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CONTENTS

Page

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

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

FRACTURE TOUGHNESS PREDICTIONS . . . . . . . . . . . . . . . . . . . . . . . 2Global Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Local Crack Closure Method . . . . . . . . . . . . . . . 3NASA Lewis 'Unique' Local Crack Closure Method . . . . . . . . . . . . . . 4

FINITE ELEMENT ANALYSIS MODELS . . . . . . . . . . . . . . . . . . . . . . . 4

RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Global Method Results. . . . 6Local Crack Closure Methods Results . . . . . . . . . . . . . . . . . . . 7

LOCAL STRESS FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

FRACTURE TOUGHNESS PARAMETERS . . . . . . . . . . . . . . . . . . . . . . . 10

PREDICTION OF COMPOSITE INTERLAMINAR FRACTURE TOUGHNESS . . . . . . . . . . 10

SUMMARY OF RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

STAR Category 24

INTERLAMINAR FRACTURE TOUGHNESS: THREE-DIMENSIONAL FINITE ELEMENT

MODELING FOR END-NOTCH AND MIXED-MODE FLEXURE

P.L.N. Murthy* and C.C. Chamist

National Aeronautics and Space AdministrationLewis Research Center

Cleveland, ':.0 44135

ABSTRACT

A computational procedure is described for evaluating End-Notch-Flexure(ENF) and Mixed-Mode-Flexure (MMF) interlaminar fracture toughness in unidirec-tional fiber composites. The procedure consists of a three-dimensional finiteelement analysis in conjunction with the strain energy release rate concept and

with composite micromechanics. The procedure is used to analyze select cases

N of ENF and MMF. The strain energy release rate predicted by this procedure is

to in good agreement with limited experimental data. The procedure is used to

Widentify significant parameters associated with interlaminar fracture tough-ness. It is also used to determine the critical strain energy release rate andits attendant crack length in ENF and/or MMF. This computational procedure has

considerable versatility/generality and provides extensive information about

interlaminar fracture toughness in fiber composites.

INTRODUCTION

Interlaminar delamination of composites is a type of fracture mode whichneeds to be carefully examined and properly considered in the design of com-posite structures. Regions prone to delaminations include free edges, loca-tions of stress concentration, ,joints, inadvertent damaged areas and defectsresulting from the fabrication procedure.

One way of properly accounting for interlaminar delamination in a designis to determine interlaminar fracture toughness parameters and then to evaluate,those stress states which are likely to induce interlaminar fracture. Severaltest methods to determine fracture toughness have been proposed and are cur-rently being used. These tests include: edge delamination, double-cantileverbeam (constant and variable thickness), cracked-lap-shear, biaxial interlaminarfracture (ARCAN), and the recently introduced three-point bend tests for ModeII (end-notch flexure (ENF)) and mixed Modes I and II fracture (MMF). Each ofthese test methods has its advantages and limitations (figs. 1 and 2). Thesetests have been the subject of discussion and evaluation at ASTM D30.02 andD30.04 subcommittee meetings and specialty symposia sponsored by these sub-committees (refs. 1 to 3).

At this time it appears that the three-point bend tests, (ENF and MMF,fig. 2) have some unique features over the others-especially for determining

*Research Associate, Cleveland State University.

tSenior Research Engineer, Aerospace Structures/Composites, StructuresDivision.

interlaminar Mode II and mixed mode fracture toughness. These unique featuresstem from (1) the simplicity of the test, and (2) the ability to measure thefracture toughness parameters directly during the test. Recent research

efforts at Lewis Research Center have focused on the development of a computa-tional method (procedure) for simulating the three-point bend test and evalu-

ating interlaminar fracture toughness in unidirectional fiber composites as

determined by ENF and/or MMF. This computational procedure consists of a

three-dimensional finite element analysis in conjunction with the strain energy

release rate concept and with composite micromechanics. The procedure is suit-able for determining global and local interlaminar fracture toughness param-eters as well as critical values of these parameters. The objective of thisreport is to describe the computational procedure in detail and resultsobtained therefrom.

A unique feature of this computational procedure is the consideration ofthe interply layer as a distinct entity and with finite thickness. The inter-ply layer has not previously been included in three-dimensional laminateanalysis (ref. 4) and in fracture mechanics-type computations. The interplylayer neecs to be considered in order to compute accurately those stress fieldswhich induce interply delamination.

FRACTURE TOUGHNESS PREDICTIONS

MSC/NASTRAN three-dimensional finite element static analysis (FEA) withsubstructuring was uses: to determine the structural response variables (dis-

placements, stresses, strains) required for fracture toughness predictions.These structural response variables were used subsequently with three differentmethods to predict the interlaminar and mixed mode fracture toughness. The

three methods used are: (1) the global method, (2) the local crack closure

method, and (3) the NASA Lewis "unique" local crack closure method developedduring this investigation. Each method is summarized below.

Global Method

The specific computational steps for this method are as follows (refer tofio e).

(1) Model the specimen with crack length (a) using three-dimensional fin-ite elements as described later.

(2) Apply a load (P) at specimen midspan.

(3) Calculate the midspan displacement v(a) using three-dimensional FEAas described later.

(4) Induce crack extension oa keeping load (P) constant.

(5) Calculate the midspan deflection [v(a + oa)).

(6) Determine the Strain Energy Release Rate (SERR), G, from

2

,,& P

6 = P x [v(a + &a) - v(a)3/2bea

(1)

where b is the specimen width.

(7) Repeat steps (4) to (6).

