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i

NASA/TP—2013–217481

Normalization of Impact Energy by Laminate 

Thickness for Compression 

After Impact Testing

A.T. Nettles and S.M. Hromisin

Marshall Space Flight Center, Huntsville, Alabama

April 2013

National Aeronautics and

Space Administration

Marshall Space Flight Center • Huntsville, Alabama 35812
ii

Available from:

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076 –1320

443–757–5802

This report is also available in electronic form at

<https://www2.sti.nasa.gov/login/wt/>

Acknowledgments

This work was funded by the National Aeronautics and Space Administration under the auspices of the Upper Stage 

Program Office at Marshall Space Flight Center.
iii

TABLE OF CONTENTS

1. INTRODUCTION ............................................................................................................. 1

1.1 Experimental Observations of Laminate Thickness on Damage Tolerance ................... 2

2. EXPERIMENTATION ...................................................................................................... 11

2.1 Laminates ..................................................................................................................... 11

2.2 Impact Testing .............................................................................................................. 12

2.3 Results .......................................................................................................................... 12

3. DISCUSSION .................................................................................................................... 25

3.1 Damage Resistance ....................................................................................................... 25

3.2 Damage Tolerance ........................................................................................................ 29

4. CONCLUSIONS ................................................................................................................ 33

REFERENCES ....................................................................................................................... 35
iv
v

LIST OF FIGURES

 1. Plot of CAI strength versus unnormalized impact energy from table 1 ........................ 4

 2. Plot of CAI strength versus normalized thickness (m=–1) from table 1 ...................... 5

 3. Plots of data presented in table 1 along with a best fit power curve 

(solid line) of data from all four thicknesses pooled: (a) m=–1.5, (b) m=–2,

and (c) m=–2.5 ............................................................................................................ 7

 4. Plot of percent difference in CAI strengths across all three laminate thicknesses 

and all three impact severity levels as a function of m .................................................. 10

 5. Schematic of the type of test specimen used in this study to assess CAI strength. 

The face sheets were cured before bonding to honeycomb in a second process 

to manufacture the test specimens ............................................................................... 11

 6. Unnormalized data from table 8 .................................................................................. 13

 7. IM7/8551-7 CAI data from table 8 normalized by specimen thickness 

to powers of (a) –1, (b) –1.5, (c) –2, and (d) –2.5 .......................................................... 15

 8. Plot of percent difference in CAI strengths across both laminate thicknesses 

and all three damage severity levels for IM7/8551-7 laminates ..................................... 16

 9. Unnormalized data from table 12 ................................................................................ 16

10. IM7/MTM-45 CAI strength data from table 12 normalized by specimen 

thickness to powers of (a) –1, (b) –1.5, (c) –2, and (d) –2.5 .......................................... 20

11. Plot of percent difference in CAI strengths combined across all three 

laminate thicknesses ..................................................................................................... 23

12. Sample infrared thermography image of 8-ply IM7/MTM-45 specimen 

impacted at 2.7 J .......................................................................................................... 26

13. Plot of damage width versus impact energy for IM7/MTM-45 laminates .................... 27

14. Impact energy needed to cause a given damage width as a function of specimen 

thickness for four different damage sizes ...................................................................... 28

15. Plot of CAI strength versus damage width for IM7/MTM-45 laminates ..................... 30

16. CAI strength data for IM7/MTM-45 specimens normalized by specimen 

thickness to the –2.13 power ........................................................................................ 31
vi

LIST OF TABLES

1. CAI data from reference 15 .................................................................................... 3

2. Difference in CAI strength values at three damage severity levels in figure 1 .......... 4

3. Difference in CAI strength values at three impact severity levels in figure 2 ........... 5

4. Percent difference in CAI strength values for unnormalized and normalized 

 data ........................................................................................................................ 6

5a. Difference in CAI strength values in figure 3 with m=–1.5 .................................... 8

5b. Difference in CAI strength values in figure 3 with m=–2 ....................................... 8

5c. Difference in CAI strength values in figure 3 with m=–2.5 .................................... 8

6a. Percent difference in CAI strength values between 24- and 32-ply specimens 

 for various IE/tm values .......................................................................................... 9

6b. Percent difference in CAI strength values between 16- and 24-ply specimens 

 for various IE/tm values .......................................................................................... 9

6c. Percent difference in CAI strength values between 16- and 32-ply specimens 

 for various IE/tm values .......................................................................................... 9

7. Lay-up of laminates used in this study ................................................................... 11

8. Results from CAI testing of IM7/8551-7 laminates ................................................ 13

9. Difference in CAI strength values at three damage severity levels from figure 6 ..... 15

10a. Difference in CAI strength values in figure 7 with m=–1 ....................................... 17

10b. Difference in CAI strength values in figure 7 with m=–1.5 .................................... 17

10c. Difference in CAI strength values in figure 7 with m=–2 ....................................... 17

10d. Difference in CAI strength values in figure 7 with m=–2.5 .................................... 17

11. Percent difference in CAI strength values between 8- and 16-ply specimens 

 for various IE/tm values .......................................................................................... 18
vii

LIST OF TABLES (Continued)

12. Results from CAI testing of IM7/MTM-45 laminates .................................................... 18

13. Difference in CAI strength values of unnormalized data ....................................... 19

14a. Difference in CAI strength values in figure 10 with m=–1 ..................................... 21

14b. Difference in CAI strength values in figure 10 with m=–1.5 .................................. 21

14c. Difference in CAI strength values in figure 10 with m=–2 ..................................... 21

14d. Difference in CAI strength values in figure 10 with m=–2.5 .................................. 21

15a. Percent difference in CAI strength values between 8- and 16-ply specimens

 for various IE/tm values .......................................................................................... 22

15b. Percent difference in CAI strength values between 8- and 24-ply specimens

 for various IE/tm values .......................................................................................... 22

15c. Percent difference in CAI strength values between 16- and 24-ply specimens

 for various IE/tm values .......................................................................................... 22

16. Infared thermography results of impacted IM7/MTM-45 specimens ............................. 26

 17. Impact levels needed to produce a range of damage widths for the three 

 laminate thicknesses ........................................................................................................ 28
viii

LIST OF ACRONYMS

ASTM American Society for Testing and Materials

CAI compression after impact

IE impact energy

IRT infrared thermography

NDE nondestructive evaluation

OHC open hole compression

TP Technical Publication
ix

NOMENCLATURE

a thickness exponent for damage resistance

b thickness exponent for damage tolerance

C arbitrary constant

DW damage width/size

hc core thickness

IE0 given impact energy

i free index in indicial notation

Lm length of moment arm

m thickness exponent

P applied load

R correlation coefficient

t laminate thickness

tf thickness of the top fact sheet

w specimen width

y vertical axis value

sf compressive stress
x
1

TECHNICAL PUBLICATION

NORMALIZATION OF IMPACT ENERGY BY LAMINATE THICKNESS 

FOR COMPRESSION AFTER IMPACT TESTING

1. INTRODUCTION

Compression after impact (CAI) strength can be a critical design parameter in many structures and thus the test method used to ascertain this value is important. CAI testing is so widely 

used that a standard was developed by the American Society of Testing and Materials (ASTM)1

in 2005. In this standard the suggested impact energy is dependent on the specimen thickness by 

a specified ratio of impact energy (IE) to specimen thickness (t) which is given as 6.7 J/mm.2 Thus, 

the suggested impact energy level used for a laminate is linearly dependent on the laminate’s thickness (i.e., if the laminate thickness doubles, then the impact energy used also doubles). In damage 

tolerance studies, it has not been uncommon to divide the impact energy by the laminate thickness 

to ‘normalize’ data.3–17 While simplistic, this normalization of the impact energy data will certainly 

result in more comparable damage tolerance data across different laminate thicknesses. For example, 

16- and 32-ply quasi-isotropic laminates of the same fiber-resin system were impacted with 31.5 J 

of energy under the same boundary conditions.15 The residual compression strength of the 16-ply 

laminate was 165 MPa and the residual compressive strength of the 32-ply laminate was 275 MPa, 

a difference of 67% more strength for the thicker laminate. This is not unexpected since the thicker 

laminate should have more damage resistance for a given impact energy. However, when the thinner 

laminate was impacted with one-half the impact energy (15.7 J), both specimens had been impacted 

with 6.7 J/mm of impact energy and the residual strength of the thin laminate increased to 236 MPa. 

