Skip to main content

Full text of "Combining fracture mechanics and ultrasonic NDE to predict the strength remaining in thick composites subjected to low-level impact"

See other formats




^ 



,\ 



t 
* 



COMBINING FRACTURE MECHANICS AND ULTRASONIC WDK TO PRF.HTrT TH E STRF.NaTH 



REMAINING IN THICK COMPOSITES SUBJECTED TO T.nw-T. F,VEL THPA^T 
Eric I. Madaras, Clarence C. Poe, and Joseph S. Heyman 



.-://■ 



^ 






NASA Langley Research Center, Hampton, Va . 23665 



ABSTRACT 

Predictions of the ultimate strength of damaged 
material have proven difficult to make. This type 
of prediction involves the combination of two 
factors: 1) an understanding of the mechanics of 
fracture, and 2) a method of measuring the 
relevant modes of damage in a non-destructive 
manner. The research reported here is focused 
upon the problem of predicting the remaining 
tensile strength of thick composites that were 
subjected to low-velocity impact damage which left 
no visible surface marks . This type of hidden 
damage can reduce the strength of thick composite 
materials significantly. For this research, 
specially fabricated thick composites were 
impacted using a one inch diameter ball as the 
indenter . These samples were non-destructively 
evaluated by ultrasonic through transmission and 
x-ray dye penetrant methods. The samples were 
then loaded in tension until failure. Predictions 
of the fracture strengths based on a fracture 
mechanics model combined with ultrasonic 
measurements generated good correlations with the 
actual measured fracture strengths. 



I. Introduction 

Thick composites are playing an • increasingly 
important role in aerospace and aeronautical 
'structures. Structures such as rocket motor 
casings and airframe components are being created 
with thicknesses of one inch or more. The 
thickness of these structures creates new 
difficulties in predicting their mechanical 
characteristics. Reliable certification of 
airworthiness is an important problem. A 
non-destructive prediction of the material 's 
useful strength while it is in service is 
necessary. 

Impact damage is a potentially serious problem in 
thick composites. Structures that employ thick 
composites are usually very massive. For example, 
a segment from NASA's space shuttle solid booster 
rocket motor weighs 17,900 to 57,700 Ibf when 
empty and between 261, 000 and 301,200 Ibf when 
loaded with fuel {see figure 1) . Thus each loaded 
rocket motor is in excess of 1,000,000 Ibf. (Each 
composite rocket motor proposed for the Shuttle 
saves almost 30, 000 Ibf in weight over the con- 
ventional steel cased motors.) These structures 
must be carefully handled because the static 
stresses involved with lifting are significant. 



Motor sections can be damaged by setting them down 
on a hard object or bumping another structure with 
,even a very low velocity. 

Most composites faiL rather catast rophically and 
give little indication of impending failure . 
Furthermore, impact damage in composites is not 
always visually evident . Impacts by sharp 
objects will leave visible scratches or puncture 
mark on the surface. In contrast, a blunt 
impacter will not leave a detectable mark for 
impact forces up tc about 17 kips (17,000 lbs), 
yet the strength of the composite could be reduced 
by as much as 37% [1], A blunt impacter will 
leave a dent or a crater for impact forces above 
17 kips. In the case of a blunt impacter, the 
degree of damage is difficult to ascertain by 
standard dye penetrant radiological means because 
the dye is not readily taken up by the composites 
used in this test. Large property variations that 
occur in the manufacturing of composite samples 
make many ultrasonic techniques unreliable. 




Figure 1 . Proposed filament wound casing 
sections for the solid rocket motors to be 
used with the space shuttle 



Eric Madaras 



Two factors will be in^ortant in order to predict 
the failure strength of these materials: 1) 
accurate knowledge of the degree of damage and 2) 
viable fracture mechanics models for failures due 
to stressing of an impacted sample . This work 
attempts to combine these two features into a 
working model for predicting the tensile strength 
of composites with invisible impact damage. 

