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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.

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.

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.

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.