Strap repairs using embedded patches: numerical analysis and experimental results

Adhesively bonded repairs offer an attractive option for repair of aluminium structures, compared to more traditional methods such as fastening or welding. The single-strap (SS) and double-strap (DS) repairs are very straightforward to execute but stresses in the adhesive layer peak at the overlap ends. The DS repair requires both sides of the damaged structures to be reachable for repair, which is often not possible. In strap repairs, with the patches bonded at the outer surfaces, some limitations emerge such as the weight, aerodynamics and aesthetics. To minimize these effects, SS and DS repairs with embedded patches were evaluated in this work, such that the patches are flush with the adherends. For this purpose, in this work standard SS and DS repairs, and also with the patches embedded in the adherends, were tested under tension to allow the optimization of some repair variables such as the overlap length (LO) and type of adhesive, thus allowing the maximization of the repair strength. The effect of embedding the patch/patches on the fracture modes and failure loads was compared with finite elements (FE) analysis. The FE analysis was performed in ABAQUS® and cohesive zone modelling was used for the simulation of damage onset and growth in the adhesive layer. The comparison with the test data revealed an accurate prediction for all kinds of joints and provided some principles regarding this technique.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

Introducing numerical analysis tools in engineering: a Scilab user case in electronics course

Software tools in education became popular since the widespread of personal computers. Engineering courses lead the way in this development and these tools became almost a standard. Engineering graduates are familiar with numerical analysis tools but also with simulators (e.g. electronic circuits), computer assisted design tools and others, depending on the degree. One of the main problems with these tools is when and how to start use them so that they can be beneficial to students and not mere substitutes for potentially difficult calculations or design. In this paper a software tool to be used by first year students in electronics/electricity courses is presented. The growing acknowledgement and acceptance of open source software lead to the choice of an open source software tool – Scilab, which is a numerical analysis tool – to develop a toolbox. The toolbox was developed to be used as standalone or integrated in an e-learning platform. The e-learning platform used was Moodle. The first approach was to assess the mathematical skills necessary to solve all the problems related to electronics and electricity courses. Analysing the existing circuit simulators software tools, it is clear that even though they are very helpful by showing the end result they are not so effective in the process of the students studying and self learning since they show results but not intermediate steps which are crucial in problems that involve derivatives or integrals. Also, they are not very effective in obtaining graphical results that could be used to elaborate reports and for an overall better comprehension of the results. The developed tool was based on the numerical analysis software Scilab and is a toolbox that gives their users the opportunity to obtain the end results of a circuit analysis but also the expressions obtained when derivative and integrals calculations, plot signals, obtain vector diagrams, etc. The toolbox runs entirely in the Moodle web platform and provides the same results as the standalone application. The students can use the toolbox through the web platform (in computers where they don't have installation privileges) or in their personal computers by installing both the Scilab software and the toolbox. This approach was designed for first year students from all engineering degrees that have electronics/electricity courses in their curricula.

Solving a signalized traffic intersection problem with an hyperbolic penalty function

Mathematical Program with Complementarity Constraints (MPCC) finds many applications in fields such as engineering design, economic equilibrium and mathematical programming theory itself. A queueing system model resulting from a single signalized intersection regulated by pre-timed control in traffic network is considered. The model is formulated as an MPCC problem. A MATLAB implementation based on an hyperbolic penalty function is used to solve this practical problem, computing the total average waiting time of the vehicles in all queues and the green split allocation. The problem was codified in AMPL.

Adhesively-bonded repair proposal for wood members damaged by horizontal shear using carbon-epoxy patches

In this work, a repair technique with adhesively bonded carbon-epoxy patches is proposed for wood members damaged by horizontal shear and under bending loads. This damage is characterized by horizontal crack growth near the neutral plane of the wood beam, normally originating from checks and shakes. The repair consists of adhesively bonded carbon-epoxy patches on the vertical side faces of the beam at the cracked region to block sliding between the beam arms. An experimental and numerical parametric analysis was performed on the patch length. The numerical analysis used the finite element method (FEM) and cohesive zone models (CZMs), with an inverse modelling technique for the characterization of the adhesive layer. Trapezoidal cohesive laws in each pure mode were used to account for the ductility of the adhesive used. To fully reproduce the tests, horizontal damage propagation within the wood beam was also simulated. A good correlation with the experiments was found. Regarding the effectiveness of the repair, for the conditions selected for this work, a full strength recovery was achieved for the bigger value of patch length tested.

