Buckling strength of adhesively-bonded single and double-strap repairs on carbon-epoxy structures

This work reports on an experimental and finite element method (FEM) parametric study of adhesively-bonded single and double-strap repairs on carbon-epoxy structures under buckling unrestrained compression. The influence of the overlap length and patch thickness was evaluated. This loading gains a particular significance from the additional characteristic mechanisms of structures under compression, such as fibres microbuckling, for buckling restrained structures, or global buckling of the assembly, if no transverse restriction exists. The FEM analysis is based on the use of cohesive elements including mixed-mode criteria to simulate a cohesive fracture of the adhesive layer. Trapezoidal laws in pure modes I and II were used to account for the ductility of most structural adhesives. These laws were estimated for the adhesive used from double cantilever beam (DCB) and end-notched flexure (ENF) tests, respectively, using an inverse technique. The pure mode III cohesive law was equalled to the pure mode II one. Compression failure in the laminates was predicted using a stress-based criterion. The accurate FEM predictions open a good prospect for the reduction of the extensive experimentation in the design of carbon-epoxy repairs. Design principles were also established for these repairs under buckling.

Mode I fracture of sheet metal

The perceived wisdom about thin sheet fracture is that (i) the crack propagates under mixed mode I & III giving rise to a slant through-thickness fracture profile and (ii) the fracture toughness remains constant at low thickness and eventually decreases with increasing thickness. In the present study, fracture tests performed on thin DENT plates of various thicknesses made of stainless steel, mild steel, 6082-O and NS4 aluminium alloys, brass, bronze, lead, and zinc systematically exhibit (i) mode I “bath-tub”, i.e. “cup & cup”, fracture profiles with limited shear lips and significant localized necking (more than 50% thickness reduction), (ii) a fracture toughness that linearly increases with increasing thickness (in the range of 0.5–5 mm). The different contributions to the work expended during fracture of these materials are separated based on dimensional considerations. The paper emphasises the two parts of the work spent in the fracture process zone: the necking work and the “fracture” work. Experiments show that, as expected, the work of necking per unit area linearly increases with thickness. For a typical thickness of 1 mm, both fracture and necking contributions have the same order of magnitude in most of the metals investigated. A model is developed in order to independently evaluate the work of necking, which successfully predicts the experimental values. Furthermore, it enables the fracture energy to be derived from tests performed with only one specimen thickness. In a second modelling step, the work of fracture is computed using an enhanced void growth model valid in the quasi plane stress regime. The fracture energy varies linearly with the yield stress and void spacing and is a strong function of the hardening exponent and initial void volume fraction. The coupling of the two models allows the relative contributions of necking versus fracture to be quantified with respect to (i) the two length scales involved in this problem, i.e. the void spacing and the plate thickness, and (ii) the flow properties of the material. Each term can dominate depending on the properties of the material which explains the different behaviours reported in the literature about thin plate fracture toughness and its dependence with thickness.

A probabilistic analysis of the future potential of evaporative cooling systems in a temperate climate

The probabilistic projections of climate change for the United Kingdom (UK Climate Impacts Programme) show a trend towards hotter and drier summers. This suggests an expected increase in cooling demand for buildings – a conflicting requirement to reducing building energy needs and related CO2 emissions. Though passive design is used to reduce thermal loads of a building, a supplementary cooling system is often necessary. For such mixed-mode strategies, indirect evaporative cooling is investigated as a low energy option in the context of a warmer and drier UK climate. Analysis of the climate projections shows an increase in wet-bulb depression; providing a good indication of the cooling potential of an evaporative cooler. Modelling a mixed-mode building at two different locations, showed such a building was capable of maintaining adequate thermal comfort in future probable climates. Comparing the control climate to the scenario climate, an increase in the median of evaporative cooling load is evident. The shift is greater for London than for Glasgow with a respective 71.6% and 3.3% increase in the median annual cooling load. The study shows evaporative cooling should continue to function as an effective low-energy cooling technique in future, warming climates.

