System for nondestructively determining composite material parameters

A method and apparatus for nondestructively determining fiber volume fraction and resin porosity of a composite material constructed of at least two different constituent materials wherein the following parameters of the composite material to be tested are known: density, elastic moduli of the constituent materials and layup sequence. Two acoustic waves of different polarizations are propagated through the composite material and the acoustic waves propagated through the composite material are sensed and the velocity of each of the two acoustic waves, V.sub.1 and V.sub.2, are determined. The thickness of the composite material is determined. The fiber volume fraction and resin porosity of the composite material are then determined using the velocities, V.sub.1 and V.sub.2, the thickness and known parameters of density, elastic moduli of the constituent materials and layup sequence.

FIELD OF THE INVENTION 
The present invention relates generally to systems for determining 
parameters of materials and, more particularly, but not by way of 
limitation to systems for nondestructive determining fiber volume fraction 
and resin porosity of composite materials constructed of at least two 
different constituent materials. 
BRIEF DESCRIPTION OF THE INVENTION 
The present invention provides a method for non-destructively determining 
fiber volume fraction and resin porosity of a composite material 
constructed of at least two different constituent materials wherein the 
following parameters of the composite material to be tested are known: 
density, elastic moduli of the constituent materials and layup sequence, 
the method comprising the steps of: propagating two acoustic waves of 
different polarizations through the composite material; receiving the 
acoustic waves propagated through the composite material; determining the 
velocity of each of the two acoustic waves propagated through the 
composite material from the received acoustic waves propagated through the 
composite material, the respective velocities being V.sub.1 and V.sub.2 ; 
determining the thickness of the composite material; and determining the 
fiber volume fraction and resin porosity of the composite material using 
the velocities, V.sub.1 and V.sub.2, the thickness and the known 
parameters of density, elastic moduli of the constituent materials and 
layup sequence. The present invention also provides an apparatus for 
nondestructively determining fiber volume fraction and resin porosity of a 
composite material constructed of at least two different constituent 
materials wherein the following parameters of the composite material to be 
tested are known: density, elastic moduli of the constituent materials and 
layup sequence, the apparatus comprising: means for propagating two 
acoustic waves of different polarizations through the composite material; 
means for receiving the acoustic waves propagated through the composite 
material and outputting the received acoustic waves in a digital format; 
means for determining the thickness of the composite material; and a 
processor receiving the two acoustic waves in a digital format and 
determining the velocity of each acoustic wave, V.sub.1 and V.sub.2, the 
processor having inputted therein the thickness of the composite material 
and having inputted therein the known parameters of density, elastic 
moduli of the constituent materials and layup sequence, the processor 
determining the fiber volume fraction and resin porosity of the composite 
material using the velocities, V.sub.1 and V.sub.2, the thickness and the 
known parameters of density, elastic moduli of the constituent materials 
and layup sequence. 
In another aspect, the present invention provides an apparatus for 
nondestructively determining fiber volume fraction and resin porosity of a 
composite material constructed of at least two different constituent 
materials wherein the following parameters of the composite material to be 
tested are known: thickness, density, elastic moduli of the constituent 
materials and layup sequence, the apparatus comprising: means for 
propagating two acoustic waves of different polarizations through the 
composite material; means for receiving the acoustic waves propagated 
through the composite material and outputting the received acoustic waves 
in a digital format; means for determining the velocity of each of the two 
acoustic waves propagated through the composite material from the received 
and sensed acoustic waves propagated through the composite material and, 
the respective velocities being V.sub.1 and V.sub.2 ; and a processor 
receiving the two acoustic waves in a digital format and determining the 
velocities, V.sub.1 and V.sub.2, of the respective acoustic waves 
propagated through the composite material, the processor having inputted 
therein the known parameters of thickness, density, elastic moduli of the 
constituent materials and layup sequence, the processor determining the 
fiber volume fraction and resin porosity of the composite material using 
the velocities, V.sub.1 and V.sub.2, and the known parameters of 
thickness, density, elastic moduli of the constituent materials and layup 
sequence.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In recent years the use of composite materials has increased significantly. 
In such materials, two different constituent materials are combined to 
optimize the properties of the resulting composite material. For example, 
high strength fibers are embedded in plastic materials to achieve a 
composite material which is light weight and has a high strength or 
stiffness to weight ratio. As used herein the term "composite materials" 
means any material constructed of at least two different constituent 
materials. 
Inhomogeneities can develop during the processing stage when the laminate 
(composite material) is cured to its final solid state. Unwanted gases may 
be introduced into the composite material from a variety of sources 
including entrainment during mixing, entrapment of air between plies 
during layup and evolution of volatiles during the curing reaction. In an 
attempt to keep porosity at a minimum, a porous bleed ply usually is 
placed in contact with the laminate (composite material). In the 
fabrication process, temperature is increased: initially to lower the 
resin viscosity for better void and resin transport and ultimately to 
promote the cure reaction. Simultaneously, pressure is applied to force 
the unwanted gases and excess resin from the composite into the bleed ply, 
which is discarded after fabrication. During the process, fibers also can 
shift position, resulting in areas which are relatively resin rich or 
resin poor. When the process works properly, the result is a void-free 
microstructure with a uniform distribution of reinforcing fibers. When the 
process breaks down, weak areas with excess resin or porosity may be 
created. 
The present invention provides a system for nondestructively determining 
fiber volume fraction, the percent of volume occupied by one of the 
constituent materials (fibers), and resin porosity, the percent of volume 
that is void or occupied by air, in composite materials. 
In the present system, the following parameters of the composite material 
to be tested are taken as known: density, elastic moduli of the 
constituent materials and layup sequence. 
