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  • 1
    Electronic Resource
    Electronic Resource
    LIMITATIONS ON THE USE OF THE STRESS INTENSITY FACTOR, K, AS A FRACTURE PARAMETER IN THE FATIGUE PROPAGATION OF SHORT CRACKS (1997)
    Oxford, UK : Blackwell Publishing Ltd
    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    Details
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— It is well known that for very short cracks the stress intensity factor K is not a suitable parameter to estimate the stress level over the small but finite Stage II process zone activation region of size rs near the crack tip, within which crack growth events take place. A critical appreciation of the reasons for the limitations on the applicability of ΔK as a fatigue crack propagation (FCP) parameter, when the crack length a is of the same order of magnitude or smaller than the size of the ‘fatigue-fracture activation region’, rs is presented. As an alternative to ΔK the range Δσs of the cyclic normal stress at a point situated at the fixed distance s=rs/2, ahead of the crack tip, inside the fatigue-fracture activation region, is proposed. It is observed that the limitation on the use of ΔK when the crack is short, is mathematical (and not physical) but this inconvenience is easily circumvented if the stress Δσs at the prescribed distance is used instead of ΔK since nowadays Δσs can be obtained numerically by using finite element methods (FEM). It follows that the parameter Δσs is not restricted by the mathematical limitations on ΔK and so it would seem that there is, a priori, no reason why the validity of the parameter Δσs cannot be extended to short cracks. It is shown that if the Paris law is expressed in terms of Δσs (πrrs)½ instead of ΔK the validity of the modified Paris law can be extended to short cracks.A coherent estimate of the value of the fatigue-fracture activation region rs is derived in terms of the fatigue limit ΔσFL obtained from S-N tests and of the threshold value ΔKth obtained from tests on long cracks where both relate to Stage II crack growth that ends in failure, namely, rs= (ΔKth/ΔσFL)2/π. An overall, threshold diagram is presented based on the simple criterion that, for sustained Stage II FCP, Δσs must be greater than ΔσFL. The study is based on a simple continuum mechanics approach and its purpose is the investigation of the suitability of both ΔK and Δσs to characterise the crack driving force that activates complex fracture processes at the microstructure's scale. The investigation pertains to conditions that lead to the ultimate failure of the component at values of Δσs 〉 ΔσFL.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1460-2695.1997.tb01521.x
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  • 2
    Electronic Resource
    Electronic Resource
    A crack in a linear-elastic material under mode II loading, revisited (1999)
    Oxford, UK : Blackwell Science Ltd
    Fatigue & fracture of engineering materials & structures 22 (1999), S. 0 
    Details
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A sharp crack in a two-dimensional infinite linear-elastic material, under pure shear (mode II) loading is re-examined. Several criteria have been proposed for the prediction of the onset and direction of crack extension along a path emanating from the tip of the initial crack. These criteria date back some three decades and are well documented in the literature. All the predictions from the different criteria are close and indicate that the crack extension takes a direction at an angle of ≈ −70° measured counterclockwise from the positive x-axis, in the case of a remotely applied positive shear stress. However, the possibility seems to have been overlooked that the crack extension may initiate not from the crack tip itself, but instead may initiate on the free surface at an infinitesimal distance behind the crack tip. The effect of crack tip plasticity on the relevant stresses in the region of the crack tip is investigated by the application of an elastic–plastic finite element program.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1046/j.1460-2695.1999.00178.x
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  • 3
    Electronic Resource
    Electronic Resource
    CRACK EXTENSION UNDER MIXED-MODE LOADING IN AN ANISOTROPIC MODE–ASYMMETRIC MATERIAL IN RESPECT OF RESISTANCE TO FRACTURE (1996)
    Oxford, UK : Blackwell Publishing Ltd
    Fatigue & fracture of engineering materials & structures 19 (1996), S. 0 
    Details
