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The analytical or numerical determination of the stress intensity factor (SIF) in cracked bodies usually assumes the body to be isolated. However, in fibre-reinforced composites, the fibre, which is the main load-carrying component, is embedded in a matrix. To clarify the effect the embedding matrix has on the SIF of the fibre, we propose a 3D computational model of an orthotropic fibre embedded in an isotropic matrix, and compute the SIF using the J-integral method. A parametric analysis based on dimensionless variables explores the effect of the fibre–matrix stiffness ratio as well as the effect of the degree of elastic orthotropy of the fibre. The results show that the SIF is strongly influenced by both factors, and that the matrix reduces the SIF by limiting the crack opening.

An analytic model has been developed for a Compact Tension specimen subjected to a controlled displacement and corresponding load within a cohesive model framework. The model is able to capture the material response while the Fracture Process Zone is being developed, obtaining the evolution of multiple variables such as the crack opening and the cohesive stresses, for an arbitrary Cohesive Law shape. The crack growth prediction based on the $${\mathcal {R}}$$ -curve and the nominal strength prediction based on Bažant’s Size Effect Law have been implemented using the output variables available from the proposed analytic model. The minimum specimen size has been found in order to properly apply $${\mathcal {R}}$$ -curve based methods. The study has concluded that only the cohesive model is able to properly capture the changes of the Specimen Geometry and Specimen Size, as unlike in other theories, no Linear Elastic Fracture Mechanics assumptions are made.

Teaching students to self-regulate enhances their mathematics performance, yet few studies have investigated the long-term differential impact of particular self-regulation strategies specifically for low-achieving students. This quasi-experimental study evaluates the effect of teaching different self-regulation strategies on mathematical problem solving in low-achieving students. The participants were 69 sixth-grade elementary school students randomly assigned to one of three experimental groups (and taught predominantly cognitive, metacognitive or volitional strategies, while verifying intervention fidelity) or a control group for 16 sessions. Mathematical problem-solving skills were evaluated prior to the intervention, upon completion, and two months later. While all three intervention groups obtained significantly better results compared to the control group immediately after the intervention, volitional and metacognitive strategies showed the strongest and most lasting positive effects. We conclude that low-achieving students could benefit from learning self-regulation strategies, particularly when these strategies take into account the affective and motivational dynamics of learning. Keywords: mathematics, metacognition, motivation, emotion, learning

Quasi-brittle materials such as fibre-reinforced composite materials develop a relatively large Fracture Process Zone where material toughening mechanisms such as matrix cracking, fibre-bridging and fibre pull-outs take place. The damage onset and damage propagation are well defined from a cohesive model point of view, although no standard procedure has been yet developed to characterize the translaminar Cohesive Law. The present work proposes an objective inverse method for obtaining the Cohesive Law with the use of an analytic model capable of predicting the load–displacement curve of a Compact Tension specimen for any arbitrary Cohesive Law shape. The softening law has been obtained for two laminates, providing an excellent agreement with the experimental results. With the obtained softening function, the nominal strengths of a Center Cracked Specimen and an Open Hole specimen have been predicted for a wide range of specimen sizes This work has been partially funded by the Spanish Government through the Ministerio de Economía y Competitividad, under contracts MAT2013-46749-R (subprogram MAT) and MAT2012-37552-C03-03

The present work addresses the damage mechanisms of polymer-based laminated composite materials under different hygrothermal conditions by means of the translaminar fracture toughness using Double Edge Notched Tensile tests of a cross-ply laminate manufactured with T800S/M21 carbon/epoxy material.Three different conditions were considered: as received-room temperature (AR/RT), wet-room temperature (WET/RT), and wet-high temperature (WET/HOT). The highest fracture toughness was for WET/HOT and the lowest for WET/RT. To observe the corresponding failure mechanisms, Scanning Electronic Microscopy (SEM) analysis was performed. The SEM inspections show that the pull-out length and the frictional coefficient are the most significant parameters that best explain the differences observed in the crack propagation and the fracture toughness. For AR/RT, the suitable adhesion between components allows stresses to be transferred from the matrix to the fibers, so the crack is practically continuous in the same failure plane and the pull-out is barely visible. However, higher pull-out lengths can be observed in WET/RT and WET/HOT, especially in the second one. For WET/RT, the crack surface shows fiber bundles at different pull-out lengths, while for WET/HOT fibers are broken individually at longer pull-out lengths. According to the moisture absorption in WET/RT and WET/HOT, a lower frictional coefficient is thought to slightly reduce the fracture toughness, which can be compared between AR/RT and WET/RT. Nevertheless, the highest fracture toughness is caused by the large pull-out lengths in WET/HOT tests, despite the reduction of the frictional coefficient The authors acknowledge the financial support of the Spanish Government under project MAT2013-46749-R. The first author would like to thank the Spanish Government for the FPI predoctoral grant BES-2010-042387 and for the mobility grant EEBBI-13-06186

