Mode-II Stress Intensity Factor by Triangular Williams Element with Generalized Degrees of Freedom

2012 ◽  
Vol 204-208 ◽  
pp. 4391-4395
Author(s):  
Hua Xu ◽  
Lu Feng Yang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Degrees Of Freedom ◽  
Crack Tip ◽  
High Accuracy ◽  
Mode Ii ◽  
Mode Ii Crack ◽  
Triangular Elements ◽  
Generalized Degrees Of Freedom

A new triangular Williams element with generalized degrees of freedom (GDOFs) was proposed for analysis of stress intensity factor (SIF) of mode II crack. The singular region around the crack tip was evenly divided into a series of triangular elements, which could be approximated by the improved Williams series. On the basis of the principle, the displacement of local field must be compatible with that of the global one, so that the SIF at the crack tip can be directly evaluated by one of the undetermined constants of the Williams series. Three important parameters for the triangular Williams element, including the radial scale factor, the number of subelements and the terms of the Williams series, were discussed in detail. Numerical example shows that the triangular Williams elements with GDOFs can directly calculate the mode II SIF with high accuracy and efficiency.

Mode-III Stress Intensity Factor by Williams Element with Generalized Degrees of Freedom

2012 ◽  
Vol 487 ◽  
pp. 242-246 ◽  
Author(s):  
Hua Xu ◽  
Lu Feng Yang ◽  
Zhen Ping She
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Crack Tip ◽  
Relative Length ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Generalized Degrees Of Freedom

Williams series are developed for mode III cracks, based on which the displacement field is defined in the singular region around the crack tip. The Williams element with generalized degrees of freedom (GDOFs) is proposed for analysis of stress intensity factor (SIF) of mode III crack. The SIF at the crack tip can be evaluated analytically by one of the undetermined constants of the Williams element. The influence of the relative length of the crack on the SIF is investigated. Three important parameters for the Williams element, including the radial scale factor, the number of subelements and the terms of the Williams series, are discussed in detail. Numerical example shows that the Williams element is of accuracy and efficiency.

Effect of Confining Pressure on Stress Intensity Factors for Cracked Brazilian Disk

2015 ◽  
Vol 07 (03) ◽  
pp. 1550051 ◽  
Author(s):  
Wen Hua ◽  
Jigang Xu ◽  
Shiming Dong ◽  
Jizhou Song ◽  
Qingyuan Wang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Intensity Factors ◽  
Confining Pressure ◽  
Mode Ii ◽  
Pure Mode ◽  
Intensity Factors ◽  
Brazilian Disk ◽  
Mode Ii Crack

An analytical model, verified by the finite element method, is developed to study the effect of confining pressure on stress intensity factors for the cracked Brazilian disk. The closed-form expressions for stress intensity factors under both confining pressure and diametric forces are obtained based on the weight function method. The results show that the confining pressure has no effect on the mode II stress intensity factor; however, the mode I stress intensity factor decreases with the increase of confining pressure and the change may be above 100% for a large confining pressure. In addition, the effect of confining pressure on the loading condition of pure mode II crack is also investigated. It is shown that the critical loading angle for pure mode II crack decreases as the confining pressure increases. Depending on the magnitude of confining pressure, the failure problem of a disk may be no longer a pure fracture problem. These results have established the theoretical foundation to measure the fracture toughness of materials under confining pressure.

Intersonic Crack Propagation—Part II: Suddenly Stopping Crack

2001 ◽  
Vol 69 (1) ◽  
pp. 76-80 ◽  
Author(s):  
Y. Huang ◽  
H. Gao
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Fundamental Solution ◽  
Crack Propagation ◽  
Auxiliary Problem ◽  
Crack Tip ◽  
Mode Ii ◽  
Static Crack ◽  
Intersonic Crack Propagation

In Part I of this series, we have obtained the fundamental solution for a mode II intersonic crack which involves a crack moving uniformly at a velocity between the shear and longitudinal wave speeds while subjected to a pair of concentrated forces suddenly appearing at the crack tip and subsequently acting on the crack faces. The fundamental solution can be used to generate solutions for intersonic crack propagation under arbitrary initial equilibrium fields. In this paper, Part II of this series, we study a mode II crack suddenly stopping after propagating intersonically for a short time. The solution is obtained by superposing the fundamental solution and the auxiliary problem of a static crack emitting dynamic dislocations such that the relative crack face displacement in the fundamental solution is negated ahead of where the crack tip has stopped. We find that, after the crack stops moving, the stress intensity factor rapidly rises to a finite value and then starts to change gradually toward the equilibrium value for a static crack. A most interesting feature is that the static value of stress intensity is reached neither instantaneously like a suddenly stopping subsonic crack nor asymptotically like a suddenly stopping edge dislocation. Rather, the dynamic stress intensity factor changes continuously as the shear and Rayleigh waves catch up with the stopped crack tip from behind, approaches negative infinity when the Rayleigh wave arrives, and then suddenly assumes the equilibrium static value when all the waves have passed by. This study is an important step toward the study of intersonic crack propagation with arbitrary, nonuniform velocities.

