NASA Technical Memorandum 10 16 19 

AVSCOM Technical Memoranchin1 89-B-006 

. 

Scaling Effects in the Static Large 

Defelction Response of Graphite- 1 

Epoxy Composite Beams 

r 

Karen E. Jackson 

Edwin L. Fasanella 

- .. 

(IASA-TH-101619) SC1LIB6 EFFECTS XI TBE 189-26843 STATIC LARGE DBFLECTIOY RESPOlSB OF 

GRAPHXTE-BPOXY COWOSITE BEARS {Army 

Aerustructores Directorate) 15 p CSCL OlC &las 63/05 0923903 

,June 1989 

m 

National Aeronauttcs and 

Space Administration 

Langley Research Center 

Hampton, Virginia 23665-5225 

US ARMY 

AVIATION 

SYSTEMS COMMAND 

AVIATION RIT ACTIVITY 
SCALING EFFECTS IN THE STATIC LARGE DEFLECTION RESPONSE 

OF GRAPHITE-EPOXY COMPOSITE BEAMS 

Karen E. Jackson 

Research Scientist 

U.S. Army Aerostructures Directorate 

NASA Langley Research Center 

Hampton, Virginia 

Edwin L. Fasanella 

Supervisor, Structures Support Unit 

Planning Research Corporation 

NASA Langley Research Center 

Hampton, Virginia 

ABSTRACT 

Scaling effects in the large 

deflection response of graphite-epoxy 

composite beams was investigated. 

Eight different scale model beams 

ranging from 1/6 to full scale were 

subjected to an eccentric axial compressive load to promote large bending 

deformations and failures. Beams 

having laminate stacking sequences 

including unidirectional, angle ply, 

cross ply, and quasi-isotropic were 

tested to examine a wide variety of 

composite response and failure modes. 

The model beams were loaded under 

scaled test conditions until 

catastrophic failure. Data acquired 

included load, end displacement, and 

strain measurements, and qualitative 

failure measurements. The experimental data is compared to a large 

rotation beam analysis and a finite 

element model analysis. Results from 

the tests indicate that the beam 

response scales in the small deflection region, but deviates as the 

response becomes nonlinear. Failure 

modes are consistent between scale 

models within a laminate family, 

however, a significant scale effect is 

observed in strength of the scaled 

beams. Small scale beams fail at 

higher normalized load and significantly higher normalized end 

displacement levels than their full 

scale prototypes. It is important 

that this phenomenon be understood 

before strength testing of scale model 

composite structures can be utilized. 

INTRODUCTION 

Scale model technology represents 

one method of investigating the structural crashworthiness of advanced, 

weight efficient composite aircraft 

components such as beams, frames, and 

rings. Impact tests on replica models 

of composite structures can provide a 

cost effective alternative to fullscale crash tests. In addition, scale 

model tests can be conducted to verify 

analysis techniques, particularly 

finite element analyses. It is important, however, to understand the 

limitations of scale modeling so that 

1 
tests on sub-scale models will generate valid data. Scaling effects in 

the response and failure of composite 

structures must be characterized 

before the technique can be used to 

full advantage. A series of tests 

were conducted by Morton [l] to examine scaling effects in the dynamic 

response of transversely impacted 

composite beams. Results from those 

tests indicated that classical scaling 

laws apply for elastic dynamic 

response, but a size effect was observed as the beams became damaged 

under greater impact loads. 

The objective of the current 

research is to investigate scaling 

effects in the static large deflection 

response of composite beams. The 

scaled beams are loaded in a beamcolumn fashion by an eccentric axial 

compressive load. This testing configuration produces large bending 

deformations and promotes global 

failure of the beams away from the 

supported ends. A dimensional 

analysis was performed on the beamcolumn system using methods outlined 

in Baker [2] to determine the nondimensional parameters or Pi terms 

which govern the scaled response. An 

experimental program designed to 

validate the scaling laws was performed and initial results are 

reported in this paper. Also, a one 

dimensional large rotation analysis 

and a Dynamic Crash Analysis of 

STructures (DYCAST) [3] finite element 

model of the composite beam were 

developed for comparison with experimental results. The results 

obtained from the static experiments 

aloiy, wi th R veri fj cd DYCAST 111ode1 

will 1,tT uscd to dovcllop ii test matrix 

for conducting impact tests and 

dynamic analyses in the future. 

