NASA ContractorReport 178018 NASA-CR-178013 19860004028

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" .ELASTIC-PLASTICDEFORMATIONOF A

METAL-MATRIXCOMPOSITECOUPON

WITHA CENTERSLOT

DanielPost, RobertCzarnek,

DuksungJoh,JinmyunJo, andYifanGuo

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VIRGINIAPOLYTECHNICINSTITUTE --.... " -

AND STATEUNIVERSITY :_ .-..,:,.,"..,,_,_,_._.,'_=,-.z_.._

Blacksburg, Virginia

Grant NAG1-343

, November1985

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Hampton, Virginia 23665

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TABLE OF CONTENTS

Page

ABSTRACT..................................................... I

INTRODUCTION.......................... • •••••••••••me•••••e••• 2

EXPERIMENTALMETHOD: MOIRE INTERFEROMETRY....................3

TEST PROCEDURE•MOIRE PATTERNS ...............................4

ANALYSIS• QUALITATIVE•eooeeooooooeoeooooeeeoooooooooeoo ..... • 5

ANALYSIS• QUANTITATIVE ....................................... 7

CONCLUSIONS .................................................. 12

ACKNOWLEDGEMENTS ............................................. 13

TABLE I ...................................................... 14

FIGURES...................................................... 15

ABSTRACT

A comprehensive experimental analysis of deformations of the

surface of a metal-matrix specimen is reported. The specimen was a 6-

. ply [0/± 45] s boron-aluminum tensile coupon with a central slot. Moire

interferometry was used for high-sensitivity whole-field measurements of

in-plane displacements. Normal and shear strains were calculated from

displacement gradients. Displacement fields were analyzed at various

load levels from 15%to 95% of the failure load. Deformations of the

boron fibers could be distinguished from those of the matrix.

Highly localized plastic slip zones occurredtangent to the ends of

the slot. Shear strains and concurrent transverse compressive strains

in the slip zones reached approximately 10%and i%, respectively. Upon

unloading, elastic recovery in surrounding regions caused a reverse

plastic shear strain in the slip zone of about 4%.

Longitudinal normal strains on the unslotted ligament peaked at the

slot boundary at about i% strain. The strain concentration factor at

the end of the slot decreased with load level and the advance of

plasticity.

KEYWORDS

composites

metal-matrix

elastic-plastic

deformation fields

strain distributions

plastic slip

moire interferometry

experimental analysis
INTRODUCTION

Understanding,and rationaldesign, with metal-matrixcomposites

requiresphenomenologicalevidenceobtainedfrom detailedmeasurements

of its behavior. Experimentalanalysisof a tensile couponwith a

severe stress concentration,a central slot, was undertakenhere. The

objectivewas a detaileddeterminationof deformationsin the vicinity

of the slot, includingthe redistributionof deformationsat higher

loads -- where theductile matrix exhibitedplasticdeformations.

Quantitativeobservationswere made up to 95% of the failure load. The

compositewas boron/aluminum,with a 6-ply stackingsequence [0/± 45]s.

Its compositionis given in Fig. I, togetherwith the specimengeometry.

Deformationswere determinedby moire interferometry.This is an

optical method that produceswhole-fieldcontourmaps of in-plane

displacementcomponentsux and Uy. Sensitivityis in the subwavelength

range, namely 16.4x10-6 inchesper fringe order. In additionto high

sensitivity,it is characterizedby high contrastinterferencefringes

and high spatial resolution,permittingdetailedanalysisof both global

and localizeddeformations. Normal strainsand shear strains can be

determinedfrom the displacementinformation. While it is similar in

many ways to classicaland holographicinterferometry-- which are

techniquesprimarilyuseful for out-of-planedisplacementmeasurements,

uz -- moire interferometryprovidesthe importantin-plane

displacements,ux and Uy.
EXPERIMENTALMETHOD: MOIRE INTERFEROMETRY

A comprehensivedescriptionof moire interferometryappears in Ref.