Numerical analysis of mixe-mode fracture of brickwork masonry with embedded discontinuity elements

One of the common pathologies of brickwork masonry structural elements and walls is the cracking associated with the differential settlements and/or excessive deflections of the slabs along the life of the structure. The scarce capacity of the masonry in order to accompany the structural elements that surround it, such as floors, beams or foundations, in their movements makes the brickwork masonry to be an element that frequently presents this kind of problem. This problem is a fracture problem, where the wall is cracked under mixed mode fracture: tensile and shear stresses combination, under static loading. Consequently, it is necessary to advance in the simulation and prediction of brickwork masonry mechanical behaviour under tensile and shear loading. The quasi-brittle behaviour of the brickwork masonry can be studied using the cohesive crack model whose application to other quasibrittle materials like concrete has traditionally provided very satisfactory results.

Estudio numérico y experimental del efecto de tamaño en modo mixto de los paneles de yeso laminado y lana de roca

Los paneles sándwich de yeso laminado y lana de roca presentan una abundante patología de fisuración debida a flechas excesivas de forjados. Existe, por tanto, la necesidad de avanzar en la simulación y predicción de comportamiento bajo solicitaciones de tracción y cortante de ese tipo de paneles, a pesar de que en las aplicaciones habituales no tienen responsabilidad estructural. El comportamiento de este material puede ser considerado cuasi-frágil, y en base a ello en este trabajo ha sido estudiado haciendo uso de modelos de fisura cohesiva, cuya aplicación a otros materiales cuasifrágiles, como el hormigón, ha aportado resultados muy satisfactorios. En esta comunicación se presenta el trabajo realizado para estudiar el efecto del tamaño del elemento de yeso laminado y lana de roca en su comportamiento mecánico-resistente. Para ello se diseñó una campaña de ensayos en modo mixto sobre probetas de diferente tamaño. Se han realizado ensayos de flexión en tres puntos en modo mixto de unas probetas entalladas, geométricamente similares y de diferente tamaño, obteniéndose las curvas carga-desplazamiento y cargaabertura de la boca de la entalla. Para simular numéricamente el comportamiento en fractura del panel en modo mixto se ha utilizado un modelo de elementos finitos con fisura embebida basado en la fisura cohesiva en el que se introducen como entrada los parámetros obtenidos a partir de la experimentación de trabajos anteriores, obteniéndose un buen ajuste. En función de estos resultados se analiza el efecto del tamaño en los paneles. Sandwich panels of laminated gypsum and rockwool have an abundant pathology of cracking due to excessive slabs deflection. Therefore, it is necessary to progress in the simulation and prediction of behaviour under tensile and shear load of such panels, although in typical applications have no structural responsability. The behaviour of this material may be considered quasi-brittle and, based on this idea, in this work has been studied using a cohesive crack model that has been applied to other quasi-brittle materials, such as concrete, and has provided very satisfactory results. This communication presents the work carried out to study the size effect of the specimen of plasterboard and rockwool in its mechanical and resistant behaviour. The authors designed an experimental campaign under mixed mode composed by testing specimens of different sizes. Assymetrical three-point bending tests have been performed on notched specimens, geometrically similar and of different size, to obtain load-displacement and load-crack moutn opening displacement curves. To numerically simulate the mixed-mode fracture behaviour of the panels we have used a finite element model with embedded crack, based on the cohesive crack model, using as input the experimental parameters obtained in previous work, obtaining a good adjustment. Based on these results we analyze the size effect of the panels

Estudio numérico y experimental del efecto de tamaño en modo mixto de los paneles de yeso laminado y lana de roca

