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The influence of the three-dimensional effects of the distribution of the stress intensity factor in the numerical calculation of plasticity-induced crack closure is analysed in this paper. The usual methodology assumes a constant distribution of K along the thickness to obtain the effective stress intensity factor of the crack. This assumption should not be transposed to models that intend to observe phenomena in the crack front vicinity, where 3-D effects are a key aspect in the results. Through numerical simulations of both fracture and fatigue of through thickness straight cracks (CT specimen in mode I), the local opening and closure moment of each crack node is obtained and compared with previous one. Corrections are proposed for numerical methodology to obtain Kop and Kcl distribution along the thickness.

Fatigue crack closure has been studied by means of the finite element method for a long time. Most work has been performed considering bi-dimensional models where the numerical methodology has been developed. A great number of bi-dimensional studies analyses different numerical parameters and optimise them. Three-dimensional models have extended lately. Nevertheless, the methodology employed was taken from the one developed for bi-dimensional cases. The current computational capabilities allow a comprehensive three-dimensional study of the influence of the different modelling parameters in a similar way to those studies carried out with bi-dimensional models. In particular, one of the key issues is related to the element size, which has a huge influence on crack opening and closure values. In the present work, a CT aluminium specimen has been modelled three-dimensionally and several calculations have been made in order to evaluate the influence of the mesh size around the crack front. The numerical accuracy is analysed in terms of crack closure and opening values. Classical bi-dimensional recommendations are updated. A similar linear relationship has been identified and a minimum mesh recommendation of 60 divisions of the Dugdale’s plastic zone size is made.

The acoustic behaviour of a tube is well known since antiquity, nevertheless, differences appear when a flexible element interferes this behaviour. The tube acoustic resonance is altered by the mechanic resonance of this element due to complex mechano-acoustic effects. In this paper, an experiment is designed to evaluate the response of a tube with a membrane at the end, subject to sound pressure at the open side of the tube. A baffle isolates both sides of the tube. A comprehensive numerical study is made to understand the behaviour of different parameter of the system as the tube length and those related with the membrane stiffness and mass. A proper numerical methodology has been developed and is described and justified. The study of the simple tube system is also accomplished finding that results match with the theoretical expected values with an effective length correction. Regarding the behaviour of the tube-membrane system, it is found that the membrane is not a transparent element, but its contribution as closing element is limited to a 10 dB sound pressure drop compared with the absence of membrane. The acoustic resonance of the tube is affected by the membrane resonance but a general pattern similar to the open-closed case is observed. No presence of the open-open case is found.

This article presents a study of the main properties (consistency, workability, leaching, unsoundness, and mechanical properties) of cement grouts prepared with cement replacement by blast furnace slag (GGBS). Mixtures have been analyzed in the absence of additives and reached high replacement percentages. As shown in the different tests presented, the observed evolution of the resistance and workability of the mixtures makes them very interesting for its application. Different types of cement (CEM-I 42.5 and CEM-I 52.5 R) and different water/binder values (1 and 0.67) are used. The results present opportunities for the steel industry by the intensive valorization of slag waste. The reduction of the use of cement in construction is also one of the key aims of this line of research. Results show improvements in the mechanical response with good fresh state properties for substitution percentages up to 70%. It is verified with leaching analysis that these products have less impact on the environment.

The dynamic behaviour of membranes has been widely studied by well-known authors for a long time. A clear distinction can be made between the behaviour of membranes without tension (plate case) and membranes subjected to large tension or pre-strain in their plane (membrane case). In classical theories, less attention has been paid to membranes subjected to a low level of tension, which solution is between both extreme cases. Recently, certain fields of research are demanding solutions for this intermediate behaviour. It is the case of membranes present in MEMS and sensor or the response of the tympanic membrane in mammals hearing system. In this paper, the behaviour of plates and circular membranes with boundary conditions clamped in the edges has been studied. The natural frequencies for both cases (plate and membrane) have been calculated using the solutions of the traditional theories and these have been compared with the numerical frequencies calculated by finite element analysis. The dynamic response of membrane with low tension, corresponding to a transition between these extreme behaviours, has also been calculated. A theoretical solution has been used complemented with a wide set of numerical finite elements calculations. The analytical and numerical solutions are very close, being the error made using both methods very low, nevertheless, there are no analytical solutions for the entire transition zone between the plate and membrane behaviour. Therefore, this range has been completed using finite element analysis. Broad ranges of geometric configurations have been studied. The transition behaviour of the membrane has been clearly identified. The main practical consequences of these results have been discussed, in particular focused on the response of the tympanic membrane.