EXPERIMENTAL PROGRAM 

Beams having unidirectional, angle 

ply, cross ply, and quasi-isotropic 

laminate stacking sequences were 

constructed of a high modulus graphite 

fiber and an epoxy matrix system 

* 

designated as AS4/3502 for the static 

tests. The full scale beam was 3 

inches wide with a 30 inch gage length 

and 48 plies thick with an average ply 

thickness of 0.0054 inches. The scale 

model beams were constructed by applying seven different geometric scale 

factors including 1/6, 1/4, 1/3, 1/2, 

2/3, 3/4, and 5/6, to the full scale 

beam dimensions. A set of scaled 

beams is illustrated in Figure 1 and 

the dimensions and lay-ups of each 

beam are listed in Table 1. The 

thickness dimension was scaled by 

reducing the number of layers in each 

angular ply group of the full scale 

laminate stacking sequence which 

consisted of at least six plies of 

similar orientation. Using this 

approach, it was not possible to 

fabricate a 1/4 or 3/4 scale quasiisotropic beam. Three replicate 

tests were conducted for each laminate 

type and size of beam. The beams were 

machined from panels which were constructed by hand from pre-preg tape 

and cured according to manufacturer's 

specifications. Slight variations 

were observed in the thickness dimensions of the cured beam specimens. 

Generally, the 1/6 scale beam was 

thicker on a per ply basis than the 

full scale beam for all laminate 

types. The maximum deviation in 

normalized thickness was approximately 

six per cent. 

During the tests each beam 

specimen was gripped in a set of 

hinges which offset the axial load 

with a moderate eccentricity, as shown 

in Figure 2. Eight sets of hinges 

were constructed to ensure that the 

e 

. 

* 

Identification of commercial products 

and companies in this paper is used to 

describe adequately the test 

materials. The identification of 

these commercial products does not . constitute endorsement, expressed or 

implied, of such products by the U.S. 

Army, the National Aeronautics and 

Space Administration, or the publishers of these conference 

proceedings. 

, 

2 
t 

end condition was properly scaled for 

each test. The hinges were pinned to 

the platens of a standard load test 

machine which applied the compressive 

vertical load. The hinged-pinned 

connection allowed the beam to undergo 

large rotations during deformation. 

Beam specimens were loaded until 

catastrophic failure, defined as loss 

of load carrying capability. 

Each beam was instrumented with 

back-to-back strain gages located at 

distances one-quarter and two-thirds 

along the length and with strain gage 

rosettes at the midpoint. Vertical 

load was measured by a load cell 

located at the base of the bottom 

hinge. End displacement was measured 

by an extensiometer attached to the 

platens of the load test machine. 

Vertical load, end displacement, and 

strain data were recorded using a 

personal computer based data acquisition system. The analog signals were 

amplified and filtered prior to being 

digitized and converted to engineering 

units. Only the load versus end 

displacement data will be presented in 

this paper. 

ANALYSIS 

A one dimensional large rotation 

"elastica" type solution was developed 

to predict the response of the composite beam-column under eccentric 

axial load. The governing equation 

for the beam was derived from equilibrium of the forces and moments on a 

beam element. The exact expression 

relating moment and curvature was 

incorporated in the analysis, thus 

allowing the solution to predict large 

rotation response. The solution of 

the governing equation is outlined in 

Timoshenko and Gere [4] for the 

"elastica" problem and was adapted for 

this problem by applying the end 

moment boundary conditions produced by 

the eccentric vertical load. The 

solution is given in terms of elliptic 

integrals and predicts the end displacement, transverse displacement of 

the midpoint of the beam, and end 

rotation for increasing load. 

The beam bending stiffness was 

derived from the method described by 

Whitney [5] in which the bending 

stiffness, EI, from classical beam 

theory is replaced by an equivalent 

stiffness for the composite beam. The 

beam is considered as a special case 

of a laminated plate in which the 

length is much larger than the width. 