Los paneles sándwich de yeso laminado y lana de roca presentan una abundante patología de fisuración debida a flechas excesivas de forjados. Existe, por tanto, la necesidad de avanzar en la simulación y predicción de comportamiento bajo solicitaciones de tracción y cortante de ese tipo de paneles, a pesar de que en las aplicaciones habituales no tienen responsabilidad estructural. El comportamiento de este material puede ser considerado cuasi-frágil, y en base a ello en este trabajo ha sido estudiado haciendo uso de modelos de fisura cohesiva, cuya aplicación a otros materiales cuasifrágiles, como el hormigón, ha aportado resultados muy satisfactorios. En esta comunicación se presenta el trabajo realizado para estudiar el efecto del tamaño del elemento de yeso laminado y lana de roca en su comportamiento mecánico-resistente. Para ello se diseñó una campaña de ensayos en modo mixto sobre probetas de diferente tamaño. Se han realizado ensayos de flexión en tres puntos en modo mixto de unas probetas entalladas, geométricamente similares y de diferente tamaño, obteniéndose las curvas carga-desplazamiento y cargaabertura de la boca de la entalla. Para simular numéricamente el comportamiento en fractura del panel en modo mixto se ha utilizado un modelo de elementos finitos con fisura embebida basado en la fisura cohesiva en el que se introducen como entrada los parámetros obtenidos a partir de la experimentación de trabajos anteriores, obteniéndose un buen ajuste. En función de estos resultados se analiza el efecto del tamaño en los paneles. Sandwich panels of laminated gypsum and rockwool have an abundant pathology of cracking due to excessive slabs deflection. Therefore, it is necessary to progress in the simulation and prediction of behaviour under tensile and shear load of such panels, although in typical applications have no structural responsability. The behaviour of this material may be considered quasi-brittle and, based on this idea, in this work has been studied using a cohesive crack model that has been applied to other quasi-brittle materials, such as concrete, and has provided very satisfactory results. This communication presents the work carried out to study the size effect of the specimen of plasterboard and rockwool in its mechanical and resistant behaviour. The authors designed an experimental campaign under mixed mode composed by testing specimens of different sizes. Assymetrical three-point bending tests have been performed on notched specimens, geometrically similar and of different size, to obtain load-displacement and load-crack moutn opening displacement curves. To numerically simulate the mixed-mode fracture behaviour of the panels we have used a finite element model with embedded crack, based on the cohesive crack model, using as input the experimental parameters obtained in previous work, obtaining a good adjustment. Based on these results we analyze the size effect of the panels.

Modelización tridimensional de ensayos de adherencia tipo viga del refuerzo NSM-FRP en hormigón

