edge-effect studies in fiber-reinforced laminates

Edge-effect Studies in Fiber-reinforced Laminates

A comparison of theoretical and experimental displacement predictions in angle-ply laminates and investigations of the relation of effects to laminate failure

by D. W. Oplinger, B. S. Parker and F. P. Chiang

ABSTRACT-~Experimentol and theoretical studies of edge effects in rectangular composite strips under tension are discussed. The objective of the study was to investigate the effect of various parameters, including reinforcement material, fiber orientation and the structure of the reinforcement, on the various quantities which are observed in the vicinity of free edges in multidirectionatly reinforced laminates. Of particular interest was the confirmation of theoretical results related ta differences in response of graphite- and boron-reinforced laminates. Experiments consisted of moir~ measurements of surface-displacement patterns which were compared with theoretical predictions, and examination of failure levels. The experiments were carried out on AVCO 5505 boron and Whitaker 5206 MODMOR II graphite-reinforced angle-ply laminates in which both stacking sequence and fiber orientation were varied parametric- ally. Moir~ techniques were developed which allowed ob- servation of displacements on both the wide surface and along the narrow edge of 1 in.-wide • 16-ply-thick (.085 in.-.1 05 in.)laminates.

List of Symbols A~t, A16, A66 ~ compliance coefficients of fiber layers

( lb-1 in.2) b = half width of laminate (in.) h ---- thickness of laminate (in.)

Gm ----" matr ix layer-shear modulus SLc, SLt- - - - longi tudinal uniaxia l s t rength of fiber

layers, compression and tension, respec- t ively (lb-in. -2)

Src, STt---- t ransverse uniaxia l s t rength of fiber layers, compression and tension, respec- t ively (lb-in. -2)

t ~ , t f = mat r ix - l aye r and f iber- layer thickness (in.)

TTL, TIL : in -p lane and in te r l aminar shear strengths ( lb- in . -2)

u ---- axial displacement (in.)

D. W, O,l inger and B. S. Parl~er are Physicist (mechanics) and Me- chanical Engineer, respectively, Army Materials and Mechanics Re- search Center, Watertown, M A 02172. F. P. Chiang is Associate Professor, Department o~ Mechanics, State University o~ N e w York, Stoney Brook, N Y 11790. Paper was presented at the Third SESA International Congress on Experimental Mechanics held in Los Angeles, CA on May 13-18, 1973.

x, y, z = cartesian coordinates with respect to geometric axes (in.)

e ---- fiber or ientat ion (deg) ~x ---- axial s train (dimensionless)

---- uniform axial s train (dimensionless) ~x, ~ , ~z, ~yz, ~xz, ~xz = stresses in cartesian coordinates

with respect to geometric axes of laminate ( lb- in . -2)

Introduction The need for taking into account three-dimensional aspects of mechanical response in f iber-reinforced materials has become increasingly recognized in recent years. Typical of the three-dimensional problem in fiber-reinforced structures is the phenomenon of edge effects occurring near the boundaries of laminated plates containing fibers oriented in several different directions. Under stretching loads, the tendency of individual layers to deform differently often gives rise, in the vicinity of free edges, to severe out-of- plane shear and bending effects. The desirability of determining the relative magnitude of these stresses and their effect on failure initiation in the plate is apparent.

The problem of tensile response of angle-ply laminates containing fibers oriented obliquely to the loading direction has been treated theoretically in Refs. I-5. Experimental work using moir& methods aimed at verifying the work of Pipes and Pagano 2 has been reported by Pipes and Daniel. 6 The present paper is aimed at further exploring the implication of edge effects in fiber-reinforced laminates. The work of Ref. 3 indicated the occurrence of certain important differences between the edge effects arising in yarn- reinforced composites such as graphite epoxy and composites reinforced with filaments arranged in well-defined sheets such as boron epoxy.

In this paper, we will consider the experimental determination of the effect of various parameters on the displacements arising from edge effects in angle- ply laminates in order to assess a number of theoretical results which have been obtained. In addition, the implications with regard to the role of edge effects on laminate strength will be explored.

