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.

Criterion for Crack Kinking out of the Interface of Two Orthotropic Layers Subjected to Thermal and Mechanical Loading

2013 ◽  
Vol 592-593 ◽  
pp. 169-172
Author(s):  
Petr Damborský ◽  
Oldřich Ševeček ◽  
Tomáš Profant ◽  
Michal Kotoul
Keyword(s):  
Residual Stresses ◽  
Mechanical Loading ◽  
Dissimilar Materials ◽  
Complex Stress ◽  
Crack Kinking ◽  
Thermal Residual Stresses ◽  
Complex Stress Intensity Factor ◽  
Finite Fracture Mechanics ◽  
T Stress ◽  
Path Stability

The problem of crack path stability along the interface between two orthotropic elastically dissimilar materials under the presence of in-plane residual stresses is analyzed using the concept of Finite Fracture Mechanics and matched asymptotic procedure. An energy based fracture criterion is introduced for this problem and it is investigated whether and how is the criterion for the prediction of crack kinking from the interface affected by residual stresses. The complex stress intensity factor and the T-stress characterizing the stress state at the crack tip are calculated both for the thermal (residual stresses) and mechanical loading using the two-state integral. The matched asymptotic procedure together with FEM is used to derive the change of the potential energy induced by the crack growth by crack increment of finite length.

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).

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.

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

Validity of the Finite Fracture Mechanics Based Asymptotic Analysis for Predictions of Crack Deflection in Thin Layers of Ceramic Laminates

2014 ◽  
Vol 627 ◽  
pp. 237-240 ◽  
Author(s):  
Oldřich Ševeček ◽  
Dominique Leguillon ◽  
Tomáš Profant ◽  
Michal Kotoul
Keyword(s):  
Potential Energy ◽  
Asymptotic Solution ◽  
Asymptotic Analysis ◽  
Crack Extension ◽  
Crack Deflection ◽  
Thin Layers ◽  
Reference Solution ◽  
Finite Fracture Mechanics ◽  
Higher Order Terms ◽  
Good Agreement

The work studies and compares different approaches suitable for predictions of the crack deflection (bifurcation) in ceramic laminates containing thin layers under high residual stresses and discuss a suitability and limits of using of the asymptotic analysis for such problems. The thickness of the thin compressive layers where the crack deflection occurs is only one order higher than the crack extension lengths considered within the solution. A purely FEM based calculation of the energy and stress conditions, necessary for the crack propagation, serves as the reference solution to the problem. The asymptotic analysis is used after for calculations of the same quantities (especially of energy release rate – ERR). This concept enables semi-analytical calculations of ERR or changes in potential energy induced by the crack extensions of different lengths and directions. Such approach can save a large amount of simulations and time compared with the pure FEM based calculations. It was found that the asymptotic analysis provides a good agreement for investigations of the crack increments enough far from the adjacent interfaces but for longer extensions (of length above 1/5-1/10 of the distance from the interface) starts more significantly to deviate from the correct solution. Involvement of the higher order terms in the asymptotic solution or other improvement of the model is thus advisable.

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