Numerical Modeling of Dynamic Crack Propagation in Finite Bodies, by Moving Singular Elements—Part 1: Formulation

1980 ◽  
Vol 47 (3) ◽  
pp. 570-576 ◽  
Author(s):  
T. Nishioka ◽  
S. N. Atluri
Keyword(s):  
Dynamic Stress ◽  
Numerical Solutions ◽  
Dynamic Stress Intensity Factor ◽  
Crack Tip ◽  
Material Behavior ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Linear Elastic ◽  
Spatial Movement ◽  
Numerical Finite Element

An efficient numerical (finite-element) method is presented for the dynamic analysis of rapidly propagating cracks in finite bodies, of arbitrary shape, wherein linear-elastic material behavior and two-dimensional conditions prevail. Procedures to embed analytical asymptotic solutions for singularities in stresses/strains near the propagating crack-tip, to account for the spatial movement of these singularities along with the crack-tip, and to directly compute the dynamic stress-intensity factor, are presented. Numerical solutions of several problems and pertinent discussions are presented in Part 2 of this paper.

Numerical Modeling of Dynamic Crack Propagation in Finite Bodies, by Moving Singular Elements—Part 2: Results

1980 ◽  
Vol 47 (3) ◽  
pp. 577-582 ◽  
Author(s):  
T. Nishioka ◽  
S. N. Atluri
Keyword(s):  
Crack Propagation ◽  
Dynamic Stress ◽  
Numerical Solutions ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Intensity Factors ◽  
Infinite Domain ◽  
Wave Interactions ◽  
Dynamic Stress Intensity Factors ◽  
Finite Domains

Using the moving-singularity finite-element method described in Part 1 of this paper, several problems of dynamic crack propagation in finite bodies have been analyzed. Discussions of the effects of wave interactions on the dynamic stress-intensity factors are presented. The obtained numerical results are compared with the corresponding infinite domain solutions and other available numerical solutions for finite domains.

An experimental investigation of dynamic crack propagation

1995 ◽  
Vol 30 (3) ◽  
pp. 175-183
Author(s):  
T H Hyde ◽  
A Yaghi
Keyword(s):  
Crack Propagation ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Initiation Site ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Thin Wall ◽  
Load Pressure ◽  
Strain Fracture ◽  
Unique Relationship

Burst tests have been performed on closed-ended thin wall tubes with axially aligned, external, semicircular, crack-like flaws. The tubes were made of Araldite CT200 with HT907 hardener. Dynamic crack propagation rates between 0.14c1 and 0.30c1 were measured, c1 being the velocity of longitudinal waves in the walls of the tubes. The fracture surfaces exhibited a smooth mirror-like appearance near the crack initiation site. This was followed by a mist region and then a hackle region. The roughness in the hackle region becomes progressively greater with distance from the initiation site and crack branching can eventually occur. The KID/KIC (where KID is the applied dynamic stress intensity factor and KIC is the plane strain fracture toughness) value at which the hackle region begins is about 3.34 and the KID/KIC value at which branching begins is about 8.75. Previously reported work only contains results for KID/KIC up to about 5. The present work contains results for KID/KIC up to about 14, which correlate with previous work for KID/KIC values less than about 4. However, previous work has indicated that a unique relationship may exist between v/c1 and KID/KIC. The present work indicates that although this is a good approximation, a systematic variation with load (pressure in this case) has been detected.

scholarly journals A method for coupling atoms to continuum mechanics for capturing dynamic crack propagation

2008 ◽  
pp. 651-662
Author(s):  
Pascal Aubertin ◽  
René de Borst ◽  
Julien Réthoré
Keyword(s):  
Fracture Mechanics ◽  
Crack Propagation ◽  
Continuum Mechanics ◽  
Crack Tip ◽  
Theoretical Background ◽  
Numerical Results ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Linear Elastic ◽  
Continuum Description

Conventionally, dynamic crack propagation is modelled using fracture mechanics (either linear elastic, or with an extension to confined plasticity). Herein, we propose a different view, based on a coupling between an atomic description at the crack tip and a classical continuum description away from it. The paper presents the theoretical background and some first numerical results.