Wave Propagation 
The equations of motion for a continuum are given by: 
EQU .rho.u.sub.i =.sigma..sub.ij,j (1) 
where 
.rho.=density 
u=particle displacement 
.sigma..sub.ij =stress tensor components 
and i signifies differentiation w.r.t. indicated subscript. By inserting 
the stress-strain relationship for an anisotropic solid: 
EQU .sigma..sub.ij =C.sub.ijkl .epsilon..sub.kl (2) 
where 
C.sub.ijkl =elasticity tensor components 
.epsilon..sub.kl =strain tensor components 
into the equations of motion, Eq. (1) becomes: 
EQU .rho.u.sub.i =C.sub.ijkl u.sub.k,lj (3) 
Assuming a plane wave solution of the form 
EQU u.sub.i =A.sub..sigma. .alpha..sub.i e.sup.i (kl.x -wt) (4) 
where 
w=frequency 
k=wave number 
l=wave normal 
A.sub..sigma. =amplitude of particle displacements 
.alpha.=displacement (direction cosines) 
we obtain the following eigenvalue equation for the velocities of 
ultrasonic wave propagation in any direction (l.sub.1, l.sub.2, l.sub.3) 
in an anisotropic material 
##EQU1## 
The geometry of the problem is illustrated in FIG. 1, where the plane of 
fiber reinforcement has been chosen to be the x.sub.2 -x.sub.3 plane. 
Since most composite applications are for plate type structures, we are 
limited for most practical cases to wave propagation in the direction 
perpendicular to the reinforcing plane, i.e., 1=(1,0,0). For this case, 
the eigenvalue equation for an orthotropic material assumes the form: 
##EQU2## 
which yields three possible wave motions: one pure mode longitudinal wave 
with velocity .sqroot.C.sub.1111/.rho. and two pure mode shear waves with 
velocities .sqroot.C.sub.1313/.rho. and .sqroot.C.sub.1212/.rho.. For 
wave propagation in any anisotropic material, one must be concerned with 
possible complications from energy flux deviations from the wave normal. 
However, for pure mode longitudinal wave propagation, energy can never 
deviate from the wave normal. Furthermore energy flux deviation is not 
observed for pure mode shear wave propagation in a direction perpendicular 
to a plane of reflection symmetry. Therefore, if we restrict our attention 
to symmetric laminates (this encompasses virtually all practical laminate 
stacking sequences), energy flux deviation may be safely neglected. 
Material Properties 
In order to assess the effects of resin porosity and fiber loading on 
ultrasonic behavior, it is necessary to first consider the behavior of a 
single ply in the context of micromechanics. Since voids will reside 
completely in the matrix, we begin by using the expressions of Boucher, 
"On the Effective Moduli of Isotropic Two-Phase Elastic Composites". J. 
Composite Materials, Vol. 8, 1974, pp. 82-89, to modify the material 
properties of an ideal matrix to account for the presence of porosity. 
The next step in the procedure is to determine the mechanical properties of 
each individual ply from the known properties of the reinforcing fibers 
and the calculated properties of the resin. This micromechanics problem 
has been the subject of extensive research using a variety of different 
approaches. Unfortunately, there are no exact solutions available for the 
problem of a random array of cylindrical reinforcing fibers embedded in an 
isotropic matrix. However, several investigators have developed suitable 
expressions (bounds) for the elastic moduli of fiber reinforced composites 
which can be used as approximations for this purpose. In this 
investigation, the expressions developed by Hashin, "On the Elastic 
Behavior of Fiber Reinforced Materials of Arbitrary Transverse Phase 
Geometry," J. Mech. Phys. Solids, Vol. 13, 1965, pp. 119-134, for the 
upper bounds on the pertinent moduli were used, based on their accuracy 
and ease of implementation on a minicomputer. 
Once the ply properties have been determined, it is then necessary to 
combine the individual properties in an appropriate manner for the 
particular stacking sequence to obtain the overall laminate properties. 
This is done using the equations of classical laminate theory. 
The procedure for determining porosity and fiber volume fraction is 
outlined below. 
Ultrasonic Velocity Measurement 
A variety of analog techniques are available for the precise determination 
of transit time for ultrasonic wave propagation, Truell, R., Elbaum, C., 
and Chick, B., Ultrasonic Methods in Solid State Physics, Academic Press, 
1969. Any of these methods would be acceptable for this purpose. However, 
the advent of high speed digital data acquisition and processing 
techniques means that this process can be automated. In this application 
we employ a technique developed by Egle, D., "Using the Acoustoelastic 
Effect to Measure Stress in Plates", UCDL-52914, Lawrence Livermore 
Laboratory (1980) to achieve this end. This process requires initially 
that the ultrasonic signals be digitized. An autocorrelation algorithm is 
then employed to estimate the transit time through the material. This 
estimate is then refined, using a curve fitting technique to find the 
maximum in the autocorrelation function. This approach has been found to 
yield the necessary accuracy in transit time measurements (to within 1 
nanosecond) for microstructure characterization. 
Data Analysis 
The effects of fiber volume fraction and resin porosity on wave propagation 
for a typical graphite-epoxy laminate configuration are shown in FIG. 2. 
This figure is based on typical values for the mechanical properties of 
the constituent materials as shown in Table 1. 
TABLE I 
______________________________________ 
Mechanical Properties of Composite 
Constituent Materials 
Density k m G 
(gm/cc) (GN/m) (GN/m) (GN/m) 
______________________________________ 
Resin 1.26 7.7 2 2 
Graphite 
1.77 14.9 5.5 24 
______________________________________ 
The layups studied in this program include a unidirectional laminate 
(shown) two cross-ply laminates, two angle ply laminates, and a 
quasiisotropic laminate. It should be noted that the velocity approach to 
fiber fraction/porosity measurement is also applicable to other composite 
systems (fiberglass, Kevlar, metalmatrix, etc.). However, resolution 
capability may vary from system to system, depending upon the relative 
differences in material properties between the fiber and matrix. 
The algebraic complexity of the problem (see theoretical section) makes it 
relatively difficult to solve explicitly for even the simple case of 
unidirectional reinforcement. For practical laminates, the situation is 
even more complicated. Clearly, an alternative approach is needed. 
Ideally, this approach should be rapid, accurate, sufficiently flexible to 
handle various composite systems and configurations, reliable and easy 
implement on a commonly available device such as a personal computer. A 
computer code with these desired characteristics was developed. 
An iterative search algorithm was devised. It is illustrated in FIG. 3. 