Our approach was to employ a fracture model for 
predicting the fracture strength of homogeneous 
materials modelled with elliptical cuts. Our NDE 
probe used through-transmission ultrasound and an 
estimate of the degree of internal damage was 
derived from this data. The NDE results were then 
used as input into the fracture mechanics model to 
predict the fracture strength. 

II. The Fracture Mechanics Model 

It is predict '^d that at the moment of a 
low-velocity impact, the strains that result from 
compressive and shearing stresses in a thick 
composite are greatest just below the surface of 
the composite (2,3] (see figure 2a for an example 
cf the static principle shear stresses). This 
implies that impacts in thick composites have a 
greater degree of damage internally than at the 
surface. In fact, there is evidence that in those 
samples which did not display visible damage at 
the surface, the surface may not have fractured in 
many cases [1,4]. Figure 2b is a schematic of a 
cross section showing what might be expected for 
the internal damage. Figure 2b shows a region 
where the fibers are broken and the matrix is 
fractured; which is surrounded by a region of 
simple matrix cracking, plus, possibly some 
delam; nations which may occur at the bottom of the 
damage. 

Fiber breakage is important to the load-carrying 
ability of these composites, and especially in the 
load-carrying hoop fibers . Figure 3a shows a 
composite with an impact damaged region. Figure 
3b shows a schematic of a surface cut on a 
composite that is the basis of our fracture model 
for predicting the mode of failure. In this 
model, we postulate that in the vicinity of the 
damage, the composite is essentially disconnected 
across the damaged region. This is probably a 
reasonable approximation since the damaged matrix 
cannot transfer the stress loads properly to 
adjacent viabl*? fibers. Thus, all the broken 
fibers in thij^ region may represent a simple 
structure like a crack or cut. The impact model 
that we employed was derived for predicting the 
fracture from an elliptical cut or crack in a 
homogeneous material. This model provides an 
exact theoretical calculation for predicting the 
strength and manner in which the samples fracture 
[5,6]. 

Qnder tensile load, this model predicts the 
samples will fracture in two steps . The first 
step, illustrated in figure 4a, shows that the 
crack will extend laterally across the specimen. 
The depth of the crack will remain constant, with 
shearing at the base of the crack. The shearing 



Static Pressure Profile 



Average contact pressure, 
Pc over the radius, R 
m — n — r 




0.0 1.0 2.0 3.0 

Radial Distance (in units of R) 



a) 




Normal composite material 
Broken fibers and cracked matrix 
Cracked matrix only 
Delaminations 



b) 



Figure 2a) Lines of constant shear stress 
in an infinite homogeneous half plane as a 
result of a hemispherical static contact 
force. b) Possible internal damage states 
in a thick composite. 



failure prediction is consistent with a composites 
low interlaminar shear strength. This results in 
a thinner section with a correspondingly lower 
strength. The remainder of the sample will 
fracture as indicated in figure 4b. This theory 
was tested on thick FWC samples with actual 
elliptical cuts made in the surface . The samples 
did indeed fail in two steps, approximately as 
predicted. The measured ultimate failure strength 
deviated somewhat from theory. This was 
attributed to the possibility of out of plane 



Eric Madaras 




Impact Damage in 
Thick Composite 




Impact Damage 
Modelled as a Crack 



Figure 3a) A thick composite coupon show- 
ing an intact damaged site, b) The intact 
damaged region modelled as a crack. 



bending forces that might occur in the load frame 
after the initial failure. Empirically, the 
remaining strength for the samples used in this 
experiment was found to approximate a power law 
given by 



S - 30,100 x^j' 



0.278 



(1) 



where S is the strength in units of KSI and x^ is 
depth of the cut in inches [1]. If the hoop 
fibers which are along the load direction were not 
damaged (less than 0.19 in.), the samples would 
then break in the vicinity of the average ultimate 
strength of 50. J. KSI [4]. The empirical result, 
equation 1, was used to predict the remaining 
strength of the samples measured in this 
experiment. 