El uso de refuerzos NSM‐FRP en estructuras de hormigón armado se ha incrementado considerablemente en los últimos años como método de refuerzo estructural. Los ensayos de arrancamiento en viga de los refuerzos NSM‐FRP permiten el estudio del comportamiento de la unión pegada. El principal objetivo del presente trabajo aborda la simulación numérica de este tipo de ensayos, con el propósito de caracterizar correctamente la adherencia entre las barras de NSM‐FRP y el hormigón. En una fase inicial se simuló un modelo bidimensional para conseguir evaluar y verificar el comportamiento de los elementos cohesivos y ver su comportamiento primero ante diferentes modelos de material y segundo ante un modo mixto de fallo, debido a la aplicación simultanea de carga axial y carga cortante. En una segunda fase se creó un modelo tridimensional para estudiar el arrancamiento de una barra de material compuesto insertada en hormigón, creando un modelo de material de hormigón y viendo el comportamiento cualitativo del sistema ante variaciones en los parámetros de los diferentes materiales. En la tercera fase, la más importante del presente trabajo, se abordó la simulación numérica del ensayo de arrancamiento en viga. Se simularon todos los componentes del ensayo y se evaluaron diferentes alternativas para representar la interfase NSM‐FRP ‐ hormigón, usando elementos cohesivos y diferentes distribuciones de los mismos en la interfase. Para conseguir representar lo más fielmente posible las condiciones del ensayo, se diseñó también un controlador PID que permite realizar las simulaciones numéricas mediante un control en desplazamientos, lo cual permite capturar más correctamente el comportamiento de reblandecimiento de la unión pegada. El controlador PID aplica técnicas de ingeniería de control para conseguir calcular a priori la amplitud necesaria del desplazamiento impuesto que provoque una evolución establecida en una variable interna del sistema. La variable usada para correlacionar los ensayos es la diferencia en desplazamientos entre dos puntos y se escoge una evolución lineal de la misma, pero en la tesis también se exponen los resultados de escoger otras posibles variables internas con diferentes evoluciones. Se compararon las simulaciones numéricas con resultados de mediciones experimentales previamente publicadas. Los resultados carga‐deslizamiento obtenidos encajan bien con los datos experimentales. El modelo propuesto es también capaz de predecir el modo de fallo en la interfase NSM‐FRP ‐ hormigón. Finalmente, también se han llevado a cabo estudios paramétricos, para evaluar la influencia de cada parámetro en los resultados. También se realizó un estudio cualitativo de cómo se comporta la unión pegada en cada momento de la simulación, mediante el uso macros y gráficas tridimensionales, para conseguir una mejor visualización y facilitar el análisis de los resultados. ABSTRACT The use of near‐surface mounted FRP reinforcement in reinforced concrete structures has seen a considerable increase in recent years as a strengthening method. Beam pull‐out tests for near‐surface reinforcement allow obtaining the local bond‐slip behavior of a bonded joint. The main objective of the current work deals with the three‐dimensional modeling of this kind of test with the purpose of characterizing suitably the mechanics of bond between FRP rods and concrete. In an initial stage, a two bidimensional in order to evaluate and to verify the behavior of the cohesive elements. Its behavior was evaluated first testing different material models and second testing the behavior when mixed mode failure appears, due to simultaneous axial and shear load. In a second stage a tridimensional model was created in order to study the pull‐out of an inserted beam of composite material in concrete. A concrete material model was created and the influence of each material parameter was studied qualitatively. The third part, the most relevant of the present work, the numerical simulation of the Beam Pull‐Out test was faced. All the parts of the Beam Pull‐Out test were included inthe simulation and different alternatives to represent the FRP bar – concrete interface have been evaluated, using cohesive elements and different distributions of them. In order to reproduce the test conditions more reliably, a PID controller has also been designed to conduct suitably the numerical tests in order to properly capture the softening branch of the load‐slip behaviour. The PID controller applies control techniques to calculate a priori the necessary amplitude of the load in order to achieve a given evolution through the simulation of an internal variable previously chosen. The variable used in order to correlate the simulation with the test results is the difference in displacements between two points and a linear evolution was chosen, but in the thesis the results of choosing other possible internal variables with different evolutions are also shown. The numerical FE simulations were compared with experimental measurements previously published. Load‐slip predictions compare well with the corresponding experimental data. The proposed model is also able to predict the failure mode at the FRP‐concrete interface. Some parametric studies have also been carried out, in order to evaluate the influence of each material parameter in the results. A qualitative study of the behaviour of the joint was also performed, using the results of the numeric simulations and through the use of macros and 3D graphs, the tensional state of each point of the joint can be visualized in each moment of the simulation.

Travel mode special reports: based on data from 1990 Nationwide Personal Transportation Survey (NPTS).

Federal Highway Administration, Washington, D.C.

Analysis of intercity modal split models. Final report.

Transportation Department, Office of the Assistant Secretary for Policy and International Affairs, Washington, D.C.

Forecasting auto ownership and mode choice for U.S. metropolitan areas. Volume II: model equations. Final report.

Transportation Department, Office of University Research, Washington, D.C.

