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.

Issue Section:
Technical Papers
Topics:
Fracture (Materials), Shear (Mechanics), Stress, Fredholm integral equations, Laplace transforms, Equations of motion, Fourier transforms
1.
Abou-Sayed
IS
Burgers
P
Freund
LB
,
1980
,
Stress Intensity Factor Due to the Parallel Impact Loading of the Faces of the Crack
,
Fracture Mechanics, 12th Conference ASTM-STP-700
(pg.
164
-
173
)
2.
Atkinson
KE
,
1997
,
The Numerical Solution of Integral Equations of the Second Kind
Cambridge University Press
New York
3.
Chen
EP
Sih
GC
,
1977
,
Transient Response of Cracks to Impact Loads
,
Elastodynamic Crack Problems
Sih
GC
Noordhoff International Publishing
Leyden, The Netherlands
4.
Debnath
L
,
1995
,
Integral Transforms and their Applications
CRC Press
Boca Raton, FL
5.
Chao
CC
,
1960
,
Dynamical Response of an Elastic Half-Space Surface Loadings
,
ASME JOURNAL OF APPLIED MECHANICS
, vol.
66
2
(pg.
559
-
567
)
Google Scholar
Crossref
Search ADS
 
6.
Freund
LB
,
1974
,
The Stress Intensity Factor due to Normal Impact Loading on the Faces of a Crack
,
Int. J. Engng. Sci
, vol.
66
2
(pg.
179
-
189
)
Google Scholar
Crossref
Search ADS
 
7.
Freund
LB
,
1990
,
Dynamic Fracture Mechanics
Cambridge University Press
New York
8.
Honig
G
Hirdes
U
,
1984
,
A Method for the Numerical Inversion of Laplace Transforms
,
J. Comp. Appl. Math
, vol.
66
2
(pg.
113
-
132
)
Google Scholar
Crossref
Search ADS
 
9.
Isida
M
,
1972
,
Data on Crack Tip Stress Intensity Factors
,
JSME
, vol.
66
2
(pg.
1127
-
1135
)
10.
Kassir
MK
Bandyopadhyay
KK
,
1983
,
Impact Response of a Cracked Orthotropic Medium
,
ASME JOURNAL OF APPLIED MECHANICS
, vol.
66
2
(pg.
630
-
636
)
Google Scholar
Crossref
Search ADS
 
11.
Lambros
J
Rosakis
A
,
1995
,
Shear Dominated Transonic Interfacial Crack Growth in a Bimaterial-I. Experimental Observations
,
J. Mech. Phys. Solids
, vol.
66
2
(pg.
169
-
188
)
Google Scholar
Crossref
Search ADS
 
12.
Liu
C
Huang
Y
Rosakis
A
,
1995
,
Shear Dominated Transonic Interfacial Crack Growth in a Bimaterial-II. Asymptotic Fields and Favorable Velocity Regimes
,
J. Mech. Phys. Solids
, vol.
66
2
(pg.
189
-
206
)
Google Scholar
Crossref
Search ADS
 
13.
Nayfeh
AH
,
1995
,
Wave Propagation in Anisotropic Media with Applications to Composites
North-Holland
Amsterdam
14.
Papoulis
A
,
1962
,
The Fourier Integral and Its Applications
McGraw-Hill
New York
15.
Parton
VZ
Boriskovsky
VG
,
1989
,
Dynamic Fracture Mechanics
,
Stationary Cracks
, vol.
66
2
Hemisphere
New York
16.
Rubio-Gonzalez
C
Mason
JJ
,
1999
,
Green's Functions for the Stress Intensity Factor Evolution in Finite Cracks in Orthotropic Materials
,
Int. J. of Fracture
submitted for publication
17.
Rosakis
AJ
,
1998
,
Plenary Lecture
The US National Congress in Applied Mechanics
Gainesville, FL
June
18.
Schwartz
MM
,
1997
,
Composite Materials: Properties, Nondestructive Testing and Repair
, vol.
66
2
Prentice-Hall
Englewood Cliffs, NJ
19.
Shindo
Y
Nozaki
H
,
1986
,
Impact Response of a Finite Crack in an Orthotropic Strip
,
Acta Mechanica
, vol.
66
2
(pg.
87
-
104
)
Google Scholar
Crossref
Search ADS
 
20.
Shivakumar
KN
Crews
JH
,
1998
,
Modified Mixed-Mode Bending Test Apparatus for Measuring Delamination Fracture Toughness of Laminates Composites
,
J. Composites Materials
to appear
21.
Shukla
A
Singh
R
Lambros
J
Rosakis
A
,
1998
,
Investigation of the Mechanics of Intersonic Crack Propagation Along a Bimaterial Interface Using Coherent Gradient Sensing and Photoelasticity
,
Proceedings of Royal Society, London
to appear
22.
Sneddon
IN
,
1966
,
Mixed Boundary Value Problems in Potential Theory
North-Holland
Amsterdam
This content is only available via PDF.
COPYRIGHT © 1999 by The American Society of Mechanical Engineers
You do not currently have access to this content.