III. Samples 

In standard FWC materials the hoop fibers which 
are under tension are oriented circumferentially . 
The fiber lay-up in the samples used in this study 
were rotated 90° in order to best test tensile 
coupons in a load frame. This orientation allowed 
the hoop fibers to be along the axis of the 
cylinders and thusavoid having to test specimens 
in their curved direction in the load frame. The 
samples used in this experiment were taken from a 
specially wound casing manufactured with both hand 
layed-up plies and fiber wound plies. Fig. 5a 
shows a schematic of the cylinder from which the 
samples were derived. The cylinder was 30 inches 
in diameter with a thickness of 1.4 inches. This 
represented a cylinder that was 1/5 full scale in 
diameter and full scale in thickness. The length 
of the sample was approximately 84 inches. This 




First 

Ligament 

Failure 




Remaining 

Ligament 

Failure 



Figure 4. A representation of how a thick 

composite will fail . a) shows the first 

step and b) illustrates the remaining 
failure. 



sample was cut into seven rings which were each 12 
inches wide. The fiber lay-up directions were 0°, 
56°, and -56°. Each of these rings were placed 
under a drop tower and impacted on the perimeter 
in two inch spacings with different masses and 
from different heights (see figure 5b) . These 
rings were then cut up into coupons 2 inches wide 
by 12 inches long, each containing one impact site 
at its center. These coupons were then non- 
destructively tested by either x-ray dye penetrant 
methods or ultrasonic testing. Finally, the 
samples were loaded in tension until failure. In 
general, these samples failed in steps as 
predicted by the fracture mechanic model, 

IV. X-ray Measurements 

Dye penetrant x-ray photographs were made on many 
of the samples. These samples contained approxi- 
mately 6% porosity and any dye exposed to the 
sides could readily be taken up, compromising the 
photographic measurements. Therefore, the dye was 
carefully exposed to the surface area just around 
the impact. The interesting feature about these 
measurements was that the dye did not enter the 
matrix very effectively when exposed to the impact 
site (see figure 6a, 7a, and 7c), indicating that 
the surface was not fractured. In figure 6b, a 
small hole was drilled into the surface at the 
impact site. The dye then entered the matrix 
region indicating the extent of the damage. 

In figure 7a, the x-ray photograph shows the 



Eric Madaras 




12 in. 



84 in. 



Fiber 
Lay -Up 

^0 



J- 56 



a) 



30 in. 



'X-^' 

<l^ 



Impacter Q Test Coupon 
»^=S= 2 in. 



30 in 




-56 

/%0 



12 in. 



„^ 



b) 



66 

Fiber 
Lay -Up 



Figure 5. Illustration of the thick fila- 
ment wound samples. Part a) shows the 
large cylinder from which smaller rings 
were cut and part b) illustrates the 
smaller rings from which the test coupons 
originated. 



.1 



Figure 6. Dye penetration into impact 
damaged thick composites. Part a) shows 
the dye uptake into an impact damaged 
coupon. Part b) shows . the same coupon 
with a small hole drilled to allow the dye 
to penetrate the interior. 



effects of the dye penetrant method when viewed 
from the top; very little evidence of the damage 
is present . Figure 7b shows the same sample 
viewed from the top after it was loaded until the 
first failure step. Here the surface has been 
fractured, and the saiqple readily absorbs the dye. 
Figure 7c shows this sample from the side view, 
before it has been loaded. As in figure 7a, the 
dye is not taken up very well, and the depth of 
the damage is not well delineated. In contrast, 
figure 7d shows a side view after loading to the 
first failure step. Here, the sample indicates 
that interlaminar shearing occurs and the damage 
is better outlined. It is difficult to determine 
if the depth of damage has increased due the 
loading failure, but at least for testing 
purposes, the dye now enters the sample. 

