Dynamic Analysis of a Mode I Propagating Crack Subjected to a Concentrated Load

2003 ◽  
Vol 70 (5) ◽  
pp. 668-675
Author(s):  
Y.-L. Chung ◽  
M.-R. Chen
Keyword(s):  
Stress Intensity ◽  
Wave Speed ◽  
Complete Solution ◽  
Crack Tip ◽  
Dynamic Effect ◽  
Mode I ◽  
S Wave ◽  
Dynamic Stress Intensity Factors ◽  
Concentrated Load ◽  
Self Similar

This work investigates the phenomenon of mode I central crack propagating with a constant speed subjected to a concentrated load on the crack surfaces. This problem is not a self-similar problem. However, the method of self-similar potential (SSP) in conjunction with superposition can be successfully applied if the time delay and the origin shift are considered. After the complete solution is obtained, attention is stressed on the dynamic stress intensity factors (DSIFs). Analytical results indicate that the DSIF equals the static stress intensity factor if the crack-tip speed is very slow and equal to zero if the crack-tip velocity approaches the Rayleigh-wave speed. However, the dynamic effect becomes obvious only if the crack-tip speed is 0.4 times faster than the S-wave speed. Moreover, the combination of SSP method and the superposition scheme can be applied to the expanding uniformly distributed load acting on a portion of the crack surfaces.

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 Analysis of Non-Symmetric Cracks Extension

2000 ◽  
Vol 16 (3) ◽  
pp. 157-167
Author(s):  
Yen-Ling Chung ◽  
Mei-Rong Chen
Keyword(s):  
Crack Tip ◽  
Mode I ◽  
Mode Ii ◽  
Mode Iii ◽  
Dynamic Stress Intensity Factors ◽  
Surface Displacements ◽  
Crack Tips ◽  
Self Similar ◽  
Rayleigh Wave Speed ◽  
Complete Solutions

ABSTRACTThis paper applies the method of self-similar potentials to analyze the dynamic behaviors of the problems of mode-I, mode-II, and mode-III cracks propagating along the x-axis with constant speed, while the constant speeds of both crack tips are not the same, called nonsymmetric crack expansion. It is assumed that an unbound homogeneous isotropic elastic material is at rest for time t < 0. However, for time t ≥ 0, a central crack starts to extend from zero length along the x-axis. On the crack surfaces of x ≥ 0, there exists uniform distributed load such that the rightmost crack tip propagates with speed ms, while the leftmost crack tip with speed s, where m > 1 and is constant. First, the complete solutions of the mode-I, mode-II, and mode-III problems are obtained. After the complete solutions are found, attention is focused on the crack surface displacements and dynamic stress intensity factors. The results of this study show that the DSIF is equal to the static SIF when the crack-tip speed is zero, and DSIF is zero as the crack-tip speed approaches the Rayleigh-wave speed. Moreover, for the special case m = 1 which indicates that the velocities of both crack tips are the same, the DSIFs of this three modes in this study is the same as those of Ref. [15].

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.

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.

Stresses Produced in a Half Plane by Moving Loads

1958 ◽  
Vol 25 (4) ◽  
pp. 433-436
Author(s):  
J. Cole ◽  
J. Huth
Keyword(s):  
Stress Field ◽  
Elastic Medium ◽  
Half Plane ◽  
Load Distribution ◽  
Wave Speed ◽  
Complete Solution ◽  
Moving Loads ◽  
Concentrated Load ◽  
Line Load ◽  
Wave Speeds

Abstract A study is made of stresses and displacements induced in an elastic half plane (plane strain) by a concentrated line load moving at a constant speed along its surface. The stress field for an arbitrary load distribution can be built up by superposition of these concentrated-load solutions. Three cases are considered: (a) The load is moving more slowly than either the longitudinal or transversal wave speeds of the elastic medium (subsonic case). (b) The load speed is between the two wave speeds (transonic case). (c) The load speed is greater than either wave speed (supersonic case). In each of these cases the nature of the singularity caused by the load is examined and the complete solution is given.