The influence of the boundary conditions on low-velocity impact composite damage

The objective of this work was to study the influence of the boundary conditions on low-velocity impact behaviour of carbon-epoxy composite plates. Experimental work and numerical analysis were performed on [04,904]s laminates. The influence of different boundary conditions on the impacted plates was analysed considering rectangular and square plates. The X-radiography was used as a non-destructive technique to evaluate the internal damage caused by impact loading. A three-dimensional numerical analysis was also performed considering progressive damage modelling. The model includes three-dimensional solid elements and interface finite elements including a cohesive mixed-mode damage model, which allows simulating delamination between different oriented layers. It was verified that plate’s boundary conditions have influence on the delaminated area. Good agreement between experimental and numerical analysis for shape, orientation and size of the delamination was obtained.

Estudo de reparações adesivas pela técnica de remendo embebido

A reparação de estruturas é um tema de primordial importância, por forma a evitar a sua substituição após a existência de dano, na medida em que permite uma redução substancial de custos associados. Entre os métodos mais comuns de reparação encontram-se a aplicação de remendos aparafusados ou as reparações adesivas. Estas últimas permitem uma diminuição das concentrações de tensões e uma aplicação mais simples, entre outras vantagens. O objetivo do tema de mestrado proposto é o estudo experimental e numérico de reparações adesivas para estruturas de alumínio pela técnica do remendo embebido. A parte experimental do trabalho consiste na fabricação e teste à tração de reparações em escala reduzida em função de alguns parâmetros pré-definidos como o ângulo das superfícies de contacto e o adesivo a utilizar, no sentido de otimização das respetivas reparações. O trabalho numérico consiste na simulação em software de Elementos Finitos ABAQUS® das várias soluções testadas, para avaliação da distribuição de campos de tensões e previsão da rotura das reparações por remendo embebido. No global, observou-se uma elevada correlação entre os resultados experimentais e as previsões numéricas, o que valida a ferramenta numérica utilizada para efeitos de previsão da rotura para reparações de remendo embebido e a utilização do mesmo para a escolha do melhor ângulo a utilizar em função da restituição de resistência pretendida.

Estruturas de suporte de terras executadas com pneus

O aproveitamento de pneus em fim de vida revela ser uma alternativa eficaz e promissora na indústria da construção civil, na utilização deste resíduo em muros de suporte. O presente trabalho tem como principal objetivo a apresentação de uma técnica de aproveitamento de pneus em fim de vida na execução de muros de gravidade, combinando solo e pneus. Neste sentido, tomou-se como referência um estudo realizado no Brasil por Sieira, Sayão, Medeiros e Gerscovich, para avaliar a eficiência e o custo deste tipo de estruturas, comparando-o com um muro de suporte tradicional de betão simples. Inicialmente, avaliou-se a segurança do muro de solo-pneus, de acordo com a metodologia proposta no Eurocódigo 7 (NP EN 1997-1, 2010), considerando a geometria e as características dos materiais apresentados no estudo referido e usando o programa de cálculo automático Slide, da Rocscience, para a verificação da estabilidade global. Reproduziu-se a análise numérica realizada no âmbito do caso de estudo brasileiro de referência, recorrendo também a uma formulação por elementos finitos com o programa de cálculo automático Phase2, da Rocscience. Por último, utilizando uma vez mais o programa Slide, definiu-se a geometria de um muro de betão simples cuja geometria garantisse o mesmo valor do fator de segurança à estabilidade global, obtido com o muro de solo-pneus e compararam-se os custos respetivos. O presente trabalho confirmou a eficiência e o baixo custo desta solução construtiva, sendo necessários, no entanto, estudos mais detalhados que reforcem estas conclusões.

Saving energy in the GFRP pultrusion process

This study addresses to the optimization of pultrusion manufacturing process from the energy-consumption point of view. The die heating system of external platen heaters commonly used in the pultrusion machines is one of the components that contribute the most to the high consumption of energy of pultrusion process. Hence, instead of the conventional multi-planar heaters, a new internal die heating system that leads to minor heat losses is proposed. The effect of the number and relative position of the embedded heaters along the die is also analysed towards the setting up of the optimum arrangement that minimizes both the energy rate and consumption. Simulation and optimization processes were greatly supported by Finite Element Analysis (FEA) and calibrated with basis on the temperature profile computed through thermography imaging techniques. The main outputs of this study allow to conclude that the use of embedded cylindrical resistances instead of external planar heaters leads to drastic reductions of both the power consumption and the warm-up periods of the die heating system. For the analysed die tool and process, savings on energy consumption up to 60% and warm-up period stages less than an half hour were attained with the new internal heating system. The improvements achieved allow reducing the power requirements on pultrusion process, and thus minimize industrial costs and contribute to a more sustainable pultrusion manufacturing industry.