Experimental Mechanics I 347

T h e o r e t i c a l C o n s i d e r a t i o n s

The theore t ica l considerat ions of present in teres t are based on resul ts discussed in Ref. 3, which we wil l br ief ly summarize at this point. The f ibe r - re in - forced lamina te [Fig. l ( a ) , l ( b ) ] is modeled as a mul t i l aye red plate [Fig. l ( c ) ] consisting of successive anisotropic and isotropic layers which represent the fiber and m a t r i x regions, respect ively.

In the case of boron- re in fo rced mate r ia l s [Fig. l ( a ) ] containing the re inforcement in the form of wel l -def ined fiber sheets, the use of the l a y e r e d - p l a t e model is r e l a t ive ly s t ra igh t forward . Fo r g raph i t e - re inforced laminates [Fig. 1 (b ) ] , the approach is less c lear cut because the y a r n - t y p e re inforcement en- forces a random dis t r ibut ion of f i laments th rough the p ly thickness. In the l a t t e r case, however , the plies m a y be represen ted in te rms of a number of sub- layers, each one-f i lament d iamete r thick. In e i ther case, the proper t ies of the compl iant layers r ep re - senting the m a t r i x ma te r i a l separa t ing the fiber layers m a y be ar t i f ic ial ly ad jus ted to re ta in the macroscopic shear modulus of the laminate . Once this is done, i t is reasonable to assume tha t the l aye red -p l a t e model gives an adequate represen ta t ion of the composite if we confine our a t ten t ion to ave r - age stresses th rough the fiber l ayers of the l aye red - p la te model.

At ten t ion wil l be res t r ic ted to the case in which a tensile load is appl ied in the x direct ion in such a way tha t stresses and displacements a re independen t of x. Among other things, it can be shown that, under this assumption, the axial strain, ,x, is independent of y and z as wel l as of x.

For ang le -p ly composites containing fibers or ien ted at +0 and --0 wi th respect to the x axis, physical considerat ions have suggested tha t the stresses of ma jo r in teres t include only ~=, ~xy and ~=~ for this type of loading. Results given in both Refs. 2 and 5 indi - cate tha t ~ , Tuz and ~z do not p l ay a significant pa r t here, a l though for laminates containing 0 or 90-deg or ientat ions they become of p r i m a r y importance.

The l aye red -p l a t e approach is then based on ap- p rox imat ing the d is t r ibut ion of d isplacements and stresses in the z direct ion by segmenta l ly l inear functions. Due to the high r ig id i ty of the fiber layers, the displacements are considered to be constant th rough the fiber layers and to va ry l inear ly th rough the ma t r i x layers. The formula t ion resul ts in a set of d i f ference-dif ferent ia l equations express ing the stresses as continuous funct ions of y and as discrete

u Z

(A) Boron Reinforced Laminate

Y I z \ ~ ~ - - ~ -

L ~ ~ / / / / / / / / / / / / / / / - - t \

"\', [ ~ [~- I ",r I ' ~ FI \ .

(B) Graphite Reinforced Laminate

Y

~ - (C) Layered Plate Mode\IL. S ~']

Fig. l--Construction of fiber-reinforced laminates and layered-plate model

functions of z for which solutions may be obta ined as a series of ma t r i x e igenvectors wi th exponent ia l mul t ip l ie rs to provide for var ia t ion wi th respect to y.

The resul ts of p r ima ry interes t are for types of s tacking sequence (see Fig. 2) des ignated as the A (a l te rna t ing) configuration [ ( + e ) / ( - - 8 ) ] n and the C (clustered) configuration [ ( + e ) n / ( - - e ) n ] . In the exper imenta l studies, the C configuration wil l be dealt wi th in terms of the so-cal led "back- to -back" C configuration, [ ( + 0) n~ ( -- 0) n] s, which, by e l imina t - ing overa l l twist in the specimen, is more sui table for moir~ measurements . Because of the lack of shear