(8) Plot results for 6 versus a or ea.

(9) Identify fracture toughness characteristics as described later.

(10) Examine complete stress state near crack tip.

(11) Compare with corresponding uniaxial composite strengths.

(12) Look for possible correlation of fracture toughness with compositeuniaxial strengths.

The global method yields the global fracture toughness without any regard toparticipating and/or dominating local fracture modes.

Local Crack Closure Method

The specific steps for this method are as follows:

(1) Perform steps (1) and (2) _s in the Global Method.

(2) Calculate (u, v, w)a at the --ack tip nodes.

(3) Induce crack extension ea keeping P constant.

(4) Calculate (u, v, w) a + ea at the same node! as in step (2).

(5) Apply unit forces (fx, f y , fz) at these nodes while keeping (P)

and (a + ea) constant.

(6) Calculate corresponding (u, v, w) displacements.

(7) Calculate local forces required to "close" the crack in its respectiveplanes (fig. 2) using the following equations

F

u(a + ea) - u(a) (2)

x u(fx)

F - v(a + ea) - v(a)(3)y v(fy)

F - w(a + ea) - w( a) (4)

z w(fz)

(8) Determine the local SERR's from

G I = F x [v(a + ea) - v(a)]/2b ea (5)

3

to^ ., -- i

GII = F x x (u;a + ea) - u(a)1/2bea (6)

GIII = F x (w(a + ha) - w(a)]/2baa (7)

(9) Repeat steps (3) to (8).

(10) Follow steps (8) to (12) in the Global Method.

The local crack closure method yields the contribution of each local

fracture erode to the composite interlaminar or mixed mode fracture toughness.The global fracture toughness can also be determined since the midspan dis-placement is available from the FEA.

NASA Lewis "Unique" Local Crack Closure Method

The specific steps `or this method are as follows:

(1) Perform steps (1) tcc _. in the Local Crack Closure Method.

(5) Apply enforced dis p lacements (single point constraints) using the stept rt oisplacements (u, v, w 1 a at the crack tip nodes.

(6) Repeat FEA with these single point constraint..(7) Calculate the corresponding forces at these constraints (Fx, Fy, Fz).

These are called the single point constraint forces in FEA.

(8) Calculate the respective SERRs using equations (5) to (7) with theFx, Fy, and F. from step (7).

(9) Repeat steps (1) to (8).

(10) Follow steps (8) to (12) in the Global Method.

The NASA Lewis method is a aviation of the local crack closure method.

The variation arises from the unique FEA feature: the single point constraintforce. It is also conceptually simpler than the local crack closure method andhas the added advantage of preserving the characteristic of monotonicallyincreasing displacement under the applied load with crack extension. On theother hand, it is possible to obtain reversal in this displacement when using

the local crack closure method. Comparisons of results predicted using thesetwo methods are made in a later section.

FINITE ELEMENT ANALYSIS MODELS

The entire specimen was modeled, including the interply layer, using thethree-dimensional finite elements available in MSC/NASTRAN. A schematic of themodel with the actual dimensions used is shown in figure 3. The specimenmodeled is the same as that currently bein g evaluated by the ASTM D30.04 sub-committee for a possible standard test method to determine Mode Ii (using ENF)

and mixed Mode I and II (using MMF) fracture toughness. The interply layersand the individual plies are modeled in the vicinity of the crack. Theremaining plies ar e grouped as shown schematically in figure 4.

4

-A

A three-dimensional computer plot of the finite element model is shown infigure 5. The specimen was modeled using 1536 solid elements for a total of6090 degrees of freedom (00F). A superelement was used in the crack vicinity.A two-dimensional computer plot of the superelement is shown in figure 6. Thesuperelement contained 360 solid elements, 450 nodes (1350 DOF). The displace-ment boundary conditions (fig. 3) are:

U. v=o at x, y=o

v=o a* x=t, y =o for ENF

x=t, y = t forMMF2

w=o at x=o and t (8)

y = o for ENF

y = t for MMF2

z = b2

A line load was applied at the specimen midspan (fig. 2). The magnitudeof this load was 120 lb. This magnitude corresponds to the experimental loadwhich induced unstable crack propagation as reported in the ASTM D30.02 sub-committee meeting (April 1984). The crack extension propagation was simulatedby progressively deleting interply layer elements and repeating the FEA as

described in the previous section. The justifications for deleting the elementinstead of the conventional line opening using double nodes are as follows:

(1) The interply layer element is very thin (about 10 percent of the

fiber diameter).

(2) Photomicrographs of the fractured surface generally show relativelylittle resin residue indicating that the interply layer is destroyed duringt!,e fracture process.

(3) The crack does not remain at the midplane of the interply layer butmeanders between the fiber surfaces of the adjacent plies.

The composite material simulated was AS-graphite fiber/epoxy matrix (AS/E)unidirectional composite. The constituent material properties are summarizedin table I assuming room temperature dry conditions. Five different unidirec-

tional composites were simulated with the following fiber volume ratios (FVR):0.30, 0.55, 0.60, 0.65, and 0.75. The unidirectional ply properties, the

interply layer thickness and its properties, and the appropriate material

properties required for the three-dimensional finite element analysis weregenerated with the aid of ICAN (Integrated Composite Analyzer), (ref. 5). The

properties for the interply layers were assumed to be the same as those for thematrix. The three-dimensional composite properties (using MSC/NASTRAN designa-tion) and interply layer thickness predicted by ICAN are summarized in

table I1.