Consequently, the transverse displacement is assumed to be a function of 

the axial coordinate only. Also, only 

the moment along the axial direction 

is assumed to be present. This is 

analogous to a plane stress assumption 

in elasticity. The transverse and 

twist curvatures are expressed in 

terms of the axial curvature and the 

bending stiffnesses, and are then 

substituted into the equation relating 

bending moment and axial curvature. 

The equivalent beam bending stiffness 

is the coefficient of the axial curvaincorporates the shear and twist 

coupling terms which are important for 

angle ply and quasi-isotropic 

laminates. 

In addition to the beam analysis, 

the nonlinear finite element structural analysis computer program DYCAST 

[3] was used to model the composite 

beam-column. Since the DYCAST program 

will be used to model the beam-column 

under impact conditions in the future, 

the static case was developed to 

verify the model and to compare with 

the large rotation beam solution. The 

composite laminate was discretized 

into 60 beam elements which were 

constrained to permit only planar 

deformations, as shown in Figure 2. 

The hinges at the top and bottom of 

the beam were modeled by two rigid 

beam elements each. The model assumed 

pinned conditions between the load 

machine and the hinge, and clamped 

conditions between the hinge and beam. 

The bending stiffness used in the 

DYCAST model was the same as used in 

the beam analysis outlined previously. 

The complete model had 192 degrees of 

freedom. The applied load was increased incrementally at one end using 

ture from this equation. It 

3 
a static full Newton iterative technique in which the stiffness matrix 

was updated in each iteration. The 

full Newton procedure was required 

since the modified Newton method which 

updated the stiffness matrix for each 

load step failed to converge in the 

nonlinear region of the response 

curve. 

RESULTS 

Normalized load versus end displacement plots and corresponding 

photographs of a complete (1/6 through 

full scale) set of failed beam 

specimens for the unidirectional, 

angle ply, cross ply, and quasiisotropic laminates are shown in 

Figures 3-6. Vertical load was normalized by the Euler column buckling 

load for the beam, and end displacement was normalized by the gage 

length. Since three repeat tests were 

performed for each laminate type and 

size of beam, the results from one 

representative test are presented 

here. Repeatability between the three 

tests was good. 

Normalized Load Versus End 

Dimlacement Results 

In general, the load versus 

displacement curves show that the 

response scales for small end displacement ratios, typically less than 

0.1. Deviation from scaled response 

is observed for all laminate types as 

the beams undergo large deflections 

and the response becomes nonlinear. 

The angle ply beams show the most 

pronounced deviation from scaled 

response, as seen in Figure 4(a). The 

small scale beams fail at a higher 

normalized load and end displacement 

lt~vcl than the full scale beam. This 

observed scale effect in failure 

behavior is significant. The 1/6 

scale twains fail at an end displacement to length ratio from 2 to 10 

times the value for the full scale 

beam depending on the laminate type. 

Failure Mechanisms 

The photographs shown in Figures 

3(b) through 6(b) indicate that while 

the failure modes for the laminate 

types considered in this study are 

different from each other, they are 

similar between scaled beams within 

the laminate family. Failure modes 

appear to be independent of specimen 

size. The unidirectional beams, shown 

in Figure 3(b), failed by fiber fractures near the midpoint of the beam. 

This failure mode is typical of all 

the unidirectional beams 1/6 through 

full scale. Failure of the angle ply 

beams occurred by transverse matrix 

cracking along 45 degree fiber lines. 

There was no evidence of fiber 

breakage, as shown in Figure 4(b). 

The cross ply laminates exhibited 

combined failure mechanisms of 

transverse matrix cracking and fiber 

fracture. As the cross ply beam 

underwent large rotations, the 90 

degree plies located in the center of 

the laminate developed transverse 

matrix cracks. The cracks were evenly 

spaced and resulted in uniform pieces 

of debris, some of which are shown in 

Figure 5(b) for the 5/6 scale beam. 

The ultimate failure of the cross ply 

beam was caused by fiber fractures in 

the 0 degree plies. The quasiisotropic beams failed through a 

combination of matrix cracking, 

delamination, and some fiber failure. 

