Crack tip stress study for elastic-perfectly plastic materials with some applications

The problems of plasticity and non-linear fracture mechanics have been generally recognized as the most difficult problems of solid mechanics. The present dissertation is devoted to some problems on the intersection of both plasticity and non-linear fracture mechanics. The crack tip is responsible for the crack growth and therefore is the focus of fracture science. The problem of crack has been studied by an army of outstanding scholars and engineers in this century, but has not, as yet, been solved for many important practical situations. The aim of this investigation is to provide an analytical solution to the problem of plasticity at the crack tip for elastic-perfectly plastic materials and to apply the solution to a classical problem of the mechanics of composite materials.^ In this work, the stresses inside the plastic region near the crack tip in a composite material made of two different elastic-perfectly plastic materials are studied. The problems of an interface crack, a crack impinging an interface at the right angle and at arbitrary angles are examined. The constituent materials are assumed to obey the Huber-Mises yielding condition criterion. The theory of slip lines for plane strain is utilized. For the particular homogeneous case these problems have two solutions: the continuous solution found earlier by Prandtl and modified by Hill and Sokolovsky, and the discontinuous solution found later by Cherepanov. The same type of solutions were discovered in the inhomogeneous problems of the present study. Some reasons to prefer the discontinuous solution are provided. The method is also applied to the analysis of a contact problem and a push-in/pull-out problem to determine the critical load for plasticity in these classical problems of the mechanics of composite materials.^ The results of this dissertation published in three journal articles (two of which are under revision) will also be presented in the Invited Lecture at the 7$\rm\sp{th}$ International Conference on Plasticity (Cancun, Mexico, January 1999). ^

Aerodynamic load characteristics evaluation and tri-axial performance testing on fiber reinforced polymer connections and metal fasteners to promote hurricane damage mitigation

Damages during extreme wind events highlight the weaknesses of mechanical fasteners at the roof-to-wall connections in residential timber frame buildings. The allowable capacity of the metal fasteners is based on results of unidirectional component testing that do not simulate realistic tri-axial aerodynamic loading effects. The first objective of this research was to simulate hurricane effects and study hurricane-structure interaction at full-scale, facilitating better understanding of the combined impacts of wind, rain, and debris on inter-component connections at spatial and temporal scales. The second objective was to evaluate the performance of a non-intrusive roof-to-wall connection system using fiber reinforced polymer (FRP) materials and compare its load capacity to the capacity of an existing metal fastener under simulated aerodynamic loads. ^ The Wall of Wind (WoW) testing performed using FRP connections on a one-story gable-roof timber structure instrumented with a variety of sensors, was used to create a database on aerodynamic and aero-hydrodynamic loading on roof-to-wall connections tested under several parameters: angles of attack, wind-turbulence content, internal pressure conditions, with and without effects of rain. Based on the aerodynamic loading results obtained from WoW tests, sets of three force components (tri-axial mean loads) were combined into a series of resultant mean forces, which were used to test the FRP and metal connections in the structures laboratory up to failure. A new component testing system and test protocol were developed for testing fasteners under simulated triaxial loading as opposed to uni-axial loading. The tri-axial and uni-axial test results were compared for hurricane clips. Also, comparison was made between tri-axial load capacity of FRP and metal connections. ^ The research findings demonstrate that the FRP connection is a viable option for use in timber roof-to-wall connection system. Findings also confirm that current testing methods of mechanical fasteners tend to overestimate the actual load capacities of a connector. Additionally, the research also contributes to the development a new testing protocol for fasteners using tri-axial simultaneous loads based on the aerodynamic database obtained from the WoW testing. ^

An energy based nanomechnical properties evaluation method for cementitious materials

Advances in multiscale material modeling of structural concrete have created an upsurge of interest in the accurate evaluation of mechanical properties and volume fractions of its nano constituents. The task is accomplished by analyzing the response of a material to indentation, obtained as an outcome of a nanoindentation experiment, using a procedure called the Oliver and Pharr (OP) method. Despite its widespread use, the accuracy of this method is often questioned when it is applied to the data from heterogeneous materials or from the materials that show pile-up and sink-in during indentation, which necessitates the development of an alternative method. ^ In this study, a model is developed within the framework defined by contact mechanics to compute the nanomechanical properties of a material from its indentation response. Unlike the OP method, indentation energies are employed in the form of dimensionless constants to evaluate model parameters. Analysis of the load-displacement data pertaining to a wide range of materials revealed that the energy constants may be used to determine the indenter tip bluntness, hardness and initial unloading stiffness of the material. The proposed model has two main advantages: (1) it does not require the computation of the contact area, a source of error in the existing method; and (2) it incorporates the effect of peak indentation load, dwelling period and indenter tip bluntness on the measured mechanical properties explicitly. ^ Indentation tests are also carried out on samples from cement paste to validate the energy based model developed herein by determining the elastic modulus and hardness of different phases of the paste. As a consequence, it has been found that the model computes the mechanical properties in close agreement with that obtained by the OP method; a discrepancy, though insignificant, is observed more in the case of C-S-H than in the anhydrous phase. Nevertheless, the proposed method is computationally efficient, and thus it is highly suitable when the grid indentation technique is required to be performed. In addition, several empirical relations are developed that are found to be crucial in understanding the nanomechanical behavior of cementitious materials.^