5

Even though room temperature dry conditions were assumed in this simula-tion, hygrothermal environmental effects can readily be simulated using the

theory (ref. 6) embedded in ICAN to predict the corresponding composite prop-erties. Other composite systems including (1) intraply hybrids, (2) interplyhybrids, (3) intra/inter ply hybrids, (4) composites with perforated interplylayers, and (5) composites with different void content can readily be simulated

using ICAN.

RESULTS AND DISCUSSION

The results obtained together with appropriate discussions, interpreta-

tions, and possible implications are summarized below first for the globalmethod and second for the local crack closure methods. The results are

presented graphically where midspan displacement and SERR are plotted versuscrack propagating length for the five different fiber volume ratios (FVR). Inaddition, graphical results are presented for the stress field behavior in the

vicinity of the crack and also the variation of maximum stress magnitudesversus crack propagating length. The maximum stress magnitudes are assumed tobe at the centroid of the interply element in the superelement ahead of thecrack tip.

Global Method Results

The midspan displacement versus crack propagating length for the fivedifferent fiber volume ratios is shown in figure 7 for the ENF specimen.. The

midspan displacement decreases with increasing fiber volume ratio. Also, themidspan deflection increases gradually with crack opening length up to abouta =1.20 in, and then increases rapidly. The corresponding SERR GII

determined using the global method described previously (Eq. (1)) is shown infigure 8. The authors interpret the behavior shown in figure 8 to beassociated with interlaminar composite fracture characteristics as follows:

(1) The initial portion of the curves (a < 1.05 in) represents slow crack

growth.

(2) The intermediate portion (1.05 in < a < 1.20 in) represents cable

crack growth.

(3) The rapid increase (rise) (a > 1.20 in) represents unstable, andtherefore rapid crack propagation to fracture.

The SERR GII varies approximately inversely with FVR as would be

expected since it is calculated from the midspan displacement which also variesinversely with FVR.

The corresponding results for MMF are shown in figure 9 for displacementand in figure 10 for SERR G. These curves exhibit the same behavior as thosefor ENF and, therefore, exhibit similar interlaminar composite fracturecharacteristics. A comparison of the curves in figures 8 and 10 reveals thatthe interlaminar fracture characteristics for ENF and MMF are almost identicalfor the same load. Again, this is anticipated since they are both determined

using the midspan displacement which is about the same for the two cases.

6

D^E

The results in figures 8 and 10 show that the anticipated "global" com-posite interlaminar fracture strain energy release rate can be predicted byconducting three-dimensional finite element analyses on ENF and MMF specimens

and using the global method. In addition, these results show similar char-acteristics for shear (Mode II) and mixed (Mode I and II) fracture. One con-

clusion from the above discussion is that the global method is quite general

for determining the mixed mode composite interlaminar fracture characteristics.Embedded cracks, multiple cracks, crack location, specimens of uniform andvariable cross sections, and different laminate configurations can be just as

easily handled as the two cases already described. The global method generallydoes not separate the contribution of each mode. However, these contributionscan be determined by the local crack closure methods as described in the nextsection.

Local Crack Closure Methods Results

The Mode II SERR, determined using the local crack closure method(eq. (6)), is shown in figure 11 (dashed line) for 0.6 FVR. The curve deter-mined using the global method is also plotted for comparison. The range of

experimental data reported in the ASTM D30.02 subcommittee meeting is shown bydashed horizontal lines. Three points are worth noting in figure 11:

(1) The global method predicts higher GII values than the local crackclosure method.

(2) The two methods predict similar composite intralaminar fracture.behavior.

(3) The measured data coincide with the rapid rise in both curves.

Accordingly, two general conclusions can be drawn:

(1) The rapid rise in the SERR (G II ) versus crack length (a) coincides

with the measured critical GII.

(2) A conservative assessment of the composite interlaminar fracturecharacteristics can be obtained by using the G II determined from the local

crack closure method.

The mixed mode (I and II) composite interlaminar fracture characteristics,

determined from the local crack closure method (eqs. (5) and (6)), are shownin figure 12 for a composite with 0.6 FVR. The fracture characteristics foreach mode (Mode I and Mode II) are compared with those predicted for the mixed

mode by using the global method (solid line) and the algebraic sum of the twomodes from the local method (short dashed line). The following observationsare worth noting in figure 12:

(1) Both the local crack closure and the global methods predict similarmixed mode (Mode I and II) fracture characteristics.

(2) The local crack closure method predicts lower mixed mode G valuesthan the global method.

o.

(3) Mode II fracture dominates the crack extension during slow and stablecrack growth (a < 1.05 in).

(4) Mode I dominates the crack extension during unstable crack growth andrapid crack propagation (a > 1.15 in).

(5) Mode I has slightly negative values (a < 1.15 in) indicating local v(predicted by eq. 5) displacement reversal.

The general conclusions to be drawn from the above observations are:

(1) The contribution of each fracture mode can be determined using thelocal crack closure method.

(2) Mode I drives the composite interlaminar delamination in MMF

specimens.

(3) The local method provides a conservative assessment of mixed modecomposite interlaminar fracture characteristics as was the case for Made II.