This resulted in a difference of 14% more strength (rather than 67%) for the thicker specimen which 

is more comparable.

A simple linear correlation of impact energy with specimen thickness may cause damage 

tolerance data to be qualitatively more comparable, but a physical basis for doing so is not readily apparent. In a test for damage resistance (perforation) of plastic film (ASTM D 1709-09)18 it is 

cautioned that, “The impact resistance of plastic film while partly dependent on thickness, has no 

simple correlation with sample thickness. Hence, impact values cannot be normalized over a range 

of thickness without producing misleading data as to the actual impact resistance of the material. 

Data from these test methods are comparable only for specimens that vary by no more than ±25% 

from the nominal or average thickness of the specimens tested.”

It is known that damage resistance (and thus damage tolerance) may not be similar for 

laminates of equal thickness made of the same material because the stacking sequence (lay-up) of 

the laminate can alter the damage resistance of a laminate despite the laminate having the same 
2

in-plane stiffnesses and equal number of plies oriented at 0°, ±45°, and 90°. For a quasi-isotropic 

laminate (25% 0°-plies, 50% ±45°-plies, and 25% 90°-plies), it has been demonstrated that the stacking sequence can influence a laminate’s damage resistance and damage tolerance. Avery and Grande19

presented data for 24-ply quasi-isotropic laminates with two different stacking sequences and found 

that less grouping of plies resulted in larger planar areas of damage, especially at high impact levels. When based on planar area of damage, the residual compression strength was similar for both 

laminates. Guynn and O’Brien4 came to similar conclusions based on 16-ply laminates. Hitchen 

and Kemp20 tested laminates of the same thickness containing 50% 0°-plies and 50% ±45°-plies (no 

90°-plies), with six different lay-ups for damage resistance and damage tolerance at an impact energy 

of 7 J. The planar damage size and shape was not always similar and the CAI strengths showed some 

variation, but this variation became less when the CAI strength was plotted versus damage size.

Thus, if a comparison of CAI strength between laminates of different thicknesses is to be 

made, similar material and stacking sequence is required. Once these parameters are satisfied, the 

question of how to normalize the CAI strength as a function of specimen thickness needs to be 

established since linear correlation may not give the most comparable results.

This correlation is important as it would be of great benefit to be able to quantitatively compare CAI data for a launch vehicle interstage structure (thick laminate) to a launch vehicle fairing 

structure (thin laminate), for example.

1.1 Experimental Observations of Laminate Thickness on Damage Tolerance

In a study by Caprino21 the effects of specimen thickness on impact resistance of laminated 

composites showed that the energy absorbed by specimens of different thicknesses at an impact 

level that produced initial damage (delamination) is proportional to the laminate thickness to the 

2.5 power. Physical reasons based on the Hertzian contact law and simple mechanics of materials 

are given that show this is not an unexpected result. In the same study it was shown that energy of 

penetration of a laminate was proportional to the thickness to the 1.5 power. 

The results from reference 21 along with the general observation of the authors was the inspiration of the current study; for given boundary conditions, thicker specimens appear to have higher 

CAI strengths, even when the impact energy is normalized (divided) by the specimen thickness. It 

was reasoned that if incident delamination damage energy is proportional to the 2.5 power of the 

thickness and the energy of penetration is proportional to the 1.5 power of the thickness, then rather 

than normalizing impact energy by the specimen thickness into the –1 power to obtain similar CAI 

strength data for specimens with the same boundary conditions, normalization of impact energy 

should be to the specimen thickness to an exponent between –2.5 and –1.5 with lower impact damage levels, perhaps having CAI strength data scaling closer to the –2.5 power of thickness and severe 

impact damage levels having CAI strength data scaling closer to the –1.5 power of thickness.

In reference 21, only the damage resistance in the form of delamination size and/or energy 

absorbed by the laminate has been considered. By attempting to relate residual compression strength 

to impact energy, the specimens’ thicknesses add yet more complexity to the problem.
3

Data from the open literature were examined for specimen thickness effects on CAI strength. 

Due to the many variables used throughout the different studies (different fiber/resin systems, layups, impact boundary conditions, and not enough data), only one set of existing data was deemed 

suitable for analysis. CAI strength data from Aoki et al.15 were reanalyzed by normalizing the 

impact energy by the thickness of the specimen to powers of –1, –1.5, –2, and –2.5. Data from 

reference  15 for quasi-isotropic laminates are presented in table 1. These specimens were of the 

stacking sequence (45, 0, –45, 90)ns, where n=2, 3, 4, and 8. The diameter of the impactor was 

15.9 mm and the specimens were clamped over a 6.35-cm circular opening during impact conforming 

to ASTM Standard D 7137-07.1 The residual strength testing also conformed to ASTM Standard 

D 7137-07.1

Table 1. CAI data from reference 15.

Specimen

Impact 

Energy

(J)

Specimen 

Thickness 

(mm)

IE/t

(J/mm)

IE/t 1.5

(J/mm1.5)

IE/t 2

(J/mm2)

IE/t 2.5

(J/mm2.5)

Failure Stress 

(MPa)

16-ply 7.5 2.3 3.3 2.2 1.4 0.9 245

16-ply 15.4 2.3 6.7 4.4 2.9 1.9 230

16-ply 19.5 2.3 8.5 5.6 3.7 2.4 230

16-ply 22.8 2.3 9.9 6.5 4.1 2.9 200

16-ply 31.5 2.3 13.7 9 6 3.9 165

24-ply 11 3.4 3.2 1.8 1 0.5 315

24-ply 15.4 3.4 4.5 2.5 1.3 0.7 305

24-ply 22.8 3.4 6.7 3.6 2 1.1 275

24-ply 31.5 3.4 9.3 5 2.7 1.5 235

24-ply 38 3.4 11.2 6.1 3.3 1.8 226

32-ply 15.4 4.7 3.3 1.5 0.7 0.3 340

32-ply 31.5 4.7 6.7 3.1 1.4 0.7 280

32-ply 34.5 4.7 7.3 3.4 1.6 0.7 305

32-ply 38 4.7 8.1 3.7 1.7 0.8 242

32-ply 45 4.7 9.6 4.4 2 0.9 240

64-ply 62.3 9.3 6.7 2.2 0.7 0.2 340

Figure 1 plots the CAI strength versus the unnormalized impact energy and, as expected, the 

thicker specimens have more strength for a given impact severity level. Each set of data for a given 

thickness has a best fit power curve applied to it so a comparison between laminates of different 

thicknesses at any given impact severity level can be made. In figure 1, low, medium, and high impact 

severity levels are noted. While rather arbitrary in nature, these levels may help give information 

about how impact severity affects the CAI strength results to be compared. The three levels were 

chosen such that little extrapolation of the best fit curves would be needed (i.e., the levels included 

most of the experimentally measured data). For a quantitative assessment, the differences in CAI 

strengths for the three thicknesses are compared at low, medium, and high impact severity levels. The 

64-ply specimen has only one data point and thus will not be included here.
4

CAI = 819(IE)–0.31

0 10 20 30

IE (J)

40 50 60 70

 F1

CAI = 649(IE)–0.29

CAI = 430(IE)–0.25

16-Ply

24-Ply

32-Ply

64-Ply

350

300

250

200

150

CAI Strength (MPa)

Low High

Medium

Figure 1. Plot of CAI strength versus unnormalized impact energy from table 1.

In figure 1 the low impact severity level will require extrapolation of the 32-ply data and 

the high impact severity level will require extrapolation of the 16-ply data. It should be noted that 

extrapolation of the curves in figure 1 need to be used with caution as the best fit equations are only 

valid for the strength degradation portion of the CAI strength versus damage severity curve. Using 

the three damage severity levels and the equations shown in figure 1 yields the results presented in 

table 2.

Table 2. Difference in CAI strength values at three damage severity levels in figure 1.