The concept of sustainability is becoming widespread every day in society, enterprises and institutions. Defining something as sustainable means that the relationship that it establishes with the environment does not represent an aggression or a threat to the latter neither when it is being utilized nor when it stops performing the function for which was designed. To make this happen we need a system in which the main priority is recycling. Everything mentioned above is related to what is called the “Circular Economy”. Concrete is one of the most widely used construction materials in the world. However, the production of portland cement, an essential constituent of concrete, leads to the release of significant amounts of CO22. The global production of concrete represents more than 5% of the anthropogenic emissions of carbon dioxide every year, mainly from the production of cement. The replacement of cement by fly ash and other industrial waste, such as steel slags, is a good example of how resource conservation can be improved and contamination can be reduced. On the other hand, future trends are predicted to increase demand for steel worldwide. Mainly due to the expected improvement in the living standards and demands of underdeveloped populations. The steelmaking process produces a by-product called slag ranging from 10 to 15% per tonne of steel, where reuse is still reduced and much of it is deposited in a landfill. This study presents laboratory test results on the total and autogenous shrinkage of medium strength concrete with partial replacement of cement by slags. Two different slags were tested, namely ladle furnaces slags (LFS) and ground granulated blast furnace slags (GGBFS). The results show the concrete shrinkage behavior when 25% of substitution are used. These data are important to predict future behavior and show that for the substitution dosages used there are no significant divergences for the shrinkage. Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.

This paper is part of a research line focused on the reduction of the use of cement in the industry. In this work, the study of work methodologies for the manufacture of green cementitious grout mixtures is studied. Grout is widely used in construction and it requires an important use of raw materials. On the other hand, the steel industry faces the problem of the growing generation of slag wastes due to the increase in steel manufacturing. The green grout aims to achieve the dual objective of reducing the demand for cement and improve the slag waste valorization. Slag is not introduced as an aggregate but through the direct replacement of cement and no additives. The research seeks a product where we can use steel slag intensively, guaranteeing minimum resistance and workability. Results with substitutions between a 25% to 50% and water/cement ratio of 1 are presented. In particular, the suitability of different slags (two Ladle Furnace Slag (LFS) and one Blast Furnace Slag (GGBS)) in the quality of the final product are analyzed. The feasibility of replacing cement with slag and the importance of the origin and pretreatment are highlighted.

This paper is focused on the methodological aspects of the numerical study of stress intensity factor (SIF) evolution through thickness. The work evaluates the modelling of an Al-alloy 2024-T351 CT specimen under mode I nominal loading in fracture. No plastic wake effect is introduced to separate the influence of plasticity-induced crack closure near the surface. Numerical models have shown the complexity 3-D behaviour in the vicinity of the crack front and finite element methods (FEM) are widely used in these problems with interesting results. However, there is a lack of literature support in many simplifying assumptions. In previous studies, authors have analysed some issues as the evolution of the plastic zone, the crack closure stress or the SIF. The current work attempts to describe and justify the key aspects of the methodology developed to address these problems by the FEM. A huge effort has been made to study main parameters involved and their influence in the results, especially in order to properly capture the SIF distribution along the thickness. Recommendations about mesh density are provided, and the main procedures to obtain K are discussed.