The mixed mode (Mode I and II) composite interlaminar fracture charac-teristics predicted using the Lewis method (local single point constraints) areshown, in figure 13. The characteristics predicted by using this method arepractically the same as those observed in figure 12. One exception is thatMode I is positive for all 'a' and, thus, this method preserves the v dis-placement monotonicity. A typical value for GI is about 0.6 psi-in at the

onset of rapid crack propagation for this type of composite. Th's coincideswith the rapid rise in Mode I (figs. 12 and 13). It is important to note thatthe contribution of each mode to mixed mode fracture can be jetermined, within

acceptable engineering accuracy, by either of the local mF'.hods describedherein. The local crack closure method, however, is easier to implementcomputationally based on the authors' research experience.

The composite interlaminar opening mode fracture was also determined bysimulating a double cantilever beam (DCB) specimen with the same geometry and

loads used in the ENF and MMF. The results are shown in figure 14 for both the

's global and the local methods. The general fracture characteristics are similar

to those determined for Mode I by the local methods of the MMF (figs. 12 and

13). The significant exception is that the opening fracture mode of the DCspecimen becomes unstable at a smaller crack opening compared to the MMFspecimen.

Apparently the presence of Mode II increases the resistance to Mode Ifracture. This is consistent with experimental observations (ref. 1). The

significant conclusion is that the local crack closure methods predict the

magnitude of the opening mode contribution and its dominance to rapid crackpropagation in mixed mode fracture reasonably well.

LOCAL STRESS FIELDS

End-Notch-Flexure. - The averaged across-the-width stress field behaviorin the interply layer in the ENF is shown in figure 15. Interestingly, allthree stresses oxx, oyy, and oxy have approximately the same magnitude in

the element next to the crack tip. The two normal stresses (oxx and oyy)

8

J4

are compressive, monotonic, and decay rapidly with distance from the crack tipas would be expected from the near-singular stress field. On the other hand,

the shear stress exhibits oscillatory behavior near the crack tip, decreasesto a relatively constant value and then slowly decays to the value predictedby simple beam theory. At this time the aithors suspect that this oscillatorybehavior may be real. Two supporting reasons are:

(1) The proper behavior of the two normal stresses gives confidence in theanalysis, and

(2) The relatively constant value of the shear stress at a distance from

the crack-tip greater than 0.05 in.

The peak stress field behavior (stress in the interply layer crack tip

element) versus the extending crack length is shown in figure 16 for 0.6 FVR.Also shown in this figure is the interlaminar shear strength predicted by usingthe composite micromechanics equations programmed in ICAN. The peak shearstress (axy) reaches relatively high values during the slow crack growthstage and remains practically constant during the stable crack growth stage(fig. 8). The peak shear stress exceeds the corresponding strength forpractically the entire extending crack distance. The peak value of the

through-the-thickness normal stress (a y) is substantial (comparable toOxx) and it is compressive throughout she extending crack distance. This

compressive normal stress will tend to close the crack and thus e-hance theinterlaminar resistance to Mode II type fracture.

It appears that the rise in the peak shear stress is associated with anincrease in the normal compressive oyy stress. The peak normal stress(oxx)• along the specimen span, is also compressive and has about the same

magnitude as ayyy. Both of the normal compressive stresses tend to crush thefractured interply layer and, therefore, provide additional credence to sim-ulating the extending crack by deleting the interply layer crack-tip element.

The significant conclusion from the above discussion is that interply ModeII fracture occurs when the corresponding shear strength is exceeded. Thisconclusion can be used to determine critical fracture toughness parameters as

will be described later.

Mixed-Mode-Flexure. - The corresponding average stress-field behavior inthe MMF is shown in figure 17. The two normal stresses (o and axx)exhibit singular monotonic stress behavior while the shear y stress (axy)exhibits oscillatory behavior near the crack tip and becomes constant there-after. Three points worth noting are:

(1) ayy has the highest magnitude in the crack-tip element.

(2) Both normal stresses are tensile while they were compressive in theENF specimen.

(3) The shear stress magnitude beyond the crack tip vicinity is about thesame as that in the ENF flexure specimen (fig. 15).

The peak stresses in the MMF specimen versus extending crack-tip distanceare shown in figure 18. Also shown in this figure are the corresponding

interlaminar shear and transverse tensile strengths predicted using ICAN.

9

Both stresses (a and ax ) exceed their corresponding strengths forpractically thentire exteiding crack-tip distance. Additionally, a

rises more r 4 :-'.dly while axy remains approximately constant for extending

crack-tip distances greater than 0.150 in. These result are consistent withthe SERR G behavior (fig. 10) and demonstrate that the MMF specimen is sub-

jected to both opening mode (Mode I) and shear mode (Mode II) type fractures.

The significant conclusion from the above discussion is that mixed mode

fracture occurs in MMF specimens when the stresses ayy and/or axyexceed their corresponding strengths. This is consistent with the conclusionstated previously for the ENF specimen. It has the same significant implica-tions and can be used to determine mixed mode fracture toughness as will be

described later.

FRACTURE TOUGHNESS PARAMETERS

During the course of this investigation, it became evident that composite

interlaminar fracture toughness is associated with several intrinsic properties

of the composite. The most obvious ones include interply .,er thickness,

interlaminar shear strength and transverse tensile strength. These are inaddition to the well known critical strain energy release rate (SERR), criticalstress intensity factor and crack length. Furthermore, the intrinsic composite

properties depend on composite constituent material properties and on fibervolume ratio (FVR) and, as a result, are not independent. Their interdepend-ence can be determined by composite micromechanics (refs. 8 and 9).