First the points corresponding to the measured velocities are located for 
varying fiber volume fractions from 25% to 75% in 5% increments for the 
coarse mesh and resin porosities 0% to 25% in 5% increments. The distance 
in velocity space is given by: 
##EQU3## 
between each of the mesh points of the coarse mesh and the point 
corresponding to the measured velocities. The mesh point closest to the 
measured point is then the one which minimizes the distance measure as 
defined above. Once this point is identified, it serves as the base point 
for a new mesh with finer increments (+1% in both porosity and fiber 
content) than that of the original coarse mesh. The process is then 
repeated to identify the nearest point among the elements of the second 
mesh to that measured. Then, the entire process is repeated one last time 
with a relatively fine mesh (+0.1% increments) to establish the final 
solution. While further refinements are possible by repeating the process 
indefinitely, differences on this order have little physical significance 
and do not justify the additional time which would be required to further 
refine the calculation. The ability of the technique to resolve fine 
microstructural differences is also limited by the time resolution 
capability of the pulseecho overlap technique. In this case, we were 
capable of measuring transit time differences of 1 nanosecond. 
Experimental Verification 
In order to assess the utility of this technique, ultrasonic test results 
were compared with microscopic measurements of porosity and fiber volume 
fraction. Test samples were machined from a 24 ply, 30.5 cm .times.30.5 cm 
unidirectionally reinforced panel manufactured by Lear Fan. This material 
was fabricated from Fiberite hy-E 1048 prepreg tape using standard 
autoclave processing techniques. 
Quantitative measurements of local fiber content and porosity and fiber 
volume fraction were made along the edges of selected samples using the 
ultrasonic technique described previously. These measured samples were 
sectioned and mounted in epoxy for microscopic analysis. Specimens were 
abrasively polished and placed in a microscope with quantitative image 
analysis capability (Quantamet) for automated measurement of 
microstructural constituents. Results from a typical sample are presented 
in FIG. 4. Good agreement, both qualitatively and quantitatively, was 
observed between the ultrasonic predictions of local fiber content and the 
microscopic measurements. Estimates of fiber loading from the two 
techniques were usually within 3% of each other. Both techniques predicted 
that there was negligible porosity present in the samples (less than 
1.5%). Since there is an inherent uncertainty of 2% in the quantitative 
image analysis system, better agreement between the two methods was not 
expected. It should also be pointed out that the two techniques are not 
measuring precisely the same quantity. The ultrasonic test is sensitive to 
material property variations in a cylindrical volume (whose diameter is 
that of the transducer of 0.31 cm in this case). The image analysis 
approach measures changes averaged over a plane area (0.49 xm .times.0.34 
cm) rather than a volume. Given the level of material inhomogeneity 
observed in the velocity scans, some differences in the measurement 
techniques are to be expected. 
Accordingly, it may be concluded that the results from the two methods are 
in substantive agreement, at least within experimental error. 
Conclusions 
1. A novel method for measuring local fiber content and porosity in 
composite materials has been developed. 
2. The method is based upon a composite micromechanics model for the 
effects of fiber content and resin porosity on mechanical properties. The 
computer code developed in this research effort requires only ultrasonic 
velocity measurements for the microstructure determination. 
3. The method is rapid, nondestructive, and applicable to virtually any 
composite material system with any stacking sequence. 
4. Tests have been conducted on samples of a unidirectionally reinforced, 
24 ply graphite-epoxy laminate to examine the utility of this method. 
Comparison of the predictions of local fiber content and porosity from the 
ultrasonic data and quantitative image analysis indicated that the two 
techniques were in substantial agreement with one another with the 
differences observed attributable to experimental error. 
Embodiment of FIG. 5 
Shown in FIG. 5 is a system 10 which is constructed to nondestructively 
determine fiber volume fraction and resin porosity of a composite material 
in accordance with the present invention and in accordance with the 
technique described in detail before. The system 10 basically includes: a 
support structure 12 for operatively supporting a shear transducer 14, a 
longitudinal transducer 16 and a linearly variable displacement transducer 
18; a multiplexer 20; a pulser-receiver 22; an analog to digital converter 
24 (designated A/D in FIG. 5); a processor 26; a power supply and signal 
conditioner 28; and a digital voltmeter 30. In one operational embodiment, 
the system 10 was constructed utilizing the following commercially 
available components: 
______________________________________ 
a. shear transducer 14 
Panametrics, 
Model V-155 
b. longitudinal transducer 16 
Panametrics, 
Model V-109 
c. linearly variable Shaevitz, 
displacement transducer 18 
Model PCA-220-005 
d. multiplexer 20 Sonotek, Inc., 
Model 23HV 
e. pulser-transducer 22 
Panametrics, 
Model 5052 
f. analog to digital Sonotek, Inc., 
converter 24 Model STR *825 
an associated 
software 
g. processor 26 Zenith, 
Model 248 
h. power supply and Albia Electronics 
signal conditioner 28 
Model DM-6 
i. digital voltmeter 30 
Hewlett Packard 
Model 3440 
______________________________________ 
In the operational embodiment just described, the particular analog to 
digital converter 24, Sonotek, Inc. STR *825, plugs directly into the 
processor 26 and the software associated with this particular analog to 
digital converter 24 is operatively disposed in the processor 26 for 
operating the analog to digital converter 24. 
The pulser receiver 22 is constructed and adapted to output timed 
excitation pulses over a signal path 32 to either the longitudinal 
transducer 16 or shear transducer 14. The pulser receiver also serves to 
amplify the sensed acoustic waves by the two transducers. The multiplexer 
20 allows the operator to automatically switch between the longitudinal 
transducer 16 or shear transducer 14 as needed. 
The excitation pulses are received by the shear transducer 14 or 
longitudinal transducer 16 and the transducers are constructed to cause an 
ultrasonic wave to propagate in the test sample, in response to receiving 
such excitation pulses. 
The shear transducer 14 and the longitudinal transducer 16 each also are 
constructed to receive ultrasonic or acoustic waves propagated through the 
composite material being tested and to output in an analog format such 
received waves. The shear transducer 14 outputs received waves propagated 
through the composite material to be tested over a signal path 38. The 
longitudinal transducer 18 outputs in an analog format received waves 
propagated through the composite material to be tested over a signal path 
40. 