In the case of very reliable materials, failures are rare events, and it is often difficult to find a sample of the product that includes instances of failure merely by analyzing feedback from experience (or performing dedicated reliability tests) in order to estimate the reliability parameters. Success often varies wildly as a function of the size of this sample. Thus, the need to understand the behavior of a long-life product before it is commissioned frequently leads to so-called accelerated life testing during the development, qualification or even production phases. This chapter presents the methodology of accelerated life testing, as well as the methods and tools used to exploit accelerated life tests, and gives a selection of examples.

The reliability of high-power mechatronic systems fundamentally depends on the reliability of film capacitors.

The purpose of this chapter is to provide the reader with an overview of the methods and modeling used in reliability prediction, that is to say, in terms of pre-project reliability. How can we quantify a failure rate for a product that is not yet on the market?

The failure of an electronic component may be described in terms of the deterioration of its electrical characteristics and is caused by modifications in the physical and chemical properties of its constituents and/or the emergence of defects. This chapter begins by discussing an experimental approach that allows these modifications to be analyzed throughout the life of a component. A description of the physicochemical techniques commonly used in laboratories is then given.

This work deals with the maximization of the fundamental frequency of laminated plates and cylinders by finding the optimal stacking sequence for symmetric and balanced laminates with neglectable bending–twisting and torsion–curvature couplings are considered. Instead of using the angle at each ply the so-called lamination parameters are used as design variables. Results for the plate problem are compared to those using analytical expressions found in the literature. The cylinder problem is solved for a large number of thickness and radius-to-length ratio combinations. Values of the optimal stacking sequence are given considering the angle can take any value between 0° and 90° or the case when the angle can only take a discrete set of values The authors acknowledge funding from the Spanish government through the Ministerio de Economía y Competitividad under contract MAT2013-46749-R

The relation between the nominal strength of open hole specimens manufactured with quasi-brittle isotropic materials with respect to the specimen size and the shape of the cohesive law is examined in the present paper. The obtained results can be used by engineers as design charts or to obtain valuable information on the failure characteristics of quasi-brittle materials.

T-bolt joints are widely used in the wind turbine industry. This paper describes the constitution and function of the different components of the joint, showing the different parameters that affect its performance, and presents a parametric analysis, useful for joint design and optimization, relating laminate thickness, bolt and cylinder diameters to pitch distance, and pretension of the bolt with external load. In order to provide information on the influence of the T-bolt geometry on the strength of the laminate in the net tension and bearing zones, tests for two different glass fiber – epoxy laminates, under different pitch/diameter ratios have been performed, forcing either bearing or tension failure modes. Stress and strain concentrations in the laminate have been estimated trough a three-dimensional finite element model that takes into account pretension effects and contact nonlinearities. How experimental results correlate with simple and finite element model analysis is discussed. Stress Point Criteria may be applied for joint tension failure with a characteristic distance of d 0 = 0.9 mm.

Materials with cellular structure are gaining prominence in recent years due to improvements in production processes, that enable the manufacture of new materials, and biomechanics, that requires mechanical analysis of cellular structures such as bones. The possibility to use the Fracture Mechanics tools developed for the continua to the fracture of cellular materials is analyzed in the present paper. As proposed by Maiti et al. the fracture toughness of cellular solids can be obtained through two procedures: taking into account the stress at crack tip or the fracture toughness of the base material. Both procedures are analyzed and the equivalent R-curve and a cohesive law is obtained in function of the cell size and structure morphology. A critical truss length exists from which crack propagation goes from being governed by the energy dissipated to being governed by the stress field.

The design of glass fibre reinforced polymer (GFRP) pultruded beams is usually governed by deformability or instability phenomena. To obtain a better use of the material properties, the GFRP profiles can be connected to concrete elements with several advantages, associated with the global stiffness and strength of the structural elements. This leads to solutions particularly useful for rehabilitation of old floors or even new construction slabs. This paper presents the results of an experimental research developed to characterize the flexural behaviour of a GFRP–concrete hybrid solution. Shear connection tests were first performed on GFRP I-profiles, connected to concrete with stainless steel bolts, to evaluate the behaviour of the shear connection. The results of those tests were then used to design simply supported GFRP–concrete hybrid beams that were tested under bending conditions. The flexural behaviour of the GFRP–concrete hybrid beams is discussed, with particular relevance to the effect of the interconnection slip. The overall behaviour of the hybrid beams is compared with that corresponding to a simple GFRP I-profile beam, demonstrating the structural advantages of this new hybrid constructive solution.

