A modified ultrasonic C-scan technique was implemented for improving the detection of a certain type of damage in composite specimens. The type of damage being studied is transverse (through the thickness) cracking of unidirectional off-axis graphite-epoxy specimens. These cracks are difficult to detect using standard through-transmission C-scan techniques. The modification is based on mode conversion to produce transmitted shear waves from incident longitudinal waves. While mode conversion is used extensively with isotropic materials, its use with composites is more limited. This is largely because the computation of wave propagation parameters is significantly more complicated with highly anisotropic materials than with isotropic materials. The appropriate incident angles to produce the desired mode conversion were computed based on the mechanical properties of the composite. Once the angles were computed the technique was simple to implement and resulted in marked improvement in detection of the transverse cracks being studied

Generazio, Edward R.

Pereira, J. Michael

English

NASA Technical Reports Server

^^^90
E5-6 50
NASA Technical Memorandum 103261
Improved Transverse Crack
Detection in Composites
J. Michael Pereira and Edward R. Generazio
Lewis Research Center
Cleveland, Ohio
Prepared for the
Society of Plastics Engineers Regional Technical Conference
Los Angeles, California, October 16-18, 1990
NASA
https://ntrs.nasa.gov/search.jsp?R=19900018559 2020-03-19T21:04:14+00:00Z
IMPROVED TRANSVERSE CRACK DETECTION IN COMPOSITES
J. Michael Pereira and Edward R. Cenerazio
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
SUMMARY
A modified ultrasonic C-scan technique was implemented for improving the
detection of a certain type of damage in composite specimens. The type of
damage being studied is transverse (through the thickness) cracking of unidi-
rectional off-axis graphite/epoxy specimens. These cracks are difficult to
detect using standard through-transmission C-scan techniques.
The modification is based on mode conversion to produce transmitted shear
waves form incident longitudinal waves. While mode conversion is used exten-
sively with isotropic materials, its use with composites is more limited.
This is largely because the computation of wave propagation parameters is sig-
nificantly more complicated with highly anisotropic composite materials than
with isotropic materials.
In this study, the appropriate incident angles to produce the desired
mode conversion were computed based on the mechanical properties of the compos-
ite. Once the angles were computed the technique was simple to implement and
resulted in marked improvement in detection of the transverse cracks being
studied.
INTRODUCTION
The ultrasonic C-scan is a common technique for detecting flaws or damage
in composite laminates as well as in many other materials- 1
 The technique is
well established, relatively simple to implement and is an effective method of
detecting local inhomogeneities in composite laminates.
	
It is particularly
effective in detecting interply delaminations which occur parallel to the lami-
nate plane and can result from applied loads or manufacturing flaws. However,
there are certain defects which are difficult to detect using the method. One
type is the transverse (through the thickness) matrix crack which may be ori-
ented perpendicular to the laminate plane in graphite/epoxy composites. This
type of damage is a common result of thermal fatigue2 and may also occur as a
result of mechanical fatigue or static in-plane loading. 3 Detection of trans-
verse matrix cracks is important because when they propagate to a ply inter-
face they may initiate delamination, further degrading the structural
integrity of the laminate.
Several methods have recently been developed to improve the ability to
detect transverse cracks in composite laminates. These include the method of
acousto-ultrasonics 2 and the use of Lamb waves. 4 These methods are sensitive
to overall changes in in-plane mechanical properties due to the presence of
transverse cracks. In this study a technique was implemented for the local
detection of this type of crack. The technique is based on the hypothesis
that oblique shear waves may be more sensitive to the presence of cracks than
are longitudinal waves propagating normal to the panel. It involves producing
only shear wave transmission through the panel, and has the advantage that
only minor changes need to be made to existing C-scan procedures.
The ability to utilize shear wave transmission results from the mode con-
version that occurs when a longitudinal wave traveling through a fluid is inci-
dent upon a solid.	 In an isotropic solid an incident longitudinal plane wave
will typically produce three refracted waves, a longitudinal wave and two shear
waves, known as P (primary compressional), SV (vertically polarized shear)
and SH (horizontally polarized shear) waves. The directions of the refracted
waves may be easily determined using Snell's law. 6
 By selecting the correct
incident angle (the "critical" angle) it is possible to produce total reflec-
tion of one of the waves, such as the P wave.
	 In addition, if the incident
plane is perpendicular to the plane of the laminate, SH waves are not gen-
erated. The mode conversion phenomenon also occurs in anisotropic media, such
as the fiber composite laminates considered here. However, the anisotropy pro-
duces several important differences that must he taken into account when com-
puting the desired incident angles. 5,6 In particular, although Snell's law
still applies, it is not sufficient to compute both wave propagation direc-
tions and angles of refraction, since the wave velocity is a function of its
direction of propagation.
In this study the wave directions and critical angles were computed for
unidirectional off-axis graphite/epoxy panels with varying fiber angles.
Ultrasonic C-scans were conducted on a 60 1 off-axis panel with an artificially
induced through-the-thickness transverse matrix crack. Scans were conducted
using both normal through-transmission and the proposed shear wave transmis-
sion technique. The results show that the crack image was significantly
enhanced using the shear wave transmission.
THEORY
An analysis was conducted to determine critical angles, phase and group
velocities, amplitudes and displacements for reflected and refracted waves
resulting from a longitudinal plane wave in a fluid incident on a composite
panel (fig. 1). The methods used were similar to those outlined in refer-
ence 6, so only a cursory discussion is given here. In the analysis, the com-
posite panel was modeled as an orthotropic solid lying in an inviscid fluid.
The ultrasonic wave was modeled as a plane wave propagating in the X2 --X3
plane with an incident angle, ^ (fig. 1). The displacement at a point x was
given as
ui = A i e
-i(k•x-Wt)
	