V. Ultrasonic Measurements 

Many NDE techniques that are sensitive to fiber 
damage proved to be inadequate in these samples 
because of the widely varying material properties. 
This was a problem not only for ultrasound and 
x-ray radiographs, but also for techniques such as 
eddy currents. Figure 8 shows a close up of one 
of the samples. The fiber lay up is not uniform 
and there is significant porosity. Transmission 
ultrasonic measurements provided an integrating 
effect upon the ultrasonic response to the 
material properties which varied from location to 
location, but not upon well localized damaged 
material. This type of measurement, however, is 
not particularly sensitive to fiber breakage. We 
made several assumptions about the nature of the 
damage that enabled us to model the damage as a 
simple system and to circumvent the problem of 
detecting fiber breakage. To test this NDE model 
we needed to measure how well the model predicted 
the actual fracture strengths, based on the 
fracture model's equation. A second test of the 
model will be to impact thick samples which will 
be disassembled into thin layers {-2 mm thick) 
that can be ultrasonically measured to assess 
damage in each individual layer. Destructive 
testing of these layers will allow the ultrasonic 
measurements to be correlated with the damage. We 
have tested the first method, which is the basis 
of this report, and the second test of the model 
is being pursued. 

A transmission measurement provides few parameters 
while these complex composites can effect those 
parameters in numerous ways. (Recall figure 2b 
which shows a schematic of the complexity of the 
damaged region within the composite.) This is, 
therefore, an indeterminate system unless we can 
simplify the system with the following 
assumptions: 1) The regions of damage can be 
separated into distinct uniform regions of 
fiber-matrix damage or matrix damage only. 2) 
The attenuation due to the broken fibers is 
linearly related to the attenuation of the fiber 
fractured material and the attenuation of the 
matrix cracked material in the following manner: 



^eff 



a 



md 



• r + a 



fd 



(2) 



where, tt^^f is an -effective** attenuation of 



Eric Madaras 




a. 



b. 




Figure 1 . A comparison of the dye 

uptake in an impact damaged coupon. 
Panel a) is the top view of dye uptake 
after impa-t, but before loading. Panel 
b) is the top view of the dye uptake 
after impact and after the first ligament 
failure. Panel c) is the side view of 
dye uj)take after impact , but before 
loading. Panel d) is the side view of 
the dye uptake after impact and after 
the first ligament failure. 



Outer Surface 




Hoop Layer Helical Larer 

Figure 8. Photograph showing a close up 
of the fiber misalignment and some 
porosity. 

damaged composite material, ^md ^^ X.h.Q 
attenuation due to natrix damaged material, r is 
the ratio of the matrix damaged material thickness 
to the fiber damaged material thickness, and OC £ ^ 
is the attenuation cf the fiber damaged material . 
3) The inverse of ihe velocity {or slowness) is 
linearly related in the following manner: 



1/v 



eff 



= r/v, 



md 



+ 1/v 



fd 



(3) 



where Vgff is cin "effective" velocity of damaged 
composite material, r is as defined in equation 2, 
Vj^^ is the velocity of matrix damaged material and 
V£^ is the velocity of the fiber damaged material. 
4) Delaminations and other modes of damage are 
negligible. 5) Tne location of broken fibers 
range uniformly from the surface into the 
composite. These assumptions simplify figure 2b 
into figure 9 . In figure 9, there are only two 
regions of interest; one is the normal good 
composite and the other an "effective" damaged 
composite region which is the important region 
related to the fiber fractured volume. 
Interestingly, this looks similar to the 
elliptical cut fracture mechanics model. These 
assumptions are somewhat extreme; their chief 
attraction is simplicity. For exampJe, at low 
crack densities, attenuation is very sensitive to 
fiber fracture, but velocity measurements are less 
so [7,83. Further research will better delineate 
the correct assumptions. 