The effects of fiber volume ratio on the fracture toughness parameters arepresented graphically in figure 19 for ENF (Mode II) fracture and for a 120 lbload. The parameters plotted are: interlaminar shear strength, SERR and

interply layer thickness for three different crack lengths (ea). The interest-ing points to be noted are:

(1) The SERR decreases with increasing FVR (rapidly at low FVR (about0.30) and more slowly at high FVR (about 0.70)).

(2) Both the interlaminar shear strength and the interply layer thicknessdecrease with increasing FVR and at a progressively faster rate.

Both of these lead to the conclusion that fiber composites with relativelyhigh FVR will have lower fracture toughness compared to those with intermediate(about 0.5) or low FVR. Another, and perhaps by far more important, conclusionis that composite mechanics in conjunction with three-dimensional finite ele-ment analysis provide unique computational analysis methods for describing/-

assessing the fracture toughness of fiber composites in general.

PREDICTION OF COMPOSITE INTERLAMINAR FRACTURE TOUGHNESS

The results of this investigation taken collectively lead to a general

computational procedure for predicting unidirectional composite interlaminarfracture toughness using the End-Notch-Flexure (ENF) and/or Mixed-Mode-Flexure(MMF) methods. In developing this procedure, the critical parameters associ-

ated with the fracture toughness of the composite are revealed. This procedureconsists of the following steps:

10

_Q;^

(1) Determine the r e q u i s i t e proper t ies a t the deslred ~ 0 n d I t l ~ n ~ using cornposlte mlcromechanlcs. These requisite proper t ies w i l l be s l m l l a r t o those s u m r l z e d l a t ab le 11.

( 2 ) Run a three-dlmenslonal f l n l t e element ana lys is on an ENF o r WF specimen ( f i g . 2) f o r an a r b l t r a r y load uslng f l n l t e element models s l m l l a r t o thosn descrlbed here ln ( f l g s . 3 and 4) . Note t h a t the superelement I s no t necessary although i t expedl tes the computations.

(3 ) Scaie the a r b i t r a r y load I n step (2 ) t o match l n te r l am lna r shear stress ar through-the-thickness normal s t ress I n t he c rack - t l p element w l t h the ln ter lamlnar shear s t rength or the through-the-thickness normal s t rength o f the composlte. Note t h a t t h l s element I s next t o the crack t i p .

(4 ) PUP several f l n l t e element analyses w l t h the scaled load and progres- s i v e l y extsndlng crack length (a) .

(5) Calculate s t r a l n energy release rates (6 ) uslng the approprtate equations (eqs. ( I ) , (5) , (6) . o r ( 7 ) ) .

(6) P lo t the curve G ca lcu la ted a t step (5) versus a. Th l r curve i s s l m l l a r t o those I n f i gu res 11 t o 13.

( 7 ) Construct two tangents t o the curve as fo l lows: (a ) through the s lowly r l s l n g p o r t l o n o f the s tab le crack ~ ; , o w t h

reg lon (b) through tCc r a p i d l y r l s l n ~ p o r t i o n o f the unstable crack growth

reglon.

(8) Select the c r ~ t i c a l G ( s t r a i n energy release ra te ) value and the c r l t i c a l crack- length from the In te rsec t i on o f the two tangents i n steC ( 7 ) . The steps fo r t h i s procedllre are s u m r l z e d together w l t h a rcher,atIc I n f i g u r e 20 f o r convenjence.

I t I s Important t o note tha t t h l s procedure has no t been v e r l f l e d w i t h appropr lzte exper:mental data other thaq t h a t descrlbed herein. lhere fore . 1~ should be used j ud i c i ous l y u n t i l s u f f i c e n t l y w e l l va l ida ted. However, I t provides a convenlent computatlonal method f o r l n l t l a l screening o t candidate composites t o se lec t those whlch should meet In ter laminar f r a c t u r e toughness deslgn requirements. I t a lso provldes a d i r e c t means f o r quan t t f y l ng values f o r c r l t l c a l s t r a i n energy re lease r a t e (G) and i t s correspnndlng c r l t l c a l length (a) on whlch deslgn c r l t e r l a can be based. I t t s the authors ' con- sidered techt.lca1 judgment t h a t proper use o f t h l s computational procedure provldes de ta l l ed in fnrmat ion whlch can be used t o describe, assess, and p r e d i c t composlte ln tc r iamlnar f r a c t u r e toughness. As a r e s u l t , composite s t ruc tures can be designed t o meet t h l s h l t h e r t o e lus l ve c r i t i c a l design requlrement. Thls computational procedure has constderable v e r s a t i l l t y and gene ra l i t y as was prev ious ly discussed.

SUWWARV OF RESULTS

The s i g n i f i c a n t r e s u l t s o f an Inves t l ga t ton of comi;osIte 1nterla;nlnar f r a c t u r e determlned by the computatlonal simulation of end-notch-'lexure (ENF) and mlxed-mode-flexure (HHF) are s u n a r l z e d below:

1. Three-dlmenslonal f l n l t e element analysis i n conjunction w l t h composl t e nechanlcs provldes a d l r e c t conputat lonal method f o r determlning the l n t e r - larnlnar f r a c t u r e toughness i n un ld l rec t l ona l composites.

2. The s i g n l f i c a n t composite proper t ies associated w l t h composlte I n t e r - lamlnar f r ac tu re toughness are: (a) ln ter lamlnar shear strength, (b) t rans- verse t e n s l l e strength, (c ) l n t e r p l y layer thickness, and (d) f l b e r volume r a t i o .