(i = 1 ,2,3)
	
(1)
where ui is the displacement in the Xi direction, Ai is the wave's ampli-
tude, k = (w/c)n is the wave vector, w is the frequency, c is the phase
velocity, n is the unit wave normal vector and t is time.
2
The velocities and displacements were found by substituting the assumed
displacement field (eq. 1) into the equations of motion, 6 giving
(C ijk0 j'Q	 pc2Sik)Ak = 0
	 (2)
where C ijkQ are the elastic stiffness constants, Sik is the kronecker delta
and p is the density. The eigenvalues, c, of equation (2) correspond to the
phase velocities of the three possible waves, while the eigenvectors are the
unit displacements. Both depend on the direction of wave propagation. The
elastic constants of the composite laminate were determined from the constitu-
ent properties using a micromechanics analysis and laminate plate theory.?
Dividing equation (2) by pc t put the equation in a form which could be used
for determining wave vectors and velocities,
(p C i jk4,m i mQ	 Sik)Ak = 0
	 (3)
where m i
 = ni/c are known as the components of the slowness vector. The
slowness vector has the same direction as the wave normal and a magnitude
equal to the inverse of the velocity. The slowness vectors were computed from
equation (3) by choosing a configuration in which the incident plane was nor-
mal to the plane of the sample. In this case m l was zero and m2
 was the
same as the X 2
 component of the slowness vector of the incident wave, 5 which
was computed independently. This left m3 as the only unknown quantity within
parenthesis of equation (3). Setting the determinant of the quantity in paren-
thesis equal to zero resulted in a sixth order polynomial in m 3 which was
solved numerically. With m l , m2, and m3 known, the velocities and normal-
ized displacements were found from the eigenvalue problem of equation (2).
EXPERIMENTAL PROCEDURE
The effect of using shear wave transmission in the C-scan rather than
longitudinal wave transmission was evaluated experimentally. A T300/934
graphite-epoxy laminate laid up in a (60) 8 configuration with a nominal thick-
ness of 1.1 mm was manufactured according to the manufacturer's specifica-
tions. A specimen was cut from the panel in such a way that the angle, 0,
(fig. 1(c)) was 30 1 . The specimen was split in two along the fibers, and the
two pieces placed back in contact and supported mechanically in such a way
that the crack was not detectable visually. Two different types of ultrasonic
C-scans were then performed. The first was a regular through - transmission
scan in which the sound travelled along a straight line between the transmit-
ting transducer and receiving transducer, normal to the plane of the sample
(fig. 1(a)). In the second scan the sound travelled along a line in the
X2 - X3
 plane but was at an angle, ^. from the X 3
 axis (fig. 1(b)). 	 In
this case an offset, S, occurred as a result of a deviation in the direction
of propagation in the solid from that in the liquid (fig. 1(b)). The angle,
^, was chosen to be slightly larger than the computed critical angle for longi-
tudinal waves so that only shear waves were transmitted through the sample.
10 MHz broadband transducers were used, with a focused transmitter and an unfo-
cused receiver.
3
RESULTS AND DISCUSSION
The mechanical properties in the material coordinate system for the unidi-
rectional composite used in this study, computed from the micromechanics analy-
sis, are shown in table I.
For unidirectional off-axis composites, the incident angle at which total
reflection of the longitudinal wave occurs is a function of fiber angle
(fig. 2).	 In particular, when the fibers are parallel to the incident plane
(0 = 90 1 ) the critical angle is quite low (91 ).	 In contrast. there is no crit-
ical angle for SV waves. That is, refracted shear waves are generated even
for grazing incidence, allowing a large range over which the incident angle
can be chosen.
Some insight into an appropriate choice for the incident angle can be
obtained from a plot of the locus of the slowness vectors (the slowness sur-
face). For the longitudinal (P) wave the direction of energy flow, which is
normal to the slowness surface, deviates significantly from the wave vector