These assumptions result in simple algebraic 
relationships for the attenuation and the velocity 
measurements. A pulsed phase locked loop system 
[91 was used to determine the changes in material 
velocity. For these experiments, the analysis 
equation is: 



Eric Madaras 



I I Viable composite material 
py^/^\ Damaged composite material 

Figure 9. A schematic of the simple 
ultrasonic model employed in the fracture 
model . 

'^d - "X t^ref - V • f^c • ^d* / 



({f 



ref 



fn.) • i^n - V^)), 



(4) 



where x^ is the damage thickness, "X ^^ ^^^ number 
of wavelengths to the phase lock point, f^ef ^^ 
the reference frequency of the phase lock loop 
system set in the normal composite region, f^^ is 
the measured frequency, v^ is the velocity of 
normal composite, and v^^^ is the velocity of 
damaged composite as defined in equation 3. For 
the attenuation measurements the equation is: 



- a^) / (a 



eff 



- a,), 



(5) 



where x^ is again the damage thickness, Xg is the 
thickness of the sample, a^ is the measured 
attenuation, OL^ is the attenuation of normal 
composite, and Ot^^^ is the attenuation of damaged 
composite defined by equation 2. Most of these 
parameters are known or can be measured in the 
experiment. We can infer the correct damage cross 
section to use in the fracture model by knowing 
the appropriate attenuation and velocity of the 
"effective" damaged composite material . 

Measurements were made near one megahertz to 
accommodate the high attenuation characteristics 
of thick composites. The transmitter was a three 
inch focussed 1.25 inch diameter transducer and 
the receiver was 0.5 inches apodized to 0.2 inch 
diame--er to approximate a point receiver. The 
sample was placed so that the top surface with the 
impact site was at the focal zone of the 
transmitter. Two-dimensional scans were made in a 
water tank on each specimen over a 50 mm by 50 mm 
region centered over the impact site, using 1 mm 
steps. The amplitude and phase of the transmitted 
ultrasonic tone burst from the pulsed phase lock 
loop system provided attenuation and relative 
velocity measurements. The composite's velocity 
was measured by separate time of flight 
measurements through the samples in regions remote 
to the impact site. The attenuation was 
calibrated by measuring the signal transmitted 
through a water path only. 

The bulk ultrasonic attenuation and velocity of 



normal composite material were 5-9 dB/cm for the 
attenuation parameter and approximately 2600 m/s 
at 0,9 MHz for the velocity. "Effective" 
attenuation of damaged composite material was 
extrapolated from measurements of thin impacted 
plates . We are presently doing experiments to 
verify our extrapolation, and our preliminary 
results tend to support our assumptions . The 
attenuation in composites was approximated as a 
linear function with frequency and characterized 
by intercept and slope terms. The intercept 
indicated contributions to the attenuation from 
interface losses or reflections which were 
frequency independent and occurred at 
delaminations and interfaces [10]. The slope of 
attenuation at the impact site predicted the bulk 
attenuation of damaged composite material. In 
thin composite material the intercept term 
represents a significant part of the attenuation. 
In thick composite materials, the bulk attenuation 
dominates and the intercept terms will be less 
significant. We assumed the intercept term to be 
negligible . An attenuation value of 15 dB/cm was 
used for damaged composite: this was a typical 
value measured for the slope of the attenuation at 
impact damage sites in similar thin composite 
material used in our lab. A velocity value of 
2250 m/s for damaged composite material was 
required to match estimates of the depth of damage 
between attenuation and velocity measurements. 
Experiments are being performed to independently 
verify this value. This velocity value was used 
in equation 4 for all the impact samples. 

The thickness of the damage material was predicted 
from equations 4 and 5 using these values for the 
"effective" attenuation and velocity of damaged 
composite. Figure 10 shows a scan image of the 
relative velocity. Similar views were evident for 
attenuation. This material displayed a large 
variance for the values of phase velocity and 
attenuation measured in the good composite 
material regions, and a bump that denotes the 
damaged region. The following algorithm was used 
to ignore the variability of normal regions and to 
determine the depth of damage. In our 
two-dimensional scans, the direction of loading 
was denoted as the y-direction. For each of the 
fifty X positions, we selected the minimum 
measured value along the y-direction scan line. 