Numerical models based on finite element method have been employed to analyse the plasticity induced crack closure phenomenon for a long time. These numerical analyses require the development of a plastic wake. During the development of the plastic wake a transient behaviour can be observed on the numerical results. Most of these previous analyses have been performed considering bi-dimensional models. The use of three-dimensional models has been extended during last years. Nevertheless, the methodology considered has been inherited from the bi-dimensional ones. Optimising the numerical parameters involved on the development of the plastic wake is a key issue to keep the computational cost under control, particularly when a three-dimensional analysis is considered. This study presents a three-dimensional analysis of the influence of the crack growth scheme on fatigue crack closure results. This three-dimensional analysis allows to study the influence of the number of loading cycles not just on plane stress or plane strain conditions but all along the thickness. In the present work, a CT aluminium specimen has been modelled three-dimensionally and several calculations have been made in order to evaluate the influence of the number of loading cycles between node releases and after releasing the last set of nodes on fatigue crack closure results. The numerical accuracy is analysed in terms of crack closure and opening values and in terms of strain and stress fields.

Plasticity Induced Crack Closure (PICC) has been studied by means of finite element method for a long time. Most of previous work was developed considering bi-dimensional models. During last years, the use of three-dimensional models has been extended. Nevertheless, the methodology employed has been inherited from bi-dimensional analyses. Many previous bi-dimensional analyses studied different numerical parameters and optimized them. Present computational capabilities allow a comprehensive study of the influence of different modelling parameter in a similar way to those bi-dimensional analyses. Moreover, the influence of these parameters on the obtained results along the thickness can be taken into consideration. In particular, one of the key issues is related to the crack growth scheme. A fatigue analysis implies a crack growth. Each change in loading and boundary conditions implies solving a nonlinear problem. It is not feasible to consider all the cycles involved in a real fatigue problem when running a finite element analysis. The computational cost is not acceptable. In the present work, a CT aluminium specimen has been modelled three-dimensionally and several calculations have been made in order to evaluate the influence of the number of load cycles between node releases. The results are analysed in terms of crack closure and opening values.

Constant-force mechanisms are designed to keep a constant or nearly constant input force along a prescribed stroke of the mechanism. The implementation of this kind of mechanisms has been approached in literature using compliant mechanisms or through a certain combination of springs and nonlinear transmissions. In this work, three new constant-force mechanisms based on the use of springs, rollers, and cams are presented and analyzed. The rolling friction forces between the rollers and the cam are included in the force equilibrium equations and considered in the integration of the cam profile. The influence of the friction force on the input force as well as the design parameters involved is studied based on numerical techniques and simulations. In fact, the results evidence that to obtain a precise constant-force mechanism, rolling friction forces must be considered in the cam profile definition. The main design guidelines for the three constant-force mechanisms proposed are described.

Recent studies have allowed us to identify a narrow region of the thickness of the crack front in fracture problems that presents interesting characteristics for the numerical-experimental correlation. Taking the three-dimensional distribution of the stress intensity factor (K) as a reference, we observe how it remains invariant and independent of the main factors influencing this type of analysis. This article presents a summary of how to identify this point through the numerical simulation of the problem and its relationship with parameters such as thickness, load level or angle of curvature. The simulations are carried out with the ANSYS software in an aluminium CT specimen subjected to a fracture loading process in mode I. Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.

Since long time, fatigue crack closure has been studied by means of finite element models. Initially by bi-dimensional models and recently, due to the higher computational capabilities, the use of three-dimensional models has been extended, providing a wider comprehension of the problem. Starting with the methodology used for 2D cases, a specific methodology for 3D models has been developed. Key parameters affecting the model have been analyzed and recommendations have been established. The numerical accuracy is evaluated in terms of crack closure and opening values. They main issues studied are the material behaviour, the loading cycles and crack growth scheme, the contact simulation, the meshing and the element size at the crack tip and along the thickness, the plastic wake computed and the opening and closure definition considered. This paper summarises the main learning and recommendations from the latest numerical modelling experience of the authors. Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.