Composite delaminations are commonly characterized using the double cantilever beam test for mode I, the end-notched flexure test or the end load split test for mode II and the mixed-mode bending test for mixed-mode. For all these tests, the mode mix remains constant and does not vary with the crack length. However, in the mixed-mode end load split test (MMELS), the delamination propagates under a varying mode mix that depends on the crack extension, which is a more realistic scenario. The MMELS test has been previously analysed by different researchers but the resulting expressions are not equivalent. A more accurate alternative analysis of the test, based on the finite element method and the virtual crack closure technique, is used in the present work for comparison. The results are compared to the predictions of approaches presented in the literature and significant findings are found for materials characterization using the MMELS test.

The mechanical behaviour of glass–fibre composites under fatigue or under long term stress is strongly influenced by the stress corrosion cracking of the fibres. In this paper, a stress corrosion model for composite materials reinforced with environment sensitive fibres has been developed and incorporated into a progressive damage model. The model is based on the definition of an effective stress, σ *( t ), which depends on the stress story, that permits the initial failure probability, given by a Weibull distribution, to be used at any later time. This methodology has been incorporated to a thermodynamically consistent constitutive model valid for early fragmentation stages. The model may be used to account for the fibre’s behaviour in numerical models based on the rule of mixtures. The ability of the extended progressive damage model to reproduce the stiffness loss of the composite under static or cyclic fatigue loads is demonstrated.

Constitutive damage models for fibre-reinforced composite materials should take into account the occurrence of the different damage mechanisms, their interaction and their influence on the resulting mechanical properties. Fibre breakage has usually been considered in damage models by means of deterministic failure criteria which thus leads to non-progressive behaviour or to a complete material collapse which is not realistic. This work presents a progressive damage model for fibre-reinforced composites based on the fragmentation analysis of the fibres. The stiffness loss of a unidirectional composite comes from the parameters of the Weibull distribution of the fibre strength and the mechanical properties of the fibre, matrix and the interface. The model has been developed for the initial stages of damage. The model is formulated in the framework of the mechanics of the continuous media. The constitutive model can be employed to simulate the contribution of fibres in damage models based on the rule of mixtures.

The present work develops an optimization procedure for a geometric design of a composite material stiffened panel with conventional stacking sequence using static analysis and hygrothermal effects. The procedure is based on a global approach strategy, composed by two steps: first, the response of the panel is obtained by a neural network system using the results of finite element analyses and, in a second step, a multi-objective optimization problem is solved using a genetic algorithm. The neural network implemented in the first step uses a sub-problem approach which allows to consider different temperature ranges. The compression load and relative humidity of the air are assumed to be constants throughout the considered temperature range.The mass, the hygrothermal expansion and the stresses between the skin and the stiffeners are defined as the optimality criteria. The presented optimization procedure is shown to yield the optimal structure design without compromising the computational efficiency The authors acknowledge the financial support of the Spanish Government under the Project DPI2009-08048

Stringer run-outs are a common solution to achieve the necessary strength, stiffness and geometric requirements of some structural solutions. The mechanical behavior and complexity of such design details requires careful and thorough studies to ensure the structural integrity of the structure. The influence of some geometric variables of the run-out in the interface of the set stringer-panel is crucial to avoid the onset and growth of delamination cracks. In this study, a damage tolerant design of a stringer run-out is achieved by a process of design optimization and surrogate modeling techniques. A parametric finite element model created with python was used to generate a number of different geometrical designs of the stringer run-out. The relevant information of these models was adjusted using Radial Basis Functions (RBF). Finally, the optimization problem was solved using Quasi-Newton method and Genetic Algorithms. In the solution process, the RBF were used to compute the objective function: ratio between the energy release rate and the critical energy release rate according to the Benzeggagh–Kenane mixed mode criterion. Some design guidelines to obtain a damage tolerant stringer-panel interface have been derived from the results The authors wish to acknowledge the Ministerio de Economía y Competitividad for the funding of the project MAT2013-46749-R and particularly to Universitat de Girona for the research Grant coded as BR2011/02