3. Three methods are su l t ab le t o computatlonally determlne the l n t e r - lamlnar s t r a i n energy release r a t e (SERR): (a) the g loba l method. (b) t he l oca l crack c losure method, (c ) the l o c a l s l ng le p o l n t constrained fo rce (Lewls) method. However, on ly the l o c a l methods are s u l t a b l e f o r determining the cont r ibu t ions o f each f r a c t u r e mode.

4. The global method p red l c t s h lgher SERR compared t o l o c a l methods dur lng slow and s tab le crack growth. However, a l l th ree methods tend t o converge dur lng rap ld l y lncreaslng s t r a i n energy release r a t e (SERR) uh lch Ind ica tes unstable crack growth.

5. Predicted SERR f o r shear (Mode 11) and mlxed mode ( I and 11) l n t e r - laminar f r ac tu re are I n good agreement w i t h l l m l t e d measured data.

6. Mode I 1 (shear) dominates ENF whi le Mode I (openlng) dominates the unstable crack growth I n MMF.

7. Mode 11 (shear) unstable crack growth occurs I n ENF when the 1nte.r- lamlnar shear stress i n t e n s i t y (as determined hereln) exceeds i t s correspondlng shear strength.

8. Mixed mode ( I and 11) unstable crack growth occurs I n MMF when the through-the-thickness normal st ress I n t e n s l t g (as determined hereln) exceeds i t s correspondlng transverse t e n s l l e strength.

9. A computatlonal procedure was developed t o determlne the c r i t i c a l SERR and i t s attendant crack length associated w l t h ENF and/or MMF f rac tu re .

REFERENCES

1. Sendeckyj, G.P., Ed., Fracture Mechanics o f Cornposltes, ASTM STP-593, American Society f o r Test lng and Mater ia ls. Phi ladelphla, PA. 1975.

2. Rel fsnider. K.L., Ed., Damage i n Com~osi te Mater ia ls , ASTM STP-775, Amerlcan Soclety f o r Test lng and Mater ia ls, Phl ladelphia. PA, 1982.

3. Wllkins. D.J., Ed., E f fec ts o f Defects i n Composite Mater ia ls. ASTM STP-836, Amerlcan Society f o r Test lng and Mater ia ls. Phl ladelphia, PA, 1984.

4. Murthy. P.L.N. and Charnls C.C., C,.rnouters and Structures, Vol. 20, No. 1-3, 1985, pp. 431 -441.

5. Uurthy. P.L.N. and Chamls, C.C., 'ICAN: In tegra ted Composites Analyzer,' AIAA Paper 84-0974, American I n s t l t u t e of Aeronautics and Astronaut ics , New York, Uay 1984.

6. Charnls, C.C., Lark, R.F., and S lnc la i r , J.H., I n Advanced C m o s i t e Mater ia ls - Envlronmental Ef fects. ASTU STP-658, J.R. Vlnson, Ed., American Soc1et.y f o r Test lng and Mater ia ls, Phlladelphla. 1978, pp. 160-192.

7. VL,1derkley, P.S., @Mode I - Mode I1 Delaminatton Fracture Toughness o f a Un ld l rec t iona l Graphlte/Epoxy Composite,' Master o f Science Thesis, Texas A L M Unlversl ty, 1981.

8. Chamls, C.C., SAUPE Quarterly, Vol. 15, No. 3, Apr. 1984, pp. 14-23.

9. Chamls, C.C., M P E Quarterly, Vol. 15, No. 4, Ju ly 1984, pp. 41-55.

TABLE I. - CONSTITUENT MATERIAL PROPERTIES USED IN THE

SIMULATION

Property Units Fiber MatrixAS-graphite intermediate-modulus

high-strength

, Symbol Value Symbol Value

!Elastic moduli i x106 psi i E fll 31.00 Em 0.5

E f22 ! 2.00Gf12 2.

Of23 1. 6m .1852Poisson's ratio' -------- vf12 ':, 0.2 vm .35

vf23 0.25Strengths ksi SfT 400 ! SmT 15

Sfc 400 Smc 35

Sms,Fiber diameter inch df I 0.0003

113

{ - 'r."'^"y —- __....ore

1

TABLE II. - COMPOSITE PROPERTIES PREDICTED BY ICAN AND USED IN THREE-DIMENSIONAL FINITE ELEMENTS

Property Units MSC/NASTRAN Designation

Symbol Fiber volume ratio

0.30 0.55 0.60 0.65 0.75

Elastic x106 lb/in2G11 12.420 20.023 21.478 22.921 25.782constants in the G21 = G12 0.734 0.629 0.615 0.602 0.583stress/strain G31 = 013 .734 .629 .615 .602 .583relationship for G41 = G14 .000 .000 .000 .000 .000unidirectional G51 - G15 .000000 .000 .000 .000AS/E composite G61 = G16 .000 .000 .000 .000 .000

G22 1.412 1.511 1.549 1.593 1.704G32 = G23 .863 .7?1 .710 .691 .654G42 - G24 .000 .000 .000 .000 .000G52 - G25 .000 .000 .000 .000 .000G62 = G26 .000 .000 .000 .000 .000

I G33 1.544 1.620 1.654 1.694 1.800G43 = 534 .000 000 .000 .000 .000

IG53 G35 .000 .000 .000 .000 .000G63 = G36 .000 I .000 j .000 .000 .000

1G44 .368 .5b6 .623 .690 I .865

654 = G45 I .000 .000 .000 LOU .000G64 = G46 .000 .000 .000

I.000 .000

G55^G65 = G56

.245 .336

.000 .000.362000

.394

.000.476.000

G66 .368 .566 .623 .690 .865Interply Byer

I

propertiesmoduli x101 lb/in 2 ` E 5 .5 .5 .5 .5

Thickness _v

incn 6.35 .35

0.1854x10-3 0.5850x10 -4.35

0.4323x10 -4.3

0.2977x10 -4.35

0.6998x10-5

1

II I

1EDGE -DELAMINATI ON

MIXED MODE

II & III

DOUBLE CANTILEVER CRACK-LAP-SHEAR

OPENING MODE (I) SHEAR MODE

III)

Figure 1. - Schematics of test methods for measuring interlaminar fracture toughness.