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— Recently, a crack path fracture criterion was proposed by Kfouri and Brown, based on maximum energy release rates at the tip of short kinks emanating from an existing crack when the main crack is subjected to mixed-mode loading. Assuming a ‘mode asymmetry’ in respect of the fracture resistances of the material, KIr, and KIIr, for pure mode I and pure mode II, respectively, i.e., KIIr, differing from KIr, generally, the modified criterion proposed that the resistance to fracture is a function of the ratio q (=k2/k1) of the mode II to the mode I stress intensity factors at the tip of the kink.The aim of the present paper is to extend the modified criterion by presenting it in a form that takes into account material fracture resistance anisotropy in addition to the fracture resistance mode asymmetry previously described. Note however that the material's elastic properties are still assumed to be isotropic. A short FORTRAN computer program has been written to predict the kink angle under mixed-mode loading for cracks in materials with mode asymmetry and material anisotropy with respect to their fracture resistance properties, and the inclination angle, θ, defining the direction of the main crack in the material. The values of four parameters, r0, r90, s and θ, described in the text, characterising the material fracture resistance asymmetrical and anisotropic properties and the orientation of the main crack, are prompted by the program, which provides, almost instantaneously, the kink angles under various loading modes and much additional relevant information. The effects of the variation of these parameters, treated singly or in combination, and the discontinuous “catastrophic” character of many of the responses at certain “transition” values of the parameters, are illustrated further. In the discussion it is recognised that the translation of the results of the analysis of a highly idealised situation to actual practical problems on real materials encountered in practice, is not straightforward but, notwithstanding, since material fracture resistance anisotropy and fracture resistance mode asymmetry may well be present in the real world, the possible influence of these factors perhaps needs to be taken into account in studies on crack paths.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1460-2695.1996.tb00929.x
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  • 4
    Electronic Resource
    Electronic Resource
    A FRACTURE CRITERION FOR CRACKS UNDER MIXED-MODE LOADING (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Fatigue & fracture of engineering materials & structures 18 (1995), S. 0 
    Details
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A fracture criterion is proposed, based on maximum energy release rates at the tips of short kinks when the main cracks are subjected to mixed mode loading. The criterion differs from existing energy based criteria in that the fracture toughness, gc, is not independent of the stress mode prevailing in the region of the tip of the kink but is a function of the ratio of the mode II to mode I stress intensity factors at the tip of the kink, i.e., gc is determined directionally by an elliptical region with major and minor axes equal to the fracture resistances of the material, KIr and KIIr, for pure mode I and pure mode II, respectively. Points inside the elliptical region are considered safe. When KIIr is equal to KIr the ellipse degenerates into a circle and the fracture criterion reverts to the existing familiar maximum energy release rate criterion based on a single value of the fracture toughness, irrespective of the active mode prevailing in the region at the tip of the kink. In this case, under pure shear (mode II) applied load, KII, the angle of inclination of the fracture crack extension to the main crack, α, is in the region of −76°, in general agreement with previous well established results. However, when the ratio r (=KIIrKIr) is less than r′ (=0.82, approximately) a different pattern emerges and, in particular, under pure mode II load, the crack advance is co-planar with the main crack, i.e., in mode II. A lower transition value r″ (=0.582, approximately) was also detected under pure mode I applied load. Thus for values of r≥r″, the crack extension is in pure mode I and is co-planar with the main crack but when r 〈 r″, the crack branches out at an angle (which can be positive or negative) in mixed modes I/II crack extension. Some implications of these results are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1460-2695.1995.tb00920.x
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  • 5
    Electronic Resource
    Electronic Resource
    COMPARISONS OF THEORETICAL AND FINITE ELEMENT STRESS ANALYSIS SOLUTIONS FOR A BIMATERIAL STRIP AND PLATE SUBJECTED TO THERMAL LOADING (1993)
    Oxford, UK : Blackwell Publishing Ltd
    Fatigue & fracture of engineering materials & structures 16 (1993), S. 0 
    Details