Impact 

Severity 

Level = IE

(J)

16-Ply CAI 

Strength 

(MPa)

24-Ply CAI 

Strength 

(MPa)

% Increase 

Over 

16-Ply

32-Ply CAI 

Strength 

(MPa)

% Increase 

Over 

16-Ply

% Increase 

Over 

24-Ply

11 236 323 37 389 65 20

25 192 255 33 302 57 18

38 173 226 31 265 53 17

As the impact severity level increases, the percent difference in CAI strength between the laminates of different thicknesses decreases slightly. Extrapolating this trend indicates that, at very severe 

impact damage levels, the CAI strengths of the different thickness specimens begin to converge. This 

makes physical sense as a very severe impact level will be akin to an open hole compression (OHC) 

test.
5

By normalizing the impact energy by the laminate thickness, the percent difference of the 

CAI strength values of the thicker laminates compared to the thinner laminates should be lessened. 

Figure 2 plots the CAI strength data versus impact energy normalized by specimen thickness to the 

–1 power from table 1 and each of the curves (one for each thickness) has a best fit power law applied 

(dashed lines).

CAI = 508(IE)–0.32

2 4 6 8

IE/t (J/mm)

10 12 14

F2

CAI = 352(IE)–0.25

Low

Medium

CAI = 454(IE)–0.28

High

350

300

250

200

150

CAI Strength (MPa)

16-Ply

24-Ply

32-Ply

64-Ply

Figure 2. Plot of CAI strength versus normalized thickness (m=–1) from table 1.

For ease of notation, the power to which the thickness of the laminate is raised to will be 

denoted by m. For example, IE/t2 implies that m=–2.

In figure 2 low, medium, and high impact severity levels are arbitrarily chosen as explained 

earlier and are noted (excluding the 64-ply laminate). Using these three impact severity levels with 

the equations in figure 2 yields the results presented in table 3.

Table 3. Difference in CAI strength values at three impact severity levels in figure 2.

Impact 

Severity 

Level = IE/t

(J/mm)

16-Ply CAI 

Strength 

(MPa)

24-Ply CAI 

Strength 

(MPa)

% Increase 

Over 

16-Ply

32-Ply CAI 

Strength 

(MPa)

% Increase 

Over 

16-Ply

% Increase 

Over 

24-Ply

3 267 334 25 357 34 7

7 216 263 22 273 26 4

11 193 232 20 236 22 2
6

Table 4 shows the percent difference in CAI strength for the unnormalized and normalized 

data from tables 2 and 3 for comparisons between the thicknesses tested at low, medium, and high 

impact damage severity levels.

Table 4. Percent difference in CAI strength values for unnormalized 

and normalized data.

Comparison of Percent Difference in CAI Strength for Different Thicknesses

(Unnormalized→Normalized)

Impact Severity Level 24- and 16-Ply 32- and 16-Ply 32- and 24-Ply

Low 37→25 65→34 20→7

Medium 33→22 57→26 18→4

High 31→20 53→22 17→2

With normalization the thicker laminates still have more CAI strength, but the magnitude of 

these differences is lessened, with the 32- and 24-ply laminate comparison being within 10% across 

all damage severity levels (less at the higher levels, as mentioned previously). 

When the impact energy is normalized by t m , m=–1, the thicker specimens still have a higher 

CAI strength for a given impact severity level. This indicates that if a similar CAI strength is to be 

obtained for a given impact severity level, the thicker specimens need to be impacted with more 

energy than what is calculated from a linear correlation (i.e., m<–1).

Figure 3 plots the CAI strength versus the impact energy to the m power for m=–1.5, –2,

and –2.5 as presented in table 1. In order to more quantitatively assess the effects of normalizing 

the impact energy by the various tm examined, each plot contains a power curve to all of the data 

pooled (solid line) with the corresponding correlation coefficient R. The closer R is to 1 the better the 

data fit the applied power curve and the more comparable the CAI strength data are for the different 

thicknesses across all impact severity levels. As with figures 1 and 2, low, medium, and high damage 

severity levels are arbitrarily chosen to include most of the experimentally measured data and are 

noted in each figure.
7

350

300

250

200

150

0 0.5 1 1.5

IE/t

2.5 (J/mm2.5)

CAI Strength (MPa)

2 2.5 3 3.5 4

Low

Medium R=0.93

CAI = 257(IE/t

2.5)–0.24

High

(c)

16-Ply

24-Ply

32-Ply

64-Ply

All

16-Ply

24-Ply

32-Ply

64-Ply

All

-

350

300

250

200

150

0 1 2 3

IE/t2 (J/mm2)

CAI Strength (MPa)

4 5 6

Low

Medium

R=0.94 CAI = 311(IE/t

2)–0.3

High

(a) (b)

0 2 4

High

6

IE/t1.5 (J/mm1.5)

8 10

Low

Medium

CAI = 401(IE/t)–0.35

R=0.88

16-Ply

24-Ply

32-Ply

64-Ply

All

350

300

250

200

150

CAI Strength (MPa)

Figure 3. Plots of data presented in table 1 along with a best fit power curve 

(solid line) of data from all four thicknesses pooled: (a) m=–1.5,

(b) m=–2, and (c) m=–2.5.
8

It appears that the data correlate well across all impact severity levels at m=–2. As m increases 

to –2.5, the data for the 32-ply specimens tend to be ‘overcorrected’ at high impact levels as the CAI 

strength results fall more below the other specimens.

A quantitative comparison of the various exponents that the specimen thickness is raised 

to can be conducted. A best fit power law for each of the three curves (representing the three thicknesses) at m=–1.5, –2, and –2.5 is applied (dashed lines in fig. 3), and then the low, medium, and high 

impact severity levels of each are used to find CAI strengths. The results are given in tables 5a–5c. 

Table 5a. Difference in CAI strength values in figure 3 with m=–1.5.

Impact Severity Level 

= IE/t 1.5

(J/mm1.5)

16-Ply CAI 

Strength 

(MPa)

24-Ply CAI 

Strength 

(MPa)

% Increase 

Over 16-Ply

32-Ply CAI 

Strength 

(MPa)

% Increase 

Over 

16-Ply

% Increase 

Over 

24-Ply

2 265 313 18 319 20 2

4 223 256 15 257 15 –

6 201 228 13 227 13 –

Table 5b. Difference in CAI strength values in figure 3 with m=–2.

Impact Severity Level 

= IE/t 2

(J/mm2)

16-Ply CAI 

Strength 

(MPa)

24-Ply CAI 

Strength 

(MPa)

% Increase 

Over 16-Ply

32-Ply CAI 

Strength 

(MPa)

% Increase 

Over 

16-Ply

% Increase 

Over 

24-Ply

1 285 321 13 310 9 –3

2.1 237 259 9 246 4 –5

 3.25 212 228 8 215 1 –6

Table 5c. Difference in CAI strength values in figure 3 with m=–2.5. .

Impact Severity Level 

= IE/t 2.5

(J/mm2.5)

16-Ply CAI 

Strength 

(MPa)

24-Ply CAI 

Strength 

(MPa)

% Increase 

Over 16-Ply

32-Ply CAI 

Strength 

(MPa)

% Increase 

Over 

16-Ply

% Increase 

Over 

24-Ply

0.5 306 330 8 301 –2 –9

 1.25 243 253 4 227 –7 –10

1.75 223 230 3 204 –9 –11

For each pair of laminate thicknesses (24–32, 16–24, and 16–32 plies), the percent difference 

in CAI strength with respect to the normalization of the impact energy to the five thickness exponents evaluated, m, are summarized in tables 6a–6c. 
9

Table 6a. Percent difference in CAI strength values between 

24- and 32-ply specimens for various IE/tm values. 

Comparison of Percent Difference in CAI Strength for 24- and 32-Ply Laminates

(33% Increase in Thickness)

Impact Severity Level Unnormalized m= –1 m= –1.5 m= –2 m= –2.5

Low 20 7 2 –3 –9

Medium 18 4 – –5 –10

High 17 2 – –6 –11

Table 6b. Percent difference in CAI strength values between 

16- and 24-ply specimens for various IE/tm values.

Comparison of Percent Difference in CAI Strength for 16- and 24-Ply Laminates

(50% Increase in Thickness)

Impact Severity Level Unnormalized m= –1 m= –1.5 m= –2 m= –2.5

Low 37 25 18 13 8

Medium 33 22 15 9 4

High 31 20 13 8 3

Table 6c. Percent difference in CAI strength values between 

16- and 32-ply specimens for various IE/tm values.

