Normal and Shear Impact of Layered Composite With a Crack: Dynamic Stress Intensification

1980 ◽  
Vol 47 (2) ◽  
pp. 351-358 ◽  
Author(s):  
G. C. Sih ◽  
E. P. Chen
Keyword(s):  
Laplace Transform ◽  
Dynamic Stress ◽  
Matrix Material ◽  
Dynamic Stress Intensity Factor ◽  
Layered Composite ◽  
The Other ◽  
Crack Plane ◽  
Time Inversion ◽  
Dual Integral Equations ◽  
The Matrix

The dynamic response of a layered composite under normal and shear impact is analyzed by assuming that the composite contains an initial flaw in the matrix material. Because of the complexities that arise from the interaction of waves scattered by the crack with those reflected by the interfaces within the composite, dynamic analyses of composites with cracks have been treated only for a few simple cases. One of the objectives of the present work is to develop an effective analytical method for determining dynamic stress solutions. This will not only lead to an in-depth understanding of the failure of composites due to impact but also provide reliable solutions that can guide the development of numerical methods. The analysis method utilizes Fourier transform for the space variable and Laplace transform for the time variable. The time-dependent angle loading is separated into two parts: one being symmetric and the other skew-symmetric with reference to the crack plane. By means of superposition, the transient boundary conditions consist of applying normal and shear tractions to a crack embedded in a layered composite. One phase of the composite could represent the fiber while the other could be the matrix. Mathematically, these conditions reduce the problem to a system of dual integral equations which are solved in the Laplace transform plane for the transform of the dynamic stress-intensity factor. The time inversion is carried out numerically for various combinations of the material properties of the composite and the results are displayed graphically.

scholarly journals Transient Elasto-Dynamic Response of a Circular Crack in a Thick Plate Under Torsion

1979 ◽  
Vol 101 (3) ◽  
pp. 207-209 ◽  
Author(s):  
E. P. Chen
Keyword(s):  
Dynamic Response ◽  
Thick Plate ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Circular Crack ◽  
Dual Integral Equations ◽  
Numerical Laplace Inversion ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Sudden Appearance

The elasto-dynamic response of a thick plate under torsion is considered in this study. A penny-shaped crack is assumed to exist in the center of the plate such that the problem is axisymmetric in nature. The crack is pressurized suddenly along its surfaces resulting in transient conditions. This problem is also equivalent to that of sudden appearance of a crack in the loaded plate. Hankel and Laplace transforms are used to reduce the problem to the solution of a pair of dual integral equations. A numerical Laplace inversion routine is used to recover the time dependence of the solution. The dynamic stress intensity factor is determined and its dependence on time and geometry is discussed.

The Preparation of Mechanically Alloyed Powders for TEM Examination

1987 ◽  
Vol 115 ◽  
Author(s):  
E. A. Kamenetzky ◽  
M. Wall ◽  
R Castro ◽  
L. E. Tanner
Keyword(s):  
High Energy ◽  
Layered Composite ◽  
The Other ◽  
Outer Diameter ◽  
Ion Milling ◽  
Mechanically Alloyed ◽  
Standard Methods ◽  
The Matrix ◽  
Energy Ball ◽  
Cold Pressed

ABSTRACTTEM specimens of mechanically alloyed elemental Ni and Nb powders are prepared by a new procedure. The alloyed powders are mixed with smaller Al powders and fill an aluminum ring (3mm outer diameter). This composite is cold pressed together with the Al powders taking most of the deformation. The compacted specimen can be mechanically thinned. Electropolishing and ion milling can then proceed by standard methods with special precautions to minimize differential polishing or milling rates.The microstructural aspects of the formation of an amorphous phase by high-energy ball milling these powders have been studied. After 6 h each particle transforms to a heterogeneous layered composite of particles of one element in the matrix of the other. Particle size ranges from 15 nm to 90 nm. Mechanical alloying for 36 h results in the formation of an apparently uniform phase interspersed with a few small (4 nm to 30 nm) elemental crystalline particles. The uniformity of composition and the presence of C, O, and Fe were studied by EDX and EELS.

Intervallic Coiflets for Numerical Calculation of Dynamic Stress Intensity Factor

2012 ◽  
Vol 562-564 ◽  
pp. 668-671
Author(s):  
Jian Ping Xuan ◽  
Yuan Feng Liu ◽  
Tie Lin Shi
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Integral Equations ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
High Accuracy ◽  
Fredholm Integral Equations ◽  
Wavelet Expansion ◽  
Dual Integral Equations

There are lots of practical problems which are related to the solution of Fredholm integral equations of the second kind. The present work proposes intervallic Coiflets for solving the equations. Illustrative problem involving dynamic stress and electric fields of a cracked piezoelectric excited by anti-plane shear wave is addressed. Permeable boundary condition has been used to obtain a pair of dual integral equations of the symmetric and antisymmetric parts which can be reduced to the solutions of two Fredholm integral equations of the second kind. The dynamic stress intensity factor is expressed in terms of the right-end values of two unknown functions in Fredholm integral equations. The two unknown functions are solved by intervallic Coiflets which have less the endpoints error. And intervallic Coiflets have low calculation cost and high accuracy due to the wavelet expansion coefficients are exactly obtained without calculating the wavelet integrations. The calculation results agree well with the existing method, which show the high accuracy of the estimation and demonstrate validity and applicability of the method.