The waves propagated through the composite material are sensed by 
transducers and outputted by the shear transducer 14 and the longitudinal 
transducer 16 over the respective signal paths 38 and 40. These analog 
signals are inputted into and received by the multiplexer 20. The 
multiplexer 20 outputs the waves propagated through the composite material 
and received from the shear transducer 14 over a signal path 42 which are 
inputted into the pulser receiver 22. The multiplexer 20 also outputs the 
waves propagated through the composite material and received from the 
longitudinal transducer 16 over a signal path 44 which are inputted into 
the pulser receiver 22. The pulser receiver 22 outputs the waves 
propagated through the composite material in an analog format received 
from the shear transducer 14 over a signal path 46 which is inputted into 
the analog to digital converter 24. The pulser receiver 22 also outputs 
the waves propagated through the composite material in an analog format 
over a common signal path 48 which is inputted into the analog to digital 
converter 24. 
The analog to digital converter 24 digitizes the received waves outputted 
by the shear transducer 14 and the analog to digital converter 24 outputs 
the digitized waves over a signal path 50. The analog to digital converter 
digitizes the waves outputted by the longitudinal transducer 16 and 
outputs the waves in a digital format over a signal path 52. The digitized 
waves outputted by the shear transducer 14 and the longitudinal transducer 
16 respectively are inputted into the processor 26 by way of the 
respective signal paths 50 and 52. 
The linearly variable displacement transducer 18 is connected to and 
receives power from the power supply and signal conditioner 28 over a 
signal path 54. The linearly variable displacement transducer 18 has a 
contact end 56 on a plunger 58 which is spring loaded and mounted within 
the casing of the linearly variable displacement transducer 18. The 
linearly variable displacement transducer 18 is constructed to output a dc 
voltage proportional to the displacement of the plunger 58 over a signal 
path 61 which is inputted into the digital voltmeter 40. The digital 
voltmeter 40 is constructed and adapted to provide a visually perceivable 
output indication of the voltage of the signal on the signal path 61 which 
is proportional to the displacement of the plunger 58 in the linearly 
variable displacement transducer 18 or, in other words, which is 
proportional to the thickness of the composite material as will be made 
more apparent below. 
The shear transducer 14, the longitudinal transducer 16 and the linearly 
variable displacement transducer 18 are operatively mounted on the support 
structure 12. More particularly, the shear transducer 14 is disposed 
through an opening in a cylindrically shaped support plate 61 and the 
upper end of the shear transducer 14 is supported a distance above the 
upper surface of the support plate 60 by way of a spring 62 which is 
disposed about the shear transducer 14 and biases the shear transducer 14 
in an upward direction. The longitudinal transducer 16 is disposed through 
an opening in the support plate 60 and the upper end of the longitudinal 
transducer 16 is support distance above the surface of the support plate 
60 by way of a spring 64 which biases the longitudinal transducer 16 in an 
upwardly direction. The linearly variable displacement transducer 18 is 
disposed through an opening in the support plate 60 and the upper end of 
the linearly variable displacement transducer is supported a distance 
above the upper surface of the support plate 60 by way of a spring 66 
which is disposed about the linearly variable displacement transducer 18. 
The support plate 60 is disposed generally below an arm 68. A shaft 70 is 
disposed through a portion of the arm 68. One end of the shaft 70 is 
secured to a central portion of the support plate 60. The opposite end of 
the shaft 70 extends through a knob 72 and the shaft 70 is secured to the 
knob 72. The shaft 70 is connected to the support plate 60 and the knob 72 
so that, by manually rotating the knob 72, the support plate 60 is 
rotated. 
An actuator post 74 is disposed through an opening in one end of the arm 68 
and the actuator post 74 is supported within this opening by way of a 
spring 76 so that one end of the actuator post 74 is supported a distance 
above the upper surface of the arm 68 by way of the spring 76. The 
actuator post 74 is supported on the arm 68 so that an actuating end 78 of 
the actuator post 74 is supported and disposed a distance above the upper 
surface of the support plate 60 in a nonactuated position of the actuator 
post 74. A set screw 80 is disposed through a portion of the arm 68 and 
one end of the set screw 80 is positioned to contact a portion of the 
actuator post 74 in one position of the set screw 80 to secure the 
actuator post 74 or the transducers 14 or 16 in a predetermined position 
within the respective openings in the arm 68 during the operation of the 
system 10 in a manner and for reasons which will be made more apparent 
below. 
One end of the arm 68 is secured to one end of a support rod 82 and the 
opposite end of the support rod 82 is secured to a base 84. The support 
rod 82 cooperates to support the arm 68 and the support plate 60 a 
distance above an upper surface 86 of the base 84. The support rod 82 also 
is sized so that the shear transducer 14, the longitudinal transducer 16 
and the linearly variable displacement transducer 18 each are supported a 
predetermined distance above the upper surface 86 of the base 84. 
In operation, the composite material to be tested is placed on the upper 
surface 86 of the base 84 in a position generally under the plunger 58 
contact end 56 of the linearly variable displacement transducer 18. The 
actuator post 74 is then pressed manually against the bias action of the 
spring 76 thereby moving the actuating end 78 into engagement with the 
upper end of the linearly variable displacement transducer 18. The 
actuator pulse 70 is manually moved in the downward direction until the 
upper end of the linearly variable displacement transducer 18 engages the 
upper surface of the support plate 60. The actuator post 74 can be secured 
in this position by the set screw 80 if desired. In this position of the 
linearly variable displacement transducer 18, the DC voltage outputted by 
the linearly variable displacement transducer 18 over the signal path 61 
is proportional to the thickness of the composite material being tested 
and this voltage proportional to thickness is outputted over the signal 
path 61 and inputted into the digital voltmeter 40. The digital voltmeter 
40 provides a visually perceivable output indication indicating the DC 
volt of the signal inputted on the signal path 61, this voltage being 
proportional to the thickness of the composite material. The operator 
manually inputs the thickness of the composite material into the processor 
26 using the processor 26 keyboard. 
It should be noted that, in a more automated form or if desired in a 
particularly application, the linearly variable displacement transducer 18 
output signal proportional to the thickness of the material can be 
inputted directly into the processor 26 thereby eliminating the manually 
steps of reading the digital voltmeter 40 in manually inputting the 
thickness into the processor 26 if desired. 