Figure 10 . Wire plot showing an x-y scan 
image of velocity where the vertical axis 
represents shifts in velocity. The up- 
wards direction indicates negative shifts 
in velocity. 



Eric Madaras 



# 

-» 



This produced a line of data across the sample in 
the x-direction representing minimum frequency 
values for the velocity scans and minimum 
airplitude values for the attenuation scans. This 
line displayed a bump in the central region where 
the damage existed. By fitting a straight line 
through the values that were remote to the damaged 
values, a dividing line between normal and damaged 
composite was generated. For the phase velocity 
measurements, this value was used as f ^^f in 
equation 4. In a similar manner, a line fitted to 
the minimum signal values of the normal regions 
was used for the a^ values in equation 5. The 
values used for f^^f and tt^ were determined for 
each individual coupon. This projected the depth 
of damage onto two dimensions . Figure 11 shows 
data calculated in the above manner from velocity 
measurements and the result of viewing the 
effective depth of damage profile in the direction 
of the applied stress . In this figure the 
vertical axis shows the depth of damage into the 
sample, and the horizontal axis is the distance 
across the coupon. An elliptical shape was fitted 
to the damage shape and was superimposed on the 
depth of damage for visual reference . These 
damage depth values are used with the fracture 
strength equation to calculate the remaining 
strength from ecjuation 1. 

VII. Results 

The remaining strength of a sample can be 
determined from equation 1 by knowledge of the 
depth of damage or, conversely, the equation can 
be solved for the equivalent depth of damage from 
the failure strength. The equivalent depth of 
damage is the depth of damage required in equation 
1 to produce the measured strength. Figure 12 
plots the X-ray measured depths of damage before 
loading versus the predicted equivalent depth of 
damage resulting from loading until fracture of 




10 20 30 40 50 

Position Across Sample (in mm) 



Figure 11 , This is a graph of a one 
dimensional scan line of the depth of 
damage derived from a velocity scan. The 
tensile load direction is perpendicular 
to the page. The negative vertical axis 
represent the depth of damage into the 
sample . 



C 



t 

P 

I 

X 



a No Visible Surface Mark 
■ Visible Surface Mark 




0.0 0.1 0.2 0.3 

Equivalent Cut Depth (in inches) 



Figure 12 . Depths of damage derived from 
X-rays compared with depths of damage 
derived from fracture mechanics. The 
solid line is the one to one correlation 
line 



the same samples. The one-to-one correlation line 
is drawn for reference only. The open symbols 
indicate impacts that left no visible surface mark 
on the samples, the impacts we are concerned with 
in this manuscript. Also shown as solid symbols 
are results from four samples where the impact 
left a dent or visible mark . The x-ray data 
indicate that the depth of damage is much smaller 
than the equivalent depth of damage predictions 
for impacts that left no surface marks. In many 
samples, the X-ray measured depth of damage was 
zero. Even in the samples with a surface 
indication, the dye uptake indicated that the 
X-ray measured depth of damage was too shallow 
compared to the equivalent depth of damage 
calculations. Thus the strengths predicted from 
X-ray data most often resulted in overestimating 
the strength of the samples. 

In figure 13, the ultrasonic attenuation and 
velocity data were used to predict the strength 
remaining in the samples using equation 1 and then 
comparing these results with the measured load 
levels at ultimate failure . Figure 13 shows the 
range of the data in units from 30 to 55 KSI, The 
one-to-one correlation line is drawn for reference 
(the solid line), as well as actual least squares 
linear fit to the data (the dashed line) . There 
were no noticeable patterns to either attenuation 
or velocity derived data to indicate either method 
as superior. In the data where the samples were 
measured to have greater than 0.16 inches of 
damage depth, the samples always broke in two 
steps. In the cases where the estimated depth of 
damage was less than . 16 inches, the samples 
often failed in a single step. 

