scholarly journals Nonlinear mechanics of cracks subjected to indentation

2006 ◽  
Vol 33 (6) ◽  
pp. 766-775 ◽  
Author(s):  
A P Selvadurai
Keyword(s):  
Stress Intensity ◽  
Boundary Element ◽  
Crack Tip ◽  
Elastic Solid ◽  
Friction Stress ◽  
Friction Angle ◽  
Element Formulation ◽  
Plastic Energy ◽  
Crack Problems ◽  
Element Technique

The paper presents the application of a boundary element technique to study the behaviour of plane cracks that are located at corner regions of an elastic solid and open during indentation. In particular, the surfaces of the planes on which indentation takes place also exhibit Coulomb frictional responses and degradation in the friction angle with plastic energy dissipation. An incremental boundary element formulation, in which special singularity elements model the behaviour at the crack tip, is used to examine the crack problems. The methodology is applied to investigate the mode I stress intensity factor at the crack tip located at the base of a V-notch in a test specimen.Key words: indented cracks, boundary element modelling, Coulomb friction, stress intensity factors

An improved boundary element formulation for calculating stress intensity factors: Application to aerospace structures

1987 ◽  
Vol 22 (4) ◽  
pp. 203-207 ◽  
Author(s):  
M H Aliabadi ◽  
D P Rooke ◽  
D J Cartwright
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Boundary Element ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Stress Fields ◽  
Element Formulation ◽  
Intensity Factors ◽  
Singular Stress ◽  
Singular Stress Field

In order to compute stress intensity factors accurately, the standard boundary element method is modified to take explicit account of the singularity in the stresses at a crack-tip. The known expansion terms of the crack tip displacement and stress fields are subtracted to remove the numerical difficulties associated with the representation of a singular stress field at the crack-tip. Hence the accuracy of calculation is much improved, without appreciably increasing the amount of computation involved. Furthermore, the stress intensity factor is directly obtained as a part of a solution and no extrapolations are required. The improved formulation is applied to a configuration, which is representative of a part of the wing in a civil transport aeroplane. This configuration consists of a pair of circular cut-outs (supply ports) near to which smaller holes exist; these small holes are particularly susceptible to cracking.

Boundary Element Analysis of Interface Cracks

2005 ◽  
Author(s):  
A. R. Hadjesfandiari ◽  
G. F. Dargush
Keyword(s):  
Stress Intensity ◽  
Boundary Element ◽  
Stress Intensity Factors ◽  
Stress Singularity ◽  
Dissimilar Materials ◽  
Quadrature Formulas ◽  
Element Formulation ◽  
Intensity Factors ◽  
Element Analysis ◽  
Crack Problems

A new boundary element formulation is developed to determine the complex stress intensity factors associated with cracks on the interface between dissimilar materials. This represents an extension of the methodology developed previously by the authors for determination of free-edge generalized stress intensity factors on bimaterial interfaces, which employs displacements and weighted tractions as primary variables. However, in the present work, the characteristic oscillating stress singularity is addressed through the introduction of modified weighting functions and corresponding numerical quadrature formulas. As a result, this boundary-only approach provides extremely accurate mesh-independent solutions for a range of interface crack problems. A number of computational examples are considered to assess the performance of the method in comparison with analytical solutions and previous work on the subject.

scholarly journals Dynamic Mixed Mode I-II Crack Kinking Under Oblique Stress Wave Loading in Brittle Solids

1990 ◽  
Vol 57 (1) ◽  
pp. 117-127 ◽  
Author(s):  
Chien-Ching Ma
Keyword(s):  
Stress Intensity ◽  
Stress Wave ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Elastic Solid ◽  
Perturbation Parameter ◽  
Intensity Factors ◽  
Linear Superposition ◽  
Dynamic Stress Intensity Factors ◽  
Brittle Solids

The dynamic stress intensity factors of an initially stationary semi-infinite crack in an unbounded linear elastic solid which kinks at some time tf after the arrival of a stress wave is obtained as a function of kinking crack tip velocity v, kinking angle δ, incident stress wave angle α, time t, and the delay time tf. A perturbation method, using the kinking angle δ as the perturbation parameter, is used. The method relies on solving simple problems which can be used with linear superposition to solve the problem of a kinked crack. The solutions can be compared with numerical results and other approximate results for the case of tf = 0 and give excellent agreement for a large range of kinking angles. The elastodynamic stress intensity factors of the kinking crack tip are used to compute the corresponding fluxes of energy into the propagating crack-tip, and these results are discussed in terms of an assumed fracture criterion.