The actuator post 74 then is released and moved by the spring 76 to the 
rest position shown in FIG. 5 thereby causing the linearly variable 
displacement transducer 18 to be moved to the rest position by the spring 
66. After the linearly variable displacement transducer 18 has been moved 
to the rest position, the operator then rotates the knob 72 thereby 
rotating the support plate 60 to position the upper end of the 
longitudinal transducer 16 generally under the actuating end 78 of the 
actuator post 74. The actuator post 74 then is moved downwardly against 
the bias action of the spring 76 with the actuating end 78 thereof 
engaging and moving the longitudinal transducer 16 in the downwardly 
direction. The longitudinal transducer 16 is moved in the downwardly 
direction by the actuator post 74 until the lower end of the longitudinal 
transducer 16 engages the upper surface of the composite material. The 
actuator post 74 is secured in this position by the set screw 80 thereby 
securing the longitudinal transducer 16 in the operating position wherein 
the lower end of the longitudinal transducer 16 engages the upper surface 
of the composite material. 
It should be noted that, prior to moving the longitudinal transducer 16 to 
the operating position just described, a high viscosity coupling agent is 
applied to the lower end of the longitudinal transducer 16 for coupling 
the ultrasonic vibrations of the longitudinal transducer 16 to the 
composite material to be tested. Also, the high viscosity coupling agent 
is applied to a portion of the upper surface of the composite material to 
be tested. One coupling agent suitable for this purpose is a resin made by 
Dow Chemical, Model V9. 
After the longitudinal transducer 16 has been moved to the operating 
position, the pulser receiver 22 is actuated to output excitation pulses 
which are multiplexed through the multiplexer 20 and inputted into the 
longitudinal transducer 16 by way of the signal path 34. The longitudinal 
transducer 16 is constructed to vibrate in a particular manner so that 
longitudinal ultrasonic waves are coupled to and propagated through the 
composite material. The ultrasonic waves induced by the longitudinal 
transducer 16 and propagated through the composite material to be tested 
propagate through the composite material and are reflected back through 
the composite material (back surface reflections in the particular 
embodiment of the invention shown in FIG. 5). The ultrasonic waves 
propagated through the composite material and reflected back through the 
composite material are sensed and received by the longitudinal transducer 
16, and the longitudinal transducer 16 outputs an analog signal on the 
signal path 40 in response to receiving the ultrasonic waves propagated 
through the composite material. These received signals are outputted on 
the signal path 40 in an analog format. The signals outputted by the 
longitudinal transducer 16 on the signal path 40 are indicative of a 
second velocity (V.sub.2), the velocity of the ultrasonic wave propagated 
through the composite material emanating from the longitudinal transducer 
16. 
The transducers 14, 16 and 18 must be positioned in the same position 
during the operation of the system 10 so the thickness measurement is 
taken and the ultrasonic waves are propagated through substantially the 
same point on the composite material. Index marks could be inscribed on 
the upper surface of the support plate 60 for alignment with one edge of 
the arm 68 to visually align each of the transducers 14, 16 and 18. In the 
alternative, index holes can be formed in the upper surface of the support 
plate 60 and a ball can be located in an opening in the lower surface of 
the arm 68 with the ball being biased toward the arm 68 by way of a 
spring. Thus, when the support plate 60 is rotated, the ball falls into 
one of the index holes in the support plate 60 to indicate that the 
support plate 60 has been rotated to a correct position. 
The signals outputted by the longitudinal transducer 16 are multiplexed 
through the multiplexer 20 and inputted into the pulser receiver 22 by way 
of the signal path 44. The pulser receiver outputs such signals on a 
signal path 46 for reception by the analog to digital converter 24. The 
analog to digital converter 24 receives the signals in the analog format 
outputted by the longitudinal transducer 16 and the analog to digital 
converter 24, operated by the processor 26 in accordance with the program 
mentioned before for operating the analog to digital converter 24, 
digitizes the analog signals outputted by the longitudinal transducer 16. 
The analog digital converter 24 outputs in a digital format the 
longitudinal transducer 16 output signals on the signal path 52 which are 
inputted into the processor 26. The processor 26 is programmed to 
determined the second velocity (V.sub.2) in response to receiving the 
inputted transducer 16 output signals in the digital format from the 
analog to digital converter 24. 
The actuator post 74 then is released and moved by the spring 76 to the 
rest position shown in FIG. 5 thereby causing the longitudinal transducer 
16 to be moved to the rest position by the spring 64. After the 
longitudinal transducer 16 has been moved to the rest position, the 
operator then rotates the knob 72 thereby rotating the support plate 60 to 
position the upper end of the shear transducer 14 generally under the 
actuating end 78 of the actuator post 74. The actuator post 74 then is 
moved downwardly against the bias action of the spring 76 with the 
actuating end 78 thereof engaging and moving the shear transducer 14 in 
the downwardly direction. The shear transducer 14 is moved in the 
downwardly direction by the actuator post 74 until the lower end of the 
shear transducer 14 engages the upper surface of the composite material. 
The actuator post 74 is secured in this position by the set screw 80 
thereby securing the shear transducer 14 in the operating position wherein 
the lower end of the shear transducer 14 engages the upper surface of the 
composite material. 
It should be noted that, prior to moving the shear transducer 14 to the 
operating position just described, a high viscosity coupling agent is 
applied to the lower end of the shear transducer 14 for coupling the 
ultrasonic vibrations of the shear transducer 14 to the composite 
material. One coupling agent suitable for this purpose is a resin made by 
Dow Chemical, Model V9, as mentioned before. 
After the shear transducer 14 has been moved to the operating position, the 
pulser receiver 22 is actuated to output excitation pulses which are 
multiplexed through the multiplexer 20 and inputted into the shear 
transducer 14 by way of the signal path 34. The shear transducer 14 is 
constructed to vibrate in a particular manner so that shear ultrasonic 
waves of a known polarization are coupled to and propagated through the 
composite material. The ultrasonic waves induced by the shear transducer 
14 and propagated through the composite material to be tested propagate 
through the composite material and are reflected back through the 
composite material (back surface reflection in the particular embodiment 
of the invention shown in FIG. 5). The ultrasonic waves propagated through 
the composite material and reflected back through the composite material 
are sensed and received by the shear transducer 14. The shear transducer 
14 outputs an analog signal on the signal path 40 in response to receiving 
the ultrasonic waves propagated through the composite material, these 
received signals being outputted on the signal path 40 in an analog 
format. The signals outputted by the shear transducer 14 on the signal 
path 40 are indicative of the velocities of the two ultrasonic waves 
((V.sub.1 and V.sub.2) propagated through the composite material by the 
shear transducer 14. 
