A numerical approach for determining weight functions in fracture mechanics

Beghini, Marco; Bertini, Leonardo; Vitale, E.

doi:10.1002/nme.1620320309

Cited by 14 publications

(6 citation statements)

References 18 publications

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“…Moreover, the pressure σ(x,y) is "read" in the new coordinates (, φ) for any fixed α, in the sense that x and y are given by (8), with r being defined by (9). If the crack has a radius equal to a the stress intensity factor becomes (13) we obtain the well-known result:…”

Section: Analytical Backgroundmentioning

confidence: 76%

“…Although not exact, this weight function, for the three-dimensional case [11], is an excellent approximation that retains all the typical characteristics of the weighted functions in [12]. In particular, in the case of a semi-axial ellipse (1, b), when eccentricity e tends to zero, the main contribution of the Oore-Burns integral differs from Irwin's analytical solution [13] for an amount equal to 2 20 e  [14]. The advantage offered by the Oore-Burns integral is to use a generic shape of the defect and the evaluation of SIF at each point of the creak contour without the need to consider the elliptical shape.…”

Section: Introductionmentioning

confidence: 90%

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Stress intensity factor for small embedded cracks in weldments

Livieri

Segàla

2019

Frattura Ed Integrità Strutturale

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In the present work, the stress intensity factor (SIF) of embedded small cracks placed at the weld toe is calculated by means of two procedures based on the Oore-Burns integral. In the first approach, the defect is considered as a circular disk and the SIF is evaluated by means of the Oore-Burns weight function. By taking advantage of a suitable change of variable, the singularity of the weight function on the crack border can be removed. In this way, the numerical evaluation of the SIF is possible without the use of specific integration algorithms, although the nominal stress field becomes singular when the crack approaches a V-sharpe notch. As an example, the obtained equations are applied to a defect located in the neighbourhood of a weld toe with an opening angle of 135 degrees under mode I loading. Subsequently, for a crack similar to a star domain with a border expressed by means of the Fourier series, the SIF is given by means of an explicit equation based on the Oore-Burns weight function.

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Section: Analytical Backgroundmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 90%

Stress intensity factor for small embedded cracks in weldments

Livieri

Segàla

2019

Frattura Ed Integrità Strutturale

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“…A discretized nodal WF was determined by Tsai and Ma using FEM with virtual crack extension (VCE) and least square fitting procedure. Beghini et al developed a technique based on FE calculations with coarse meshes, which can be regarded as intermediate between pure analytical and numerical methods, but accuracy of the WFs is not so good. Fett et al performed FE computations for kinked edge crack and the results for point forces provide the WF through a fit procedure .…”

Section: Numerical Weight Function Methodsmentioning

confidence: 99%

A review and verification of analytical weight function methods in fracture mechanics

2019

Fatigue Fract Eng Mat Struct

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The weight function method is a powerful method for the determination of key parameters of stress intensity factors and crack opening displacements that are fundamental for crack analyses in fracture mechanics. The method has a remarkable computational efficiency without compromising solution accuracy and is especially suited for cracks in real‐world components with complex stress gradients. A critical issue for successful development and reliable application of the weight function method is how to achieve verifiable and high solution accuracy. This paper provides several reflections on the current state of the art in weight function methods, including a brief historical perspective and description of several analytical and numerical weight methods, with main focus on the two‐dimensional (2D) analytical approaches. A variety of typical application examples are presented. A platform for point‐by‐point accuracy assessment by using the Green's functions is established on a completely independent numerical approach with validated accuracy. Rigorous and systematic verification of the accuracy levels of different 2D analytical weight function approaches are conducted using several benchmark crack geometries. The sources of inaccuracy of different analytical weight function methods are analysed. A brief account on weight function methods for analysing three‐dimensional (3D) crack problems with arbitrary univariant and bivariant stress distributions is provided.

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“…The weight function method has been used for SIF calculation in different problems, and it has proved to be efficient 13–17 . In fact, due to the dependence of the WF only on geometric parameters, the SIF calculation reduces to a numerical integration along the crack face of the WF multiplied by the stress acting in an uncracked body.…”

Section: Introductionmentioning

confidence: 99%

A mode II weight function for subsurface cracks in a two‐dimensional half‐space

Mazzù

2002

Fatigue Fract Eng Mat Struct

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The general properties of a mode II Weight Function for a subsurface crack in a two‐dimensional half‐space are discussed. A general form for the WF is proposed, and its analytical expression is deduced from the asymptotic properties of the displacements field near the crack tips and from some reference cases obtained by finite elements models. Although the WF has general validity, the main interest is on its application to the study of rolling contact fatigue: its properties are explored for a crack depth range within which the most common failure phenomena in rolling contact are experimentally observed, and for a crack length range within the field of short cracks. The accuracy is estimated by comparison with several results obtained by FEM models, and its validity in the crack depth range explored is shown.

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A numerical approach for determining weight functions in fracture mechanics

Cited by 14 publications

References 18 publications

Stress intensity factor for small embedded cracks in weldments

Stress intensity factor for small embedded cracks in weldments

A review and verification of analytical weight function methods in fracture mechanics

A mode II weight function for subsurface cracks in a two‐dimensional half‐space

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