Effective Use of Commercial FEM Software in 2-Dimentional Crack Problems

2008 ◽  
Vol 33-37 ◽  
pp. 103-108
Author(s):  
Hironobu Nisitani ◽  
Kuniharu Ushijima ◽  
D.H. Chen ◽  
Akihide Saimoto
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
High Accuracy ◽  
Intensity Factors ◽  
Structural Problems ◽  
Crack Problems ◽  
Accuracy Of Results ◽  
Element Technique ◽  
Effective Use

Finite element method (FEM) is used widely for various structural problems. However, in general, it is difficult to guarantee the accuracy of results obtained by commercial software of FEM. In this paper, a practical finite element technique for calculating the stress intensity factors with high accuracy is proposed. This technique is based on the characteristics of stress field due to a crack. In this study, the proposed method is applied to 2-dimentional crack problems.

Nodal Collocation for the P-Convergent Scheme in Boundary Element Technique

2013 ◽  
Vol 405-408 ◽  
pp. 3139-3142
Author(s):  
Kwang Sung Woo ◽  
Won Seok Jang ◽  
Yoo Mi Kwon ◽  
Jun Hyung Jo
Keyword(s):  
Boundary Element ◽  
Higher Order ◽  
Kernel Functions ◽  
Element Formulation ◽  
Shape Functions ◽  
Collocation Points ◽  
Element Technique ◽  
Scheme Selection ◽  
Shaped Domain ◽  
Hierarchical Pattern

The concept of thep-convergent boundary element modeling has been presented to analyze the potential problem with L-shaped domain. The details of thep-convergent boundary element formulation are discussed. These include the equations of nodal collocation for thep-convergent scheme, selection of higher order hierarchical shape functions, techniques for integrating the product of the kernel functions and corresponding shape functions, strategies for selecting collocation points used in approximating the unknowns associated with the higher order shape functions, and program organizations. A numerical example that demonstrates the performance of thep-convergent boundary element formulation is shown with respect to different arrangement of collocation points including both symmetric non-hierarchical pattern and non-symmetric hierarchical pattern.

scholarly journals Stiffness Derivative Finite Element Technique to Determine Nodal Weight Functions With Singularity Elements

1983 ◽  
Author(s):  
George T. Sha
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Weight Functions ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Crack Face ◽  
Crack Geometry ◽  
Crack Problems

The use of the stiffness derivative technique coupled with “quarter-point” singular crack-tip elements permits very efficient finite element determination of both stress intensity factors and nodal weight functions. Two-dimensional results are presented in this paper to demonstrate that accurate stress intensity factors and nodal weight functions can be obtained from relatively coarse mesh models by coupling the stiffness derivative technique with singular elements. The principle of linear superposition implies that the calculation of stress intensity factors and nodal weight functions with crack-face loading, σ(rs), is equivalent to loading the cracked body with remote loads, which produces σ(rs) on the prospective crack face in the absence of crack. The verification of this equivalency is made numerically, using the virtual crack extension technique. Load independent nodal weight functions for two-dimensional crack geometry is demonstrated on various remote and crack-face loading conditions. The efficient calculation of stress intensity factors with the use of the “uncracked” stress field and the crack-face nodal weight functions is also illustrated. In order to facilitate the utilization of the discretized crack-face nodal weight functions, an approach was developed for two-dimensional crack problems. Approximations of the crack-face nodal weight functions as a function of distance, (rs), from crack-tip has been successfully demonstrated by the following equation: h a , r s = A a √ r s + B a + C a √ r s + D a r s Coefficients A(a), B(a), C(a) and D(a), which are functions of crack length (a), can be obtained by least-squares fitting procedures. The crack-face nodal weight functions for a new crack geometry can be approximated using cubic spline interpolation of the coefficients A, B, C and D of varying crack lengths. This approach, demonstrated on the calculation of stress intensity factors for single edge crack geometry, resulted in a total loss of accuracy of less than 1%.

scholarly journals Fracture analysis of cracked thermopiezoelectric materials by BEM

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
Qing-Hua Qin
Keyword(s):  
Boundary Element ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Element Model ◽  
Element Formulation ◽  
Multiple Crack ◽  
Brief Assessment ◽  
Crack Problems ◽  
Piezoelectric Solid ◽  
Thermopiezoelectric Materials

The boundary element formulation for analysing cracked thermopiezoelectric materials due to thermal and electroelastic loads is reviewed in this paper. By way of Green's functions for piezoelectric solid with defects and variational principle, a boundary element model (BEM) for a 2-D thermopiezoelectric solid with various defects is discussed. The method is applicable to multiple crack problems in both finite and infinite solids. Finally a brief assessment of the boundary element formulation is made by considering some numerical examples for stress and electric displacement (SED) intensity factors at a particular crack-tip in a crack system of piezoelectric materials.

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