Although the photograph in Figure 6(b) 

does not give a good indication, the 

damaged quasi-isotropic beams are 

highly curved. The sequence of 

failure events occurred such that the 

remaining intact section of the beam 

consisted of an unsymmetric laminate, 

resulting in the observed curvature. 

Analytical Results 

Comparison of the experimental 

data for the 1/6 and full scale 

specimens with the large rotation beam 

analysis and the DYCAST finite element 

analysis is plotted in Figures 7(a) 

through 7(d) for each of the laminate 

types. Agreement between the two 

4 
. 

. 

analysis methods is excellent, even 

though they approach the problem in 

different manners. The beam solution 

assumes an inextensible beam, while 

the DYCAST model allows in-plane 

deformations due to membrane loads. 

Also, the large rotation beam analysis 

incorporates the exact nonlinear 

expression for beam curvature, while 

the DYCAST model uses the linear 

expression. However, these factors do 

not appear to be important in the 

response prediction. DYCAST appears 

to be sufficiently accurate for future 

dynamic analyses of the scaled beam 

since a closed form "elastica" type 

analysis is not available. 

Good correlation is obtained 

between the experiment and the beam 

solution and DYCAST for small load 

ratios, generally less than 0.4. 

However, both the large rotation beam 

solution and the DYCAST model typically overpredict the experimental 

beam response as the load ratio and 

normalized end displacement values 

increase and beam rotations become 

large. This is true for all of the 

laminates tested. The slope of the 

response curve in the large deflection 

region (normalized end displacement 

greater than 0.2) as predicted by both 

analyses is in good agreement with 

experiment, as shown in Figures 7(a), 

7(c), and 7(d). Overprediction of the 

response by the large rotation beam 

analysis and DYCAST may be due in part 

to certain assumptions made in the 

analysis including constant stiffness 

assumptions. The stiffness of the 

beam is reduced due to nonlinear 

material properties and damage events 

:;IICII {I:; I t-:iit:;vvr:;~- III:II I I x c.r;ic.k In[; 

which are not modeled by the analysis. 

DISCUSSION 

The results presented here indicate that a significant scale effect 

exists in the failure behavior since 

the smaller scale beams fail at a 

higher normalized load and much higher 

normalized end displacement value than 

the full scale beam. Stress and 

strain based failure criterion such as 

maximum stress, maximum strain, TsaiHill, or Tsai-Wu, would not be able to 

predict the observed scale effect. 

According to classical scaling laws, 

stress and strain should scale as 

unity. Consequently, under perfectly 

scaled experimental test conditions 

the stress and strain in a model beam 

will be the same as for the prototype. 

A stress analysis of the scaled test 

will predict one value of end displacement to length ratio at which 

failure should occur. Morton [l] 

discusses a linear elastic fracture 

mechanics approach to the strength 

scaling of transversely impacted 

composite beams and shows that a 

theory for a notch-sensitive or 

brittle material can predict scaling 

effects in a cracked plate. 

Application of these theories to a 

stress analysis of the beam-column 

problem is planned as a continuation 

of the experimental and analytical 

results presented here. 

CONCLUDING REMARKS 

Scaling effects in the large 

deflection response and failure behavior of graphite-epoxy composite 

beams was investigated. A series of 

static tests on scale model composite 

beams having unidirectional, angle 

ply, cross ply, and quasi-isotropic 

laminate stacking sequences was 

conducted. The beams were loaded 

under an eccentric axial compressive 

load to promote large bending deformations and global failure. Plots of 

iioriiiii I I zc.cl 1 oiitl v(xrsiis t*iitl ti i si) 1 iicc~- 

ment were generated to compare with a 

one dimensional large rotation composite beam analysis and a DYCAST 

finite element model. 