1. Briefly,a high frequencycrossed-linediffractiongrating is

replicatedon the specimensurfaceusing a specialmold, as illustrated

in Fig. 2a. The result is a thin -- usually 0.001 in. -- reflective

phase grating firmly adhered to the specimen,which deforms together

with the specimen surface. The specimengrating is observed in an

optical arrangementillustratedschematicallyin Fig. 2b. Two beams of

light incidentat angles_ and -_ form a virtual referencegrating,with

its grating lines perpendicularto the plane of the figure. Its

frequencyis f = (2 sin _)/x, where _ is the wavelengthof the light.

This referencegrating interactswith the similarlyoriented lines of

the specimengrating to form the interferencepattern recorded in the

camera. When the referencegrating lines are perpendicularto the x

axis, the pattern is a contour map of displacementsgovernedby the

relationship

ux = _ Nx (i)

where ux is the in-plane x component of displacement at any point and Nx

is the fringe order at that point in the fringe pattern.

The crossed-line specimen grating was applied in the xy plane with

lines perpendicular to the x and y axes. In the optical arrangement

used in these experiments, two additional beams (not shown) produced a

virtual reference grating perpendicular to that of Fig. 2b. Individual

patterns of Nx or Ny were obtained by blocking the light of the

alternate virtual reference grating. Whenthe reference grating lines

were perpendicular to the y axis, in-plane displacements Uy were

obtained from fringe orders Ny by
Uy = _ Ny (2)

Frequencyf was 60,960 lines/in.(2400 _/mm). An argon ion laser was

used at wavelength20.3 uin. (0.514_m) and 100 mW power.

Strainscan be calculatedfrom the displacementfields by the

(small strain)relations

•m BUx 1 _Nx

Cx _x - f _x (3)

_y = _y = T _y (4)

_ux _Uy 1 _Nx _N

- + =T (5)

The accuracyof the calculatedstrains is substantiallyless than the

accuracyof the displacements. Regardlessof the method used to

determinethe derivatives,differentiationof experimentaldata always

results in a band of uncertaintythat is much broaderthan the

uncertaintyin the data. However,satisfactorystraindeterminations

are achieved in the presentwork becausethe closely spaced fringes of

the displacementfields provide an abundanceof high accuracy data.

TEST PROCEDURE,MOIRE PATTERNS

The metal-matrixspecimenwas suppliedby NASA Langley Research

Center; the central slot was producedby an electricspark discharge ,.

technique. The specimengrating and electricresistancestrain gage

(1/4 inchgage length,gage CEA-06-250UW-350, MeasurementsGroup Inc.,

Raleigh,NC) indicatedin Fig. 1 were applied at VPI & SU. The specimen

was installedin a mechanicalloadingfixtureequippedwith strain gage

transducersto measure the applied load, P; the Fixturewas attached to
a vibration isolation table that also supported the optical elements of

the moire interferometry system.

Following initial adjustments, the specimen was loaded in a

sequence of loading steps; for each step the load and strain gage

readings were recorded and the Nx and Ny patterns were photographed.

After loading to 95% of the predicted failure load, the load was removed

and patterns of the residual displacement fields were photographed.

Relevant loading data are shown in Table I. The predicted failure load,

Pf, is the average of failure loads for similar specimens tested at

NASALangley Research Center.

The moire interferometry fringe patterns of Ny and Nx are shown in

Figs. 3(a) - 3(I) for loads P/Pf ranging between 15% and 95%. The

residual displacement fields, after the specimen was unloaded to 1.3% of

Pf, are shown in Figs. 4(a),(b).

ANALYSIS, QUALITATIVE

At 15%of Pf (Fig. 3a), the fringes are most closely spaced near

the ends of the slot, indicating zones of largest displacement gradients

or strains. The fringes are smoothly or systematically spaced however,

in contrast to the abrupt changes in fringe gradients seen in the Ny

patterns for all the higher loads. These abrupt changes, which occur in

narrow vertical zones tangent to the slot ends, are strong

concentrations of shear strains; they are undoubtedly associated with

localized plasticity of the matrix material which permits relative slip

of the 0° boron fibers in the outer ply. They will be called plastic

slip zones. Whereas the intensity of these shear strains and fiber

displacements increases with load level, it is curious that the length
of each slip zone increasesrather slowly,much more slowly than

proportionalto the load.