It is important to note that the data now scatter 
about the one-to-one line and that, except for 
four points, all the data lie within a few percent 
of the one-to-one 'correlation line. This is a 
very encouraging result because in eighteen 



Eric Madaras 




— Slope = 1.00 
'-* Slope = 0.916 



35 40 45 50 

Measured Strength (in KSI) 



55 



Figure 13. Predicted strengths based on 
the ultrasonic measurements compared with 
the measured fracture strengths . The 
solid line is the one to one correlation 
line, and the dashed line is the linear 
fit to the data. 



undamaged samples, the measured strengths had 
variances of about 10% . Thus, the scatter in 
figure 13 is reasonable for the samples tested and 
may be due to variations in the materials. 

VIII. Discussion 

The goal of this set of experiments was to couple 
NDE measurements to fracture mechanics to predict 
the ultimate strength of composite sanples loaded 
in tension . Transmission measurements of 
ultrasonic velocity and attenuation as well as 
radiographic techniques were used. The samples 
studied were thick FWC composites with nonvisible 
impact damage on the san^le surface. 

Radiographic x-ray measurements proved to be of 
little use as an NDE tool because the dye was not 
taken up by the samples. It was postulated that 
the surface sustained little or no damage so that 
the radio-opaque dye could not penetrate the 
surface . The x-ray measurements were very 
informative in viewing the damage after the first 
ligament failure. They indicated that the samples 
did not just fracture as a simple crack as 
pictured in figure 4a, but rather with many 
surface fractures in the region of the impact site 
that were oriented along the fiber lay up 
directions. Furthermore, the shearing in the 
samples was complicated, indicating shearing 
across ply layers and in more than one shear 
plane, unlike the picture shown in figure 4a. 
This indicated some of the limits of the fracture 
theory that we applied to impacted thick 
composites, particularly in predicting the first 
fracture step. The x-ray photographs do point to 
the fact that the samples did fracture to depths 
which appeared to be related to the degree of 
impact damage. Therefore, the remaining strength 
could be calculated by knowing the impact's depth 
of damage. 



The ultrasonic measurements were made in 
transmission and were based on both attenuation 
and velocity measurements. Ultrasonic backscatter 
measurement techniques were tried but did not 
identify fiber fracture specifically, and did not 
generally provide reasonable resolution of the 
damaged regions from other regions of porosity or 
sample variability. By using a linear 
approximation to the relationship between 
different types of damage, a simple model was 
derived that could approximately relate the depth 
of fiber damage to the ultrasonic measurement. 
This model assumes that the regions of matrix only 
damage and regions of fiber and matrix damage 
scale together. Presently, there is no direct 
experimental support for the linear assumption. 
It is the simplest first approximation that can be 
employed. The fact that these approximations 
resulted in a model similar in configuration to 
the fracture model is attractive. Generally, 
fiber breakage will occur at higher damage levels 
than matrix fracture, and therefore, one might 
expect a cut-off to the relationships defined by 
equations 4 and 5. Similarly, either attenuation, 
velocity or both could exhibit a non-linear 
relationship between the different damage modes. 
The ultrasonic predictions indicated reasonably 
good correlations with the actual strengths, 
displaying about a 10% variance. This 10% 
variance of the strength was within the 
variability measured for undamaged samples, and is 
considered a reasonable strength predictor 
variance. 