Fig. 2--Laminate stacking sequences + O 1 + Pt I ,

- e - I - (-7 - j

- H - 2 .... + ~ - 2

Matrix Layers

Clustered Sequence Alternatin9 Sequence

348 I S e p t e m b e r 1 9 7 4

TABLE 1--ASSUMED MECHANICAL CONSTANTS OF FIBER-REINFORCED MATERIALS

Boron Graphite Epoxy Epoxy

Elastic Constants EL (106 psi) 30.0 25.0 ET (106 psi) 3.0 1.0 GLT (106 psi) 1.0 .5 ~LT 0.2 0.2

Strength Constants SLt (ksi) 240* 170" SLc (ksi) 400.0 100.0 STt (ksi) 5.0 6.0 STc (ksi) 30.0 20.0 TLT (ksi) 15.0 15.0

Interlaminar Constants Gm (10 +6 psi) 0.10"* .12"* Filament diameter (mils) 4.00 0.20 tm (mils) 1.00 0.05 Tin, IL shear strength (ksi) 15.00 15

Ply Thickness Number of filaments 1 25 Thickness in mils 5.00 6.25

* From test results, ,. * * In fer red f rom moire measurements, 10-deg laminates.

coupling across the symmetry plane of the back- to- back C configuration, the two halves act independent ly and should, therefore, give rise to the same level of edge effects as the simple C configuration. The A and C configurations effectively represent l imit ing cases for invest igat ing edge effects in angle-ply laminates containing fibers oriented symmetr ical ly about the loading axis.

Two types of theoretical results are of interest in the present paper. Figure 3 shows, first of all, the general na ture of the axial displacement profiles seen at the surface of a back- to-back C configuration laminate under tension. The ampli tude of the curves, Umax may be expressed in terms of the laminate by a

dimensionless ratio with respect to the laminate thickness, h, as follows:

2Umax A16 1 (tStm) 1/2

h 2All (GmA6d) 2/2 ts -F tm

where A i~'s are f iber-layer compliances, Gm is matr ix shear modulus and Kn, a funct ion of the number of layers n, is general ly close to 1.5. Here A86' ---- A66

- - A216/A~l is modified value of shear compliance, while the quanti t ies t~ and t,~ are the f iber-layer and mat r ix - layer thicknesses, respectively. One of the ma in objectives of the exper imenta l work was to determine to what extent the predicted surface displacements are valid in actual laminates. Pipes and Daniel 2 obtained results quite similar to the upper curve in Fig. 3, for a graphi te-epoxy laminate. In the present study, we will show measurements of this type for both the wide face and the nar row edge of the laminate (lower curve of Fig. 3). Our objective in the moir6 studies is to provide verification of the main features of the analysis for boron as well as for graphite laminates.

The second objective of the s tudy is to explore the implications of the theoretical results with respect to fa{lure of the laminate. Fai lure may be considered, as usual, by t ransforming the stresses in each layer to the "material axes" (coordinates oriented parallel and normal to the fiber direction) of the layer and applying a mul t iaxia l failure rule such as Hoffman's criterionY It should be noted that the stresses vary in the y and z directions, resul t ing in different predicted failure loads for the inter ior of the bar where vx reaches a max imum and Txy is nonzero, vs. the edge region where ~x reaches a minimum, ~xy is zero and significant levels of in te r laminar shear stress ~z are present. Figure 4 shows the predicted mean axial stress for onset of failure at the center and edge regions. The solid curve denoted "edge failure" ignores the effect of in te r laminar shear stress while the dashed curve indicates the correction that mus t be made to the "edge failure" curve to allow for ILS. The predictions are based on the level of stresses predicted together with the uniaxia l s t rength data

2b

~

AXIAL DEFORMATIONS

-o

z

L: i i ! i i _ o

/

Fig. 3--Shear displacements in angle-ply laminate under tension

Experimental Mechanics I 349

TABLE 2- -LAMINATE CONFIGURATIONS FOR EXPERI MENTAL STUDIES

A Configuration

+ 0

- - 0

+ 0

- - 0

i

C Configuration

[ - -018 16 PLIES

8 PLIES [ + o ] 4

GRAPHITE EPOXY BORON EPOXY (Modul i te 5206 Prepreg. MODMOR II Graphite}

(A'VCO Rigidite 5505 Prepreg.}

Unidirectional A C Unidirectional A C (8 lyrs.) (8 lyrs.)