On the left side, the slot seems to terminatepartly through a

boron fiber. That fiber appears to have broken at a load between 15%

and 25% of the failure load. The apparentbreak first appears in Fig.

,t

3(c), along the centerlineof the slot. On the right side, the slot

appears to terminatein the matrix materialand the first continuous

fiber beyond the slot remains unbrokenthroughoutthe test.

The Nx patternsshow that compressivestrains are substantially

larger in the slip zone than in surroundingregions. Plasticityin the

matrix comprisingthe slip zone appears to be accompaniedby two

conditions,elevatedcompressivestrains and large shear strains.

The first evidenceof inter-fiberplasticityoccurs between the

first continuousfiber outside the slot and the neighboringfiber

interceptedand cut by the slot. Subsequently,at a higher load, severe

plastic deformationappears to develop in the matrix between the next

inboard pair of fibers (towardthe specimencenterline),where a second

slip zone is formed.

Except for the lowest load levels, Ny fringes near the slip zones

are seen to have an irregularor zig-zagcharacter. These are real

deformationeffects,and not optical noise in the experiments. They

signify largervalues of _Uy/BXin the matrix and smallervalues in the

fibers. This translatesto largershear strains in the matrix between t

fibers and smaller shear strains in the fibers.

The Nx fringes show a similar cyclicalbehaviorabove and below the

center of the slot. This is where the average compressive_x strains

are large. The zig-zag fringes in this region are especiallypronounced

6
in Figs. 3(j) and 3(1). They have relatively horizontal segments, where

aUx/aX is very small, and inclined segments where aUx/aX is large. The

former corresponds to fiber locations (where _x is small) and the latter

to matrix locations (where _x is large). The period of the cyclic

disturbances is 0..007 in., which corresponds to the fiber spacing. In

both cases -- shear along the fibers and compression across the fibers

-- the deformation proceeds in harmony with the compliance of the

material and deformations are larger in the more compliant matrix.

In fact, the magnitude of this disparity of deformations in matrix

and fibers is somewhat masked by the experimental method. While the

specimen grating is very thin, its thickness is finite. Shear lag in

the grating thickness introduces some difference between the

deformations at the surface of the specimen and at the surface of the

grating. The effect appears to be small enough that it will not change

the trends or influence the conclusions of these tests.

Figure 4 shows dramatic residual deformations. Permanent

deformations are evident throughout the field, even far from the slot.

Strong permanent deformations are evident in the slip zones tangent to

the slot ends and in the compression zones near the center of the slot.

ANALYSIS, QUANTITATIVE

Figure 5 shows the stress-strain curve for the specimen at zones

remote from the slot. The data correspond to those in Table I, where

the far-field strains are determined by the strain gage. The

longitudinal stress-strain behavior is mildly non-linear from low stress

levels to 95% of the specimen failure load.

7
Figures 6 and 7 are plots of the Uy and ux displacementsnear the

slot. Figure 6 shows the displacementsfor one load level,P/PF = 80%,

for the 4 horizontallines indicatedin the figure. The displacements

for 4 load levels are plotted in each of Figs. 7(a)-(d),but for

differentdistancesfrom the slot. The figures show the gradual

intensificationof displacementgradientsat locationsapproachingthe

slot; and they show the gradual intensificationof gradientswith

increaseof load.

These data, and those used in all subsequentfigures,were taken

from the first quadrant (upper-rightsection)of the fringe pattern.

While deformationsin the four quadrantsare not identical,they are

sufficientlysimilar that the results for the first quadrantcan be

taken to representthe behaviorof the entire specimen.

In Figs. 6 and 7, the line segmentsof very large slopes, at and

near x = O, correspondto the slip zones. These segmentsare drawn as

straightlines, since fringes in these very narrow zones were not

resolved. The shear strains interpretedfrom these straightsegments

are assumed to be uniform acrossthe width of the slip zone. It is

possibleand even probablethat these displacementswould be better

representedby shallowS-shapedcurves, which would lead to higher

valuesof shear strainsalong the centerlineof the slip zone.