A framework for using real data with distributed low cost sensors

Currently, due to the widespread use of computers and the internet, students are trading libraries for the World Wide Web and laboratories with simulation programs. In most courses, simulators are made available to students and can be used to proof theoretical results or to test a developing hardware/product. Although this is an interesting solution: low cost, easy and fast way to perform some courses work, it has indeed major disadvantages. As everything is currently being done with/in a computer, the students are loosing the “feel” of the real values of the magnitudes. For instance in engineering studies, and mainly in the first years, students need to learn electronics, algorithmic, mathematics and physics. All of these areas can use numerical analysis software, simulation software or spreadsheets and in the majority of the cases data used is either simulated or random numbers, but real data could be used instead. For example, if a course uses numerical analysis software and needs a dataset, the students can learn to manipulate arrays. Also, when using the spreadsheets to build graphics, instead of using a random table, students could use a real dataset based, for instance, in the room temperature and its variation across the day. In this work we present a framework which uses a simple interface allowing it to be used by different courses where the computers are the teaching/learning process in order to give a more realistic feeling to students by using real data. A framework is proposed based on a set of low cost sensors for different physical magnitudes, e.g. temperature, light, wind speed, which are connected to a central server, that the students have access with an Ethernet protocol or are connected directly to the student computer/laptop. These sensors use the communication ports available such as: serial ports, parallel ports, Ethernet or Universal Serial Bus (USB). Since a central server is used, the students are encouraged to use sensor values results in their different courses and consequently in different types of software such as: numerical analysis tools, spreadsheets or simply inside any programming language when a dataset is needed. In order to do this, small pieces of hardware were developed containing at least one sensor using different types of computer communication. As long as the sensors are attached in a server connected to the internet, these tools can also be shared between different schools. This allows sensors that aren't available in a determined school to be used by getting the values from other places that are sharing them. Another remark is that students in the more advanced years and (theoretically) more know how, can use the courses that have some affinities with electronic development to build new sensor pieces and expand the framework further. The final solution provided is very interesting, low cost, simple to develop, allowing flexibility of resources by using the same materials in several courses bringing real world data into the students computer works.

Estudo comparativo da resistência à tração de juntas adesivas de sobreposição simples e dupla

O método de união com ligações adesivas está cada vez mais a ser utilizado na conceção de estruturas mecânicas, por causa das vantagens significativas desta técnica em comparação com as ligações tradicionais. De facto, as juntas com ligação adesiva estão sob investigação intensa há bastante tempo. Entre as vantagens, destaca-se a redução de peso e possibilidade de unir diferentes materiais, incluindo compósitos, sem danificar as estruturas a ligar. Os adesivos comerciais variam desde resistentes e frágeis (por exemplo, Araldite® AV138) a menos resistentes e dúcteis (por exemplo, Araldite® 2015). Uma nova família de adesivos de poliuretano combina elevada resistência e ductilidade (por exemplo, Sikaforce® 7888). Este trabalho compara o desempenho à tração dos três adesivos supracitados, em juntas de alumínio (Al6082-T651) de sobreposição simples e dupla, com variação dos valores de comprimento de sobreposição (LO). A análise numérica de modelos de dano coesivo (MDC) foi realizada para analisar as tensões de arrancamento (oy) e as de corte (txy) na camada adesiva, para estudar a variável de dano do MDC durante o processo de rotura e para avaliar a capacidade MDC na previsão da resistência da junta. A análise da resistência e da variável de dano ajudou na compreensão das diferenças entre os adesivos no que se refere ao processo de rotura e resistência da junta. Observou-se que as juntas de sobreposição dupla apresentam uma distribuição de tensões bastante mais favorável relativamente às juntas de sobreposição simples, principalmente devido à eliminação da flexão do substrato interior. Como resultado, a resistência destas juntas foi tipicamente superior ao dobro da observada para as juntas de sobreposição simples, com exceção de algumas configurações de junta em que houve plastificação extensa ou mesmo rotura dos substratos por tração. O trabalho proposto permitiu também concluir que as previsões MDC são tipicamente precisas, e qual a família de adesivos é mais adequada para cada configuração de junta, com a clara vantagem para o Sikaforce® 7888. Como resultado deste trabalho, foram propostas diretrizes de conceção para juntas adesivas.

