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 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.

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.

Impact Response of a Cracked Orthotropic Medium

1983 ◽  
Vol 50 (3) ◽  
pp. 630-636 ◽  
Author(s):  
M. K. Kassir ◽  
K. K. Bandyopadhyay
Keyword(s):  
Stress Intensity ◽  
Dynamic Stress ◽  
Fourier Transforms ◽  
Dynamic Stress Intensity Factor ◽  
Orthotropic Materials ◽  
Dynamic Stress Intensity Factors ◽  
Transient Problem ◽  
Numerical Laplace Inversion ◽  
The Laplace Transform ◽  
Applied Stresses

A solution is given for the problem of an infinite orthotropic solid containing a central crack deformed by the action of suddenly applied stresses to its surfaces. Laplace and Fourier transforms are employed to reduce the transient problem to the solution of standard integral equations in the Laplace transform plane. A numerical Laplace inversion technique is used to compute the values of the dynamic stress-intensity factors, k1 (t) and k2 (t), for several orthotropic materials, and the results are compared to the corresponding elastostatic values to reveal the influence of material orthotropy on the magnitude and duration of the overshoot in the dynamic stress-intensity factor.

scholarly journals Torsional Impact Response of a Penny-Shaped Interface Crack in Bonded Materials With a Graded Material Interlayer

2002 ◽  
Vol 69 (3) ◽  
pp. 303-308 ◽  
Author(s):  
C. Li ◽  
Z. Duan ◽  
Z. Zou
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Interface Crack ◽  
Singular Integral ◽  
Dynamic Stress ◽  
Mixed Boundary ◽  
Dynamic Stress Intensity Factor ◽  
Cauchy Kernel ◽  
Dynamic Stress Intensity Factors

In this paper, the dynamic response of a penny-shaped interface crack in bonded dissimilar homogeneous half-spaces is studied. It is assumed that the two materials are bonded together with such a inhomogeneous interlayer that makes the elastic modulus in the direction perpendicular to the crack surface is continuous throughout the space. The crack surfaces are assumed to be subjected to torsional impact loading. Laplace and Hankel integral transforms are applied combining with a dislocation density function to reduce the mixed boundary value problem into a singular integral equation with a generalized Cauchy kernel in Laplace domain. By solving the singular integral equation numerically and using a numerical Laplace inversion technique, the dynamic stress intensity factors are obtained. The influences of material properties and interlayer thickness on the dynamic stress intensity factor are investigated.

Use of Jˆ-Integral in Dynamic Analysis of Cracked Linear Viscoelastic Solids by Finite-Element Method

1982 ◽  
Vol 49 (1) ◽  
pp. 75-80 ◽  
Author(s):  
K. Kishimoto ◽  
S. Aoki ◽  
M. Sakata
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Computational Method ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Element Method

A computational method using the path (area)-independent Jˆ-integral is developed to analyze viscoelastic problems. Since the displacement field near the crack tip of a viscoelastic solid is dependent upon the complete past history of the dynamic stress-intensity factors, the Jˆ-integral is represented by a hereditary integral of the dynamic stress-intensity factors. We assume that the stress and strain rates vary in proportion to time during each increment of time and derive a formula to obtain the current value of the dynamic stress-intensity factor from the time increment of the Jˆ-value. Both pure and mixed mode problems of a suddenly loaded crack are analyzed by making use of the formula together with the conventional finite-element method. In order to demonstrate the capability and reliability of the present method, problems of a center crack and an oblique crack in viscoelastic rectangular plates are solved.