0 ~ X ~ ~ X ~

_ i 0 ~ - - X X ~ X X

• ~ - - . . . . X • ~ X X ~ ~ - -

• ~ - - - - X - - X X

t ion of a selected set of the tests with closer at tent ion to this aspect of the problem may be warranted.

Moir~ Measurements

Approach From the outset, it was desired to employ an ex-

perimental technique that was capable of providing accurate surface-displacement measurements on both the nar row edge as well as the wide face of the laminate. To achieve this capability, the moir6 method was selected. The techniques consisted of uti l izing cemented film gratings ra ther than photoprinted gratings, since the la t ter technique would be difficult to apply to the side of a th in specimen and would tend to give poor contrast at the boundaries. Kodak "Kodalith" str ipping film has proven to be an excel- lent medium for providing specimen gratings. It has practically no reinforcing effect because of its th in-

given in Table 1. The assumed elastic constants shown in Table 1 were used in carrying out the stress analysis.

The present approach is used pr imar i ly to focus at tent ion on regions of performance where the in ter - l aminar shear stress can be considered significant enough to have a potential effect on failure. In the ensuing, the curves of Fig. 4 will be used to get pre- l iminary insight into which of the available mechan- isms are controlling failure.

Experimental Studies Experimental studies were carried out on boron-

epoxy and graphi te-epoxy laminates fabricated in the two stacking sequences shown in Table 2. The or ientat ion angles which were studied for the two materials are also given.

Moir~ measurements to be discussed in the next section were carried out on the back- to-back C configuration laminates under tensile load. From the theoretical results it was expected that the magni tude of edge effects would be considerably reduced in the A configuration, and it was decided to restrict the moir4 measurements to the C configuration, since the surface displacements associated with the edge effects would be easiest to determine with this type of laminate. Fai lure studies were carried out on both configurations, however.

The details of the specimens used for both moir6 measurements and failure studies are shown in Fig. 5. Scotchply 1002 fiberglass loading tabs were bonded at 350 ~ F with FM1000 film adhesive, using a specially designed jig to ma in ta in adequate curing pressure and planar i ty of the overall arrangement .

In the moire measurements , the loads were applied at .05 in . /min unt i l the desired level was achieved, then held constant or readjusted from time to time to compensate for specimen relaxation. The load rate for the failure tests was held at .05 in . /min up to failure. Relaxation effects could not be completely accounted for in the moir6 measurements, and repeti-

t

200 ~ ' ~ ' ~ N Graphite Epoxy [(+0)/(-0)] 4

~ 100 re enter Fa,lure

< 0

._ 300 - ~ Boron Epoxy [/+O~/(-0)] 4

~ 200

,~ Edge \

~100

10 20 30 40 50 60 Fiber Orientation in Degrees

Fig. &-Test-specimen details

f 30~ ~ . ~

t" 3" * I

l'~ 12 .. . . .

Dimension "t"

Materia~ Configuration Dimension "t" Be A 0.042""

C 0.085" Ge A 0.055"

D 0.104"

Fig. 5- -Theoret ica l fa i lure predic t ions for graphi te-epoxy and boron-epoxy angle-ply laminates

350 t September 1974

hess (.0005 in.) and affords a considerable degree of convenience which is desirable for studies where ex- tensive parametr ic investigations are reqired.

The gratings were prepared by contact pr in t ing a glass master on Kodak "Kodalith" str ipping film using the technique described in Ref. 8. In order to insure proper a l ignment of the grat ing on the specimen, a reference l ine was marked on the film backing perpendicular to direction of the l ine array. This was done wi th the aid of an optical comparator (100X magnification).

The grat ing was cemented to the specimen surface using s tandard s train-gage procedures. An epoxy adhesive (BLH EPY 150) was used. Special care was taken to insure a l ignment of the reference l ine on the film with the edge of the specimen. For opaque specimens, a reflective coating of flat white paint was sprayed on prior to cementing of the grating.