Comparison of Percent Difference in CAI Strength for 16- and 32-Ply Laminates

(100% Increase in Thickness)

Impact Severity Level Unnormalized m= –1 m= –1.5 m= –2 m= –2.5

Low 65 34 20 9 –2

Medium 57 26 15 4 –7

High 53 22 13 1 –9

A cursory examination of tables 6a–6c shows that the exponent, m, that gives the most comparable CAI strength data is dependent mainly upon the difference in thicknesses of the specimens 

to be compared. The impact severity level shows a smaller effect on the comparability of the CAI 

strength data, although it should be noted that for comparison of the two thickest laminates at the 

high impact severity level (table 6a, last row), the commonly used m=–1 appears to fit well.

According to tables 6a–6c for the CAI strength data given in table 1, the impact energy data 

should be normalized by the specimen thickness to the –1.5 power for comparing 24- and 32-ply 

CAI strength data, to the –2.5 power for comparing 16- and 24-ply CAI strength data, and to the 

–2 power for comparing 16- and 32-ply CAI strength data. It thus appears that normalizing the 

impact energy by the specimen thickness raised to a power to compare CAI strength results will not 

be a ‘one size fits all’ proposition for various increases in laminate thicknesses. Figure 4 is a plot of 

the average of all the percent differences for any given value of m as a function of m. Note the large 

standard deviation values since data across all impact severity levels and thicknesses are being considered (i.e., tables 6a–6c are combined).
10

40

30

20

10

0

–10

–3 –2.5 –2 –1.5

Value of m

Average Percent Difference in CAI Strength

–1 –0.5 0 0.5

F4

–2.2

Figure 4. Plot of percent difference in CAI strengths across all three laminate 

thicknesses and all three impact severity levels as a function of m.

From a least squares linear fit of the data in figure 4, the percent difference in CAI strengths is 

zero at m=–2.2. This value is close to that found by a visual assessment of the three plots in figure 3 

in which m=–2 appeared to give the most comparable CAI strength data across all impact severity 

levels.

This experimental data, while limited, demonstrates that in order to correlate CAI strength of 

laminates that are similar, differing only in thickness, that the impact energy used needs to be higher 

for thicker specimens by more than just a linear correlation.

A systematic study was performed to compliment the data shown thus far to support or refute 

the premise that normalizing impact energy by the specimen thickness to a power between –1.5 

and –2.5 gives more uniform results for the CAI strength data of specimens of similar lay-ups but 

different thicknesses under the same impact boundary conditions.

It should be noted that detailed information about failure mechanisms due to the impact 

event and during compression to failure testing are not presented in this study and only the impact 

energies and associated compression after impact strengths are presented since these are the values 

of interest for the premise of this Technical Publication (TP).
11

2. EXPERIMENTATION

2.1 Laminates

CAI testing was performed on two groups of specimens. The first group had laminates of 

8 and 16 plies composed of IM7/8551-7 carbon/epoxy. The second group had laminates of 8, 16, 

and 24 plies composed of IM7/MTM-45 carbon/epoxy. Table 7 gives the specific lay-up and nominal 

thicknesses of the laminates manufactured.

Table 7. Lay-up of laminates used in this study.

Material Lay-Up

Number

 of Plies

Nominal Laminate

Thickness 

(mm)

IM7/8551-7 (45,0,–45,90)S 8 1.07

IM7/8551-7 (45,0,–45,90)2S 16 2.14

IM7/MTM-45 (45,0,–45,90)S 8 1.09

IM7/MTM-45 (45,0,–45,90)2S 16 2.18

IM7/MTM-45 (45,0,–45,90)3S 24 3.28

Laminates were manufactured by curing 3,721-cm square sections of prepreg in a heated 

platen press according to the manufacturer’s recommended cure cycle. After cure, these panels had 

one side prepared for bonding to honeycomb core since the four-point-bend method was to be utilized to assess CAI strength.22 This was achieved by sanding the surface to be bonded with 120 grit 

abrasive paper followed by an alcohol wipe. This was repeated until water would remain on the entire 

surface without beading after being removed from immersion. The bottom (tensile) face sheet was 

identical to the top face sheet. The core density used for these specimens was 192 kg/m3 and the core 

thickness was 3.81 cm. The top and bottom face sheets were bonded to the honeycomb with FM-300 

film adhesive. Once these bonds had cured, the panels were cut into 5.1-cm-wide test specimens (fig. 5).

F5

5.1 cm

55.9 cm

5.1 cm

3.81 cm

Steel ‘Load Spreaders’ Upper Span

(4 Total)

Lower Span

Top Face Sheet

Figure 5. Schematic of the type of test specimen used in this study to assess 

CAI strength. The face sheets were cured before bonding to honeycomb in a second process to manufacture the test specimens.
12

2.2 Impact Testing

Each sandwich specimen was impacted at its geometric center on the top (compression) face 

sheet. The impactor had a diameter of 6.4 mm and the specimen was placed on a solid steel plate during impact to give the highest rigidity, and thus most damage possible for a given impact energy.23,24

This also ensured similar boundary conditions for all impacts.

An instrumented drop-weight impact apparatus was used to inflict damage to the specimens. 

The impact energy was measured by measuring the velocity of the impactor at the point of contact 

with the specimen since some of the initial potential energy of the drop weight was lost due to friction with the guide posts. 

As mentioned previously, the sandwich four-point-bend method22 was utilized to generate 

compressive forces in the damaged laminate. This methodology was chosen over end loading since 

an abundance of prepreg, film adhesive, and honeycomb core was available while strain gauges were 

not and the end loading method requires four strain gauges per specimen.1 The compressive stress in 

the face sheet between the upper span was calculated from:

σ f = P

w

L( m )

h c

2

+ t

f

tf hc + t ( f )

2 ⎡

⎣

⎢ ⎤

⎦

⎥

⎡

⎣

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

, (1)

where σf is the compressive stress, w is the specimen width, P is the applied load, Lm is the length of 

moment arm (25.4 cm), tf is the thickness of the top face sheet, and hc is the core thickness (3.81 cm). 

The cross head rate used was 2.5 mm/min which caused the typical test to last approximately 

1–2 min. All failures were similar in that fiber fracture occurred across the width of the specimen 

through the point of impact.

2.3 Results

2.3.1 IM7/8551-7 Material

The results from the residual compression strength testing for the IM7/8551-7 material are 

given in table 8 and are plotted in figure 6.
13

Table 8. Results from CAI testing of IM7/8551-7 laminates.

Number 

of Plies

Thickness 

(mm)

Impact Energy 

(J)

Number of

 Specimens

CAI

Strength (MPa)

8 1.14 0.9 5 377 ± 22

8 1.14 1.5 6 344 ± 16

8 1.14 2.6 5 311 ± 8 

8 1.14 3.8 5 294 ± 20

16 2.29 3.8 3 438 ± 24

16 2.29 6.2 7 372 ± 16

16 2.29 8 3 348 ± 15

450

400

350

300

250

0 2 4 6

IE (J)

CAI Strength (MPa)

8 10

Low

Medium

CAI = 369(IE)–0.17

High

CAI = 663(IE)–0.31

8-Ply

16-Ply

Figure 6. Unnormalized data from table 8.

Using the three damage severity levels shown in figure 6 with the equations in figure 6 yields 

the results presented in table 9. The undamaged compression strength of this laminate was measured 

as 684 MPa, thus the extrapolated 16-ply data should not be above this value. The OHC strength of 

this laminate was measured at 270 MPa, thus the extrapolated 8-ply data should not be below this 

value.
14

Table 9. Difference in CAI strength values at three 

damage severity levels from figure 6.

Impact Severity 

Level = IE

(J)

8-Ply CAI

 Strength 

(MPa)

16-Ply CAI 

Strength 

(MPa)

% Increase 

Over 8-Ply

2 328 535 63

4 292 431 48

6 272 380 40

Without normalization, the 16-ply laminate has between 40% and 63% more strength than 

the 8-ply laminate, depending on the impact severity level. As the impact severity level increases, the 

percent difference in CAI strength values between the two different thicknesses used is lessened.

