Evaluation of the Higher Order Terms of the Wedge-Splitting Specimen Based on the SBFEM

2013 ◽  
Vol 477-478 ◽  
pp. 25-29 ◽  
Author(s):  
Feng Lin Xu ◽  
Jun Yu Liu ◽  
Bao Kuan Ning ◽  
He Fan
Keyword(s):  
Radial Direction ◽  
High Accuracy ◽  
Higher Order ◽  
Asymptotic Field ◽  
Crack Tip Asymptotic Field ◽  
Higher Order Terms ◽  
T Stress ◽  
Crack Stability ◽  
Scaled Boundary Finite Element ◽  
Wedge Splitting

The scaled boundary finite element method (abbr. SBFEM) is a semi-analytical method developed by Wolf and Song. The analytical advantage of the solution in the radial direction allows SBFEM converge to the Williams expansion. The coefficients of the Williams expansion, including the stress intensity factor, the T-stress, and higher order terms can be calculated directly without further processing. In the paper the coefficients of higher order terms of the crack tip asymptotic field of typical wedge splitting specimens with two different loading arrangements are evaluated using SBFEM. Numerical results show the method has high accuracy and effectiveness. The results have certain significance on determining crack stability of the wedge-splitting specimen.

Evaluation of the T-Stress and the Higher Order Terms of the Elastic Crack Based on the SBFEM

2013 ◽  
Vol 838-841 ◽  
pp. 2275-2278 ◽  
Author(s):  
Jun Yu Liu ◽  
Feng Lin Xu ◽  
Bao Kuan Ning ◽  
He Fan
Keyword(s):  
Edge Crack ◽  
Crack Tip ◽  
High Accuracy ◽  
Higher Order ◽  
Elastic Plates ◽  
Single Edge ◽  
Higher Order Terms ◽  
T Stress ◽  
Elastic Crack ◽  
Scaled Boundary Finite Element

The Scaled Boundary Finite Element Method (abbr. SBFEM) developed by Wolf and Song is a numerical method which has a half analytical nature. In the paper, the asymptotic fields of central crack tip and single edge crack tip of the plane elastic plates are evaluated based on the SBFEM. Numerical examples are provided to demonstrate its high accuracy and effectiveness, and the numerical results show that SBFEM can calculate the SIFs, T-stress and the coefficients of higher order terms with higher efficiency and accuracy. The singular fields of crack-tip with complex configuration can be evaluated combining the sub-structuring technique (or super-element).

Crack Deflection from the Interface between Two Orthotropic Materials-Effect of Higher Order Terms in Asymptotic Analysis

2013 ◽  
Vol 577-578 ◽  
pp. 157-160
Author(s):  
Petr Damborský ◽  
Oldřich Ševeček ◽  
Tomáš Profant ◽  
Michal Kotoul
Keyword(s):  
Fracture Criterion ◽  
Input Parameter ◽  
Complex Stress ◽  
Higher Order ◽  
Crack Deflection ◽  
Orthotropic Materials ◽  
Complex Stress Intensity Factor ◽  
Higher Order Terms ◽  
T Stress ◽  
Main Input

The problem of crack deflection from the interface between two orthotropic materials is analyzed using the concept of Finite fracture mechanics and matched asymptotic procedure. A fracture criterion based on the energy approach is introduced for this problem. The main input for such criterion is the complex stress intensity factor calculated e.g. using the two-state integral. However for more precise predictions of the crack propagation also higher order terms of the asymptotic expansion are advisable to involve in the fracture criterion. To this end a T-stress term will be calculated and considered as the second input parameter. The matched asymptotic procedure together with FEM is used to derive the change of the potential energy induced by the incremental crack growth.

Using the Multi-Parameter Fracture Mechanics for more Accurate Description of Stress/Displacement Crack Tip Fields

2013 ◽  
Vol 586 ◽  
pp. 237-240 ◽  
Author(s):  
Lucie Šestáková
Keyword(s):  
Stress Distribution ◽  
Fracture Mechanics ◽  
Boundary Conditions ◽  
Displacement Field ◽  
Singular Term ◽  
Crack Tip ◽  
Higher Order ◽  
Precise Description ◽  
Accurate Knowledge ◽  
Higher Order Terms

Most of fracture analyses often require an accurate knowledge of the stress/displacement field over the investigated body. However, this can be sometimes problematic when only one (singular) term of the Williams expansion is considered. Therefore, also other terms should be taken into account. Such an approach, referred to as multi-parameter fracture mechanics is used and investigated in this paper. Its importance for short/long cracks and the influence of different boundary conditions are studied. It has been found out that higher-order terms of the Williams expansion can contribute to more precise description of the stress distribution near the crack tip especially for long cracks. Unfortunately, the dependences obtained from the analyses presented are not unambiguous and it cannot be strictly derived how many of the higher-order terms are sufficient.

The Skyrme model and higher order terms

1990 ◽  
Vol 235 (1-2) ◽  
pp. 141-146 ◽  
Author(s):  
Luc Marleau
Keyword(s):  
Higher Order ◽  
Skyrme Model ◽  
Higher Order Terms

scholarly journals Experimental determination and finite element analysis of coefficients of the multi-parameter Williams series expansion in the vicinity of the crack tip in linear elastic materials. Part I

2020 ◽  
pp. 237-249
Author(s):  
L. V Stepanova
Keyword(s):  
Series Expansion ◽  
Digital Image ◽  
Power Series Expansion ◽  
Crack Tip ◽  
Higher Order ◽  
Accurate Estimation ◽  
Principal Stresses ◽  
Isochromatic Fringe ◽  
Higher Order Terms ◽  
Fringe Patterns

This study aims at obtaining coefficients of the multi-parameter Williams series expansion for the stress field in the vicinity of the central crack in the rectangular plate and in the semi-circular notched disk under bending by the use of the digital photoelasticity method. The higher-order terms in the Williams asymptotic expansion are retained. It allows us to give a more accurate estimation of the near-crack-tip stress, strain and displacement fields and extend the domain of validity for the Williams power series expansion. The program is specially developed for the interpretation and processing of experimental data from the phototelasticity experiments. By means of the developed tool, the fringe patterns that contain the whole field stress information in terms of the difference in principal stresses (isochromatics) are captured as a digital image, which is processed for quantitative evaluations. The developed tool allows us to find points that belong to isochromatic fringes with the minimal light intensity. The digital image processing with the aid of the developed tool is performed. The points determined with the adopted tool are used further for the calculations of the stress intensity factor, T-stresses and coefficients of higher-order terms in the Williams series expansion. The iterative procedure of the over-deterministic method is utilized to find the higher order terms of the Williams series expansion. The procedure is based on the consistent correction of the coefficients of the Williams series expansion. The first fifteen coefficients are obtained. The experimentally obtained coefficients are used for the reconstruction of the isochromatic fringe pattern in the vicinity of the crack tip. The comparison of the theoretically reconstructed and experimental isochromatic fringe patterns shows that the coefficients of the Williams series expansion have a good match.

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