VIII. Conclusion 

Decisions on product certification are frequently 
based on history of usage, such as hours of 
flight, or on the detection of damage by an NDE 
technique without knowledge of the actual 
remaining strength. This research afforded an 
interesting opportunity to combine ultrasonic 
techniques with fracture mechanics theory. We 
were able to calculate an **ef fective" depth of 
damage from ultrasonic transmission measurements. 
We could predict the strength of a sample under a 
tensile load within a 10% accuracy using fracture 
mechanics and this depth of damage prediction. 
Although the ultrasonic measurements were made in 
transmission, this technique should be general 
enough to be applicable to a single sided 
reflection based measurement with the possible 
inclusion of a diffraction correction. It is 
possible that this type of measurement could be 
coupled with the current FWC testing system, 
(called SUTRA), to better evaluate solid rocket 
motor segments. 

Much work remains to be done to better define the 
limits of the algorithms and to develop 
refinements to reduce the errors. The results of 
this work will hopefully lead to a reliable 
predictor of tensile strength, including the first 
ligament failure point as well as the remaining 
ligament failure. 

IX. Acknowledgements 

The authors are grateful to Jeff Knutson for his 



9 



Eric Madaras 



invaluable technical assistance in making the 
ultrasonic measurements. 

X. Bibliography 

1. C. C. Poe, Jr., W. Illg, and D. P. Garber, 
"Tension Strength of a Thick Graphite /Epoxy 
Laminate after Impact by a 1/2 In. Radius 
inpacter**, NASA Technical MemQcandum 67771, 1986. 

2. A. E. H. Love, "The Stress Produced in a 
Semi-infinite Solid by Pressure on Part of the 
Boundary", Phil. Trans, Royal Sqc. Lond. A, vol. 

228, 1929, pp. 377-420. 

3 . L. B. Greszczuk, "Damage in Composite 
Materials due to Low Velocity Impact", Impact 
Dynamics r John Wiley and Sons, Inc., 1982, pp. 
55-94. 

4. C. C. Poe, Jr., W. Illg, and D. P. Garber, "A 
Program to Determine the Effect of Low-Velocity 
Impacts on the Strength of the Filament-Wound 
Rocket Motor Case for the Space Shuttle", NASA 
Technical Memorandum 87589. Sept. 1985. 

5. J. C. Newman, Jr., and I. S. Raju, "Stress- 
Intensity Factor Equations for Cracks in 
Three-Dimensional Finite Bodies" . Fracture 
Mschanics: Fourteenth symposium — volume i : 

Theory and Analyais r ASTM STP 791, J. C. Lewis and 
G. Sines, Eds . , American Society for Testing 
Materials, 1983, pp. I-238-I-265. 

6. I. S. Raju, and J. C. Newman, Jr., 
"Stress-Intensity Factors for a Wide Range of 
Semi-Elliptical Surface Cracks in Finite-Thickness 
Plates", Engineering Fracture Mechanics , Vol. 11, 
No. 4, 1979, pp. 817-829. 

7. J. H. Cantrell, Jr., W. P. Winfree, J. S. 
Heyman, and J. D. Whit comb, "Multiparameter 
Characterization of Fatigue Damage in 
Graphite/ Epoxy Composites from Ultrasonic 
Transmission Power Spectra", 19BQ IEEE ultrasonics 

Sympoaium Proceedinga, 80CH1602, b. r. McAvoy, 
Ed., No. 2, pp 954-956. 

8 . H. I . Ringermacher, "Ultrasonic Velocity 
Characterization of Fatigue Damage in 
Graphite/Epoxy Composites", 19B0 ieee ultiraaQniea 

Sympoaium Proceedings. 80CH1602, B. R. McAvoy, 

Ed., No. 2, pp 957-960. 

9. J. S. Heyman, "Pulsed Phase Locked Loop Strain 
Monitor", NASA Patent Disclosure LAR 12772-1, 

(1980) 

10. T. A. Shoup, J. G. Miller, J. S. Heyman, and 
W. Illg, "Ultrasonic Characterization of Fatigue 
and Impact Damage in Graphite Epoxy Composite 

Laminates", XMZ I££E UltraaonJca SympQaium 

Proceedings^ 82CH1823-4, B. R. McAvoy, Ed., No. 
2, pp 960-964.