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State of the art of corner point singularities under in-plane and out-of-plane loading
No full textThe linear elastic analysis of homogeneous, isotropic cracked bodies started in the 1900s. The existence of three dimensional corner point effects in the vicinity of a corner point where a crack front intersects a free surface was investigated in the late 1970s. An approximate solution by Bažant and Estenssoro explained some features of corner point effects but there were various paradoxes and inconsistencies. Results derived from finite element models showed that the analysis is incomplete. The stress field in the vicinity of a corner point appears to be the sum of two singularities
Corner point singularities under in-plane and out-of-plane loading: A review of recent results
No full textThe linear elastic analysis of homogeneous, isotropic cracked bodies started in the 1900s. The existence of three dimensional corner point effects in the vicinity of a corner point where a crack front intersects a free surface was investigated in the late 1970s. An approximate solution by Bažant and Estenssoro explained some features of corner point effects but there were various paradoxes and inconsistencies. Results derived from finite element models showed that the analysis is incomplete. The stress field in the vicinity of a corner point appears to be the sum of two different singularities (i.e. stress intensity factors and corner point singularities). In this paper some recent results for the corner point singularities under in and out of plane loadings is reviewed and discussed
Coupled fracture modes of discs and plates under anti-plane loading and a disc under in-plane shear loading
No full textThree-dimensional effects near crack tips have been deeply investigated in the past, but the topic is still ongoing and under investigation. However, the understanding is in some cases limited, and the problem requires further attention. Three-dimensional effects are in fact neglected in situations where they may play an important role. The main aim of this review paper is to summarise some recent results of a study carried out on the coupled in-plane fracture mode induced by a nominal anti-plane (mode III) loading applied to plates and discs weakened by a straight crack. Only linear elastic conditions are considered herein. The results derived by a large bulk of finite element models allow a better understanding of coupled modes generated by anti-plane loading. The influence of plate/disc bending on three-dimensional stress fields is considered in the investigation, showing that it becomes non-negligible as the thickness decreases. Some considerations on the trend of KIII as the corner point is approached are also part of this paper. In addition, the trend of the strain energy density (SED) in a volume surrounding the crack tip is shown and commented on. This parameter allows the precise determination of the weakest point of the component through the thickness becoming a useful tool. Some new results for a disc under in-plane shear loading are included. These results clarify the influence of disc bending under anti-plane loading. © 2016 Wiley Publishing Ltd
Three-dimensional stress states at crack tip induced by shear and anti-plane loading
No full textIt was known for a long time that shear and anti-plane fracture modes are coupled. It means that shear or anti-plane loading of an elastic plate with a through-the-thickness crack also generates a coupled three-dimensional anti-plane or shear singular stress state, respectively. These singular stress states (or coupled fracture modes) are currently largely ignored in theoretical and experimental investigations as well as in standards and failure assessment codes of structural components, in which it is implicitly assumed that the intensities of these modes as well as other three-dimensional effects are negligible in comparison with the stress field generated by the primary modes (modes I, II and III). In this paper we provide an overview of recent theoretical studies carried out by the authors, which demonstrate that the account for these coupled modes can totally change the classical (two-dimensional) view on many fracture phenomena. In particular, this relates to a generation of the coupled modes by non-singular (in two-dimensional sense) shear and anti-plane stress fields. The theoretical results indicate the existence of a strong plate thickness effect on the intensity of the coupled modes, which can significantly influence fracture conditions. © 2013 Elsevier Ltd
Induced out-of-plane mode at the tip of blunt lateral notches and holes under in-plane shear loading
No full textAs it is well known the Poisson's effect in a cracked plate subjected to anti-symmetric plane loading leads to the generation of a coupled out-of-plane singular mode. Recent theoretical and numerical analyses have shown that this effect is present also in plates weakened by sharp V-notches and might play a role in failure initiation phenomena of notched plates subjected to Mode II loading, especially in the presence of a large notch opening angle. Dealing with blunt notches with a large notch radius, and not just with sharp notches, the presence or not of an out-of-plane mode does not appear to have been systematically investigated in the past. The main aim of this work is to confirm the existence of the stress field associated with the out-of-plane mode (Mode O) and to describe its main features in the presence of a notch radius significantly different from zero. The analyses include U-notches, as well as circular and elliptic holes. The strain energy density in a 3D control volume is utilized to identify the most critical zone (with respect to failure initiation) through the plate thickness at the notch tip. © 2012 Blackwell Publishing Ltd
Three-dimensional effects on cracked components under anti-plane loading
Full text linkThe existence of three-dimensional effects at cracks has been known for many years, but understanding has been limited, and for some situations still is. Understanding improved when the existence of corner point singularities and their implications became known. Increasingly powerful computers made it possible to investigate three-dimensional effects numerically in detail. Despite increased understanding, three-dimensional effects are sometimes ignored in situations where they may be important. The purpose of the present investigation is to study by means of accurate 3D finite element (FE) models a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic plates. An extended version of the present work has recently been published in the literature. The results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked components under anti-plane loading. The influence of plate bending is increasingly important as the thickness decreases. It appears that a new field parameter, probably a singularity, is needed to describe the stresses at the free surfaces. Discussion on whether KIII tends to zero or infinity as a corner point is approached is futile because KIII is meaningless at a corner point. The intensity of the local stress and strain state through the thickness of the cracked components has been evaluated by using the strain energy density (SED) averaged over a control volume embracing the crack tip. The SED has been considered as a parameter able to control fracture in some previous contributions and can easily take into account also coupled three-dimensional effects. Calculation of the SED shows that the position of the maximum SED is independent of plate thickness. Both for thin plates and for thick ones the maximum SED is close to the lateral surface, where the maximum intensity of the coupled mode II takes place