Estudo da resistência de juntas adesivas em L entre alumínio e material compósito

As ligações adesivas são frequentemente utilizadas na fabricação de estruturas complexas que não poderiam ou não seriam tão fáceis de ser fabricadas numa só peça, a fim de proporcionar uma união estrutural que, teoricamente, deve ser pelo menos tão resistente como o material de base. As juntas adesivas têm vindo a substituir métodos como a soldadura, e ligações parafusadas e rebitadas, devido à facilidade de fabricação, menor custo, facilidade em unir materiais diferentes, melhor resistência, entre outras características. Os materiais compósitos reforçados com fibra de carbono são amplamente utilizados em muitas indústrias, tais como de construção de barcos, automóvel e aeronáutica, sendo usados em estruturas que requerem elevada resistência e rigidez específicas, o que reduz o peso dos componentes, mantendo a resistência e rigidez necessárias para suportar as diversas cargas aplicadas. Embora estes métodos de fabricação reduzam ao máximo as ligações através de técnicas de fabrico avançadas, estas ainda são necessárias devido ao tamanho dos componentes, limitações de projecto tecnológicas e logísticas. Em muitas estruturas, a combinação de compósitos com metais tais como alumínio ou titânio traz vantagens de projecto. Este trabalho tem como objectivo estudar, experimentalmente e por modelos de dano coesivo (MDC), juntas adesivas em L entre componentes de alumínio e compósito de carbono epóxido quando solicitados a forças de arrancamento, considerando diferentes configurações de junta e adesivos de ductilidade distinta. Os parâmetros geométricos abordados são a espessura do aderente de alumínio (tP2) e comprimento de sobreposição (LO). A análise numérica permitiu o estudo da distribuição das tensões, evolução do dano, resistência e modos de rotura. Os testes experimentais validam os resultados numéricos e fornecem mecanismos de projecto para juntas em L. Foi mostrado que a geometria do aderente em L (alumínio) e o tipo de adesivo têm uma influência directa na resistência de junta.

Adhesive selection for single lap bonded joints: Experimentation and advanced techniques for strength prediction

The integrity of multi-component structures is usually determined by their unions. Adhesive-bonding is often used over traditional methods because of the reduction of stress concentrations, reduced weight penalty, and easy manufacturing. Commercial adhesives range from strong and brittle (e.g., Araldite® AV138) to less strong and ductile (e.g., Araldite® 2015). A new family of polyurethane adhesives combines high strength and ductility (e.g., Sikaforce® 7888). In this work, the performance of the three above-mentioned adhesives was tested in single lap joints with varying values of overlap length (LO). The experimental work carried out is accompanied by a detailed numerical analysis by finite elements, either based on cohesive zone models (CZM) or the extended finite element method (XFEM). This procedure enabled detailing the performance of these predictive techniques applied to bonded joints. Moreover, it was possible to evaluate which family of adhesives is more suited for each joint geometry. CZM revealed to be highly accurate, except for largely ductile adhesives, although this could be circumvented with a different cohesive law. XFEM is not the most suited technique for mixed-mode damage growth, but a rough prediction was achieved.

Strength improvement of adhesively-bonded scarf repairs in aluminium structures with external reinforcements

Adhesively bonded techniques are an attractive option to repair aluminium structures, compared to more traditional methods. Actually, as a result of the improvement in the mechanical characteristics of adhesives, adhesive bonding has progressively replaced the traditional joining methods. There are several bonded repair configurations, as single-strap, double-strap and scarf. Compared with strap repairs, scarf repairs have the advantages of a higher efficiency and the absence of aerodynamic disturbance. The higher efficiency is caused by the elimination of the significant joint eccentricities of strap repairs. Moreover, stress distributions along the bond length are more uniform, due to tapering of the scarf edges. The main disadvantages of this technique are the difficult machining of the surfaces, associated costs and requirement of specialised labour. This work reports on an experimental and numerical study of the tensile behaviour of two-dimensional (2D) scarf repairs of aluminium structures bonded with the ductile epoxy adhesive Araldite® 2015. The numerical analysis, by Finite Elements (FE), was performed in Abaqus® and used cohesive zone models (CZM) for the simulation of damage onset and growth in the adhesive layer, thus enabling the strength prediction of the repairs. A parametric study was performed on the scarf angle (α) and different configurations of external reinforcement (applied on one or two sides of the repair, and also different reinforcement lengths). The obtained results allowed the establishment of design guidelines for repairing, showing that the use of external reinforcements enables increasing α for equal strength recovery, which makes the repair procedure easier. The numerical technique was accurate in predicting the repairs’ strength, enabling its use for design and optimisation purposes.