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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 crack propagation is influenced by what happens at both the surface and the interior of the component. Traditional experimental tools allow the surface behaviour to be characterised accurately but the information obtained from the bulk is much more limited. In this work, a study of both bulk and surface behaviour is presented. The material behaviour is studied by powerful 3D ultrafine finite element analysis in terms of the crack tip plasticity for a range of different conditions. The analysis is performed on a wedged opening loaded specimen made of an Aluminium alloy. The results are then validated with full-field digital image correlation data. The validation is used to enhance the model used in our analyses.

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.

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.

A circular economy is a current tenet that must be implemented in the field of construction. That would imply the study of the possibilities of the use of waste generated, for obtaining materials the used in construction as replacements for the raw material used. One of these possibilities is the substitution of the cement by slag, which contributes to the reduction of cement consumption, decreasing CO2 emissions, while solving a waste management problem. In the present paper, different types of concrete made by cement substitution with different type of slags have been studied in order to evaluate the properties of these materials. Cement is replaced by slag from different steel mills, both blast furnace and ladle furnace slag. The percentages of slag substitution by cement are 30%, 40% and 50% by weight. Mechanical, physical and environmental properties have been evaluated. Compressive and flexural strength have been analysed as the main mechanical properties. As far as physical properties go, density and porosity tests were be reported and analysed, and from an environmental point of view, a leachate study was performed. It has been found that some kinds of slag (blast furnace slag) are very suitable as substitutes for cement, providing properties above those of the reference concrete, while other types (ladle furnace slag) could be valid for non-structural applications, contributing in both cases to a circular economy. Agência financiadora Center of Industrial Technological Development (CDTI) of the Ministry of Economy and Competitiveness IDI-20160509 info:eu-repo/semantics/publishedVersion

Concrete consumption greatly exceeds the use of any other material in engineering. This is due to its good properties as construction material and the availability of its components. Nevertheless, the present worldwide construction increase and the high-energy consumption for cement production means a high environmental impact. On the other hand, one of the main problem in iron and steel industry is waste generation and by-products that must be properly processed or reused to promote the environmental sustainability. One of these by-products are blast furnace slag. Cement substitution by slag strategy achieves two goals, raw materials consumption reduction and waste management. In the present work, four different concrete mixtures are evaluated. 25% cement is substituted by different blast furnace slag. Tests are made to evaluate the advantages and drawbacks of each mixture. Depending on the origin, characteristics and treatment of the slag, concrete properties change. Certain mixtures provide proper concrete properties. Stainless steel slag produces a fluent mortar that reduces the water consumption whit a slight mechanical strength loss. Mixture with electric arc slag furnace properties are better to the reference concrete (without slag) when slag is treated similarly to the cement.

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 presents a numerical study of the influence of the load level and the crack front curvature on the plastic zone in the area close to the crack front. The aim of the work is to determine the influence of these parameters on fatigue crack closure. For this, a CT aluminum specimen has been modelled tri-dimensionally and several finite elements calculations have been made considering a large combination of the variables under consideration.

Many mechanical components are subjected to multiaxial fatigue. These conditions are typically coming from external loads, the geometry of the component and/or residual stresses. However the majority of experimental data available in the literature are focused on the simpler uni-axial fatigue problem. The present work describes a series of experimental tests conducted to characterise in a comprehensive way the multiaxial behaviour of a ST52-3N structural steel. First, the monotonic properties of the steel were obtained experimentally. Then cyclic properties were also measured both in the longitudinal and torsional axes. Finally another series of tests were carried out to study the multiaxial response of the material. Both in-phase (proportional) and out-of-phase (non proportional) loadings were employed, thus providing a complete database for improving current models which describe the multiaxial behaviour of materials.

r Fatigue crack closure is strongly influenced by the plastic wake developed because of the action of precedent cycles. It is related to the load sequence and is an additional difficulty for its determination. Finite-element method has been an alternative for the study of crack closure, commonly in constant-amplitude loading. However, such analyses are complex and computationally expensive, the length of the wake simulated being a critical parameter. In this paper, a comprehensive study of the effect of the plastic wake in fatigue crack closure is made. It is structured in two parts: one regarding the correct numerical modelling process and the other focussed on the influence of the wake under moderate variable-amplitude loading. After a brief description of the numerical methodology, results for different wake lengths are reported. The plastic wake is modelled with a new approach in which the final crack tip is fixed. Information regarding potential error is provided. Second, the load sequence effect is discussed. Crack closure is obtained for several load ratios, with wakes developed with different stress ratios. This permits the analysis of the influence of the load sequence over the crack-driving force compared with constant-amplitude loading.