To view the moir~ fringes, a glass master was used which was a direct copy of the str ipping film just prior to the film's application to the model. Timing of the copying step is crucial because of the fact that the film shrinks after drying, thus creating a l inear compressive mismatch. While mismatch can usual ly be used advantageously in moir~ measurements , in this s tudy it would have the adverse effect of reducing the sensit ivi ty of the moir~ fringes to the edge effect.

Pet ro leum je l ly was used as a coupling agent between the master and model gratings. Scotch tape

was used to hold the glass plate in place. Two min i - spot lamps were used to i l luminate the specimen. In - cremental loads were applied to the model and the moir~ fringes were recorded photographically.

No part icular difficulty was encountered in this process. There seemed to be no debonding problem between the pairs of surfaces. It is important to note that the thickness of the paint and adhesive were kept to a m i n i mum to insure accurate reproduction of the surface displacements.

As compared with the process of vacuum deposit- ing a reflective surface and photoengraving gratings on the model, the present approach has several ad- vantages; namely, it is simpler and less t ime con- suming and does not require special equipment such as a vacuum metall izer and vacuum frame. Fur the r - more, it would be extremely difficult to vacuum deposit and photoprint on the nar row side of models, which were as thin as .085 in. In addition, the photo- pr in t ing process tends to produce gratings with poor qual i ty at the edges which were the locations of pr imary interest in this study.

The moir4-fr inge pat terns were obtained with 1000-lines/in. (lpi) gratings, except for the edge views obtained for the • 45-deg graphi te-epoxy laminates in which case a grating density of 100 l ines / ram was used.

Fig. 6--Moird-fringe patterns for various laminates, [(+sh/(--o)4]s configuration: face view--lX; edge view--2X. (Reduced approximately 50 percent upon reproduction)

Fig. 7--Moire-fringe patterns for various laminates, [(+20=)4/(-20~ under developing load. Face view-- 1X; edge view--2X. (Reduced approximately 50 percent upon reproduction)

Experimental Mechanics [ 351

+0.4

=+0.2

% o

o

-0.2

-0.4 0

[ (+ 10~ ~ 8/(+ 100)4 ] - - Theoretical - - - Experimental

(4 Fringes) 82.5 ksi

[ ; __~ \ \ i [ -0.1 - 0 . 2 +0.2 +0.1

Distance from Edge, in .~Distance from Edge, m.

+0f .~+0.2 ~\

~0,

-0.41 , 0 -0.1 -0.2 +0.1

Distance from Edge, in.~.~Distance from Edge, m.

Fig. 8--Comparison of experimental and t h e o r e t i c a l shear d i s p l a c e m e n t s ~ b o r o n e p o x y (face view)

[(+20o)4/(-20o)8/(+200) 4 ] - - - Experimental


+0.41

+0.2]

%

o

i5 -0.2

-0.4

\

[ (+10~ 10~ 10~ 4 ]

- - Theoretical - - - Experimental


\ \ \ \ %

1 I "~ \ I I - . 1 -0.2 \ \+0 .2 +0.1

Distance from Edge, in .~Dis tance from Edge, in.

+0'41 [(+30o)4/(-30o)8/(+30o)4 ]

2~\~ - - - Experimental E \ {5 Fringes}

+-+0. ~- 23.8 ksi

i5_0.

-0.41 I I \ \ ,

-0.1 -0.2 \ \+0.2 +0.1 Distance from Edge, in .~ ~Distance from Edge, in.

Fig. 9 - - C o m p a r i s o n of e x p e r i m e n t a l and t h e o r e t i c a l shear d i s p l a c e m e n t s - - g r a p h i t e e p o x y ( face v iew)

E x p e r i m e n t a l R e s u l t s

Figures 6 and 7 show the moi re - f r inge pat terns which were obtained on the wide and nar row edges of the specimens. A notable difference in character of the fr inges is observed, in that considerably more definition is observed in the fringes obtained on the nar row edge. This suggests that the measurement of total shear displacement obtained from the edge view can be made more precise that that obtained f rom the face view.