An experimental method for evaluating mode II stress intensity factor from near crack tip field

2015 ◽  
Vol 197 (1) ◽  
pp. 119-126 ◽  
Author(s):  
Zhuang He ◽  
Andrei Kotousov ◽  
Andrea Fanciulli ◽  
Filippo Berto
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Experimental Method ◽  
Crack Tip ◽  
Mode Ii ◽  
Crack Tip Field

A No-Slip Interface Crack

1980 ◽  
Vol 47 (2) ◽  
pp. 347-350 ◽  
Author(s):  
A. F. Mak ◽  
L. M. Keer ◽  
S. H. Chen ◽  
J. L. Lewis
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Interface Crack ◽  
Crack Tip ◽  
Mode I ◽  
Mode Ii ◽  
Shear Stresses ◽  
Rough Interface ◽  
Adhesive Fracture

Adhesive fracture of an interdigitated or very rough interface is investigated by considering an interface crack with no-slip zones. Both the normal and the shear stresses are singular at the crack tip with the Mode II stress-intensity factor being generally smaller than that of the Mode I.

A new type of cracks adding to Griffith–Irwin cracks

2019 ◽  
Vol 485 (2) ◽  
pp. 162-165
Author(s):  
V. A. Babeshko ◽  
O. M. Babeshko ◽  
O. V. Evdokimova
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Tip ◽  
Stress Concentrations ◽  
New Type

The distinctions in the description of the conditions of cracking of materials are revealed. For Griffith–Irwin cracks, fracture is determined by the magnitude of the stress-intensity factor at the crack tip; in the case of the new type of cracks, fracture occurs due to an increase in the stress concentrations up to singular concentrations.

scholarly journals Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Bing Yang ◽  
Zhanjiang Wei ◽  
Zhen Liao ◽  
Shuwei Zhou ◽  
Shoune Xiao ◽  
...  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Plastic Zone ◽  
Relative Error ◽  
Crack Tip ◽  
Image Correlation ◽  
Preconditioned Conjugate Gradient ◽  
Loading Process ◽  
Tip Position

AbstractIn the digital image correlation research of fatigue crack growth rate, the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor, thereby affecting the life prediction. This paper proposes a Gauss-Newton iteration method for solving the crack tip position. The conventional linear fitting method provides an iterative initial solution for this method, and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix. A noise-added artificial displacement field is used to verify the feasibility of the method, which shows that all parameters can be solved with satisfactory results. The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result, and the relative error between the two is only − 0.621%; The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip, and the maximum relative error with the test plastic zone area is − 11.29%. The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05%. The crack tip coordinates, stress intensity factors, and plastic zone contour changes in the loading and unloading phases are explored. The results show that the crack tip change during the loading process is faster than the change during the unloading process; the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process; under the same load, the theoretical plastic zone during the unloading process is higher than that during the loading process.

Application of Extended Finite Element Method (XFEM) to Stress Intensity Factor Calculations

2015 ◽  
Author(s):  
Do-Jun Shim ◽  
Mohammed Uddin ◽  
Sureshkumar Kalyanam ◽  
Frederick Brust ◽  
Bruce Young
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Degrees Of Freedom ◽  
Extended Finite Element Method ◽  
Partition Of Unity ◽  
Extended Finite Element ◽  
Element Method

The extended finite element method (XFEM) is an extension of the conventional finite element method based on the concept of partition of unity. In this method, the presence of a crack is ensured by the special enriched functions in conjunction with additional degrees of freedom. This approach also removes the requirement for explicitly defining the crack front or specifying the virtual crack extension direction when evaluating the contour integral. In this paper, stress intensity factors (SIF) for various crack types in plates and pipes were calculated using the XFEM embedded in ABAQUS. These results were compared against handbook solutions, results from conventional finite element method, and results obtained from finite element alternating method (FEAM). Based on these results, applicability of the ABAQUS XFEM to stress intensity factor calculations was investigated. Discussions are provided on the advantages and limitations of the XFEM.

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