Dynamic Anti-Plane Characteristic of Two Dissimilar Piezoelectric Media with an Interfacial Crack

2009 ◽  
Vol 417-418 ◽  
pp. 869-872
Author(s):  
Tian Shu Song ◽  
Dong Li ◽  
Tammam Merhej
Keyword(s):  
Stress Intensity ◽  
Dynamic Stress ◽  
Piezoelectric Materials ◽  
Dynamic Stress Intensity Factor ◽  
Interfacial Crack ◽  
Physical Parameters ◽  
Dynamic Stress Intensity Factors ◽  
Piezoelectric Media ◽  
Time Harmonic ◽  
Electric Loads

Dynamic anti-plane characteristic is investigated theoretically on two dissimilar piezoelectric media with an interfacial crack subjected to time-harmonic incident anti-plane shearing in this paper. The formulations are based on the method of complex variable and Green’s function. Dynamic stress intensity factors at the crack’s tip are obtained by solving boundary value problems with the methods of conjunction and crack-division technique. The calculating results are plotted to show how the frequencies of incident wave, all kinds physical parameters of two dissimilar piezoelectric materials, applied electric loads and the dimension of the interfacial crack influence upon the dynamic stress intensity factor (DSIF). And some of the calculating results are compared with other published documents.

Influence of Rotatory Inertia on Steady-State Crack Propagation in a Finite Plate Subjected to Out-of-Plane Bending

1978 ◽  
Vol 45 (1) ◽  
pp. 130-134 ◽  
Author(s):  
A. F. Fossum
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Wave Velocity ◽  
Release Rate ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Crack Tip ◽  
Out Of Plane ◽  
Tip Velocity

A dynamic stress-intensity factor and energy release rate are obtained for a running semi-infinite crack traversing a strip of elastic material subjected to out-of-plane bending. It is shown that the maximum ratio of crack tip velocity to shear wave velocity is identical to the maximum ratio of flexural wave velocity to shear wave velocity in the limit of vanishingly small wavelength. The dynamic stress-intensity factor is written as the product of a static stress-intensity factor multiplied by a function of Poisson’s ratio and crack tip velocity the function decreasing monotonically with increasing crock tip velocity. The energy release rate is shown to be independent of crack tip velocity for this type of problem.

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.

Dynamic Stress Intensity Factor Due to Concentrated Loads on Semi-Infinite Cracks in Orthotropic Materials

2000 ◽  
Author(s):  
C. Rubio-Gonzalez ◽  
C.-Y. Wang ◽  
J. J. Mason
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Dynamic Stress ◽  
Fourier Transforms ◽  
Asymptotic Expression ◽  
Dynamic Stress Intensity Factor ◽  
Crack Tip ◽  
Orthotropic Materials ◽  
Isotropic Case

Abstract The transient elastodynamic response due to concentrated normal or shear impact loads on the faces of a semi-infinite crack in orthotropic materials is examined. Solution for the stress intensity factor history around the crack tip is found. Laplace and Fourier transforms together with the Wiener-Hopf technique are employed to solve the equations of motion in terms of displacements. An asymptotic expression for the stress near the crack tip is analyzed which leads to the dynamic stress intensity factor in modes I and II. Similar to the isotropic case, it is found that the stress intensity factor has a singularity and discontinuity when the Rayleigh wave emitted from the load arrives at the crack tip. Results are presented for a typical orthotropic material.

On the Characterization of the Transient Stress Field Near the Tip of a Crack

1987 ◽  
Vol 54 (1) ◽  
pp. 72-78 ◽  
Author(s):  
K. Ravi-Chandar ◽  
W. G. Knauss
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Crack Tip ◽  
Transient Conditions ◽  
Dynamic Stress Field

The dynamic stress field near a propagating crack tip is usually characterized in terms of one parameter, namely, the dynamic stress intensity factor. While analytically this is an exact representation at the crack tip itself, under transient conditions, the domain of dominance of the stress intensity factor varies as discussed by Ma and Freund (1986). In this paper, we present experimental results which show that while the stress intensity factor may dominate the near tip stress field under transient conditions as long as the crack velocity is small, it may not be dominant over an appreciable region under other transient conditions of crack tip motion, thus making it difficult to determine this quantity experimentally.

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