Response of Finite Cracks in Orthotropic Materials due to Concentrated Impact Shear Loads

1999 ◽  
Vol 66 (2) ◽  
pp. 485-491 ◽  
Author(s):  
C. Rubio-Gonzalez ◽  
J. J. Mason
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Laplace Transform ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Shear Loading ◽  
Orthotropic Materials ◽  
Plane Shear ◽  
Shear Loads

The elastodynamic response of an infinite orthotropic material with a finite crack under concentrated in-plane shear loads is examined. A solution for the stress intensity factor history around the crack tips is found. Laplace and Fourier transforms are employed to solve the equations of motion leading to a Fredholm integral equation on the Laplace transform domain. The dynamic stress intensity factor history can be computed by numerical Laplace transform inversion of the solution of the Fredholm equation. Numerical values of the dynamic stress intensity factor history for several example materials are obtained. The results differ from mode I in that there is heavy dependence upon the material constants. This solution can be used as a Green's function to solve dynamic problems involving finite cracks and in-plane shear loading.

Calculation of Dynamic Stress Intensity Factor by the Boundary Element - Laplace Transform Method

2014 ◽  
Vol 989-994 ◽  
pp. 1825-1828
Author(s):  
Wei Zhang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Laplace Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Boundary Integral ◽  
Inverse Laplace Transform

Using the Laplace transform and freezing time variable, the problem in the time domain into the frequency domain to solve the problem. The establishment of a crack unit model in the frequency domain, and the boundary integral equation and discrete form containing the crack unit has been deduced. While using Durbin algorithm suitable for transient dynamic response of the inverse Laplace transform, the amount of stress intensity factor of a set of transformation parameters corresponding to the frequency domain into a time domain to obtain the dynamic stress intensity factor of time curve, and calculate the stress intensity factor compared to the boundary finite element method has a Laplace transform high precision, easy to save CPU time and data preparation features, we recommend using this method to calculate the dynamic stress intensity factor.

scholarly journals THE FINE STRUCTURE AND ARRANGEMENT OF MICROCYLINDERS IN THE LUMINA OF FLAGELLAR FIBERS IN CRICKET SPERMATIDS

1970 ◽  
Vol 45 (2) ◽  
pp. 416-430 ◽  
Author(s):  
Jerome S. Kaye
Keyword(s):  
Fine Structure ◽  
Matrix Material ◽  
The Other ◽  
Amorphous Substance ◽  
Mean Diameter ◽  
The Matrix ◽  
Cytoplasmic Microtubules ◽  
The Mean ◽  
Center Distance ◽  
Electron Lucent

Flagellar structure in spermatids of several species of cricket was studied with the electron microscope. The flagella of mid-spermatids contain the usual 9 + 2 set of fibers and a set of nine accessory fibers. At first all are hollow, then the lumina become filled with an electron-opaque matrix material in which narrow electron-lucent microcylinders are embedded. The accessory fibers and one central fiber become filled first, then the B subfibers and the other central fiber, and finally the A subfiber. In all but the B subfibers, microcylinders are arranged in a circular or oval group that lies against the wall of the lumen and encloses one or several additional microcylinders. In accessory fibers there are 9–11 microcylinders in the outer group and 4–5 in the inner group. In the central fibers and the A subfibers there are 7–9 microcylinders that enclose one or two more. In the B subfibers there is a crescentic group of 6–7 microcylinders that partially encloses 2–3 more. Microcylinders become packed as though they are independent units; the matrix appears to be an amorphous substance that fills the spaces around the microcylinders. The mean diameter of the microcylinders is 36 A, and they have a center-to-center distance of 56 A. In both respects they resemble wall subunits of flagellar fibers and microtubules and they may be similar structures but with a different localization. The diameter of accessory fibers is about 350 A, which is 25% greater than that of the other flagellar fibers and of cytoplasmic microtubules. Rotation tests suggest that the accessory fibers have 16 wall-subunits.

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.

scholarly journals The effect of couple-stresses on the stress concentration around a moving crack

1981 ◽  
Vol 4 (1) ◽  
pp. 165-180 ◽  
Author(s):  
S. Itou
Keyword(s):  
Dynamic Stress ◽  
Couple Stress Theory ◽  
Dynamic Stress Intensity Factor ◽  
Expansion Method ◽  
Infinite Medium ◽  
Dual Integral Equations ◽  
Moving Crack ◽  
Stress Theory ◽  
Finite Crack ◽  
Series Expansion Method

The problem of a uniformly propagating finite crack in an infinite medium is solved within the linearized couple-stress theory. The self-equilibrated system of pressure is applied to the crack surfaces. The problem is reduced to dual integral equations and solved by a series-expansion method. The dynamic stress-intensity factor is computed numerically.

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.

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