The results shown in Fig. 6 represent a composite of the results obtained at various or ientat ion angles. For the _ 45-deg cases, the applied load was considerably l imited by low axial tensile s t rength of the laminates and only a min imal edge effect was generated. The edge effect was almost absent from the face view and these are not shown in Figs. 6. The edge views give a fair ly clear indication of an edge effect in the _ 45-deg laminates a l though considerable var ia t ion is present f rom fringe to fringe. F ig- ure 7 shows typical variat ions of the fr inge pat terns with applied load for a boron-epoxy laminate.

Displacement measurements obtained f rom the face-v iew pat terns for various laminates are compared in Figs. 8 and 9 wi th theoret ical predictions. The method of calculat ing the shear displacement from the moi re - f r inge pat terns is based on a simpli- fied formula which applies here because of the con-

dition of uniform axial strain. We note that the axial deviat ion of a given fringe, d=, from a fixed axial position, bears the same ratio to the fr inge spacing, Ax, as the displacement du corresponding to dx bears to AU, the displacement difference be tween successive fringes (i.e., Au = inverse of grat ing l ine densi ty) . Since A u / A x is equal to the axial s train then the relat ion

du -- e= d=

is obtained. The displacement plots are therefore obtained by measur ing dx wi th respect to a reference point on a given fr inge (for example, the s t raight portions of the face-v iew fringes) and using the axial strain ~x as a mul t ip l ier to generate d~.

In addition, it is noted that the above formula can be transposed to give

du dx --

ex

If the system response is linear, then the ratio du/e.~ is a constant, so that one expects the fr inge distortion dx to be re la t ive ly independent of load. Examinat ion of the fringes shown in Fig. 7 seems to bear this out.

The theoret ical curves in Figs. 8 and 9 were generated by first adjust ing the ma t r ix shear modulus Gm to get a good fit for the cases of 10-deg fiber orientation. The values given in Table 1 for G~ were ar r ived at in this manner. The theoret ical curves for

352 I September 1974

~+0.4 ~- ~" ~ :r

,!' t,i ' L

I -1 0 +1

2_~z h

Fig. 10--Comparison of theoretical and experimental edge-view displacements, boron epoxy [(+20~ (--20~176

- - - - - Scaled Theoretical ~; ]; ~ Experimental

(No, of Fringes = 5) o x = 64.7 x 103 Ib-in.-2

20-deg boron epoxy and 30-deg graphite epoxy were then generated using the parameters obtained from the 10-deg cases.

It should be noted from physical considerations that a low value of the assumed Gm should be expected in order to make the layered-pla te model give an in te r l aminar shear modulus equivalent to the actual f iber-reinforced materials. This observat ion stems from considering the relat ive stiffnesses of laminates constructed from plane homogeneous layers vs. fiber-reinforCed mater ia ls whose consti- tuents have the same elastic constants as the layered material . For example, a comparison was made between the theoretical macroscopic in t e r l aminar shear modulus of a p lane- layer - re inforced mater ia l and a c ircular-f iber-reinforced material , using theoretical results given in Refs. 3 and 9, respectively. (A square ar ray was assumed for the fiber~reinforced material .) If perfectly rigid "fiber" layers 'are~assumed for the p lane- layer reinforcement, the assumed Gm must be reduced from that for fiber re inforcement by a factor close to 0.6, in order to obta in equal composite in te r - l aminar shear modulus. The actual shear modulus of typical epoxies being close to 0.17 • 106 psi, the Table 1 values of Gm are not far removed from 0.6 X 0.17 • 106 = .102 • 106 psi. Thus, the Table 1 values of Gm are reasonably consistent with the physical considerations which must be observed in applying the layered-pla te model.

As indicated in Figs. 8 and 9, the var ia t ion in both the ampli tude and boundary - l aye r thicknesses ob-

ta ined at the higher or ientat ion angles was considerably greater than for the cases of 10-deg fiber or ien- tation. A consistent difference in the fringes between the right and left edges of the specimen was typical ly observed at the higher orientations, in addit ion to a relat ively random var ia t ion among fringes along a given edge.

