) and cohesive zone models (CZMs). The extended finite element method (XFEM) is employed as the discretization method and cracks in both homogeneous and bimaterial solids are considered in this work. First, a novel set of enrichment functions within the framework of XFEM is proposed for the LEFM analysis of interface cracks in bimaterials. The motivation for the new enrichment set stems from the revelation that the accuracy of the widely accepted 12-fold bimaterial enrichment functions significantly deteriorates with the increase in material mismatch. To this end, we propose an 8-fold material-dependent enrichment set, derived from the analytical asymptotic displacement field, that well captures the near-tip oscillating singular fields of interface cracks, including the transition to weak discontinuities of bimaterials. The new enrichment set is tested on various examples and found to outperform the 12-fold set in terms of accuracy, conditioning, and total number of degrees of freedom (DOFs). The formulation is then extended to include high-order enrichment functions and accurate stress and displacement fields are obtained. The complex stress intensity factors (SIFs) of interface cracks are evaluated by employing Irwin's crack closure integral. To this end, a closed-form SIF formulation in terms of the enriched DOFs is derived by matching the leading term in the XFEM with an analytical expression of Irwin's integral. Hence, the SIFs of interface cracks can be directly obtained upon the solution of the XFEM discrete system without cumbersome post-processing requirements. The proposed method is shown to work well on several benchmark examples involving straight and curved interface cracks, giving accurate SIF results. Another contribution of the work is the application of Irwin's integral to the estimation of SIFs for curved homogeneous cracks. At the core, the proposed approach employs high-order enrichment functions to accurately capture the near-tip fields and evaluates the original definition of Irwin's integral through closed-form formulations in terms of enriched DOFs. An improved quadrature scheme using high-order isoparametric mapping together with a generalized Duffy transformation is proposed to integrate singular fields in tip elements with curved cracks. The proposed extraction approach is shown to yield decomposed SIFs with excellent accuracy and avoid the need for auxiliary fields as in J-integral method. Second, with respect to cohesive fracture, a discrete damage zone model (DDZM) is proposed following a rigorous thermodynamic framework similar to that of continuum damage mechanics (CDM). For the modeling of mixed-mode delamination, a novel damage evolution law is proposed to account for the coupled interaction between opening and sliding modes of interface deformations. A comprehensive comparison made with several popular CZMs in the literature demonstrates the thermodynamic consistency of the DDZM. The proposed interface model is integrated with the XFEM and the effectiveness of this framework has been validated on various benchmark problems. Finally, a novel continuous/discontinuous method is proposed to simulate the entire failure process of quasi-brittle materials: from the nucleation of diffuse damage to the development of discrete cracks . An integral-type nonlocal continuum damage model is coupled in this framework with DDZM with a new numerical energetic coupling scheme. The transition from the continuous (CDM) to the discontinuous approach (DDZM) can be triggered at any damage level with a weak energetic equivalence preserved. A few benchmark problems involving straight and curved cracks are investigated to demonstrate the applicability and robustness of the coupled XFEM cohesive-damage approach.

Progressive collapse is a failure mechanism that causes local damage of one structural element to progress throughout the whole structure leading to collapse of the entire structure. Recent catastrophic structural collapses in the world have drawn attention from structural engineers to the importance of designing structures that will continue to be operational even after some local failures occur. For some bridge types, although the design of each single member follows the proper design standards, they still cannot provide sufficient degree of redundancy to withstand a local failure without the total collapse of the entire structural system. In this study, two truss-type bridges, a half-through pedestrian bridge and a through-truss bridge, are investigated. The design configurations follow the AASHTO specifications, and they are usually classified as fracture-critical, non-redundant structures. Furthermore, traditional design and evaluation procedures generally classify through-truss bridges as single-load-path structures. However, due to the configuration of this bridge type, alternative load paths in the bridge could exist, indicating that this type of structural system has the ability to continue sustaining further loads after one of its members reaches its ultimate capacity by using different load paths. It is important to note that, since the structural load-carrying capacity strongly depends on the location of the damaged area, the progressive collapse mechanism of a structure could change substantially under different damage conditions. For the pin-connected pedestrian bridge model, the analysis showed that the failure of a local member is not responsible for the bridge’s collapse. Instead, it is the global buckling (instability) of top chord system that led the bridge to collapse. A modified 2D structure was studied to properly match the buckling load and its associated deformed shape with those obtained in the 3D model’s top chord system. The conclusions of this study verified that the collapse mechanism of this type of bridge is linked to the instability of the top chord system. For the same pedestrian bridge with beam-type connection, the bridge’s failure mechanism is instead associated with the local buckling of an upper chord element that led the bridge to collapse. Therefore, the pedestrian bridge should not be considered a fracture-critical structure since the failure mechanisms that led to its collapse were associated with large compression forces in the upper chord. Looking at deterioration effects on bridge performance, corrosion is one of the dominant causes of deterioration in steel bridges due to aggressive environment and inadequate maintenance. The effects of corrosion damage could alter significantly the bridge behavior depending on the extent of deterioration on the bridge structure. Comprehensive nonlinear analyses were conducted to investigate the changes in collapse mechanisms considering various corrosion level and different corroded locations. Results from the deteriorated pedestrian bridge analyses showed that the deterioration of corroded top chord members could significantly reduce the load-carrying capacity of the bridge and lead the structure to sudden catastrophic failure even for a load lower than the one used in the original design. For the through-truss bridge model, the cases with a corroded middle diagonal member revealed similar load-carrying capacities and collapse mechanisms to the undamaged bridge. These models show similar collapse mechanisms, related to the bending failure of the middle bottom chord and the local buckling of the middle top chord. When the corrosion of the top chord element is severe, the collapse mechanism of the bridge is still linked to the buckling failure of upper chord together with the bending failure of the middle bottom chord. However, the load-carrying capacity of this damaged bridge could drop considerably when compared to that of the undamaged model. Among all the cases analyzed in this study, the corrosion of the end post element represents the most critical case: here, the results indicated a considerable decrease in the load-carrying capacity of this damaged bridge model when compared to that of the undamaged bridge. In addition, this study also focused on the effects of support settlements on the load-carrying capacity and on the collapse mechanism of deteriorated bridges. It was found that, even with only a slight differential settlement support, the bridge model with a localized corroded diagonal element reached its ultimate capacity much earlier in the loading process than the bridge with fixed boundaries, with a reduction of the original load-carrying capacity of about 15%.