If the impact energy is normalized by the specimen thickness raised to a power between –1 

and –2.5, the data will result as shown in figure 7. In figure 7, all of the data are pooled and a best fit 

power curve is applied for impact energy normalized by the specimen thickness to powers of –1, –1.5, 

–2, and –2.5. 
15

0 0.5 1 1.5 2

IE/t2.5 (J/mm2.5)

2.5 3

Low

Medium

CAI = 356(IE/t R=0.97 2.5)–0.21

High

 

8-Ply

16-Ply

All

450

400

350

300

250

CAI Strength (MPa)

(d)

0.5 1 1.5 2

IE/t2 (J/mm2)

2.5 3

Low

Medium

CAI = 374(IE/t R=0.89 2)

–0.23

High

8-Ply

16-Ply

All

450

400

350

300

250

CAI Strength (MPa)

(c)

IE/t

1.5 (J/mm1.5)

Low Medium

CAI = 386(IE/t R=0.69 1.5)

–0.19

High

8-Ply

16-Ply

All

450

400

350

300

250

1 1.5 2

CAI Strength (MPa)

2.5 3 3.5

(b)

0.5

450

400

350

300

250

0.5 1 1.5 2

IE/t (J/mm)

CAI Strength (MPa)

2.5 3 3.5 4

F7

CAI = 380(IE/t) R=0.43 –0.11

8-Ply

16-Ply

Low All

Medium

High

(a)

Figure 7. IM7/8551-7 CAI data from table 8 normalized by specimen thickness to powers 

of (a) –1, (b) –1.5, (c) –2, and (d) –2.5.

The thickness exponent m appears to fit the data for both thicknesses across all impact severity levels best at a value of m=–2.5. A best fit power law for each of the two curves at each of the 

four values of m is applied; then, arbitrarily selected low, medium, and high impact severity levels (as 

noted in figs. 8 and 9) are used to find CAI strengths. The results are given in tables 10a–10d.
16

60

50

40

30

20

–10

0

10

–3 –2.5 –2 –1.5

Value of m

Average Percent Difference in CAI Strength

–1 –0.5 0 0.5

F8

–2.3

-

Figure 8. Plot of percent difference in CAI strengths across 

both laminate thicknesses and all three damage 

severity levels for IM7/8551-7 laminates.

8-Ply

16-Ply

24-Ply

CAI Strength (MPa)

500

450

400

350

300

250

0 1 2 3 4

IE (J)

5 6 7 8

 F9

Low

Medium

CAI = 349(IE)–0.15

High

CAI = 505(IE)–0.28

CAI = 690(IE)–0.33

Figure 9. Unnormalized data from table 12.
17

Table 10a. Difference in CAI strength values in figure 7 with m=–1.

Impact 

Severity Level 

= IE/t

(J/mm)

8-Ply CAI 

Strength 

(MPa)

16-Ply CAI 

Strength 

(MPa)

% Increase 

Over 8-Ply

1 361 512 42

2.25 315 398 26

3.5 292 347 19

Table 10b. Difference in CAI strength values in figure 7 with m=–1.5.

Impact 

Severity Level 

= IE/t

1.5

(J/mm1.5)

8-Ply CAI 

Strength 

(MPa)

16-Ply CAI 

Strength 

(MPa)

% Increase 

Over 8-Ply

1 357 449 26

1.8 323 374 16

2.75 301 328 9

Table 10c. Difference in CAI strength values in figure 7 with m=–2.

Impact 

Severity Level 

= IE/t 2

(J/mm2)

8-Ply CAI 

Strength 

(MPa)

16-Ply CAI 

Strength 

(MPa)

% Increase 

Over 8-Ply

0.7 375 441 18

1.5 329 348 6

 2.25 308 307 –

Table 10d. Difference in CAI strength values in figure 7 with m=–2.5.

Impact 

Severity Level 

= IE/t 2.5

(J/mm2.5)

8-Ply CAI 

Strength 

(MPa)

16-Ply CAI 

Strength 

(MPa)

% Increase 

Over 8-Ply

0.5 393 431 10

1.1 343 338 –1

 1.75 317 293 –8

For the two laminate thicknesses, the percent difference in CAI strength with respect to the 

thickness exponent, m, are summarized in table 11. 
18

Table 11. Percent difference in CAI strength values between 8- and 

16-ply specimens for various IE/tm values.

Comparison of Percent Difference in CAI Strength for 8- and 16-Ply Laminates

(100% Increase in Thickness)

Impact Severity Level Unnormalized m= –1 m= –1.5 m= –2 m= –2.5

Low 63 42 26 18 10

Medium 48 26 16 6 –1

High 40 19 9 – –8

A cursory examination of table 11 shows that the exponent that gives the most comparable 

CAI strength data across all impact severity levels is m=–2.5 and that the impact severity level 

shows a larger effect on the comparability of the CAI strength data than for the data examined in 

tables 6a–6c. This may be due to the thinner specimens for these data, having one-half the thickness 

of the thinnest specimens from the previous data set.

Figure 8 is a plot of the average of all the percent differences in CAI strength across all three 

impact severity levels for any given value of m as a function of m. From a least squares linear fit of 

the data in figure 8, the percent difference in CAI strengths is zero at m=–2.3. This value is close to 

that found by a visual assessment of the plots in figure 7 where m=–2.5 appeared to give the most 

comparable CAI strength data across all impact severity levels. 

2.3.2 IM7/MTM-45 Material

The results from the residual compression strength testing for the IM7/MTM-45 material are 

given in table 12 and the results plotted in figure 9.

Table 12. Results from CAI testing of IM7/MTM-45 laminates.

Number 

of Plies

Thickness 

(mm)

Impact 

Energy 

(J)

Number

of 

Specimens

CAI 

Strength 

(MPa)

8 1.11 1.5 1 350

8 1.11 2.7 3 306 ± 29

8 1.11 3.8 4 290 ± 19

16 2.18 2.9 4 425 ± 17

16 2.18 5.3 3 344 ± 19

16 2.18 7.7 3 319 ± 18

24 3.28 4.5 4 477 ± 43

24 3.28 8 3 390 ± 7.3

24 3.28 11.2 3 354 ± 16
19

In figure 9 each severity level chosen will require extrapolation of some of the data. The 

undamaged compression strength of this laminate was measured as 690 MPa and the OHC strength 

measured as 270 MPa. These are the approximate upper and lower compression strength limits to 

curve extrapolation. Using the three damage severity levels shown in figure 9 with the equations in 

figure 9 yields the results presented in table 13.

Table 13. Difference in CAI strength values of unnormalized data.

Impact Severity 

Level = IE

(J)

8-Ply CAI 

Strength 

(MPa)

16-Ply CAI 

Strength 

(MPa)

% Increase 

Over 8-Ply

24-Ply CAI 

Strength 

(MPa)

% Increase 

Over 8-Ply

% Increase 

Over 16-Ply

2 315 414 31 549 74 33

3.5 289 354 22 456 58 29

5.5 270 312 16 393 46 26

As the impact severity level increases, the percent difference in CAI strength between the 

laminates of different thicknesses decreases. 

By normalizing the impact energy by the specimen thickness to a power between –1 and –2.5, 

the data fall as shown in figure 10. In figure 10, all of the data are pooled and a best fit power curve is 

applied for impact energy normalized by the specimen thickness to powers of –1, –1.5, –2, and –2.5.
20

Figure 10. IM7/MTM-45 CAI strength data from table 12 normalized by specimen thickness 

to powers of (a) –1, (b) –1.5, (c) –2, and (d) –2.5.

The thickness exponent m appears to fit the data for all three thicknesses across all impact 

severity levels best at a value of m=–2. Using m=–2.5 results in overcorrection of the CAI strength 

data for high impact severity levels.

0 0.5 1 1.5 2 2.5

IE/t2.5 (J/mm2.5)

3

Low

Medium

CAI = 343(IE/t R=0.95 2.5)–0.18

High

8-Ply

16-Ply

24-Ply

All

CAI Strength (MPa)

500

450

400

350

300

250

0 0.5 1 1.5 2 2.5

IE/t2 (J/mm2)

3 3.5

Low

Medium

CAI = 368(IE/t R=0.98 2)–0.25

High

8-Ply

16-Ply

24-Ply

All

CAI Strength (MPa)

500

450

400

350

300

250

(c) (d)

(a) (b)

0.5 1 1.5 2 2.5

IE/t (J/mm1.5)

3 3.5

Low

CAI = 414(IE/t R=0.96 1.5)–0.32

 

CAI Strength (MPa)

500

450

400

350

300

250

8-Ply

16-Ply

24-Ply

All

Medium

High

F10

1 1.5 2 2.5

IE/t (J/mm)

3 3.5 4

Low

Medium

CAI = 445(IE/t) R=0.71 –0.27

High

CAI Strength (MPa)

500

450

400

350

300

250

8-Ply

16-Ply

24-Ply

All
21

A best fit power law for each of the three curves at each of the four values of m is applied; then 

low, medium, and high impact severity levels are used to find CAI strengths. The results are given in 

tables 14a–14d.