Effects of architectural features of air-permeable roof cladding materials on wind-induced uplift loading

Widespread damage to roofing materials (such as tiles and shingles) for low-rise buildings, even for weaker hurricanes, has raised concerns regarding design load provisions and construction practices. Currently the building codes used for designing low-rise building roofs are mainly based on testing results from building models which generally do not simulate the architectural features of roofing materials that may significantly influence the wind-induced pressures. Full-scale experimentation was conducted under high winds to investigate the effects of architectural details of high profile roof tiles and asphalt shingles on net pressures that are often responsible for damage to these roofing materials. Effects on the vulnerability of roofing materials were also studied. Different roof models with bare, tiled, and shingled roof decks were tested. Pressures acting on both top and bottom surfaces of the roofing materials were measured to understand their effects on the net uplift loading. The area-averaged peak pressure coefficients obtained from bare, tiled, and shingled roof decks were compared. In addition, a set of wind tunnel tests on a tiled roof deck model were conducted to verify the effects of tiles' cavity internal pressure. Both the full-scale and the wind tunnel test results showed that underside pressure of a roof tile could either aggravate or alleviate wind uplift on the tile based on its orientation on the roof with respect to the wind angle of attack. For shingles, the underside pressure could aggravate wind uplift if the shingle is located near the center of the roof deck. Bare deck modeling to estimate design wind uplift on shingled decks may be acceptable for most locations but not for field locations; it could underestimate the uplift on shingles by 30-60%. In addition, some initial quantification of the effects of roofing materials on wind uplift was performed by studying the wind uplift load ratio for tiled versus bare deck and shingled versus bare deck. Vulnerability curves, with and without considering the effects of tiles' cavity internal pressure, showed significant differences. Aerodynamic load provisions for low-rise buildings' roofs and their vulnerability can thus be more accurately evaluated by considering the effects of the roofing materials.

Aerodynamic Load Characteristics Evaluation and Tri-Axial Performance Testing on Fiber Reinforced Polymer Connections and Metal Fasteners to Promote Hurricane Damage Mitigation

Damages during extreme wind events highlight the weaknesses of mechanical fasteners at the roof-to-wall connections in residential timber frame buildings. The allowable capacity of the metal fasteners is based on results of unidirectional component testing that do not simulate realistic tri-axial aerodynamic loading effects. The first objective of this research was to simulate hurricane effects and study hurricane-structure interaction at full-scale, facilitating better understanding of the combined impacts of wind, rain, and debris on inter-component connections at spatial and temporal scales. The second objective was to evaluate the performance of a non-intrusive roof-to-wall connection system using fiber reinforced polymer (FRP) materials and compare its load capacity to the capacity of an existing metal fastener under simulated aerodynamic loads. The Wall of Wind (WoW) testing performed using FRP connections on a one-story gable-roof timber structure instrumented with a variety of sensors, was used to create a database on aerodynamic and aero-hydrodynamic loading on roof-to-wall connections tested under several parameters: angles of attack, wind-turbulence content, internal pressure conditions, with and without effects of rain. Based on the aerodynamic loading results obtained from WoW tests, sets of three force components (tri-axial mean loads) were combined into a series of resultant mean forces, which were used to test the FRP and metal connections in the structures laboratory up to failure. A new component testing system and test protocol were developed for testing fasteners under simulated tri-axial loading as opposed to uni-axial loading. The tri-axial and uni-axial test results were compared for hurricane clips. Also, comparison was made between tri-axial load capacity of FRP and metal connections. The research findings demonstrate that the FRP connection is a viable option for use in timber roof-to-wall connection system. Findings also confirm that current testing methods of mechanical fasteners tend to overestimate the actual load capacities of a connector. Additionally, the research also contributes to the development a new testing protocol for fasteners using tri-axial simultaneous loads based on the aerodynamic database obtained from the WoW testing.