Results from the experiments show 

that beam response scales in the small 

deflection, elastic region; however, 

deviations from scaled response appear 

as the beams undergo large deflections 

and rotations. The degree of variation from scaled response is dependent 

on laminate stacking sequence. Angle 

5 
ply laminates exhibited the greatest 

deviation from scaled response. A 

significant scale effect in strength 

behavior was observed even though 

failure modes were consistent between 

scale model beams and the prototype 

within the same laminate family. The 

one dimensional large rotation beam 

analysis and DYCAST finite element 

model gave good agreement with the 

experimental data for low load ratios, 

typically less than 0.4. The DYCAST 

analysis and the large rotation beam 

analysis overpredicted the beam 

response in the large deflection 

region compared with the experiment, 

but predicted the shape of the 

response curve well. 

The results of this study indicate that an important scale effect 

exists in the modeling of failure 

behavior of composite structures. 

Further work is required to identify 

the micromechanical mechanisms involved in this effect and to 

understand how they interact on a 

macroscopic level to produce the 

observed scale effect in ultimate 

failure of the structure. 

REFERENCES 

1. Morton, John., "Scaling of Impact 

Loaded Carbon Fiber Composites, It 

Proceedings of the 28th SDM 

Conference, Part l., Monterey, CA., 

April 1987, pp. 819-826. 

2. Baker, W.E., Westine, P.S., and 

Dodge, F.T., Similaritv Methods in 

Engineering - Dvnamics, Hayden Book Co., 

Rochelle Park, N.J., 1973. 

3. Pifko, A. B., Winter, R., and 

Ogilvie, P., "DYCAST - A Finite 

Element Program for the Crash Analysis 

of Structures," NASA Contractor Report 

4040, January 1987. 

4. Timoshenko, S., and Gere, J., 

Theory of Elastic Stabilitv, 2nd 

edition, McGraw-Hill, New York, 1961, 

pp. 76-82. 

5. Whitney, J., Structural Analysis 

of Laminated Anisotrooic Plates, 

Technomic Publishing Co., Lancaster, 

1987, pp. 68-74. 

Table 1. Scdle model beam test specimen (iimensions and lay-ups. 

SCALE BEAM DIMENSION UNIDIRECTIONAL ANGLE PLY CROSS PLY QUASI-ISOTROPIC 

1/6 0.5" X 5.0" 

I//I 0.15" X 1.5" 

1/3 1.0" X 10.0" 

1/2 1.5" X 15.0" 

2/3 2.0" X 20.0" [0132T [458/-4581s 

3/4 2.25" X 22.5" [0136T [45c)/-4591 s 

5/6 2.5" X 25.0" Io140T 14510/-45101 s 

6/6 3.0" X 30.0" [0148T [4512/-45121s 

.- 

6 
Figure 1. Fhotograph of scaled camposite beam spec-. 

ORIGINAL PAGE 

BLACK AND WHITE PHOTOGRAPH 

rlcl 

length 

Figure 2. Schematic drawing of the test configuration. 

7 
ORIGlNAL PAGE 

BLACK AND WHITE PHOTOGRAPH 

0.7 I 

0.6 

0.b 

0.4 

0.s 

I 

I I I I I I I I I 

0 02 0.4 0.6 04 1 

p(D~ENl/LENcTw 

(a) Normalized load versus end displacement. 

(b) Failed beam spec-. 

Figure 3. Unidirectional graphite-epow composite beam results8 
I. 

i. 

ORiG!pJrSL PAGE 

BLACK AND IUMTE PHOT3G9APH 

0.6 

0.5 

0.4 

0.3 

0.1 

0 

0 0.2 0.4 0.6 

D(DOKPWEUOM/LP(GRI 

0.8 

(a) Normalized load versus end displa-nmt. 

(b) Failed beam specimenS. 

Figure 4. Angle ply graphite-epxy composite beam results. 

9 
C"'" h I \? ! ?.! :";L i ',2G E 

BLACK AND Wtll-iE PHOTOGRAPH 

0.7 

05 7 

0.4 

0.s 

02 

0.1 

0 

4 

w3 - 

- 3/4 

0 0.2 

- 

v3 - 

Q.4 0.6 0.8 

(a) Normalized load versus end displacement. 

1 

(b) Failed beam specime.ns. 

Figure 5. Cross ply graphite-epoxy camposite beam res'u.lts. 