Accordingly,shear strains in the slip zone are assessedconservatively

in the subsequentFigures. _:

Figure8 shows the distributionsof strains along the y and x axes

for one load level,P/Pf = 80%. In (a) the normaland shear strains are

plotted as a functionof distancealong the y axis; in (b) the normal

strainsare plotted againstdistancealong the x axis. Note the
different scales for €x and Ey, indicatingthey have opposite signs.

Clearly,the shear strains near the slot are very much largerthan the

normal strains. This high shear strain is the dominantfeature in the

" specimendeformation. The peak shear reaches a strain level near 8%,

well into the plastic range of the matrix material. The peak shear

occurs near the slot, but it is locatedabove the centerlineof the

slot; at the centerline,the shear strain must be zero.

Figure 8(b) illustratesthe normal strains along the unslotted

ligament. The Peak value•of Ey occurs at the slot boundary,but it is

an order of magnitudesmaller than the peak shear strain.

Normal strain €x is very small at the slot boundary,indicatinga

very small effectivePoisson's•ratio•at that point. This may be

associatedwith the underlying± 45° fibers;these fibers are not

continuous,but instead they terminateat theslot boundary. Remote•

from the slot, at x = 1.3a and y = O, •theratio Ex/Ey is approximately

0.2._

A comparisonis made in Fig' 9 of the shear strainsalong the y

axis (alongthe line markedA) and along the adjacentline marked B.

The load levelwas P/Pf = 80%. The severeplasticdeformationalong

line B began at a higher load level and the peak shear strain along B

_ remainedsubstantiallylower than that along A -- where severe plastic

deformationfirst appeared.

Figure 10 shows the residualstrainsalong the y and x axes, after

the load was reduced to only 1.3% of Pf. The residualshear strains

(Fig. lOa) are large,peaking at about 4.7% strain. For comparison,the

peak shear strain at the highest load level (P/Pf= 95%) was about 8.8%

strain. The difference(4.1% shear strain)cannot be attributedto
elasticrecovery snce a recoveryof several percent cannot be elastic.

Instead,the elastic recoveryof adjacentregions of the specimen,

includingthe underlying± 45° plies, must have caused a reverse plastic

deformationin the high shear zones. This suggeststhat low-cycle

fatiguemight be an importantparameterin the materialperformance.

Comparingthe normal strains in the slip zone (Figs. 10a and 8a),

residuallongitudinalstrains Cy are relativelylow near the slot. This

signifiessubstantialrecoveryfrom the maximum load condition. On the

other hand, residual transversestrains Ex are more than half as large

as those for the maximum load condition,indicatinga modest recovery.

While these compressivestrains in the maximum load conditionswere only

0.1% and less, the matrix material in that zone was well into its

plastic state because of the very high shear strains;the absence of

strongrecoveryof these small compressivestrains is attributedto the

plasticityof the matrix.

The longitudinalresidualstrains,Ey, along the x axis (Fig. lOb)

are nearly constantremote from the slot. Near the slot, however, they

dip to a low residualstrain level. The change of shape of the curve,

relativeto the Cy curve for the loadedcondition(Fig. 8b), is curious.

What might be viewed as excessiverecoveryof € near the slot must

Y

result from a differentmode of deformationin the unloadingprocess,

relativeto that in the loadingprocess. An explanationsuch as workhardeningof the matrixwould fit the observation,wherein more plastic

deformationwould occur during loadingthan unloading.

Figures 11(a) and 11(b) show plots of longitudinalstrains E along Y

the x axis for various load levels; in (a) the strains are normalized

with respect to the far-fieldstrain_ff, while in (b) they are

10
normalized with respect to the far-field stress, o. Normalization with

respect to far-field strain seems the more informative.