Finite element method has been broadly used to study fatigue crack closure. The simulated plastic wake length is one of the key modelling parameters involved. This paper presents a complete analysis in fatigue crack closure 3-D models. It is aimed at two aspects: the influence on the calculation of opening and closure values, and the effect on other main results. Conclusion indicates a 0.6 times Dugdale’s plastic size length to stabilise results as plastic zone or contact area, but a reduced length could be acceptable in terms of crack closure results. This suggests some independence among this parameter and fatigue crack closure.

The study of crack tip fields in mode I is often conducted assuming a homogeneous behaviour through the thickness. Depending on the specimen thickness, a state of plane stress or plane strain is normally presumed. However, recent studies have shown a more complex behaviour along the thickness. On the one hand, plasticity-induced crack closure effects affect mainly to a small region close to the specimen surface. On the other hand, the plastic zone evolution along the thickness is not as simple as the classic dog-bone shape normally described in Fracture Mechanics textbooks. Unlike what is normally expected, the size of the plastic zone decreases in a very small region close to the surface, as we move from the interior to the surface of the specimen. These two effects can be detected if the mesh used in the finite element model is sufficiently fine. Both effects are probably related to an uneven distribution of the load along the thickness. One of the consequences of these effects on the fatigue crack growth is the curvature of the crack front which can be explained by two mechanisms. The first one is related to the crack closure effect near the surface, it would imply a smaller effective Δ K close to the surface, and therefore a slower crack growth rate. The second one (plastic zone size decrease in a small region close to surface) is probably due to Δ K being smaller near the surface than in the interior. The current work attempts to evaluate numerically both effects in order to separate their individual influence and their magnitude. This is done by evaluating the K distribution along the thickness at different planes on an Al 2024-T35 compact tension specimen under mode I nominal loading. The plastic wake effect is removed from the model in order to distinguish between both effects.

Crack front curvature is evidence in most experimental crack advance test. When classical linear elastic fracture mechanic theory deals with bi-dimensional crack configurations, it ignores the three-dimensional effects of crack propagation. Issues as the influence of the specimen thickness and the crack front curvature are not considered. Previous numerical studies have shed light on out-of-plane plastic zone development or stress state. Nevertheless, these numerical studies are based on the assumption that the crack front is ideally straight; despite it is well known that the crack front has some kind of curvature. In the present work, a CT aluminium specimen has been modelled three-dimensionally and several calculations have been made considering a huge combination of different single load levels, specimen thicknesses and crack front curvatures. Due to the abrupt transition from plane strain to plane stress, an ultrafine mesh along the thickness has been applied. The analysis of the evolution of the plastic zone and the stress state along the thickness provides information about the combined influence of these parameters on fracture mechanics.

Concerning bi-dimensional crack configurations, classical linear elastic fracture mechanic theory ignores the three-dimensional effects of crack propagation. Issues as the influence of the specimen thickness are not considered. Nevertheless, real cracks show some effects difficult to explain. It is the case of the load effect on fatigue crack closure. The yielded zone size close to the crack front is an important factor in fracture and fatigue of metallic materials. They are related to the two extreme stress states: plane stress or plane strain, but no clear information about out-of-plane plastic zone development or stress state has been provided. In the present work, a CT aluminium specimen has been modelled three-dimensionally and several calculations have been made considering a huge combination of different single load levels and specimen thickness. Due to the abrupt transition from plane strain to plane stress, an ultrafine mesh along the thickness has been applied. The analysis of the evolution of the plastic zone and the stress state along the thickness provides information about the combined influence of these parameters on fracture mechanics.

This paper focuses on the study of the plastic zone in fatigue crack closure based on the results obtained by means of 3D Finite Element Analysis (FEA). These results show the crack behavior through the thickness. The plastic zone is visualized and quantified. It does not correspond to the classical shape. The plastic zone in the interior surface is similar to those obtained in 2D plane strain conditions and a reduced effect of closure is observed. However, close to the external surface, 2D plane stress results are not reproduced, the plastic zone size is smaller and an important change is observed. This transition is developed in a thin external portion of the specimen and it can only be captured if a fine mesh of the thickness is done.