Fracture Toughness and Subcritical Crack Growth in Polycrystalline Silicon

2005 ◽  
Vol 73 (5) ◽  
pp. 714-722 ◽  
Author(s):  
I. Chasiotis ◽  
S. W. Cho ◽  
K. Jonnalagadda
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Crack Growth ◽  
Critical Stress ◽  
Polycrystalline Silicon ◽  
Subcritical Crack Growth ◽  
Crack Tip ◽  
Critical Stress Intensity Factor ◽  
Mode I ◽  
Intensity Factors

The fracture behavior of polycrystalline silicon in the presence of atomically sharp cracks is important in the determination of the mechanical reliability of microelectromechanical system (MEMS) components. The mode-I critical stress intensity factor and crack tip displacements in the vicinity of atomically sharp edge cracks in polycrystalline silicon MEMS scale specimens were measured via an in situ atomic force microscopy/digital image correlation method. The effective (macroscopic) mode-I critical stress intensity factor for specimens from different fabrication runs was 1.00±0.1MPa√m, where 0.1MPa√m is the standard deviation that was attributed to local cleavage anisotropy and grain boundary effects. The experimental near crack tip displacements were in good agreement with the linearly elastic fracture mechanics solution, which supports K dominance in polysilicon at the scale of a few microns. The mechanical characterization method implemented in this work allowed for direct experimental evidence of incremental (subcritical) crack growth in polycrystalline silicon that occurred with crack increments of 1-2μm. The variation in experimental effective critical stress intensity factors and the incremental crack growth in brittle polysilicon were attributed to local cleavage anisotropy in individual silicon grains where the crack tip resided and whose fracture characteristics controlled the overall fracture process resulting in different local and macroscopic stress intensity factors.

The Effect of Crack-Tip Plasticity on the Determination of Dynamic Stress-Intensity Factors by the Optical Method of Caustics

1981 ◽  
Vol 48 (2) ◽  
pp. 302-308 ◽  
Author(s):  
A. J. Rosakis ◽  
L. B. Freund
Keyword(s):  
Stress Intensity ◽  
Plastic Zone ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Crack Tip ◽  
Inertial Effects ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Elastic Crack ◽  
Crack Tip Plasticity

The shadow spots which are obtained in using the optical method of caustics to experimentally determine dynamic stress-intensity factors are usually interpreted on the basis of a static elastic crack model. In this paper, an attempt is made to include both crack-tip plasticity and inertial effects in the analysis underlying the use of the method in reflection. For dynamic crack propagation in the two-dimensional tensile mode which is accompanied by a Dugdale-Barenblatt line plastic zone, the predicted caustic curves and corresponding initial curves are studied within the framework of plane stress and small scale yielding conditions. These curves are found to have geometrical features which are quite different from those for purely elastic crack growth. Estimates are made of the range of system parameters for which plasticity and inertia effects should be included in data analysis when using the method of caustics. For example, it is found that the error introduced through the neglect of plasticity effects in the analysis of data will be small as long as the distance from the crack tip to the initial curve ahead of the tip is more than about twice the plastic zone size. Also, it is found that the error introduced through the neglect of inertial effects will be small as long as the crack speed is less than about 20 percent of the longitudinal wave speed.

Experimental Study on K-Dominance of Static Crack Tip in Functionally Gradient Materials

2007 ◽  
Vol 348-349 ◽  
pp. 789-792 ◽  
Author(s):  
Wei Xu ◽  
Xue Feng Yao ◽  
Lin Zhi Wu
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Mode I ◽  
Intensity Factors ◽  
Functionally Gradient Materials ◽  
Property Variation ◽  
Gradient Materials ◽  
Functionally Gradient ◽  
Static Crack

In this paper, coherent gradient sensing (CGS) and digital speckle correlation method (DSCM) are introduced to study the K-dominance of static crack tip in functionally gradient materials (FGMs) with a crack oriented along the direction of the elastic gradient. And the numerical simulation is analyzed through finite element method (FEM). Firstly, the CGS and DSCM equations at the mode-I static crack tip of FGMs are developed, which can be used to calculate the stress intensity factors of FGMs. Secondly, three kinds of FGMs specimens with different variation of the modulus are prepared to observe the influences of the property variation on the K-dominance. Then three-point-bending experiments are carried out. The interference fringe pictures of CGS and the speckle patterns for DSCM on the specimens are shot through the camera. Thirdly, based on the results of the experiments, the stress intensity factors of three kinds of FGMs specimens are calculated by CGS and DSCM. Meanwhile, the stress intensity factors are obtained by FEM. Finally, comparing the results from CGS, DSCM and FEM, the K-dominance of mode-I static crack tip in FGMs is discussed in detail. It is found that the K-dominance of FGMs and homogenous material is almost same when the gradient index in FGMs is relatively small.

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