Remote from the slot, the curves cluster together (Fig. lla),

indicating that strains in the remote regions are essentially

proportional to the load. More accurately, these normalized strains

rise gradually with load level -- consistent with Fig. 5, which shows a

gradual increase of compliance with stress level.

Very close to the slot, the behavior is reversed (Fig. lla).

Normalized strains _y/_ff decrease as the applied load increases.

Strains Cy are rather high in this region, and the matrix material

becomes increasingly plastic as the load increases. This presumably

distributes the local forces more effectively to adjacent fibers and

depresses the strain concentration that would otherwise be developed.

Figure 12 shows the strain concentration Cy/Cff at the end of the

slot as a function of applied load on the specimen. This strain

concentration reduces significantly with load level, from about 8 at 15%

of failure load to about 4 at 95% of failure load. The trend of the

curve is clear, although scatter of data points is greater here than in

preceeding graphs. This is because the moire fringes surrounding these

points of peak strain are less distinct than elsewhere.

Figures 13(a) and (b) show the shear strains along the y axis,

where they are normalized with respect to far-field strains and

stresses, respectively. The character of the curves for different load

levels is basically the same, except for the 15% load, which shows a

much smaller shear strain concentration near the slot. At higher loads,

the plastic slip band (in the matrix adjacent to the first continuous

fiber) is fully developed and the curves represent shear strains in this

slip zone.

11
Shear strains in the slip zone are, by far, the highest strains

developedin the specimen,higherthan others by an order of magnitude.

Their magnitudesare undoubtedlyunderestimated,too, for reasons

alreadymentioned-- shear lag through the grating thicknessand

averagingacross the slip zone. The region of highest shear strain

occurs in a very small part of the slip zone, but very substantialshear

strainsoccur throughoutthe slip zone.

Figure 14 is a plot of the shear concentrationYxy/Cff,at the

point where Yxy is maximum, as a functionof load level. This strain

concentrationbecomes exceedinglyhigh as soon as the slip zone is

formed, and it continuesto rise with the load. The dashed line

representsan estimateof performanceat lower load levels,where the

strain concentrationis assumed to be nearly constantprior to

developmentof the Slip zone.

CONCLUSIONS

A comprehensiveexperimentalanalysisof deformationsof the

surface of a metal-matrixtensile specimenwith a central slot is

reported. Deformations,specificallyin-planedisplacementsand

strains,were determinedat several load levels,from 15% to 95% of the

failure load. Deformationsof the fiberscould be discriminatedfrom

those of the matrix.

The dominant feature of deformation was a plastic slip zone tangent

to the end of the slot. It occurred in the matrix material adjoining

the last continuous fiber adjacent to the slot. At 95% of the failure

load, shear strains in the slip zone reached approximately 10%.

Concurrently, compressive normal strains acting perpendicular to the

12
slip zone reached approximately1%. The matrix materialexhibited

highly plastic behavior. The shear strain concentrationfactor Yxy/_ff,

where _ff is the far-fieldlongitudinalstrain, jumped to a value of 23

- when the slip band first occurred,and it rose to about 30 at 95% of the

failure load.

Longitudinalnormal strainson the unslottedligament (x axis)

peaked at the slot boundaryat about i% strain,which was well into the

plastic range of the matrix material. This strain concentrationfactor

decreasedwith the advanceof plasticityfrom about 8 to about 4.

Upon unloadingfrom 95% of the failure load, permanentdeformation

remainedthroughoutthe specimen. Residual shear strain and residual

compressivestrain in the slip zone reached approximately5% and 0.6%,

respectively. Elastic recoveryin surroundingregions caused a reverse

plastic shear strain in the slip zone of about4%. Along the unslotted

ligament,the residuallongitudinalstrain peaked at a significant

distance from the slot at about 0.1% strain.

ACKNOWLEDGEMENTS

Dr. W. S. Johnson of NASA Langley ResearchCenterwas the NASA

TechnicalOffice For this research. His assistanceand valuable

discussionsare greatelyappreciated.

REFERENCE

1. Post, D., "Moire Interferometryat VPI & SU," Experimental

Mechanics,23(2), June 1983, pp. 203-211.