10 
0.7 

1 

OS 

0.4 

0.3 

0.2 

0.1 

va - - 2/3 

I I I I I I I I 

0 0.2 0.4 0.6 0.0 

ocoolwwEmm/LP(CIH 

(a) Normalized load versus end displacement. 

(b) Failed beam specimens. 

Figure 6. Quasi-isotropic graphite-epoq canrposite beam de. 

11 
0.7 

0.6 

0.5 

g 0.4 

A 

3 

W ' 0.3 

? 

0.2 MCASPANALYSIS 

A mmrunxncxmms~s 

0.1 -- 

0 

0 0.2 0.4 0.6 0.0 1 

END DI-OJT / mCM 

(a) Unidirectional beam results. 

' 

0.6 

An 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

(b) Angle ply beam results. 

AUL 

. 

b 

Figure 7. 

experimental data for 1/6 and full scale beams with DYCAST finite ekme.nt 

analysis and larye rotation exact solution. 

Comparison of normalized load versus end displacement 

12 
l 

0 0.2 0.4 0.6 0.8 1 

WDISPUCEUPST/LMGTH 

(c) Cross ply beam results. 

0.6 4 

NLLsCAr.E- f 

Os' a 

0 t 

0 0.2 0.4 0.6 

END OlSPUCEYENl/ LE" 

(d) Quasi-isotropic beam results. 

0.0 

FiWe 7. 

VriInental data for 1/6 and full scale beams with DYCAST finite e1-t 

analysis and large rotation exact solution. 

Comparison of normalized load versus end displacement 

13 
Report Documentation Page 

I. Report No. 2. Government Accession No. 

NASA TM-101619 

AVSCOM TM-89-B-006 

4. Title and Subtitle 

Scaling Effects in the Static Large 

Deflection Response of Graphite-Epoxy 

Composite Beams 

19. Security Classif. 20. Security Classif. (of this page) 21. No. of pages (of this report) 

Unclassified Unclassified 14 

7. Authoris) 

Karen E. Jackson 

Edwin L. Fasanella 

22. Price 

A0 3 

9. Performing Organization Name and Address 

NASA Langley Research Center 

Ae ros t r uc t ures Direct or ate 

Hampton, VA 23665-5225 

2. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Washington, DC 20546-0001 and 

U.S. Army Aviation Systems Command 

St. Louis, MO 63120-1798 

USAARTA- AVS COM 

5. Supplementary Notes 

3. Recipient's Catalog No. 

~~~ 

5. Report Date 

June 1989 

6 Performing Organization Code 

8. Performing Organization Report No. 

10. Work Unit No. 

505-63-01-11 

11. Contract or Grant No. 

13. Type of Report and Period Covered 

Technical Memorandum 

14. Sponsoring Egency Code 

Karen E. Jackson: U. S. Army Aerostructures Directorate 

Edwin L. Fasanella: Planning Research Corporation, Hampton, VA 

This paper was presented at the AHS National Technical Specialists' 

Meeting on Advanced Rotorcraft Structures, October 25-27, 1988, 

Williamsburq, VA. 

Scaling effects in the large deflection response of graphiteepoxy composite beams was investigated. Eight different scale model 

beams ranging from 1/6 to full-scale were subjected to an eccentric 

axial compressive load to promote large bending deformations and 

failures. Beams having laminate stacking sequences including unidirectional, angle ply, cross ply, and quasi-isotropic were tested 

to examine a wide variety of composite response and failure modes. 

The model beams were loaded under scaled test conditions until catastrophic failure. Data acquired included load, end displacementr 

and strain measurements, and qualitative failure measurements. The 

experimental data is compared to a large rotation beam analysis and 

a finite element model analysis. Results from the tests indicate 

that the beam response becomes nonlinear. Failure modes are consistent between scale models within a laminate family, however, a 

significant scale effect is observed in strength of the scalnd beams 

6. Abstract 

17. Key Words (Suggested by Author(s)l I 18. Distribution Statement 

Composite material 

Scale modeling 

Nonlinear response 

Failure 

Unclassified - Unlimited 

Subject Category 05