Fatigue crack closure has been studied numerically with 2D finite element models as alternative to experimental methods. In a few cases fatigue crack closure behaviour has been analyzed with tri-dimensional models. In this work, a compact C(T) aluminium specimen has been modelled tri-dimensionally. The minimum element size is smaller than common accepted recommendation. This parameter limits the mesh size along the thickness. The number of divisions of the thickness is a special issue studied in this work. Different thicknesses, range of loads and stress relations have been calculated. The results show the crack behaviour through the thickness. The plastic zone is visualized and quantified. An abrupt transition is observed in a thin external slice of the specimen; only captured with a fine meshing of the thickness. Crack closure/opening along the thickness have been computed. Results show that closure is only relevant in this small external area and its size is not affected by the thickness. Results match experimental observation and have been correlated with experimental tests.

The fatigue life of metallic materials is strongly influenced by crack closure effects. Finite element (FE) methods allow the study of crack closure with great detail and can provide valuable information about phenomena occurring in the bulk of the material. In this work the distribution of stresses through the thickness of a cracked specimen has been studied using 3D FE simulations. It was found that the transition between the interior of the specimen (plane strain) and the surface (plane stress) differs from that predicted by 2D plane stress models. In addition, an attempt is presented to experimentally validate the results at the surface level. For this purpose full-field image correlation technique was utilized. This allowed direct comparison between the displacement field predicted by the numerical simulations and the experimental results measured by digital image correlation.

Plasticity-induced crack closure is an observed phenomenon during fatigue crack growth. However, accurate determination of fatigue crack closure has been a complex task for years. It has been approached by means of experimental and numerical methods. The finite element method (FEM) has been the principal numerical tool employed. In this paper the results of a broad study of fatigue crack closure in plane stress and plane strain by means of FEM are presented. The effect of three principal factors has been analysed in depth, the maximum load, the crack length and the stress ratio. It has been found that the results are independent of maximum load and the crack length, and there exists a direct influence of the stress ratio. This relation has been numerically correlated and compared with experimental results. Differences have also been established between opening and closure points and between the different criteria employed to compute crack closure.

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.

This article analyses fatigue crack growth under random loading using experimental results taken from literature on the subject and from growth simulations carried out using the Strip Yield Model. The capacity of the Strip Yield Model in representing the retardation effects produced during the growth process is analysed. The effect of different statistical parameters of the random load process and of the representative histories of the same on the crack growth life and on the variability of the results obtained in different representative tests of the same real load process is likewise studied. Some of the parameters considered are the bandwidth of the random loading process, the number of cycles of the load histories employed and the effect of truncating the histories. It can be seen that under certain conditions, the numerical model employed can quite closely predict some of the behaviours of the crack growth. Likewise, it can also be seen that the bandwidth has a significant effect on the fatigue life, and that the length of the histories employed in tests or simulations has a great effect on the variability of the obtained results. It can also be seen that, although the elimination of the overloads tends to give rise to shorter lives, in certain cases, from a statistical point of view, it may be the origin of non-conservative predictions.

Measuring opening or closure stress is a complex process that influences the low accuracy of obtained data. Finite element models have been one of the available ways to deal with this problem. The difficulty of modelling the whole process of crack growth (due to the great number of cycles implied) as the great complexity of the phenomenon itself (with a high plastic strain concentrated in a small area, with elevated stress gradients) has made the results to be quite varied, being influenced by a great number of modelling parameters. Of those parameters, the minimum size of the element used to mesh the area around the crack tip vicinity presents a great influence on the results. In this work, a detailed analysis of the influence of this parameter in the results in terms of closure or opening stress is presented. The effect that different meshing criteria can have on the result is complex and it has been necessary to reduce the element size around the crack tip to a size that had not been reached before. Procedures and modelling criteria stricter than the ones shown in the current bibliography are proposed. A methodology for the correct interpretation of the results is also established.