direction near the critical angle (fig. 3). For the transverse shear wave,
however, the direction of energy flow is almost collinear with the wave vector
direction, meaning that for a thin laminate the offset, S, (fig. 1(b)) will be
relatively small.
These results allow some simplification in an experimental arrangement
for using shear wave propagation to detect damage. Because the energy of the
P wave is deflected significantly near the critical angle, some error is per-
missible in the experimental apparatus used for orienting the transmitter-
receiver pair relative to the sample to produce the calculated incident
angle. That is, for incident angles somewhat less than the critical angle,
the energy of a refracted P wave would be directed far enough away before
emerging from the other side of the sample that it may not be sensed by the
receiving transducer. For the detection of transmitted SV waves on the
other hand, very little correction needs to be made for a lateral shift, S,
(fig. 1(b)) in the path of an ultrasonic beam due to the change in direction
of energy flow. From a practical point of view, this means that for thin
samples, the proposed method may be implemented by simply changing the angular
orientation of the transmitter-receiver pair relative to the sample.
The use of transmitted SV waves rather than longitudinal waves led to a
significant improvement in the ability of the C-scan to detect the presence of
a through-the-thickness transverse crack (fig. 4). Figure 4(a) is a conven-
tional C-scan (fig. 1(a)) of the specimen, in which the P-wave propagates nor-
mal to the plane of the composite panel. The transverse crack in the specimen
can be seen extending from the upper left of the figure to the lower right.
Figure 4(b) is a C-scan of the same crack using the shear wave transmission
technique. In this figure the crack appears wider and is easier to detect vis-
ually. For this experiment, the critical angle for longitudinal waves was com-
puted to be 18 0 . An incident angle of 20 1 was used to generate the shear
waves. The plane of incidence was parallel to the longitudinal axis of the
sample.
These results indicate that the use of transmitted shear waves can be use-
ful in detecting this particular type of damage. Although more involved than
for isotropic materials, the computation of critical angles is relatively
4
straightforward. One of the principal advantages of this method over other
methods of detecting transverse cracks is that in many cases, it can be imple-
mented simply by changing the orientation of the transmitter-receiver trans-
ducer pair in a standard C-scan facility.
REFERENCES
1. T. Liber, I.M. Daniel, and S.W. Schramm, "Ultrasonic Techniques for
Inspecting Flat and Cylindrical Composite Specimens," Nondestructive
Evaluation and Flaw Criticality for Composite Materials, ASTM STP 696,
R.B. Pipes, ed., American Society for Testing and Materials (1979),
pp. 5-25.
2. J.H. Hemann, P. Cavano, H. Kautz, and K. Bowles, ''Trans-ply Crack Density
Detection by Acousto-Ultrasonics," Acousto-Ultrasonics Theory and Appli-
cation, J.C. Duke, ed., Plenum Press, New York, (1988).
3. P.A. Lagace, "Static Tensile Fracture of Graphite/Epoxy," Sc.D. Thesis.
Massachusetts Institute of Technology (1982).
4. B. Tang, and E.G. Henneke, II., "Lamb-Wave Monitoring of Axial Stiffness
Reduction of Laminated Composite Plates," Mater. Eval., vol. 47, p. 928
(1989).
5. F.I. Federov, Theory of Elastic Waves in Crystals, Plenum Press, New York
(1968).
6. S.I. Rokhlin, T.K. Bolland, and L. Adler, "Reflection and Refraction of
Elastic Waves on a Plane Interface Between Two Generally Anisotropic
Media," J. Acoust. Soc. Am., vol. 79 (4), p. 906 (1986).
7. P.L.N. Murthy, and C.C. Chamis, "Integrated Composite Analyzer (ICAN)
Users and Programmers Manual," NASA TP-2515 (1986).
TABLE I. - MECHANICAL PROPERTIES FOR T300/934
GRAPHITE/EPDXY COMPOSITE IN THE MATERIAL
COORDINATE SYSTEM
E11 = 144.2	 GPa	 G 1 2 = 4.098 GPa	 v 12 = 0.26
E 22 =	 8.729 GPa	 G 13 = 4.098 GPa	 v 13 = .26
E 33 
=	 8.729 GPa	 G23 = 2.475 GPa	 v23 = .42
5
-^ X 2
t X3
(a) Normal through-transmission C-scan.
►
 x 2
(b) Oblique shear wave transmission C-scan.
Crack
X2
Fiber–/
X1
	