The signals outputted by the shear transducer 14 are multiplexed through 
the multiplexer 20 and inputted into the pulser receiver 22 by way of the 
signal path 44. The pulser receiver outputs such signals on a signal path 
46 for reception by the analog to digital converter 24. The analog to 
digital converter receives the signals in the analog format outputted by 
the shear transducer 14 and the analog to digital converter 24, operated 
by the processor 26 in accordance with the program mentioned before for 
operating the analog to digital converter 24, digitizes the analog signals 
outputted by the shear transducer 14. The analog to digital converter 24 
outputs in a digital format the shear transducer 14 output signals on a 
signal path 52 which are inputted into the processor 26. The processor 26 
is programmed to determined the first velocity (V.sub.1) (the velocity of 
the factor of the two shear waves) in response to receiving the inputted 
transducer 16 output signals in a digital format from the analog to 
digital converter 24. 
Prior to starting the operation of the system 10, the operator manually has 
inputted into the processor 26 certain parameters of the composite 
material to be tested, namely, density, elastic moduli of the constituent 
materials and layup sequence, which are stored in the processor 26. The 
processor 26 previously has the thickness of the composite material also 
has been inputted into the processor 26 in the manner described before. 
The processor 26 is programmed to store the inputted thickness of the 
composite material to be tested. After the processor 26 has determined the 
first and second velocities, V.sub.1 and V.sub.2, the processor 26 then is 
programmed to determined the fiber volume fraction and resin porosity of 
the composite material based on the determined parameters of thickness and 
first and second velocities, V.sub.1 and V.sub.2, and the inputted known 
parameters of density, elastic moduli of the constituent materials and 
layup sequence in accordance with the procedures graphically shown in 
FIGS. 2 and 3 and described before. In one particular embodiment, the 
processor 26 was programmed with the following program to enable the 
processor 26 to determine the fiber volume fraction and resin porosity of 
the composite material to be tested in the manner just described, the 
program being outlined below in the FORTRAN and C (subroutine PLT.sub.-- 
Time) languages: 
##SPC1## 
The signals outputted by the longitudinal transducer 16 and the shear 
transducer 14 comprise a first series of pulses generally referred to in 
the art as the "main bang" followed after a time delay by another series 
of pulses referred to generally in the art as "first back surface 
reflections", followed after a time delay by another series of pulses 
commonly referred to in the art as "second back surface reflections". This 
sequence of a series of pulses followed by a time delay and then another 
series of pulses is repeated. The analog to digital converter 24 digitizes 
this signal. The processor 26 could then be programmed to determine the 
velocity (V.sub.1) or (V.sub.2) by determining the time delay between 
corresponding peaks of the first and the second back surface reflections. 
However, in accordance with the program described above and in accordance 
with one mode of operating the present invention, the processor 26 is 
programmed to determine this time delay and thus determine the first and 
the second velocities, (V.sub.1) and (V.sub.2), using a quadratic fit to 
find the maximum in the autocorrelation function to determine the peak in 
each of the first and the back surface reflections and the time delay 
between these two peaks then is utilized to determine the respective 
velocities, (V.sub.1) and (V.sub.2). 
It also should be noted that the particular analog to digital converter 24 
describe before digitizes at a rate of 25 MKz. This rate of digitizing 
does not provide the accuracy desired in most applications of the system 
10. Thus, the program mentioned before in connection with the particular 
analog to digital converter 24 cooperates the analog to digital converter 
24 to artificially induce a higher accuracy by shifting the point in the 
analog signal to be digitized eight times thereby providing an effective 
digitizing rate or sample rate of 200 MHz in this particular example. 
Rather than using the autocorrelation function system for determining the 
peaks for the purpose of measuring the velocities, (V.sub.1) and 
(V.sub.2), the processor 26 could be programmed to simply measure or 
determine the time delay between the peaks of the digitized signal. This 
is not done in the particular embodiment described before because this has 
been found not to be as accurate as the method previously described 
because of dispersion and attenuation phenomena. However, if the analog to 
digital converter 24 could be operated at a higher sampling or digitizing 
rate, this peak to peak method could be utilized for higher data 
acquisition. 
With the particular model shown in FIG. 5 and particularly with the 
specific embodiment shown described before, the outputs of the shear 
transducer 14 and the longitudinal transducer 16 are displayed by the 
processor 26 so the operator can determine whether or not the received 
signals are adequate for processing in accordance with the present 
invention. The operator is observing these signals on the processor 26 
display to ascertain whether or not the amplitudes are high enough or, in 
other words, whether or not this is a detectable signal. The processor 26 
in some applications could be programmed to make this determination 
automatically. 
As specifically described before, the system 10 utilizes a shear transducer 
14 and a longitudinal transducer 16. In the shear transducer 14, 
vibrations are generated in response to the received excitation pulses and 
these vibrations result in the first ultrasonic wave being emitted from 
the shear transducer 14 and propagated through the composite material to 
be tested. Assuming "l" equals a vector describing the direction of 
propagation of the ultrasonic wave normal, and ".alpha." equals a vector 
describing the direction of particle vibration in the composite material, 
then the ultrasonic wave propagated through the composite material as a 
result of a shear transducer 14 represent a circumstance where "l" is 
perpendicular to ".alpha.". 
As specifically described before, the system 10 also utilizes a 
longitudinal transducer 16. In the longitudinal transducer 16, vibrations 
are generated in response to the received excitation pulses and these 
vibrations result in the second ultrasonic wave being emitted from the 
longitudinal shear transducer 16 and propagated through the composite 
material to be tested in this circumstance, "l" is parallel to ".alpha.". 
Assuming "l" equals a vector describing the direction of propagation of 
the ultrasonic wave normal, and ".alpha." equals a vector. 
Thus, the waves propagated through the composite material as induced by the 
shear transducer 14 and the longitudinal transducer 16 have different 
polarizations, one instance, being were "l" is parallel to ".alpha." in 
the case of the longitudinal transducer 16 and the other being were "l" is 
perpendicular to ".alpha." in the case of the shear transducer 14. In the 
present invention, it only is important that two acoustic waves are 
propagated through the composite material to be tested having different 
polarizations and the present application is not limited to the particular 
polarizations described before with respect to the longitudinal and the 
shear transducers 16 and 14. 
