Weight functions and stress intensity factors for embedded cracks subjected to arbitrary mode I stress fields

Glinka, G.; Reinhardt, Wolf

doi:10.1016/s1566-1369(99)80041-7

Cited by 8 publications

(8 citation statements)

References 9 publications

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“…Using the weight function approach (Glinka, 1996), maximum stress intensity factors ( K Imax ) were calculated for the crack profiles seen in Figures 13 and 14 along with a few others. The weight function method was preferred since the equations accounted for the thickness of the samples, which on average was about 3.56 mm.…”

Section: Resultsmentioning

confidence: 99%

Variability on nucleation and growth of short fatigue cracks due to material anisotropy in aluminum 2024-T351

Makas

Avallone

MacKinnon

et al. 2012

Journal of Intelligent Material Systems and Structures

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Early fatigue life behavior is important for the prediction of residual useful life of aerospace structures via computational modeling. In particular, the influence of rolling-induced anisotropy on fatigue properties has not been studied extensively, but it is likely to be an important effect. Therefore, fatigue behavior of a 2024-T351 plate was studied using notched uniaxial samples with load axes along either longitudinal or long transverse directions. Interrupted fatigue testing at stresses close to yielding was performed to nucleate and propagate short cracks, and local nucleation sites were located and characterized using optical and electron microscopy techniques. Results show that crack nucleation occurred due to fractured particles for longitudinal samples, while either debonded or fractured particles led to nucleation for transverse samples. Crack nucleation from debonded particles reduced life till matrix fracture because sharper flaws were generated when compared to those from fractured particles. Longitudinal samples experienced multisite crack initiation because of preferential fracture of inclusions for that loading direction. Conversely, long transverse samples showed reduced particle fracture, which eliminated multisite cracking. Crystallography of individual grains also played a role related to bulk plasticity in the grains, as estimated by their individual Taylor factors, and to environmental effects.

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Section: Resultsmentioning

confidence: 99%

Variability on nucleation and growth of short fatigue cracks due to material anisotropy in aluminum 2024-T351

Makas

Avallone

MacKinnon

et al. 2012

Journal of Intelligent Material Systems and Structures

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“…The LEFM model applied by Krug and others (2014) is similar to the van der Veen (1998b) model in that the net Cauchy stress is multiplied by a single weight function and integrated over the depth of the crack to obtain the net SIF. Thus, using the weight function method, net SIF at the tip of a surface crevasse is calculated as and at the tip of a basal crevasse is calculated as where β is the universal weight function provided in Appendix C (Glinka, 1996). The term ‘universal weight function’ is slightly deceiving here because the parameters M i in the expression for β (see Appendix C) change with the geometry and boundary conditions of the cracked body.…”

Section: Lefm Models and Methodsmentioning

confidence: 99%

On the evaluation of the stress intensity factor in calving models using linear elastic fracture mechanics

Jiménez

Duddu

2018

J. Glaciol.

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We investigate the appropriateness of calving or crevasse models from the literature using linear elastic fracture mechanics (LEFM). To this end, we compare LEFM model-predicted stress intensity factors (SIFs) against numerically computed SIFs using the displacement correlation method in conjunction with the finite element method. We present several benchmark simulations wherein we calculate the SIF at the tips of water-filled surface and basal crevasses penetrating through rectangular ice slabs under different boundary conditions, including grounded and floating conditions. Our simulation results indicate that the basal boundary condition significantly influences the SIF at the crevasse tips. We find that the existing calving models using LEFM are not generally accurate for evaluating SIFs in grounded glaciers or floating ice shelves. We also illustrate that using the ‘single edge crack’ weight function in the LEFM formulations may be appropriate for predicting calving from floating ice shelves, owing to the low fracture toughness of ice; whereas, using the ‘double edge crack’ or ‘central through crack’ weight functions is more appropriate for predicting calving from grounded glaciers. To conclude, we recommend using the displacement correlation method for SIF evaluation in real glaciers and ice shelves with complex geometries and boundary conditions.

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“…Another simple approximate method was proposed by G‐S . In this method, 3D SIFs at two points are considered.…”

Section: Wfms For 3d Crack Problemsmentioning

confidence: 99%

“…The choice of geometric condition is inconsistent: m" = 0 was used in the previous study 46 with fixed constant of M 2 = 3, and m' = 0 was used in another study. 107 For the surface point, the FIGURE 13 Ratio of the two multiple reference states (MRS) Green's functions (GFs) for an edge crack in a circular disc, based on the same reference load cases and geometric condition m" = 0, by using Glinka-Shen universal weight function method (UWFM) and Fett-Munz direct adjustment method (DAM) weight function method (WFM), respectively geometric condition in the G-S UWF is replaced by a condition that the WF must vanish at the surface by considering the "boundary layer effect" in which the stress singularity "r −1/2 " vanishes. Another problem with this method is that only SIFs due to stresses varying in one direction (x or y, so called univariant stress) can be considered.…”

Section: Wfms For 3d Crack Problemsmentioning

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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Weight functions and stress intensity factors for embedded cracks subjected to arbitrary mode I stress fields

Cited by 8 publications

References 9 publications

Variability on nucleation and growth of short fatigue cracks due to material anisotropy in aluminum 2024-T351

Variability on nucleation and growth of short fatigue cracks due to material anisotropy in aluminum 2024-T351

On the evaluation of the stress intensity factor in calving models using linear elastic fracture mechanics

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

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