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— A study is made on a bimaterial beam of length 2L and height 2h, composed of a lower half-beam made from material A and an upper half-beam made from material B, under thermal loading. The geometrically identical half-beams are bonded together at the interface. Materials A and B have similar elastic properties, i.e., Young's modulus E(=207 GPa) and Poisson's ratio v(=0.3) are the same for both materials but the coefficients of linear thermal expansion are αA for material A and αB for material B, where αA 〉 αB.A theoretical solution based on simple beam theory is derived for the stress-strain-displacement fields at a temperature T1 〉 T0 where T0 corresponds to an initial stress-free state, when the beam is held at the centre only to prevent rigid-body motion. The main purpose of the investigation is to compare the results of the theoretical solution with those obtained from elastic, plane-stress, finite element analyses, using two different meshes. The case when the ends of the beam are held down is also examined.Finally the analogous axisymmetric problem of a bimaterial circular plate comprising a lower and an upper half-plate bonded together, is investigated and a theoretical solution of the biharmonic equation, using Legendre polynomials, is derived. The results from the theoretical solutions are compared with the results from an axisymmetric finite element analysis and also from a simulation plane-stress analysis using E1 as the effective modulus of elasticity, where E1=E/(1 –v). Some interesting features and oddities arising from these investigations are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1460-2695.1993.tb00746.x
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  • 6
    Electronic Resource
    Electronic Resource
    ELASTIC-PLASTIC FINITE ELEMENT ANALYSES OF CRACKED NOTCHES IN PLATES UNDER MIXED-MODE LOADING (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Fatigue & fracture of engineering materials & structures 15 (1992), S. 0 
    Details
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Plates containing inclined elliptical notches with and without cracks are analysed for five different major axis inclinations, namely, θ equal to 0, 11.25, 22.5, 33.75 and 45˚. Short cracks emanating from the roots of such inclined circular and elliptical notches are analysed. Under various mixed-mode loading conditions, when cracks are present, a simple method is described for the evaluation of the Mode I and Mode II stress intensity factors, for the elastic state. Values of the J integral along three different contours are also evaluated in the elastic and elastic-plastic states, as well as the Mode I and Mode II components of the crack tip opening displacenient (CTOD), the maximum principal stresses, the maximum average equivalent plastic strains and the location of the elements in which they occur. Comparisons of the different loading conditions are presented and the implications of the effects of mixed-mode loading on fracture and fatigue crack propagation are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1460-2695.1992.tb00054.x
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  • 7
    Electronic Resource
    Electronic Resource
    A Boussinesq wedge analysis of the tensile stress region in a rail head beneath compressive and traction point loads (2004)
    PO Box 1354, 9600 Garsington Road, Oxford OX4 2XG, UK. : Blackwell Science Ltd
    Fatigue & fracture of engineering materials & structures 27 (2004), S. 0 
    Details
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Investigations into the causes of damage to rail heads and on rolling contact fatigue, date back a considerable time and are described in a large number of expertise literature on the many different aspects of this complex problem. The present paper is prompted by the naïve observation that fatigue crack propagation is more likely to occur in a tensile stress environment than in a highly compressive one and it therefore seeks to locate a region of radial or longitudinal tensile stresses on a rail head during the rectilinear motion of the train, providing favourable conditions for mode I or mixed-mode crack propagation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1460-2695.2004.00812.x
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  • 8
    Electronic Resource
    Electronic Resource
    An elastic-plastic finite element analysis of crack tip fields under biaxial loading conditions (1974)
    Springer
    International journal of fracture 10 (1974), S. 393-404 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Résumé On a étudié par éléments finis une tôle carrée comportant une fissure centrale et soumise à tensions biaxiales. L'analyse élastique montre que le COD et la tension de séparation en avant de l'extrémité de l'entaille ne sont pas influencés par le mode de mise en charge biaxiale; il en résulte que le facteur d'intensité d'entaille donne une description adéquate de la situation de l'extrémité de l'entaille dans un continuum élastique. L'analyse élastoplastique, qui implique un écoulement plastique plus étendu à l'extrémité de l'entaille, conduit à des solutions différentes pour les champs de contraintes à l'extrémité de l'entaille et pour les déplacements des lèvres de la fissure, selon les différentes modes de mise en charge biaxiale. La mise en charge équi-biaxiale est celle qui cause la contrainte de séparation la plus élevée, mais aussi le plus petit COD et la plus faible étendue de déformation plastique par cisaillement. La mise en charge par cisaillement, par contre, provoque la contrainte de séparation la plus faible et les COD et étendue de zone plastique les plus grands.