Table 14a. Difference in CAI strength values in figure 10 with m=–1. .

Impact 

Severity Level 

= IE/t

(J/mm)

8-Ply CAI 

Strength 

(MPa)

16-Ply CAI 

Strength 

(MPa)

% Increase 

Over 8-Ply

24-Ply CAI 

Strength 

(MPa)

% Increase 

Over 

8-Ply

% Increase 

Over 

16-Ply

1.4 332 410 23 473 42 15

2.4 306 353 15 396 29 12

3.5 289 318 10 349 21 10

Table 14b. Difference in CAI strength values in figure 10 with m=–1.5.

Impact 

Severity Level 

= IE/t 1.5

(J/mm1.5)

8-Ply CAI 

Strength 

(MPa)

16-Ply CAI 

Strength 

(MPa)

% Increase 

Over 8-Ply

24-Ply CAI 

Strength 

(MPa)

% Increase 

Over 

8-Ply

% Increase 

Over 

16-Ply

0.75 361 438 21 477 32 9

1.5 326 361 11 380 17 5

2.4 303 316 4 325 7 3

Table 14c. Difference in CAI strength values in figure 10 with m=–2. 

Impact 

Severity Level 

= IE/t 2

(J/mm2)

8-Ply CAI 

Strength 

(MPa)

16-Ply CAI 

Strength 

(MPa)

% Increase 

Over 8-Ply

24-Ply CAI 

Strength 

(MPa)

% Increase 

Over 

8-Ply

% Increase 

Over 

16-Ply

0.4 395 467 18 483 22 3

1.1 339 351 4 346 2 –1

1.75 316 309 –2 297 –6 –4

Table 14d. Difference in CAI strength values in figure 10 with m=–2.5.

Impact 

Severity Level 

= IE/t 2.5

(J/mm2.5)

8-Ply CAI 

Strength 

(MPa)

16-Ply CAI 

Strength 

(MPa)

% Increase 

Over 8-Ply

24-Ply CAI 

Strength 

(MPa)

% Increase 

Over 

8-Ply

% Increase 

Over 

16-Ply

0.25 420 478 14 463 10 –3

0.75 356 351 –1 322 –10 –8

1.25 330 304 –8 272 –18 –11
22

For each pair of laminate thicknesses, the percent difference with respect to the thickness 

exponent, m, are summarized in tables 15a–15c.

Table 15a. Percent difference in CAI strength values between 8- and 

16-ply specimens for various IE/tm values.

Comparison of Percent Difference in CAI Strength for 8- and 16-Ply Laminates

(100% Increase in Thickness)

Impact Severity Level Unnormalized m= –1 m= –1.5 m= –2 m= –2.5

Low 31 23 21 18 14

Medium 22 15 11 4 –1

High 16 10 4 –2 –8

Table 15b. Percent difference in CAI strength values between 8- and 

24-ply specimens for various IE/tm values.

Comparison of Percent Difference in CAI Strength for 8- and 24-Ply Laminates

(200% Increase in Thickness)

Impact Severity Level Unnormalized m= –1 m= –1.5 m= –2 m= –2.5

Low 74 42 32 22 10

Medium 58 29 17 2 –10

High 46 21 7 –6 –18

Table 15c. Percent difference in CAI strength values between 16- and 

24-ply specimens for various IE/tm values.

Comparison of Percent Difference in CAI Strength for 16- and 24-Ply Laminates

(50% Increase in Thickness)

Impact Severity Level Unnormalized m= –1 m= –1.5 m= –2 m= –2.5

Low 33 15 9 3 –3

Medium 29 12 5 –1 –8

High 26 10 3 –4 –11

A cursory examination of tables 15a–15c shows that the exponent that gives the most comparable CAI strength data is dependent mainly upon the difference in thicknesses of the specimens 

to be compared. The impact severity level shows a smaller effect on the comparability of the CAI 

strength data.

For the data given, the impact energy data should be normalized by the specimen thickness to 

the –2.5 power for comparing 8- and 16-ply CAI data, to the –2 power for comparing 16- and 24-ply 

data, and to the –2 power for comparing 16- and 24-ply data. Figure 11 is a plot of the average of 

all the percent differences across all thicknesses and impact severity levels for any given value of m
23

as a function of m. From the least squares linear fit of the data in figure 11, the percent difference in 

CAI strengths is zero at m=–2.2, which is close to the value of m=–2 as determined by the visual 

examination of figure 10.

40

30

20

–10

0

10

–3 –2.5 –2 –1.5

Value of m

Average Percent Difference in CAI Strength

–1 –0.5 0 0.5

F11

–2.2

Figure 11. Plot of percent difference in CAI strengths 

combined across all three laminate thicknesses.

Thus, from three sets of data (one from the literature and two produced in this study), normalizing the impact energy by the specimen thickness raised to a power will result in more comparable CAI strength results for different laminate thicknesses tested. It is apparent that, depending on 

the severity of impact and the difference in thickness, the exponent of thickness that gives the best 

fit of the CAI strength data will differ. However, for the range of impact energies examined thus far, 

acursory examination of the data shows that despite this difference, CAI strength can be better compared by normalizing the impact energy to a specimen thickness raised to a power between –2.2 and 

–2.3.
24
25

3. DISCUSSION

The CAI strength of a damaged laminate will depend upon the laminate’s damage resistance 

and its damage tolerance. One example of the effect of specimen thickness on damage resistance will 

be that the planar damage size as measured by a nondestructive evaluation (NDE) technique may be 

different for different thicknesses at a given impact energy and with the same boundary conditions. 

Assuming a nonlinear relationship and a smaller damage size for thicker specimens,

DW ∝ IE0/t a , (2)

where DW is damage size, IE0 is a given impact energy, t is the laminate thickness, and a is the 

thickness exponent for damage resistance. (If the damage size increases with increasing specimen 

thickness, then the exponent, a, will be negative).

As the thickness of a specimen goes up, the CAI strength (damage tolerance) is assumed to 

go up for a given damage size. Assuming a nonlinear relationship and more strength for a thicker 

specimen,

CAI ∝ DW(t b) , (3)

where CAI is compression after impact strength, DW is a given planar damage size, t is the laminate 

thickness, and b is the thickness exponent for damage tolerance.

Combining equations (2) and (3), 

CAI ∝ IE0(t)–a(t b) ∝ IE0t (b–a) . (4)

Examination of the data may help determine the exponents a and b for the laminates used in this 

study and thus the relative contribution of damage resistance and/or damage tolerance to cause 

thicker laminates to have a higher CAI strength for a given impact energy.

3.1 Damage Resistance

As mentioned previously, the CAI strength of a laminate consists of both the damage resistance and damage tolerance of the material. An examination of the damage resistance aspects of the 

IM7/MTM-45 laminates of three thicknesses will be presented in an effort to better understand the 

dependence of the CAI strength on the specimen thickness.

3.1.1 Size of Impact Damage

The width of the damage formed in the composite laminates due to impact was assessed 

with infrared thermography (IRT) techniques. The damage width as detected by IRT was used as 
26

ameasure of damage size (DW) since this has been shown to be a good predictor of CAI strength.24

A sample IRT image is shown in figure 12.

F12

Loading (0°) Direction

Damage

Width

Figure 12. Sample infrared thermography image of 8-ply IM7/

MTM-45 specimen impacted at 2.7 J.

The damage widths of impact observed for the IM7/MTM-45 specimens used in this study 

are presented in table 16 in the appendix. Each specimen thickness had four impacts at a given 

energy level and the width results were averaged. The impact energy versus damage width data from 

table 16 are plotted in figure 13 and a logarithmic curve fit of the form y=C0+C1log(x) applied. 