13
TABLE I

LOADAND FAR-FIELD STRESSAND STRAIN

Far-field

Stress,

Load, (Ibs)P % Failure (P/Pf)load* Strain, (.in./in_) _ is (psi)

i ................

200 15% 290 5,860

336 25% 555 9,850

538 40% 1025 15,800

803 60% 1700 23,500

1070 80% 2410 31,400

1270 95% 3010 37,200

18 1.3% 710 530

*Pf = Failure load (average) = 1340 Ibs.

..?

14
t t Specimen

Metal Matrix Composite

6 ply layup [0/+_45]s

Boron/Aluminum

boron fiber dia.= 0.14mm

6.62 44% fiber by volume

Grating--"L, Aluminum 6061 annealed

Slot--- _

Strain

Gage--.

H

--_0.758.-

(inch)

--_ ,- 0.045

Fig. 1 Specimenand loading.

15
Uncured_ .,_

A_hesiv7e;111111111_F.m

Specimen/_ _o.,o_\\\\\\\\\_ c.

oooo..0. ./.

Sur

S.

face

c_me

t \

n_\\\\\\\\\_ \ _ \ \ \ \ \(

_ \/

F,,m

Metallic _Mold

Film ....... _Cured

t'/rT/7-//-M/77/77/7T/7:'a*" Adhesive

Spueci rfacemen""_j___]

Beamfrom

Laser

Specimen

._____= Lens _ (b)

Camera

Fig. 2 (a). Replicationtechniqueto form a high-frequency,highreflectancegrating on the specimen.

(b). Optical arrangementfor moire interferometry.

16
Fig. 3 (a). Ny pattern depicting the Uy displacement field. Contour

interval is 16.4 uin./fringe order in all patterns. P/Pf

= 15%.

17
Fig. 3 (b). Nx pattern for P/Pf = 15%.

18
ii

Fig. 3 (c). Ny pattern for P/Pf = 25%. Numbers give the numerical

values of fringe orders Ny for each contour line, i.e.,

along the center!ine of each fringe.

19
i ̧ ̧

Fig. 3 (d). Nx pattern for P/Pf = 25%. Numbers give the numerical

values of Nx.

2O
Fig. 3 (e). Ny patter n for P/Pf = 40%.

21
Fig. 3 (f). Nx pattern for P/Pf = 40%.

22
Fig. 3 (g). Ny pattern for P/Pf = 60%.

23
Fig. 3 (h). Nx pattern for P/Pf = 60%.

24
Fig. 3 (i). Ny pattern for P/Pf = 80%.

25
i

Fig. 3 (j). Ny pattern for P/Pf = 80%.

26
Fig. 3 (k). Ny pattern for P/Pf = 95%.

27
Fig. 3 (I). Nx pattern for P/Pf = 95%.

28
Fig. 4 (a). Ny pattern depicting the residual Uy displacement field

after specimen was unloaded to P/Pf = 1.3%.

29
Fig. 4 (b). Residual Nx pattern for P/Pf = 1.3%.

3O
O" (psi)

40,000 -

30,000

20,000

I0,000

I I I

0 0 0.001 0.002 0.003 _ Eff

Fig. 5 Longitudinal stress vs. strain for the specimen remote from the

slot. Strains were measured bY the strain gage. Subscript ff

denotes far field.

31
Uy (_in)

I000_

I

8OO

0 I I I I=x

-IOa -OSa 0 0.5a

O T 1 1 1-_'x

-I00

-200

-500 o y = 1.5a

y= I.Oa

"y =0.5a -400

• y : O.Ila

Ux(/.dn)

Fig. 6 Deformation near the slot for P/Pf = 80%. Displacements Uy and

ux are plotted vs. position for 4 horizontal lines.

32
Uy (/..,.in)

I000 -

800 - 600 -

400 -

200

0 I I I I I I- x

-IDa -0.5a 0 O,.Sa

o -:_x

-I00

here-----_ " _ -

-200 - _--- --y=1.5a p/pf

o 95%

_ '--'--'-- - -_x z_80%

-300 - I'- 2a-- o 60 %

• 25%

Ux(Fin)

Fig. 7 (a). Displacements Uy and ux along line y = l.Sa for 4 load

levels.

