Simulating three-dimensional stress intensity factors by the least-squares method

The analysis of cracked brittle mechanical components considering linear elastic fracture mechanics is usually reduced to the evaluation of stress intensity factors (SIFs). The SIF calculation can be carried out experimentally, theoretically or numerically. Each methodology has its own advantages but the use of numerical methods has become very popular. Several schemes for numerical SIF calculations have been developed, the J-integral method being one of the most widely used because of its energy-like formulation. Additionally, some variations of the J-integral method, such as displacementbased methods, are also becoming popular due to their simplicity. In this work, a simple displacement-based scheme is proposed to calculate SIFs, and its performance is compared with contour integrals. These schemes are all implemented with the Boundary Element Method (BEM) in order to exploit its advantages in crack growth modelling. Some simple examples are solved with the BEM and the calculated SIF values are compared against available solutions, showing good agreement between the different schemes.

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“…• The Least Squares method was used by Ju (1998) to extract the KIII SIF through a least square fit of the stress solution obtained from the FEM.…”

Section: Introductionmentioning

confidence: 99%

A New Displacement-based Approach to Calculate Stress Intensity Factors With the Boundary Element Method

González

Teixeira

Wrobel

et al. 2015

Lat. Am. j. solids struct.

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“…16. The 3D mixed-mode cracked problems in Ju's article (Ju 1998) were analyzed using the current method and found to be in good agreement with the theoretical solutions, so this section only discusses the results of sharp V-notch problems. Example 1 This example examines a thin plate with a sharp V-notch subjected to uniform tension σ 0 , as shown in Fig.…”

Section: Numerical Validationsmentioning

confidence: 91%

“…The least-squares method has been applied to experimental and finite element methods for calculation of the SIFs of cracked bodies (Hyde and Warrior 1990; Ju 1996Ju , 1998Ju et al 2006). In this study, the leastsquares method incorporating the finite element analysis was employed to find the mixed-mode SIFs of a sharp V-notch.…”

Section: Least-squares Methods To Find Sifs Of a Sharp V-notchmentioning

confidence: 99%

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Accuracy and limit of a least-squares method to calculate 3D notch SIFs

Chung

2007

Int J Fract

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To evaluate the three-dimensional (3D) stress intensity factors (SIFs) of a sharp V-notch using the finite element result is limited in the literature. Thus, this study developed a least-squares method to solve this problem as well as study its restriction and accuracy. First, the William's eigenfunction and complex stress function approach are deduced into a least-squares form, and then stress field from the finite element analysis is substituted into the least-squares equation to evaluate the 3D SIFs. Numerical simulations in this article show that the least-squares method can be used to calculate SIFs accurately if more than two stress terms are included. The calculated SIFs of this least-squares method are not sensitive to the maximum and minimum radiuses of the area from which data are included. The major advantage of the proposed method is that the procedure is simple and systematic, so it can be applied to any finite element code without difficulties.

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“…Because elastic constants for cubic QCs are not available presently [6], the material parameters are assumed as follows: C 11 = 4 GPa, C 12 = 2 GPa, C 44 = 3 GPa,…”

Section: Basic Equationsmentioning

confidence: 99%

Finite Element Method for Static Problems of Cubic Quasicrystals

Yang¹,

He²,

Gao³

2014

Acta Phys. Pol. A

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We put forward a nite element method for static problems of cubic quasicrystals by variation of a suitable general potential functional. As an example we study a quasicrystal column containing a penny-shaped crack. The comparison with analytical results shows that the precision and eciency of the numerical solution are satisfactory. The procedure can be used to solve more complicated boundary value problems and can be extended towards more sophisticated methods of crack tip loading analysis.

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Simulating three-dimensional stress intensity factors by the least-squares method

Cited by 20 publications

References 12 publications

A New Displacement-based Approach to Calculate Stress Intensity Factors With the Boundary Element Method

A New Displacement-based Approach to Calculate Stress Intensity Factors With the Boundary Element Method

Accuracy and limit of a least-squares method to calculate 3D notch SIFs

Finite Element Method for Static Problems of Cubic Quasicrystals

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