It also should be noted that two waves having different polarizations can 
be caused to be propagated through the composite material to be tested 
using only a single shear transducer. In this instance, the composite 
material to be tested is placed in one position under the single shear 
transducer for inducing the first ultrasonic wave to be propagated through 
the composite material. The composite material then is moved and 
repositioned under the shear transducer for propagating the second 
ultrasonic wave through the composite material. If the composite material 
is moved in a proper manner to different positions as just described, two 
waves having different polarizations can be induced in the composite 
material using the signal shear transducer. 
The specific program described before is particularly adapted for composite 
materials wherein the fiber constituent is disposed in the other material 
constituent in a two dimensional pattern. The present invention also could 
be utilized for three dimensional patterns; however, the processor 26 
program would have to be modified to accommodate such three dimensional 
patterns. In general, the program would have to be modified in the 
following manner to accommodate three dimensional patterns for woven 
reinforcements, or for carbon-carbon materials. 
EMBODIMENT OF FIG. 6 
Shown in FIG. 6 is a system 10a which also is constructed in accordance 
with the present invention for nondestructively determining fiber volume 
fraction and resin porosity of a composite materials. The system 10a 
generally comprises a modified support structure 12a which is disposed in 
a reservoir 90 containing water, the support structure 12a being immersed 
in the water. 
The support structure 12a is connected to cross beams 92 and 94 which are 
supported on the upper end of the reservoir 90. In this embodiment, the 
composite material to be tested also is immersed within the reservoir as 
generally illustrated diagrammatically in FIG. 6 wherein the composite 
material is designated by the reference numeral 96. 
The support structure 12a includes a modified support plate 60a which is 
rollingly connected to the cross beams 92 and 94 by way of a support beam 
98, one end of the support beam 98 being secured to the support plate 60a 
and the opposite end of the support beam 98 being rollingly connected to 
the cross beams 92 and 94 so the support plate 60a can be moved along the 
support beam 92 and alternatively along the support beam 94 for 
positioning the support plate 92 in various positions within the reservoir 
90 and with respect to the composite material 96. 
In this embodiment, four longitudinal transducers are used. One pair (100 
and 104) are employed at normal incidence for longitudinal wave 
propagation. A second pair (14 and 16) are employed at an incidence angle 
other than 90.degree. and are used to generate shear waves via mode 
conversion. In this way, transducers 100 and 104 can be used for thickness 
measurement (since they are a known distance apart and the sound velocity 
in water is constant) as well as for longitudinal wave propagation. 
One end of a curved arm 102 is connected to the support plate 60a. The arm 
102 extends a distance from the support plate 60a so the opposite end of 
the arm 102 is positioned generally below and spaced a distance from the 
first thickness transducer 100. A second thickness transducer 104 is 
supported in the end of the arm 102, opposite the end connected to the 
support plate 60a, so that the second thickness transducer 104 is aligned 
with the first thickness transducer 100. The second thickness transducer 
104 also is constructed and operates exactly like the longitudinal 
transducer 16 described before. 
The transducers 14, 16, 100 and 104 each are connected through the 
multiplexer 20, the pulser receiver 22, the analog to digital converter 24 
and the processor 26 in a manner exactly like that described before with 
respect to the transducers 14 and 16. 
In operation, the composite material to be tested is disposed in the 
immersion bath within the reservoir 90. The support structure 12a is 
positioned on the cross beam 92 or the cross beam 94 so that transducer 
100 is positioned generally above a point on the composite material 96 and 
transducer 104 is positioned generally on the opposite side of the 
composite material 96 and aligned with the first thickness transducer 100. 
In this position, the transducer 14 is angularly disposed within the 
support plate 60a so that the ultrasonic wave emitted by the transducer 14 
impinges on the point immediately below the first thickness transducer 100 
and generally between the first and the second thickness transducers 100 
and 104. In this position, transducer 16 is angularly disposed within the 
support plate 60 so that the ultrasonic waves generated in the part by 
transducer 14 will be received by transducer 16. 
Transducer 14 and transducer 16 are operated in a pitch-catch mode rather 
than the pulse-echo mode described in FIG. 5. Otherwise, they are used to 
provide shear velocity information analogous to that provided by the 
single contact shear transducer shown in FIG. 5 (14). 
Transducer pair 100 and 104 are used for two purposes. The first purpose is 
to determine the thickness of the composite sample. For this purpose, 
transducer 100 is excited by the pulser receiver 22 to generate a 
longitudinal wave in the water. This wave propagates to the upper surface 
of the composite material where part of the energy is reflected back to 
transducer 100. The reflected wave and successive reflections are sensed 
by this transducer. Since the velocity of sound wave propagation in water 
is a known constant (1,460 m/s), by digitizing the response of transducer 
to the first two water path reflections, the distance between transducer 
100 can be determined. In a similar fashion, by exciting transducer 104 
and digitizing the same two water path echoes, its position relative to 
the lower surface of the composite is determined. Since the total distance 
between the surface of transducer 100 and transducer 104 is fixed, this 
procedure yields the thickness of the composite. 
The second purpose of the transducer pair is to determine the velocity of 
longitudinal wave propagation in a direction perpendicular to the plane of 
reinforcement. The device may be operated in a pulse-echo mode with a 
single transducer (either 100 or 104) serving as generator and receiver or 
with one transducer serving as generator and the other as receiver. By now 
analyzing successive internal reflections within the composite, the 
transit time for this digital mode can be measured. This, in conjunction 
with the thickness measurement, yields the desired longitudinal velocity 
(V.sub.2). 
In this operation of system 10a, the first and second velocities are 
determined in a manner similar to that described with respect to system 10 
and the processor is programmed to calculate resin porosity and fiber 
volume fraction as in system 10. The processor is also programmed to 
translate the transducer assembly over the surface of the part so that 
resin porosities and fiber volume fraction measurements can be performed 
for the entire part. 
EMBODIMENT OF FIG. 7 
Shown in FIG. 7 is another modified system 10c which is constructed in 
accordance with the present invention for nondestructively determining 
fiber volume fraction and resin porosity of a composite material, the 
composite material being diagrammatically shown in FIG. 7 and designated 
therein by the reference numeral 106. In this system 10c, the transducer 
14 and the transducer 16 each are supported in a support plate (not shown) 
in a manner exactly like described before with respect to the system 10a 
shown in FIG. 6. Further, transducer 100 is supported in the support plate 
in a manner exactly like described before with respect to the system 10a 
shown in FIG. 6. Transducer 104 is supported so the second thickness 
transducer 104 is disposed and oriented with respect to the first 
thickness transducer 100 in a manner exactly like that described before 
with respect to the system 10a shown in FIG. 6. 