A

Y,v

a --+

l

ORIGIN END-NOTCH-FLEXURE (ENF)--SHEAR MODE (I1)

X, u p

Z, w

r—a-

MIXED-MODE-FLEXURE (MMF) —MIXED MODE (I II)

Figure Z - Schematic of flexural test for interlaminar fracture mode toughness.Note: Origin at left support bottom,

niw IV

P • 120 lb

Z

0.5" 1--- V

Figure 3. - Model geometry and F. F. schematic.

1 "/A

2

X

-{ 0. 5" 1---

INTER PLYLAYERS

Figure 4 - Schematic of F. L model through-the-thicknessietails.

I

y, i

CS

)ELEMENTSHEDRANS ANDWEDRANSI

6090 DOF

SUPER ELEMENT IN CRACKREGION

tl

Figure 5.- 3-D finite element model.

Figure 6. - Crack region superelement model details-front view. Superelement statistics:360 solid elements (326-node pentahedrans, 328 8-node bricks) 450 nodes, 1350 DOF.

1.0"r120 Ib ti ^ a

12'

^MIDSPAN

55

60

65

75

FVR

.30

c

ziOUWzaNcm

. .V

1.0 1.05 1.10 1.15 1.20 1.25CRACK LENGTH, a, in

Figure 7. - Fiber volume ratio effects on midspan deflection. End-notch-flexure (AS1E).

120 Ib

0T^MIDSPAN 17.7

DEFLECTION (W) FVR6.0 4 0^ —__^ 0.30

c48a

0.55

0.60j,43.6

W \

2.40.75

> 0.65

W 1,2zW

0

1,00 1.05 1.10 1.15 1.20 1.25CRACK LENGTH, a, in

Figure 8. - Fiber volume ratio effects on Mode II energy release rate,End-notch-flexure (ASIE).

120 lb

2"

L wnf DAKI

FVR

0.30

0. 550.600.650.75

20

c .16

^ .12r-c.>

o .08zo-0f .04

6.0

c4,8

6V

3.6

W

tJ 2.4

c^

iz 1.2

1, I

.._7117

0 1 1 1 1 1 1

1.0 1.05 1.10 1.15 1.20 1.25CRACK LENGTH, a, in

Figure 9. - Fiber volume ratio effects on midspan deflection, Mixed-mode-flexure (ASIE).

120 lb a^

017 2"

i MIDSPAN 17,7

DEFLECTION IWI

D 1 — I I 1 1 1

1.00 1.05 1.10 1.15 1.20 1.25CRACK LENGTH, a, in

Figure 10, - Fiber volume ratio effects on mixed mode ( I & III. Mixed-mode-flexure (ASIE).

1.0"^120 Ib ^ ate{

0:r2I

T ^MIDSPAN r

DEFLECTION lWl 14 }`-- — 4.0" — — •^ 11

1 MODE (II)—"'--^---'—"— t---^ MEASURED

RANGE3 ------ /'—^\ --- Jt-----

2

cleQ /

WN /GLOBAL

} 1 ---- LOCAL

wZ D I IW

1.0 1.1 1.2 1.3CRACK LENGTH, a, in

Figure 1L - End-notch flexure energy release rate-comparison,

5 17.7 17.1 }14.6

11o1.0"^

120 lb I ^• a—^

4r

3 ,: I MIDSPAN iDEFLECTION IW1

s

2 sf f

> I

o"c ( GLOBAL MIXED lI & III

1 ; ----- LOCAL MIXED 41 & 11)/ LOCAL I

/' — -- LOCAL 11

1.0 1.1 1,2 1.3CRACK LENGTH, a, in

Figure 12. - Mixed-made-flexure energy release rate and components (ASIE). Local closuremethod,

-C

5 17.0117,73 14.5

i

1.0" ^`120 lb a

4

_ ► ' 01iS i ►

3 ' ^ MIDSPAN'^

.

Z-' ► I DEFLECTION W

Ioc ►

1 MODE

GLOBAL MIXED lI & III

— LOCAL MIXED Q& III0^ --- LOCAL I

LOCAL II

-1.01.0 1.1 1.2 1.3

CRACK LENGTH, a, in

Figure 13. - Mixed-made flexure energy release rate and components (ASIEI. Singlepoint constrained (Lewis) method.

1000

c

n 100

aWN

WQ'

10d'W-LW

1.0 1 1 1 1 1 ,

1.0 1.1 1.2 1.3CRACK LENGTH, a, in

Figure 14, - Double-cantilever energy release rate-comparisons(AS IE).

NNW

C4

15

O X7

12°x7 ' °Yz ' °zz ' 0 y ^^LAYER

9 x

z

6 oxy CRACK

TIP

Y 3

z o yy

N 0W1N 3°xx

-6

acyy-12

150 .050 .100 .150 .200 .250

DISTANCE FROM CRACK-TIP, in

Figure 15. - Stress field in interply layer near crack tip, End -notch -f;exure (ASIE).