33
Uy (Fin)

Displ(]cements y

here--,,_ _

I000' - _ _ ___y=a _

' _X

8OO

6O0

400 -

200 -

0 I I I I I I_x

-I.Oa -0.5a 0 0.5Q

o r-'-x

-I00

w%

-200 o 95 %

" 80%

n 60%

-300- " 25%

Ux (p.in)

Fig. 7 (b). Displacements Uy and ux along line y = a for 4 load

levels.

34
Uy (Fin)

I000 _._ _ Displocemenfs

• here Y

8O0

600 xQ

4OO

2OO

0 I I I I I I. x

-I.0o -0.50 0 0.5o

0 x

-I00 -

-2ooo 95 % _

-500 - " 80 7o

__ . " 60% • • 25%

-400 -

Ux (/.dn)

Fig. 7 (c). Displacements Uy and ux along line y = 0.5a for 4 load

levels.

35
Uy (_in)

I000, -

_-Displacements

800 __ " _ _here

600.i --"Y

400 _ 1_2a--

2OO

0 X

-I.Oa -0.5a 0 05a

0 I I I I I _--X

-I00

-200

-300

P/Pf

o 95%

-400 _ 80%

u 65%

• 25%

-500

Ux (M.in)

Fig. 7 (d). Displacements Uy and ux along line y = O.lla (tangent to

edge of slot) for 4 load levels.

36
7'xy, E'x

-0.08 -

I\ S,r.,ns,Y -006,_, ,',er_

-oo,,ik I_ ° :"xy

-0.02 -

- _ \ - 0.010

,- _- 0.005

, , ...,- ,,.. y

0 0 0.5a I.Oa 1.Sa

Fig. 8 (a). Normal and shear strains along the y axis.

37
tttt

Ey Strain

here-__.

0.010

A Ey

0.006 0 Ex

0.004

E X

0.002 - -0.002

- -0.001

0----

0 I ! I _x

0 0.5a I.Oa 1.5a

Fig. 8 (b). Normal strains along the x axis.

38
7'xy

-0.08 -

tttt

-0.06

)7 in

I --12ol--

I

-o.oo I'

/f=8 %

I

I

A

-0.02

-- I

I

I

I I .y 0 0 0.5a l.Oa 1.5a

F_g. 9 Comparisonof shear strains along lines A and B.

39
-0.06 -

-0.05-- here._l A A 4 A

-0.04 i_ _ _StrainS"3h, ere

A Ey P/Pf= 1.3Yo

-o.o2i \ °_ ,,Ey

-o.o, - \ _o.o,oo.oo_?- °_' _''

_'-"Y

o

0 _ I a I a--]-O.O00 _o5

.oo,o

0 0 0.5a I.Oa 1.5a 0 0.5a I.Oa 1.5a _'-X

Fig. I0 (a). Residual strainsalong the y axis.

(b). Residual strainsalong the x axis.
r

_ _.o t t t.t

w_

3.0 o 95 %

A 80%

" 60%

• 40%

• 2_5%

• 15%

2.0

1.0

0 I I I_x

0 0.5a l.Oa 1.5a

Fig. ii (a). Strains _y along the x axis, normalized with respect to

the far-field strain, Eff.

41
/_in/in

EY/o" (ps , )

tttt '

0.4 -

OP/Pf

o 95%

80%

0,2_ '-' 60%

• 40%

A 25%

• 15%

0.1

0 I I I_x

0 0.5a l.Oa 1.5a

Fig. ii (b). Strains Cy along the x axis, normalizedwith respect to

the far-fieldstress, o.

42
EY/Eff

tttt

IO -

B6

4

0

2 -

i

0 I I I I I .= Pip. (%)

.-[ 0 20 40 60 80 I00

Fig. 12 Strain concentrations Cy/Eff at x = y = O, vs. load level.