Dynamic Stress Intensity Factor for a Radial Crack on a Circular Cavity in a Piezoelectric Medium

2010 ◽  
Vol 452-453 ◽  
pp. 273-276
Author(s):  
Tian Shu Song ◽  
Dong Li ◽  
Ming Yue Lv ◽  
Ming Ju Zhang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Dynamic Stress ◽  
Radial Crack ◽  
Dynamic Stress Intensity Factor ◽  
Crack Tip ◽  
Piezoelectric Medium ◽  
Circular Cavity ◽  
Dynamic Stress Intensity Factors

The problem of dynamic stress intensity factor is investigated theoretically in present paper for a radial crack on a circular cavity in an infinite piezoelectric medium, which is subjected to time-harmonic incident anti-plane shearing. First, a pair of electromechanically coupled Green’s functions are constructed which indicate the basic solutions for a semi-infinite piezoelectric medium with a semi-circular cavity. Second, based on the crack-division technique and conjunction technique, integral equations for the unknown stresses’ solution on the conjunction surface is established, which are related to the dynamic stress intensity factor at the crack tip. Third, the analytical expression on dynamic stress intensity factor at the crack tip is obtained. At last, some calculating cases are plotted to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the geometry of the crack and the circular cavity influence upon the dynamic stress intensity factors. While some of the calculating results are compared with the same situation about a straight crack and with static solutions.

Mechanics of dynamic debonding

1991 ◽  
Vol 433 (1889) ◽  
pp. 679-697 ◽  
Keyword(s):  
Steady State ◽  
Stress Intensity ◽  
Rayleigh Wave ◽  
Wave Speed ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Crack Tip ◽  
Interface Fracture ◽  
Dynamic Stress Intensity Factors ◽  
Rayleigh Wave Speed

Singular fields around a crack running dynamically along the interface between two anisotropic substrates are examined. Emphasis is placed on extending an established frame work for interface fracture mechanics to include rapidly applied loads, fast crack propagation and strain rate dependent material response. For a crack running at non-uniform speed, the crack tip behaviour is governed by an instantaneous steady-state, two-dimensional singularity. This simplifies the problem, rendering the Stroh techniques applicable. In general, the singularity oscillates, similar to quasi-static cracks. The oscillation index is infinite when the crack runs at the Rayleigh wave speed of the more compliant material, suggesting a large contact zone may exist behind the crack tip at high speeds. In contrast to a crack in homogeneous materials, an interface crack has a finite energy factor at the lower Rayleigh wave speed. Singular fields are presented for isotropic bimaterials, so are the key quantities for orthotropic bimaterials. Implications on crack branching and substrate cracking are discussed. Dynamic stress intensity factors for anisotropic bimaterials are solved for several basic steady state configurations, including the Yoffe, Gol’dshtein and Dugdale problems. Under time-independent loading, the dynamic stress intensity factor can be factorized into its equilibrium counterpart and the universal functions of crack speed.

Dynamic Crack Propagation Analysis by Moving Singular Boundary Elements

1992 ◽  
Vol 59 (2S) ◽  
pp. S158-S162 ◽  
Author(s):  
Rafael Gallego ◽  
Jose´ Dominguez
Keyword(s):  
Crack Propagation ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Singular Boundary ◽  
Singular Element ◽  
Infinite Domain ◽  
Propagation Analysis ◽  
Finite Domains

An efficient boundary element procedure for the dynamic analysis of crack propagation in unbounded and arbitrary shape finite bodies is presented. The procedure is based on the direct time domain formulation of the boundary element method. A moving singular element and a remeshing technique have been developed to model the asymptotic solution of the stresses near the propagating crack tip. These ideas are easily implemented for a boundary discretization as opposed to similar procedures previously developed in a finite element context. The method is applied to problems of dynamic crack propagation in finite and infinite elastic domains. The obtained numerical results are compared with infinite domain analytical solutions and with available numerical solutions for finite domains.

Numerical Study of Dynamic Crack of 1D Hexagonal and 3D Icosahedral Quasicrystals

2013 ◽  
Vol 734-737 ◽  
pp. 2306-2309
Author(s):  
Li Ping Du ◽  
Xiu Juan Xu ◽  
Yi Li Tan
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Dynamic Stress ◽  
Dynamic Behaviour ◽  
Numerical Study ◽  
Dynamic Stress Intensity Factor ◽  
Dynamic Equations ◽  
Dynamic Crack ◽  
Icosahedral Quasicrystals

According to a new version of equations of elasodynamics of quasicrystals suggested by Ref, a finite difference method of the anti-plane elastic dynamic equations of 1D hexagonal and 3D icosahedral quasicrystals is developed. Further the dynamic behaviour of the material with a model III crack under impact loading is given.The results show dynamic stress intensity factor of the crack tip, in which the similar and different features with conventional materials are discussed, especially the phonon,phason and phonon-phason coupling effects are explored.

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