Delamination Arrestment in Bonded-Bolted Composite Structures by Fasteners

Thesis (Ph.D.)--University of Washington, 2016-06

Application of the finite element method to problems in fracture mechanics

Numerical techniques have been finding increasing use in all aspects of fracture mechanics, and often provide the only means for analyzing fracture problems. The work presented here, is concerned with the application of the finite element method to cracked structures. The present work was directed towards the establishment of a comprehensive two-dimensional finite element, linear elastic, fracture analysis package. Significant progress has been made to this end, and features which can now be studied include multi-crack tip mixed-mode problems, involving partial crack closure. The crack tip core element was refined and special local crack tip elements were employed to reduce the element density in the neighbourhood of the core region. The work builds upon experience gained by previous research workers and, as part of the general development, the program was modified to incorporate the eight-node isoparametric quadrilateral element. Also. a more flexible solving routine was developed, and provided a very compact method of solving large sets of simultaneous equations, stored in a segmented form. To complement the finite element analysis programs, an automatic mesh generation program has been developed, which enables complex problems. involving fine element detail, to be investigated with a minimum of input data. The scheme has proven to be versati Ie and reasonably easy to implement. Numerous examples are given to demonstrate the accuracy and flexibility of the finite element technique.

Shear induced toughening in bonded joints:experiments and analysis

Bonded joint specimens were fabricated from composite adherends and either an epoxy or a urethane adhesive. In mixed-mode fracture experiments, the epoxy bonded specimens generally failed by subinterfacial fracture in the composite, while specimens bonded with urethane failed very close to the adhesive/substrate interface. For the epoxy bonded specimens, fracture toughness did not change significantly with mode-mix, but for urethane bonded joints, fracture toughness increased with increasing shear load. Finite element analysis, which modeled specimens bonded with the two adhesives, showed similar trends. The different toughening behaviors for the two bonded joints can be attributed to dissipation of energy through inelastic deformation, which was insignificant in the epoxy-bonded joints but substantial when the urethane was used as the bonding agent.

The role of material characterisation in the crush modelling of thermoplastic composite structures

The predictive capability of high fidelity finite element modelling, to accurately capture damage and crush behaviour of composite structures, relies on the acquisition of accurate material properties, some of which have necessitated the development of novel approaches. This paper details the measurement of interlaminar and intralaminar fracture toughness, the non-linear shear behaviour of carbon fibre (AS4)/thermoplastic Polyetherketoneketone (PEKK) composite laminates and the utilisation of these properties for the accurate computational modelling of crush. Double-cantilever-beam (DCB), four-point end-notched flexure (4ENF) and Mixed-mode bending (MMB) test configurations were used to determine the initiation and propagation fracture toughness in mode I, mode II and mixed-mode loading, respectively. Compact Tension (CT) and Compact Compression (CC) test samples were employed to determine the intralaminar longitudinal tensile and compressive fracture toughness. V-notched rail shear tests were used to measure the highly non-linear shear behaviour, associated with thermoplastic composites, and fracture toughness. Corresponding numerical models of these tests were developed for verification and yielded good correlation with the experimental response. This also confirmed the accuracy of the measured values which were then employed as input material parameters for modelling the crush behaviour of a corrugated test specimen.

Experimental and analytical study of cracks under biaxial fatigue

Most mechanical components experience multi-axial cyclic loading conditions during service. Experimental analysis of fatigue cracks under such conditions is not easy and most works tend to focus more on the simpler but less realistic case of uni-axial loading. Consequently, there are many uncertainties related to the load sequence effect that are now well known and are not normally incorporated into the growth models. The current work presents a new methodology for evaluating overload effect in biaxial fatigue cracks. The methodology includes evaluation of mixed-mode (KI and KII) stress intensity factor and the Crack Opening Displacement for samples with and without overload cycle under biaxial loading. The methodology is tested under a range of crack lengths. All crack-tip information is obtained with a hybrid methodology that combines experimental full-field digital image correlation data and Williams' elastic model describing the crack-tip field.