Figure 10 shows a comparison of the theoretical and exper imental displacements for the edge-view fringes in the case of • 20-deg boron epoxy. The true theoretical curve, as indicated in Table 3, was some- what smaller in ampli tude than the exper imenta l results. The "scaled theoretical" curve shown in Fig. 10 was adjusted by a mult ipl icat ive constant to yield agreement in the max imum amplitudes, and is presented main ly to demonstrate the relat ive agreement between the theoretical and exper imental edge-view profiles. The exper imenta l results were obtained with the aid of a curve digitizing accessory to a Hew- lett Packard 9100 desk calculator and plotter which allowed the fringes to be replot ted from a 5X magni - fication of the original photograph with an addit ional magnification in the z direction of about 12: 1. The results shown in Fig. 10 are, thus, considerably "stretched out" in the z direction in comparison wi th the fringes seen in Fig. 6. Notwiths tanding the re- quired ampli tude ad jus tment of the theoretical curve, the trends in the exper imental and theoretical results of Fig. 10 appear to be in reasonable agreement,

Detailed comparisons of this type were not made for the remaining cases. However, Table 3 summar - izes the measurements of displacement amplitude, Umax, wh ich were made from the edge views, as well as giving a comparison wi th the values obtained f rom the face views. As suggested earlier, the precision which can be obtained from the e dge - v i e w fringes appears to be general ly greater, as indicated by the smaller s tandard deviations which were usual ly obtained. Measurements on the 45-deg laminates were hampered by a lack of definition and repeatabi l i ty in the fringe pat terns for these cases and are not shown here.

Fai lure - tes t Resul ts

Figures 11 and 12 show the results of tensile tests which were made on C and A configuration laminates

TABLE 3--SUMMARY OF DISPLACEMENT MEASUREMENTS

Boron Epoxy 10 deg

Graphite Epoxy 20 deg 10 deg 30deg

�9 x(Ib-in.-~) 82.3 Face View L No. of Fringes 4

U max, .001 in. .18 (Std. Dev., .001 in.) (.050) Edge View No. of Fringes 4 U max, .001 in. .22 (Std. Dev., .001 in.) (.014) Theoretical U max, .001 in. .219

R L 4 7

.23 .344 (.033) (.084)

4 .32

(.013)

64.7 57.7 24.0 R L R L R

8 4 4 5 5 .442 .247 .251 .234 .272

(.084) (.025) (.017) (.088) (.063)

5 10 .281 .21

(.021) (.031)

.243 .201 .163

Experimental Mechanics 353

/ • a [(+•)4/(-0)8/(+0) 4] (Clustered) 300 o [ (+O} / ( -0 ) ] 4 (Alternating)

.c" 8

E

~100 "..--..~. \

0 10 20 30 40 50 60 Fiber Orientation, degrees

Fig. l l - -Failure-test results, boron epoxy

[(+0)4/(-0)8/(+0) 4 ] (Clustered}

~200 L o [(+e)l(-e)]4 (Alternating)

v

;lOO E

'~ 0 , 10 20 30 40 50 60

Fiber Orientation, degrees

Fig. 12--Failure-test results, graphite epoxy

with orientations from 0 deg to +_ 45 deg. As noted in Table 2, the unidirect ional (0 deg) specimens were 8 layers thick, corresponding to the number of layers in the A configuration. The exper imental results for each mater ial are compared in Figs. 11 and 12 with the theoretical curves shown in Fig. 4. As seen in these figures, the results for the C configuration gen- erally were quite close to the predicted "edge-failure" curves, the largest deviation occurring for the 10-deg boron-epoxy mater ial with an exper imental value of 129 • 103 ( • 5 • 103) psi vs. the theoretical value of 106 • 103 psi, a deviation of about 22 percent from the theoretical result. The A configuration results general ly fell above the "edge-failure" curves, the largest deviation occurring for the boron-epoxy 10-deg case with an exper imental value of 180 ( • 9 • 103) psi vs. the 106 • 103 psi theoretical value.