X0_°xz ' 3 Y ' a zz ° 0 Y

J-- x

21.0 z CRACK TIPr o xy ELEMENT

z 12.0

W

3.0

°xx-6.0

a yy J0 .05 .10 .15 .20 .25

EXTENDING CRACK-TIP DISTANCE, in

Figure 16.- Peak stress behavior in interply layer with crack extension. End-

notch-flexure (AS/E).

i

-3 ;

0 .05 .lo0 .150 .200 .2M DISTANCE FRW CRACK-TIP. i n

Figure 17. - Stress field Ir! interply layer near cradt tip. Mixed-mcde-flexure MSIEI,

\ L' - ELEMENT

.05 . l o I S .n .a EXTENDING CRACK-TIP DISTANCE. in

Figure 18 - Peak s t r m behavior at crack tip with crack extension. Mixed-mode- fracture MSIEI.

0 INTERLAMINAR SHEAR STRENGTH A INTERPLY LAYER THICKNESS 000 MODC ;: EiGRGY RELEASE RATE

20- - 10-3

- k l-llo-6 5 0.0 a30 a% a 7 0 aw

FIBER VOLUME RATIO

Figure 19. - Flber volume ratio effect on lnter lamlnar f raclure toughness parameters. End-notch-flutura (ASIELI

DETERMINE REQUISITE PROPfRlTES AT DESIRED CONDITIONS USING COMPOSITE

MICRWCHANICS

RUN 9 0 FINITE ELEMENT ANAlYSlS ON ENF lMMFl SPECIMEN FOR AN ARBITRARY LOAD

SCALE LOAD TO MATCH INTERLAMINAR SHEAR STRESS AT ELEMEM NXT TO CRACK-TIP

W m t SCALED LOAD DTEND CRACK AND PLOT STRAIN ENRGY REEASE PATE VS CRACK LENGTH G - - - - -- - SELECT C.RITICAL "G" _

AND CRITICAL "a" I ,-

I

METHOD HAS VERSATIUNIGENERALITY Extended crack length, a

Figure 20. - Genera! p r o c d u r e for p r d i c t i m ~ wmposlte lrlterlamlnar frac'ure toughness using the end-n,!tch-flexure lENFl or m l x d m c d e - f l u u r e IMMF) method

1. Aepoft ,.,. 2. Oo¥emment Acceulon No.

NASA TM-81138 • . TItle and Subtitle

InterlaM1nar Fracture Toughness: Three-01mens1onal F1n1te Element Mode11ng For End-Notch and M1xed­Mode Flexure

7. Aut!tof(a,

P.L.N. Murthy and C.C. Cham1s

I . PerformIng OrgMlUlion NMIe and Add .....

Nat10nal Aeronaut1cs and Space Adm1n1strat1on Lew1s Research Center Cleve~and, Oh10 44135

12. 8poneorIng Agency NMIe and Add .....

Nat10nal Aeronaut1cs and Space Adm1n1strat1on wash1ngton, D.C. 20546

15. Supplementary Not"

3. Reclplent'a cataIoO No.

5. ~Det •

•. Perfonnlng 0fgM1zal1on Code

505-33-18 • . Perfonnlng 0fgM1zal1on Aepoft No.

E-2626

10. Wotk Unit No.

11. Contraet or Orant No.

13. Type 01 Report and '-loci eo-.d

Techn1cal Memorandum 1 •. Sponeoring Aeency Code

Prepared for the S)mpos1um on Toughened Compos1tes sponsored by the Amer1can Soc1ety for Test1ng and Mater1als. Houston. Texas, March 13-15, 1985.

" . Abetraet

A computat10na1 procedure 1s descr1bed for evaluat1ng End-Notch- Flexure (ENF) and M1xed-Mode-flexure (MMF) 1nterlam1nar fracture toughness 1n un1d1rect1onal f1ber compos1tes. The procedure rons1sts of a three-d1mens1onal f1n1te element analys1s 1n conjunct10n w1th the stra1n energy release rate concept i~~ w1th compos1te m1cromechan1cs. The procedure 1s uied to analyze select cases of ENF and MMF. The stra1n energy release rate pred1cted by th1s procedure 15 1n good agreement w1th l1m1ted exper1mental data. The procedure 1s used to 1dent1fy s1gn1f1cant parameters assoc1ated w1th 1nterlam1nar f racture toughness. It 1s also used to determ1ne the cr1t1cal stra1n energy release rate and 1ts attendant crack length 1n ENF and/or MMF. Th1s computat1onal procedure has cons1derable versat1l1ty/genera11ty and prov1des extens1ve 1nformat1on about 1nterlam1nar ~racture toughness 1n f1ber compos1tes.

17. Key Wordl (Suggelted by Authol1l))

~tational procedure; Stra\n-energy release rate; CaIpos\te m\cranechan\cs; Shear node; Pbie II fracture; Open\~ node; ftode 1 fracture,' Global _tloI' local methods' Three-dimenstona stresses; ~tte ftrengths; Graphtte ftber· Epolty matrb; Crick open ng; Interply layer; Fr"ciunt toughness

18. Dlltrlbullon Statement

Unclass1f1ed - un11m1ted STAR category 24

11. Security Cle .. lI. (01t1111 report,

Unc lass H 1ed 20. Security CI .. III. (01 tl111 page,

Unc las s H1 ed 21 . No. 01 paget

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