When plotting impact damage size versus impact energy, there typically is a critical impact energy at 

which damage begins, and as the impact energy increases, the damage size begins to level out as more 

severe damage is formed.25 A plot of damage size versus impact energy can be represented well by

a logarithmic curve fit.26

Table 16. Infared thermography results of impacted 

IM7/MTM-45 specimens.

Number 

of Plies

Thickness 

(mm)

Impact 

Energy 

(J)

Average 

Damage 

Width 

(mm)

8 1.11 1.5 11.8 ± 2.1

8 1.11 2.7 14.9 ± 1.8

8 1.11 3.8 16 ± 2.1

16 2.18 2.9 9 ± 0.7

16 2.18 5.3 13.3 ± 0.4

16 2.18 7.7 14.7 ± 1.1

24 3.28 4.5 8.9 ± 1.7

24 3.28 8 11.8 ± 0.6

24 3.28 11.2 13.5 ± 1
27

8-Ply

16-Ply

24-Ply

18

16

14

12

10

8

0 2 4 6 8

IE (J)

Damge Width (mm)

10 12

Zone of Similar

Damage Widths

Figure 13. Plot of damage width versus impact energy 

for IM7/MTM-45 laminates.

The equations defining the curves in figure 13 are given by:

 8-ply: DW1 = 10.2 + 10.6 log(IE1) , (5)

16-ply: DW2 = 2.1 + 14.9 log(IE2) , (6)

and

24-ply: DW3 = 1.3 + 11.9 log(IE3) , (7)

where DWi indicates damage width and IEi is the impact energy. The subscripts 1, 2, and 3 correspond to the 8-, 16-, and 24-ply laminates, respectively. 

3.1.2 Impact Energy to Produce a Given Damage Width

Now that a relation of damage width versus impact energy has been estimated from the best 

fit logarithmic curves in figure 13 and equations (5)–(7), the three energies needed to produce a given 

damage width for each of the three thicknesses of laminates can be deduced. To use a damage width 

outside the zone of damage widths common to all three thicknesses means reliance that extrapolation of the data beyond what was experimentally measured is required.
28

Table 17 shows a range of damage widths and the impact energy needed to produce the given 

damage width using equations (5)–(7). 

Table 17. Impact levels needed to produce a range 

of damage widths for the three laminate 

thicknesses.

DW

(mm)

IE1

(J)

IE2

(J)

IE3

(J)

11 1.2 3.9 6.5

12 1.5 4.6 7.9

13 1.9 5.3 9.5

14 2.3 6.2 11.6

The data in table 17 are plotted in figure 14 as IE versus number of plies/8 plies. This gives the 

thinnest laminate a thickness value of unity and a specimen twice as thick a thickness value of 2 and 

a specimen three times as thick a thickness value of 3. A best fit power curve is applied to each of the 

damage widths plotted.

12

10

8

6

4

2

0

1 2

Thickness (Plies/8)

14 mm

13 mm

12 mm

11 mm

Damage Width

Damge Width (mm)

3

Figure 14. Impact energy needed to cause a given damage 

width as a function of specimen thickness for 

four different damage sizes.
29

The best fit power curves for the four damage widths are given by,

11 mm: IE=1.2(t) 1.56 , (8)

12 mm: IE=1.5(t) 1.53 , (9)

13 mm: IE=1.9(t) 1.49 , (10)

and

14 mm: IE=2.3(t) 1.46 . (11)

The coefficients in each of the above equations are the impact energy needed to cause the 

associated damage width for the thinnest specimens (i.e., 1.2 J to cause a damage width of 11 mm in 

an 8-ply specimen, 1.5 J to cause a damage size of 12 mm in an 8-ply specimen, etc.). Notating these 

coefficients as IEDW (impact energy to cause a certain damage width), equations (8)–(11) can be written in the form IE=IEDW t a; or rearranging,

IEDW =IE/t a . (12)

The average of the exponents (denoted by a) for the four curve fits in figure 14 is a=1.51, 

which is close to the value of 1.5 as found in reference 21 for energy of penetration of an impacted 

laminate versus thickness. Thus, to obtain a given damage width, the impact energy must be divided 

by the specimen thickness to the 1.51 power and the exponent, a, in equation (2) is thus 1.51.

The next part of relating residual strength to specimen thickness is to determine the residual 

strength as a function of damage size for different specimen thicknesses.

3.2 Damage Tolerance

In order to gain insight into the relation of damage tolerance of the laminates examined in this 

study, the data from tables 12 and 16 can be used to plot CAI strength as a function of damage width for 

the IM7/MTM-45 specimens used in this study. The results for the three thicknesses are shown in figure15.
30

8-Ply

16-Ply

24-Ply

500

450

400

350

300

250

8 10 12 14 16

Damage Width (mm)

CAI Strength (MPa)

18 20

Figure 15. Plot of CAI strength versus damage width 

for IM7/MTM-45 laminates.

The equations defining the curves in figure 15 are given by:

8-ply: CAI1 = 1,569(DW1) –0.607 , (13)

16-ply: CAI2 = 1,499(DW2) –0.573 , (14)

and

24-ply: CAI3 = 2,280(DW3) –0.716 , (15)

where CAIi indicates residual compression strength and DWi is the damage width. The subscripts 1, 

2, and 3 correspond to the 8-, 16-, and 24-ply laminates, respectively. 

The average of the exponents in equations (13)–(15) is –0.63, thus CAI ∝ DW(t) –0.63 and 

b=–0.63 in equation (3).

Thus, equation (4) gives CAI ∝ IE0t 

(–0.63–1.5) ∝ IE0/t 2.13.

The data for the MTM-45 laminates are plotted in figure 16 for m=–2.13.
31

500

450

400

350

300

250

0 0.5 1 1.5 2 2.5

IE (J/mm2.13)

CAI Strength (MPa)

F16

R=0.97 CAI = 328(IE/t

2.13)–0.23

8-Ply

16-Ply

24-Ply

All

Figure 16. CAI strength data for IM7/MTM-45 specimens 

normalized by specimen thickness to the –2.13 power.

The data in figure 16 actually fit no better than the data for m=–2 (fig. 10). However, the relative contribution of the thickness on the CAI strength of a laminate is seen to be mostly comprised 

of the effects of damage resistance and less so on damage tolerance.
32
33

4. CONCLUSIONS

The conclusions are as follows:

• A definitive exponent that the specimen thickness must be raised to in order to normalize impact 

energy to give comparable CAI strength results across all impact damage severities probably cannot be achieved. An approximate exponent is the most that can be achieved in an attempt to compare CAI strength data across a range of impact damage severity levels.

• Care must be taken when comparing CAI strength data since the lay-up and material can have 

a large influence on results of laminates of the same thickness.

• As the impact severity level increases, the difference between the unnormalized CAI strengths 

becomes less, which makes physical sense as the specimens are essentially nearing the OHC strength 

of the laminate.

• For the data examined in this TP, an exponent of m=–2.2 appears to give the best overall comparison of CAI strength values across the range of thicknesses and impact severity levels used.

• Material type appears to play an important role as CAI strength data for IM7/8551-7 was much 

more dependent upon damage severity level than the CAI strength data of IM7/MTM-45.

• If only ‘severe’ impact severity levels are considered, then an exponent of m=–1.5 appears to give 

the best overall comparison of CAI strength data.

• Since ASTM D 7137 called for relatively thick specimens being impacted at a ‘severe’ level compared to the laminates and impact levels considered in this TP, no change is needed although normalization with m=–1 appears to favor the thicker laminate.

• For relatively thick laminates, normalizing impact energy by the specimen thickness gives fairly 

comparable CAI strength results, especially at high impact severity levels.

• For high impact severity levels, a lower value of m gives more comparable CAI strength data, and 

for low impact severity levels, a higher value of m gives more comparable CAI strength data.

• Most of the difference in CAI strength values for laminates of different thicknesses is due to 

a change in damage resistance.

• Once a given planar damage area forms, the CAI strength varies inversely by ≈0.63, although this 

value is quite dependent on specimen thickness.
34
35

REFERENCES

 1. ASTM Standard D 7137-07, Standard Test Method for Compressive Residual Strength Properties of Damaged Polymer Matrix Composite Plates, West Conshohocken, PA, 2009.