Dynamic fracture of metals is a fascinating multiphysics-multiscale problem that often results in brittle and/or ductile fracture of structural components. Additionally, under high strain rates such as impact or blast loads, a failure phenomena known as shear banding may also occur, which is a common precursor to fracture. Both fracture and shear banding are instability processes leading to strong discontinuities and strain localization, respectively. Namely, shear bands are zones of highly localized plastic deformation, while brittle/ductile cracks are material discontinuities due to cleavage and/or void coalescence. Furthermore, while fracture events are mostly driven by triaxial tensile loading, shear bands are driven by shear heating caused by inelastic deformations and high temperature rise. In this work, fracture is modeled through a phase field formulation coupled to a set of equations that describe shear bands. While fracture is governed by a strong length scale that propagates at a fast time scale, shear bands are dominated by a weak length scale and propagate slower. These are two different failure modes with distinct spatial and temporal scales. This thesis is aimed at the development of analytical and numerical methods to determine the onset of both shear band localization and fracture. The main contribution of this thesis is the formulation of analytical criteria, based on the linear perturbation method, for the onset of fracture and shear band instabilities. We first propose a stability framework for shear bands that account for a non-constant Taylor Quinney coefficient. In addition, we apply the linear perturbation method to the phase field formulation of fracture to study the onset of unstable crack growth. The derivations lead to an analytical, energy based criterion for the phase field method in linear elastic and visco-plastic materials. The stability criterion not only recovers the critical stress value reported in the literature for simple elastic cases but also provides a criterion for visco-plastic materials with a general degradation function and fracture induced by cold-work. Finally, we analyze the physical stability of both failure modes and their interaction. The analysis provides insight into the dominant failure mode and can be used as a criterion for mesh refinement. Several numerical results with different geometries and a range of strain rate loadings demonstrate that the stability criterion predicts well the onset of failure instability in dynamic fracture applications. For the example problems considered, if a fracture instability precedes shear banding, a brittle-like failure mode is observed, while if a shear band instability is initiated significantly before fracture, a ductile-like failure mode is expected. In any case, fracture instability is stronger than a shear band instability and if initiated will dominate the response. Another contribution of this thesis is the development of numerical type stability methods based on the discretized model which can be employed within any finite element method. In this approach, a novel methodology to determine the onset of shear band localization is proposed, by casting the instability analysis as a generalized eigenvalue problem with a particular decomposition of the element Jacobian matrix. We show that this approach is attractive, as it is applicable to general rate dependent multidimensional cases and no special simplifying assumptions ought to be made. Furthermore, this technique is also applied to the fully coupled dynamic fracture problem and is shown to agree well with the analytical criteria. Finally, we propose an alternative for identifying the instability point following a generalized stability analysis concept. In this framework, a stability measure is obtained by computing the instantaneous growth rate of the vector tangent to the solution. Such an approach is more appropriate for non-orthogonal problems and is easier to generalize to difficult dynamic fracture problems.

Stability of a simple elastic structure, namely a Chilver structure, is to be investigated. The study will concentrate on the effect of structural imperfections on the critical load of the structure. A computer program will be developed to search for the critical direction of the imperfection,i.e., the direction in which the load carrying capacity of the structure is a minimum for any given amplitude of the imperfection. This study will help structural engineers understand the behavior of imperfect structures.Ball State UniversityMuncie, IN 47306

Thesis (M.S.)--Mississippi State University. Department of Aerospace Engineering. / Title from title screen. Includes bibliographical references.

Thesis (M.E.-Res.)--University of Wollongong, 2008. / Typescript. Includes bibliographical references: leaf 163-172.