43
7xY/Ef -_

tttt

Strainst y

-30 - he_

-.t2o -

-25 -

-20

P/Pf I

-15 -- I o 95%

I

I

_ 80%

m 60%

-I0 -

• 40%

• 25%

= 15%

-5 - I

I

i

!

I

.J-- 1 y

0 0 0.5a l.Oa 1.5a

:i

Fig. 13 (a). Shear strains Yxy along the X axis, normalizedwith

respect to the far-fieldstrain, off.

44
(pinlin

_'_,'o_,-,) t ttt

Strains_

-2.5 - here-_ y

===l

!

-2.0 -

0"

-I.5 --

PIPf

o 95%

A 80%

-I.0 - [] 60°Io

• 40% I

I • 25% • 15%

-0.5 -

I

I

I

0 ._z_ 1 Y

0 0.5a I.Oa 1.5a

Fig. 13 (b). Shear strains Yxy along the y axis, normalizedwith

respect to the far-fieldstress, o.

45
YxY/Eff

-55 -

-30 - o 0

-25 -

I

-=o_ I, ffff

-15 - I

I "e_eD

I -_2a_

-_o - I

I

_5 ---_ __

I I I I I _ (%) 0 0 20 40 60 80 I00 "-

Fig. 14 Shear strain concentrationsYxy/_ff at point where shear strain

Yxy is maximum, vs. load level.

46

Standard Bibliographic Page

1.NAsARep178013 ortcR_N°" 12. Government Accession No. 3. Recipient's Catalog No.

I

4. Title and Subtitle 5. Report Date

ELASTIC-PLASTICDEFORMATIONOF A METAL-MATRIX November 1985

COMPOSITECOUPONWITH A CENTRALSLOT 6.PerformingOrganizatiCoonde

7. Author(s)

Daniel Post, RobertCzarnek,Duksung Joh, JinmyunJo, 8.Performing Organization ReportNo.

and Yifan Guo

9. Performing Organization Name and Address 10. Work Unit No.

Virginia Polytechnic Institute and State University

Engi neeri ng Science and Mechanics Dept. ii.' Contracort GrantNo.

Blacksburg, VA 24061 NAG1-343

12. Sponsoring Agency Name and Address 13. Type of Report and Period Covered

Contractor Report National Aeronautics and Space Administration

Washington,DC 20546 14.Sponsoring AgencCode y

506-43-11-04

15. Supplementary Notes

Langley Technical Monitor: W. Steven Johnson

16. Abstract

A comprehensive experimental analysis of deformations of the surface of a metalmatrix specimen is reported. The specimen was a 6-ply [0/+ 45]_ boron-aluminum

tensile coupon with a central slot. Moire interferometryWas u_ed for high-sensitivity whole-field measurements of in-plane displacements. Normal and shear

strains were calculated from displacement gradients. Displacement fields were

analyzed at various load levels from 15% to 95%of the failure load. Deformations

of the boron fibers could be distinguished from those of the matrix.

Highly localized plastic slip zones occurred tangent to the ends of the slot. Shea_

strains and concurrent transverse compressive strains in the slip zones reached

approximately 10%and 1%, respectively. Upon unloading, elastic recovery in surrounding Hegions caused a reverse plastic shear strain in the slip zone of about 4%

Longitudinal normal strains on the unslotted ligament peaked at the slot boundary

at about 1% strain. The strain concentration factor at the end of the slot

decreased with load level and the advance of plasticity.

-.i

17. Key Words (Suggested by Authors(s)) 18. Distribution Statement

Composites Plastic slip

Metal-matrix Moire interferometry Unclassified - Unlimited

Elastic-plastic Experimental analysis

Deformation fields Subject Category 27 Strain distributions

19"rep°rt)uncl Security ass Cl_a'2'sif' i Ti ed this (°f 20.._e page)unc ctti-ity IaSSCli_f.(of 1T1e this . I21"4_"°f Pages122_r_ce

For sale by the National Technical Information Service, Springfield, Virginia 22161

NASA Langley Form 63 (June 1985)

i

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