It is apparent from these results that, for the boron epoxy, the A configuration does tend to reduce the strength degradation caused by the stresses occurring in the vicinity of the laminate free edge. The difference is less clear cut in the case of the graphi te-epoxy results. In either case the "edge-failure" prediction appears to provide a lower bound on the strength values.

C o n c l u s i o n s

The most important considerations regarding the role of edge effects in the mechanical response of angle-ply laminates appears to have been borne out. The expected features of the surface-deformation

profiles have been obtained for both boron- and graphite-reinforced materials over the range of orientat ion angles from ___ 10 deg to • 30 deg, al- though, as expected from the theoretical resu!ts, 3 at + 45 deg the tensile loads which can be developed are insufficient to give rise to significant levels of shear deformation. The role of the edge effect in the failure of angle-ply laminates was also borne out. The use of an a l ternat ing (A configuration) stacking sequence to disperse the effects of in te r laminar shear stresses near the edge appears to be a beneficial approach, part icular ly for boron-re inforced materials.

The use of cemented film gratings for moir~ measurements on composite materials has proven to be an attractive approach, from the standpoint of both convenience and the capabili ty it provides for exploring the details of mechanical behavior along narrow edges of composite laminates.

Fur ther study is needed to obtain a more complete quant i ta t ive agreement between the theoretically predicted surface displacement profiles of laminates in the fiber or ientat ion range of • 20 deg to _ 30 deg. The role of nonl inear response is one obvious factor which is needed in the theoretical approach since shear deformation modes are of key importance in controll ing the edge effect. At tent ion to viscoelastic effects, both in the theory and in the experimental approach, is also needed, since as noted in the section on "Experimental Studies" it was not possible, in the approach which was taken, to completely compensate for relaxat ion effects which were present.

Finally, it is noted that the predicted results were based to a large extent on assumed elastic and strength constants of the fiber layers. The general agreement between the predicted "edge-failure" curves of Figs. 11 and 12 based on these parameters and the exper imental results for the C configuration indicates that in te r laminar shear stresses did not have the expected degrading effect on strength. It is noted that the failure curves which were adjusted for in te r laminar shear stress (the dashed curves in Figs. 11 and 12) were below the failure levels which were observed. The independent determinat ion of the mechanical constants used in the predictions together with an exper imental approach which brings out the actual details of failure ini t iat ion appears to be needed.

R e ] e r e n c e s

1. Puppo, A. H. and Evensen, H. A., "Interlamlnar Shear in Composite Laminates Under Generalized Plane Stress," J. Comp. Marl., 4, 204 (1970).

2. Pipes, It. B. and Pagano, N. ]., "'Interlaminar Stresses in Composite Laminates Under Axial Extension," ]. Comp. Marl., 4, 538 (1979).

3. Oplinger, D. W., "'Edge Effects in Angle Ply Composites," AMMRC, Watertown, MA, TR-71-62 AD Number 747343 (1971).

4. Pipes, R. B. and Pagano, N. ]., "'Interlaminar Stresses in Com- posite Laminates--An Approximate Elasticity SoT.ution, "" Mechanics and Structures Research Report No. 73-1, Drexel University, Phila- delphia, PA (1973).

5. Oplinger, D. W., "'Analytical Studies of Edge Effects in Fiber Reinforced Laminates," Fourth Canadian Cong. of Appl. Mech., Montreal, Canada (May 1973).

6. Pipes, R. B. and Daniel, I. M., "'Moird Analysis of Interlamlnar Shear Edge Effect in Laminated Composites," 1. Comp. Marl., 5, 225 (1971).

7. Hoffman, 0. , "'The Brittle Strength of Orthotropic Materials,'" J. Comp. Marl., I, 200 (I967).

8. Chlang, F. P., "'Production of High-density Moir5 Grids,'" EXPEBI~NIENTAL MECHANICS, 9(6), 286-288 (1969).

9. Tsai, S. Vd., Adams. D. F. and Doner, D. R., "'Analysis of Composite Structures," NASA Contractor Iteport NASA-CIt-620 (1966).

354 1 September 1974

edge-effect studies in fiber-reinforced laminates

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