In system 10c, a pair of water jets 112 are associated with each of the 
transducers 14, 16, 100 and 104. The water jets associated with the 
transducers 14, 16, 100 and 104 are schematically shown and represented in 
FIG. 7 by a pair of arrows associated with each transducer and designated 
by the reference numerals 110 and 112. The water jets associated with the 
transducer 14 are designated as 110d and 112d in FIG. 7, the water jets 
associated with the transducer 100 are designated 110e and 112e in FIG. 7, 
the water jets associated with the transducer 16 are designated 110f and 
112f in FIG. 7 and the water jets associated with the transducer 104 are 
designated 110s and 112s in FIG. 7. The water jets 110 and 112 associate 
with each of the transducers are oriented to supply a jet of water 
generally between the end of the transducer and the surface of the 
composite material 106. 
The water jets or streams provided by the water jets 110 and 112 provide a 
coupling for coupling the ultrasonic waves between the transducers and the 
composite material 10 thereby eliminating the need for immersing the 
transducers and the composite material in a reservoir containing the 
coupling agent as described before in connection with FIG. 6. 
In this embodiment of the invention, the transducers 14, 16, 100 and 104 
can be moved freely about the composite material 106. This embodiment of 
the invention permits the testing of large parts which are incapable of 
being immersed practically in a reservoir. 
In this embodiment of the invention, the fiber volume fraction and resin 
porosity of the composite material are determined by the processor 26 in a 
manner exactly like that described before with respect to the system 10a 
shown in FIG. 6. 
The procedures prescribed in detail before assume the state of cure of the 
composition material is known and therefore the elastic modulii of the 
constituent materials also are known. The elastic moduli of the 
constituent materials of the composite material vary with the state of 
cure and, where the state of cure is not known, procedures must be 
effected to measure the effect of the cure reaction in the composite 
material. Preferably, the procedures are compatible with ultrasonic sound 
measurements. In general, dielectric property measurements (conductivity, 
capacitance, permitivity, loss factor) can be used to accomplish this 
purpose. 
Since ionic mobility is directly related to the extent of polymerization, 
measurement of conductivity can be correlated to the degree of cure. 
Hence, mechanical properties (Young's modulus, shear modulus, Poisson's 
ration, viscosity, etc.). It should be pointed out that these correlations 
are empirical and must be done for each resin system under consideration. 
See Marvin Bramm Berg, David Day, Huan Lee and Kimberly Russell "New 
Applications For Dielectric Monitoring and Control In Advanced Composites: 
The Latest Developments", Published by American Society of Metals (1986, 
pages 307-311). These relationships are the basis for the present method 
of compensating for local variations in the extent of cure. It should also 
be mentioned that low frequency probes must be used for accurate cure 
measurements. 
Initially, what is sometimes referred to herein as a "state of cure data 
base" is accumulated. Sample composite materials, each having the same 
constituent material as the composite material to be tested and each 
having a known state of cure, initially are established. Each of these 
sample composite materials is cured to various known states of cure, such 
as ten percent (10%) cured, twenty percent (20%) cured . . . one hundred 
percent (100%) cured, for example. The elastic moduli (shear and Young's 
moduli for example) and the dielectric property (e.g. conductivity) of 
each of these resin samples then is determined. 
From this set of experimental or empirical data, curves plotting two 
independent elastic moduli such as shear and Young's versus conductivity 
for each of the sample composite materials are developed. These curves 
comprise the state of cure data base which is inputted into the processor 
26. In a more preferred form, a formula is developed representing each of 
these curves and these formulae comprise the state of cure data base which 
is inputted into the processor 26. In either case, the state of cure data 
base is inputted into and stored in the processor 26. 
The dielectric property measuring device outputs a signal which is 
indicative of the conductivity of the composite material to be tested. 
Dielectric property devices which are capable of providing an output 
proportional to the capacitance of the composite material to be tested are 
well known in the art and one such device which can be used in the present 
invention is commercially available from Micromet Instruments, Inc , 
Eumetric System II 
The dielectric constant indicating device outputs an indication of the 
dielectric constant of the composite material being tested, and this 
output is digitized and inputted into the processor 26. Where the 
dielectric constant indicating device more particularly outputs an 
indication of the conductivity of the composite material to be tested, the 
processor 26 is programmed to determine the dielectric constant of the 
material to be tested from the inputted indication of measured 
conductivity. 
The processor 26 has stored therein the state of cure data base, and the 
processor 26 is programmed to determine the shear modulus and the Young's 
modulus from the inputted output of the dielectric constant indicating 
device either from the curves stored in the state of cure data base or the 
formula stored in the state of cure data base. 
After determining the required elastic modulii, the processor 26 then 
determines the other composite material parameters in the manner described 
before, but using the shear modulus and the Young's modulus determined in 
the manner just described. 
With respect to the device as shown in FIGS. 6 and 7, the dielectric 
constant indicating device cannot be incorporated with the other 
transducers since water is used as the transmitting medium In these cases, 
the dielectric constant indicating device which provides an output of the 
capacitance of the composite material being tested cannot be used in a 
water medium In these instances where water is used as a transmitting 
medium, the dielectric constant indicating device separately is utilized 
to determine the dielectric constant of the composite material being 
tested. 
Further, with respect particularly to the embodiment shown in FIGS. 6 and 
7, it should be noted that the state of cure may, and in many instances 
will, vary over the area of composite material being tested For example 
only, the state of cure along the edges of the composite material may be 
quite different as compared to the state of cure over the central portion 
of the composite material to be tested. The dielectric property of the 
composite material to be tested is determined at a plurality of points 
over the entire area of the composite material to be tested and the 
determined dielectric property are correlated with the other measured 
parameters for determining the parameters in accordance with the present 
invention. 
Changes may be made in the construction and the operation of the various 
components and assemblies described herein and changes may be made in the 
steps or the sequence of steps of the methods described herein without 
departing from the spirit and the scope of the invention as defined in the 
following claims.