ro
(c) Through-the-thickness transverse crack.
Figure 1.—Schematic of the experiments showing the relative
locations of the transmitting (T) and receiving (R) transducers
for the two types of C-scans used to detect the crack shown
in (C).
6
40
30
a^
a^
20
U
.r
U
10
0 10	 20	 30	 40	 50	 60	 70	 80	 90	 100
Fiber angle, deg
Figure 2.--Critical incident angle for full reflection of longitudinal
waves, as a function of fiber angle, 6.
1.0
X3
.6
E	 IncidentE -2	 wave	
x20
m No
_	 SH
E 2	 SV	 P	 Ray vector
Wave vector_ 	 direction
6 direction (SV wave) —	 (P wave)
Ray vector	 Wave vector direction
direction (SV wave) -- _ _ _	 (P-wave)
-1.0 '	
1	 1	 1	 I	 1
—1.6
	
—1.0	 —.3	 .3	 1.0	 1.6
M2 (µsec/mm)
Figure 3.—Slowness surfaces for incident and refracted waves for a
60 degree off axis (0 = 30 degrees) sample. Near the critical angle
the energy flow (ray) direction for longitudinal waves deviates
significantly from the wave direction. For SV waves the ray and
wave directions are approximately the same.
7
(a) Normal through-transmission.
(b) Oblique shear wave transmission.
Figure 4.—Images of a transverse crack in a 60 degree off-axis unidirec-
tional sample using the two types of C-scans. The shear wave method
produces an enhanced image. Arrows indicate location of crack.
8
NASA	 Report Documentation PageNational Aeronautics and
Space Administration
1.	 Report No. 2. Government Accession No. 3. Recipient's Catalog No.
NASA TM-103261
4. Title and Subtitle 5. Report Date
Improved Transverse Crack Detection in Composites
6. Performing Organization Code
7. Author(s) 8. Performing Organization Report No.
J. Michael Pereira and Edward R. Generazio E-5650
10. Work Unit No.
505-63-1B
9. Performing Organization Name and Address
11. Contract or Grant No.
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio	 44135-3191 13. Type of Report and Period Covered
Technical Memorandum12. Sponsoring Agency Name and Address
National Aeronautics and Space Administration 14. Sponsoring Agency Code
Washington, D.C.	 20546-0001
15. Supplementary Notes
Prepared for the Society of Plastics Engineers Regional Technical Conference, Los Angeles, California,
October 16-18, 1990.
16. Abstract
A modified ultrasonic C-scan technique was implemented for improving the detection of a certain type of damage
in composite specimens. The type of damage being studied is transverse (through the thickness) cracking of
unidirectional off-axis graphite/epoxy specimens. These cracks are difficult to detect using standard through-
transmission C-scan techniques. The modification is based on mode conversion to produce transmitted shear waves
from incident longitudinal waves. While mode conversion is used extensively with isotropic materials, its use
with composites is more limited. This is largely because the computation of wave propagation parameters is
significantly more complicated with highly anisotropic composite materials than with isotropic materials. In this
study, the appropriate incident angles to produce the desired mode conversion were computed based on the
mechanical properties of the composite. Once the angles were computed the technique was simple to implement
and resulted in marked improvement in detection of the transverse cracks being studied.
17. Key Words (Suggested by Author(s)) 18. Distribution Statement
Ultrasonic flow detection Unclassified — Unlimited
Composite materials Subject Category 24
Elastic anisotropy
Wave reflection
19.	 Security Classif. (of this report) 20.	 Security Classif. (of this page) 21. No. of pages 22.	 Price'
Unclassified Unclassified 10 A02
NASA FORM 1626 OCT 86	
*For sale by the National Technical Information Service, Springfield, Virginia 22161


Improved Transverse Crack Detection in Composites

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server