    Abstract: Zusammenfassung Man untersucht mit dem Verfahren der endlichen Elementen eine viereckige Platte mit einem zentralen Riß unter biaxialer Spannung. Eine elastische Untersuchung zeigt daß die Rißöffnungsausdehnung und die Trennungsspannung von der Rißspitze nicht durch die Art von biaxialen Belastung beeinflußt werden und daher werden die Begebenheiten and der Rißspitze passend durch den Spannungsintensitätfaktor in einem elastischen Medium beschrieben. Eine elastisch plastische Untersuchung die mehr als nur örtliches Fliessen an der Rißspitze·berücksichtigt liefert verschiedene Lösungen für Rißspitzenspannungsfelder und Rißseitenverschiebungen für die verschiedenen Arten von biaxialer Belastung. Die equibiaxiale Belastung erzeugt die größte Trennungsspannung aber die kleinste plastische Querverformung und Rißausdehnung. Die Querkraft Belastung erzeugt die größte plastische Querverformung und Rißausdehnung aber die kleinste Trennungsspannung der Rißspitze.
    Notes: Abstract A square plate containing a central crack and subjected to biaxial stresses has been studied by a finite element analysis. An elastic analysis shows that the crack opening displacement and stress of separation ahead of the crack tip are not affected by the mode of biaxial loading and therefore the stress intensity factor adequately describes the crack tip states in an elastic continuum. An elastic-plastic analysis involving more than localized yielding at the crack tip provides different solutions of crack tip stress fields and crack face displacements for the different modes of biaxial loading. The equi-biaxial loading mode causes the greatest separation stress but the smallest plastic shear ear and crack displacement. The shear loading system induces the maximum size of shear ear and crack displacement but the smallest value of crack tip separation stress.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00035500
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  • 9
    Electronic Resource
    Electronic Resource
    Continuous crack growth or quantized growth steps? (1979)
    Springer
    International journal of fracture 15 (1979), S. 23-29 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Résumé On examine la théorie suivant laquelle la vitesse de relaxation de l'énergie de Griffith non évanescente requiert une singularité du type r −1 au sommet d'une fissure pour exprimer l'intensité d'énergie, à savoir le produit de la contrainte et de la dilatation. Si l'existence de telle singularité est critiquée sur les bases physiques, des considérations d'équilibre d'énergie de mécanique des milieux continus suggèrent qu'une extension initiale d'une fissure instable s'effectue par un ressaut de croissance discrète caractérisé par une dimension Δa.
    Notes: Abstract The assertion that a non-vanishing Griffith energy release rate requires an r −1 type singularity at the tip of a crack for the energy intensity, i.e. the product of stress and strain, is examined. When the existence of such a singularity is denied on physical grounds continuum mechanics energy balance considerations suggest that initial unstable crack extension is by a discrete growth step of characteristic size Δa.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00115905
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  • 10
    Electronic Resource
    Electronic Resource
    Stresses in a partly yielded notched bar - An assessment of three alternative programs (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 63-73 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The results of three finite element stress analysis programs are compared for the problem of the elasto-plastic bending of a notched beam under plane strain conditions. Both Tresca and von Mises yield criteria are considered and the numerical results are compared with an available analytical solution based on slip-line field theory. The general conclusion is drawn that finite element methods can be used with confidence in elasto-plastic stress analysis.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060108
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