Micromechanical Modeling of FRCs Containing Matrix Cracks and Partially Debonded Fibers

1999 ◽  
Vol 121 (4) ◽  
pp. 445-452
Author(s):  
X. D. Wang ◽  
S. A. Meguid
Keyword(s):  
Stress Intensity ◽  
Incident Wave ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Matrix Crack ◽  
Micromechanical Modeling ◽  
Failure Behavior ◽  
Dynamic Stress Intensity Factors ◽  
Matrix Cracks ◽  
The Matrix

This study is concerned with the treatment of the dynamic antiplane failure behavior of fiber reinforced composites involving matrix cracks and partially-debonded fibers. The matrix/fiber interphase was modeled as a thin interfacial layer with varying elastic modulus. The steady-state theoretical solution of this class of problems is formulated using a newly developed pseudo-incident wave method, thus reducing the original interaction problem into the solution of coupled single fiber/crack solutions. By using Fourier transform technique and solving the resulting singular integral equations, the dynamic stress intensity factor at the matrix crack was obtained analytically. Numerical examples were provided to show the effect of the location and material property of fibers, the size of debonded layer, and the frequency of the incident wave upon the dynamic stress intensity factors of the matrix crack.

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.

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.

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.

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.

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.

Antiplane Response of Cylindrical Inclusion with Eccentric Crack to Incident SH Waves

2014 ◽  
Vol 887-888 ◽  
pp. 970-974
Author(s):  
Jie Yang ◽  
Dong Li
Keyword(s):  
Stress Intensity ◽  
Green Function ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Cylindrical Inclusion ◽  
Fredholm Integral Equations ◽  
Mode Iii ◽  
Dynamic Stress Intensity Factors ◽  
Sh Waves ◽  
Eccentric Crack

The analytical solution to a cylindrical inclusion with an eccentric crack impacted incident SH waves was studied by using the methods of Green function and conjunction. Firstly, Green function was constructed, which was an essentical solution of displacement field for an elastic half space containing a half cylindrical inclusion while bearing out-of-plane harmonic line source force at any point of its horizontal boundary. Secondly, the whole space was divided into two parts via conjunction technology, a series of unknown forces were loaded at the linking sections to satisfy continuity conditions.Thirdly, the Fredholm integral equations of the first kind were set up through the continuity conditions and the Green function. Finally, a example for dynamic stress intensity factor for mode III at the crack tip was given. Numerical results show that the dynamic stress intensity factors is influenced by wave numbers and media parameters.

Dynamic Crack Analysis Under Coupled Thermoelastic Assumption

2000 ◽  
Vol 68 (4) ◽  
pp. 584-588 ◽  
Author(s):  
P. Hosseini-Tehrani ◽  
M. R. Eslami ◽  
H. R. Daghyani
Keyword(s):  
Stress Intensity ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Dynamic Crack ◽  
Intensity Factors ◽  
Displacement Fields ◽  
Dynamic Stress Intensity Factors ◽  
Thermoelastic Field ◽  
Comparison Of The Results ◽  
Domain Discretization

A boundary element method using Laplace transform in time domain is developed for the analysis of fracture mechanic under coupled thermoelastic assumption. The transient coupled thermoelastic field is solved without need for domain discretization. The singular behavior of the temperature and displacement fields in the vicinity of the crack tip is modeled by quarter-point elements. Thermal dynamic stress intensity factors for mode I are evaluated from computed nodal values, using the well-known displacement and traction formulas. The accuracy of the method is investigated through comparison of the results with the available data in literature. The conditions where the inertia term plays an important role is discussed and variations of the dynamic stress intensity factor is investigated.

Dynamic Stress on a Partially Bonded Fiber

1991 ◽  
Vol 58 (2) ◽  
pp. 404-409 ◽  
Author(s):  
Andrew Norris ◽  
Yang Yang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Interfacial Crack ◽  
Resonance Phenomenon ◽  
Dimensionless Frequency ◽  
Asymptotic Results ◽  
The Matrix

The dynamic stress on a partially bonded fiber is analyzed for shear wave incidence, with particular attention given to the stress intensity factor at the neck joining the fiber to the matrix. The problem is formulated in terms of the unknown stress across the neck and the remainder of the fiber-matrix interface is modeled as a curved interfacial crack. Explicit asymptotic expressions are derived for the near and farfields that are valid in the frequency range in which the recently discussed resonance phenomenon occurs (Yang and Norris, 1991). This resonance is a rattling effect that is most prominent when the neck becomes very thin, and can occur at arbitrarily small values of the dimensionless frequency ka, where a is the radius of the fiber. The asymptotic results indicate that the dynamic stress intensity factor becomes unbounded as the neck vanishes, in contrast to the prediction of a purely quasistatic analysis that the stress intensity factor vanishes in the same limit.

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