 2. ASTM Standard D 7136-05, Standard Test Method for Measuring the Damage Resistance 

of a  Fiber-Reinforced Polymer Matrix Composite to a Drop-Weight Impact Event, West 

Conshohocken, PA, 2009.

 3. Husman, G.E.; Whitney, J.M.; and Halpin, J.C.: “Residual Strength Characterization of Laminated Composites Subjected to Impact Loading,” in Foreign Object Impact Damage to Composites, ASTM STP, Vol. 568, pp. 92–113, 1975.

 4. Guynn, E.G.; and O’Brien, T.K.: “The Influence of Lay-Up and Thickness on Compositer 

Impact Damage and Compression Strength,” in Proceedings, AIAA/ASME/ASCE/AHS 26th 

Structures, Structural Dynamics and Materials Conference, Orlando, FL, Vol. 26, pp. 187–196, 

April 15–17, 1985.

 5. Avva, V.S.; Vala, J.R.; and Jeyaseelan, M.: “Effect of Impact and Fatigue Loads on the Strength 

of Graphite/Epoxy Composites,” in Composite Materials Testing and Design (7th conference), 

ASTM STP, Vol. 893, pp. 196–206, 1986.

 6. Cano, R.J.; and Dow, M.B.: “Properties of Five Toughened Matrix Composite Materials,” 

NASA TP–3254, NASA Langley Research Center, Hampton, VA, 58 pp., October 1992.

 7. Strait, L.H.; Karasek, M.L.; and Amateau, M.F.: “Effects of Stacking Sequence on the Impact 

Resistance of Carbon Fiber Reinforced Thermoplastic Toughened Epoxy Laminates,” Journal 

of Composite Materials, Vol. 26, No. 12, pp. 1725–1740, 1992.

 8. Bannister, M.; Callus, P.; and Herszberg, I.: “Compression After Impact Behavior of Multilayer 

Woven Glass/Vinyl Ester Composites,” in Proceedings 21st International Council of the Aeronautical Sciences, Vol. 5.9.1, pp. 1–7, Melbourne, Australia, September 13–18, 1998.

 9. Ishikawa, T.; Sugimoto, S.; Matsushima, M.; and Hayashi, Y.: “Some Experimental Findings 

in Compression-After-Impact (CAI) Tests of CF/PEEK (APC-2) and Conventional CF/Epoxy 

Flat Plates,” Composites Science and Technology, Vol. 55, pp. 349–363, 1995.

10. Tai, N.H.; Yip, M.C.; and Lin, J.L.: “Effects of Low-Energy Impact on the Fatigue Behavior of 

Carbon/Epoxy Composites,” Composites Science and Technology, Vol. 58, pp. 1–8, 1997.
36

11. Duarte, A.; Herszberg, I.; and Paton, R.: “Impact Resistance and Tolerance of Interleaved Tape 

Laminates,” Composite Structures, Vol. 47, pp. 753–758, 1999.

12. Khondker, O.A.; Leong, K.H.; Herszberg, I.; and Hamada, H.: “Impact and CompressionAfter-Impact Performance of Weft Knitted Glass Textile Composites,” Composites: Part A,

Vol. 36, pp. 638–648, 2005.

13. Mourtis, A.P.: “Comment on the Impact Damage Tolerance of Stitched Composites,” Journal of 

Material Science Letters, Vol. 22, pp. 519–521, 2003.

14. Byun, J.-H.; Song, S.-W.; Lee, C.-H.; et al.: “Impact Properties of Laminated Composites with 

Stitching Fibers,” Composite Structures, Vol. 76, pp. 21–27, 2006.

15. Aoki, Y.; Kondo, H.; and Hatta, H.: “Effect of Specimen Thickness on Impact-Induced Delamination and CAI Behavior,” CD–ROM, Paper No. TM1–03, 39th International SAMPE Technical Conference, Cincinnati, OH, October 29–November 1, 2007.

16. Uda, N.; and Ono, K.: “Compression Fatigue Failure of CFRP Laminates with Impact Damage,” 

CD–ROM, Paper No. TuHAZ–01, 16th International Conference on Composite Materials, 

Kyoto, Japan, July 8–13, 2007.

17. Hoshi, H.; Nakano, K.; and Iwahori, Y.: “Study on Repair of CFRP Laminates for Aircraft 

Structures,” CD–ROM, Paper No. ThuIA2–01, 16th International Conference on Composite 

Materials, Kyoto, Japan, July 8–13, 2007.

18. ASTM Standard D 1709-09, Standard Test Methods for Impact Resistance of Plastic Film by 

the Free Falling Dart Method, West Conshohocken, PA, 2009.

19. Avery, W.B.; and Grande, D.H.: “Influence of Materials and Layup Parameters on Impact 

Damage Mechanisms,” 22nd International SAMPE Technical Conference, Vol. 22, pp. 470–483, 

Boston, MA, November 6–8, 1990.

20. Hitchen, S.A.; and Kemp, R.M.J.: “Effect of Stacking Sequence on Impact Damage in a Carbon 

Fiber/Epoxy Composite,” Composites, Vol. 26, No. 3, pp. 207–214, 1995.

21. Caprino, G.; Lopresto, V.; Scarponi, C.; and Briotti, G.: “Influence of Material Thickness on 

the Response of Carbon-Fabric/Epoxy Panels to Low Velocity Impact,” Composites Science and 

Technology, Vol. 59, pp. 2279–2286, 1999.

22. Nettles, A.T.; Jackson, J.R.; and Gates, T.S.: “Compression After Impact Testing of Sandwich 

Structures Using a Four Point Bend Test,” CD–ROM, Paper No. SSIB–03, SAMPE Fall Technical Conference and Exhibition, Memphis, TN, September 8–11, 2008.
37

23. Tomblin, J.S.; Ng, Y.C.; and Raju, K.S.: “Material Qualification and Equivalency for Polymer 

Matrix Composite Material Systems,” Final Contract Report DOT/FAA/AR-00/47, Wichita 

State University, Witchita, KS, 2001.

24. Nettles, A.T.; and Jackson, J.R.: “Developing a Material Strength Design Value Based on Compression After Impact (CAI) Damage for the ARES I Composite Interstage,” NASA/TP—2009–

215634, Marshall Space Flight Center, AL, 52 pp., January 2009.

25. Lee, S.M.; and Zahuta, P.: “Instrumented Impact and Static Indentation of Composites,” Journal of Composite Materials, Vol. 25, pp. 204–222, 1991.

26. Nettles, A.T.; Jackson, J.R.; and Hodge, A.J.: “Change in Damage Tolerance Characteristics of 

Sandwich Structure with a Thermal Protection System (TPS),” Journal of Composite Materials, 

Vol. 46, pp. 211–226, 2012.
38

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Normalization of Impact Energy by Laminate Thickness 

for Compression After Impact Testing

A.T. Nettles and S.M. Hromisin

George C. Marshall Space Flight Center

Huntsville, AL 35812

National Aeronautics and Space Administration

Washington, DC 20546–0001

Unclassified-Unlimited

Subject Category 24

Availability: NASA CASI (443–757–5802)

Prepared by the Materials & Processes Laboratory, Engineering Directorate

M–1357

Technical Publication

NASA/TP—2013–217481

impact, composite laminates, compression strength, thickness, damage tolerance

01–04–2013

UU 52

NASA

U U U

The amount of impact energy used to damage a composite laminate is a critical parameter when assessing residual strength 

properties. The compression after impact (CAI) strength of impacted laminates is dependent upon how thick the laminate is and 

this has traditionally been accounted for by normalizing (dividing) the impact energy by the laminate’s thickness. However, when 

comparing CAI strength values for a given lay-up sequence and fiber/resin system, dividing the impact energy by the specimen 

thickness has been noted by the author to give higher CAI strength values for thicker laminates. A study was thus undertaken 

to assess the comparability of CAI strength data by normalizing the impact energy by the specimen thickness raised to a power 

to account for the higher strength of thicker laminates. One set of data from the literature and two generated in this study were 

analyzed by dividing the impact energy by the specimen thickness to the 1, 1.5, 2, and 2.5 powers. Results show that as laminate 

thickness and damage severity decreased, the value which the laminate thickness needs to be raised to in order to yield more 

comparable CAI data increases.

STI Help Desk at email: help@sti.nasa.gov

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