Coupled fracture modes of discs and plates under anti-plane loading and a disc under in-plane shear loading
No full textThree-dimensional effects near crack tips have been deeply investigated in the past, but the topic is still ongoing and under investigation. However, the understanding is in some cases limited, and the problem requires further attention. Three-dimensional effects are in fact neglected in situations where they may play an important role. The main aim of this review paper is to summarise some recent results of a study carried out on the coupled in-plane fracture mode induced by a nominal anti-plane (mode III) loading applied to plates and discs weakened by a straight crack. Only linear elastic conditions are considered herein. The results derived by a large bulk of finite element models allow a better understanding of coupled modes generated by anti-plane loading. The influence of plate/disc bending on three-dimensional stress fields is considered in the investigation, showing that it becomes non-negligible as the thickness decreases. Some considerations on the trend of KIII as the corner point is approached are also part of this paper. In addition, the trend of the strain energy density (SED) in a volume surrounding the crack tip is shown and commented on. This parameter allows the precise determination of the weakest point of the component through the thickness becoming a useful tool. Some new results for a disc under in-plane shear loading are included. These results clarify the influence of disc bending under anti-plane loading
Three-dimensional effects on cracked discs and plates under nominal Mode III loading
Full text linkThe existence of three-dimensional effects at cracks has been known for many years, but understanding has been limited, and for some situations still is. Understanding improved when the existence of corner point singularities and their implications became known. Increasingly powerful computers made it possible to investigate three-dimensional effects numerically in detail. Despite increased understanding, threedimensional effects are sometimes ignored in situations where they may be important. The purpose of the present contribution is to review the study carried out by the same authors in some recent investigations, in which a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic discs and plates has been analysed by means of accurate 3D finite element (FE) models. The results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked components under anti-plane loading. The influence of plate bending is increasingly important as the thickness decreases. It appears that a new field parameter, probably a singularity, is needed to describe the stresses at the free surfaces. Discussion on whether KIII tends to zero or infinity as a corner point is approached is futile because KIII is meaningless at a corner point. The intensity of the local stress and strain state through the thickness of the cracked components has been evaluated by using the strain energy density (SED) averaged over a control volume embracing the crack tip. The SED has been considered as a parameter able to control fracture in some previous contributions and can easily take into account also coupled three-dimensional effects. Calculation of the SED shows that the position of the maximum SED in the discs case is a function of the thickness. In the plates case instead the position of the maximum SED is independent of plate thickness, contrary to disc results
Coupled fracture mode of a cracked disc under anti-plane loading
No full textThe existence of three-dimensional effects at cracks has been known for many years, but understanding has been limited, and for some situations still is. Understanding improved when the existence of corner point singularities and their implications became known. Despite increased understanding, three-dimensional effects are sometimes ignored in situations where they may be important. The purpose of the present investigation is to study by means of accurate 3D finite element (FE) models a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic discs. The results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked discs under anti-plane loading. The influence of plate bending is increasingly important as disc thickness decreases. It appears that a new field parameter, probably a singularity, is needed to describe the stresses at the disc surfaces. Calculation of the strain energy density (SED) in a control volume at the crack tip shows that the position of the maximum SED is a function of disc thickness
Coupled fracture mode of a cracked disc under anti-plane loading
Full text linkThe existence of three-dimensional effects at cracks has been known for many years, but understanding has been limited, and for some situations still is. Understanding improved when the existence of corner point singularities and their implications became known. Increasingly powerful computers made it possible to investigate three-dimensional effects numerically in detail. Despite increased understanding, three-dimensional effects are sometimes ignored in situations where they may be important. The purpose of the present investigation is to study by means of accurate 3D finite element (FE) models a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic discs. The results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked discs under anti-plane loading. The influence of plate bending is increasingly important as disc thickness decreases. Bazant and Estenssoro's analysis works well for the symmetric mode (mode I), but it is incomplete for the asymmetric mode (a combination of modes II and III). It appears that a new field parameter, probably a singularity, is needed to describe the stresses at the disc surfaces. Discussion on whether K-III tends to zero or infinity as a corner point is approached is futile because K-III is meaningless at a corner point. Calculation of the strain energy density (SED) in a control volume at the crack tip shows that the position of the maximum SED is a function of disc thickness
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