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THIS DOCUMENT HAS BEEN REPRODUCED FROM MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED IN THE INTEREST OF MAKING AVAILABLE AS MUCH INFORMATION AS POSSIBLE
1 LL
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CONTENTS
Page ABSTRACT .
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INTRODUCTION .
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FRACTURE TOUGHNESS PREDICTIONS . . . . . . . . . . . . . . . . . Global Method Local Crack Closure Method . . . . . . NASA Lewis 'Unique' Local Crack Closure
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FINITE ELEMENT ANALYSIS MODELS .
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RESULTS AND DISCUSSION . . . . . . . . Global Method Results. . . . Local Crack Closure Methods Results
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6 6 7 8
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LOCAL STRESS FIELDS
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FRACTURE TOUGHNESS PARAMETERS
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PREDICTION OF COMPOSITE INTERLAMINAR FRACTURE TOUGHNESS SUMMARY OF RESULTS . REFERENCES .
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. 12
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 Administration Lewis Research Center Cleveland, ':.0 44135
ABSTRACT A computational procedure is described for (ENF) and Mixed-Mode-Flexure (MMF) interlaminar tional fiber composites. The procedure consists element analysis in conjunction with the strain with composite micromechanics. The procedure is
N to
evaluating End-Notch-Flexure fracture toughness in unidirecof a three-dimensional finite energy release rate concept and used to analyze select cases
of ENF and MMF. The strain energy release rate predicted by this procedure is in good agreement with limited experimental data. The procedure is used to
Widentify significant parameters associated with interlaminar fracture toughness. It is also used to determine the critical strain energy release rate and its 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 which needs to be carefully examined and properly considered in the design of composite structures. Regions prone to delaminations include free edges, locations of stress concentration, ,joints, inadvertent damaged areas and defects resulting from the fabrication procedure. One way of properly accounting for interlaminar delamination in a design is to determine interlaminar fracture toughness parameters and then to evaluate, those stress states which are likely to induce interlaminar fracture. Several test methods to determine fracture toughness have been proposed and are currently being used. These tests include: edge delamination, double-cantilever beam (constant and variable thickness), cracked-lap-shear, biaxial interlaminar fracture (ARCAN), and the recently introduced three-point bend tests for Mode II (end-notch flexure (ENF)) and mixed Modes I and II fracture (MMF). Each of these test methods has its advantages and limitations (figs. 1 and 2). These tests have been the subject of discussion and evaluation at ASTM D30.02 and D30.04 subcommittee meetings and specialty symposia sponsored by these subcommittees (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, Structures Division.
interlaminar Mode II and mixed mode fracture toughness. These unique features stem from (1) the simplicity of the test, and (2) the ability to measure the fracture toughness parameters directly during the test. Recent research efforts at Lewis Research Center have focused on the development of a computational method (procedure) for simulating the three-point bend test and evaluating 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 suitable for determining global and local interlaminar fracture toughness parameters as well as critical values of these parameters. The objective of this report is to describe the computational procedure in detail and results obtained therefrom. A unique feature of this computational procedure is the consideration of the interply layer as a distinct entity and with finite thickness. The interply layer has not previously been included in three-dimensional laminate analysis (ref. 4) and in fracture mechanics-type computations. The interply layer neecs to be considered in order to compute accurately those stress fields which induce interply delamination.
FRACTURE TOUGHNESS PREDICTIONS MSC/NASTRAN three-dimensional finite element static analysis (FEA) with substructuring was uses: to determine the structural response variables (displacements, stresses, strains) required for fracture toughness predictions. These structural response variables were used subsequently with three different methods 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 developed during this investigation. Each method is summarized below.
Global Method
fio
The specific computational steps for this method are as follows (refer to e).
(1) Model the specimen with crack length (a) using three-dimensional finite elements as described later. (2) Apply a load (P) at specimen midspan. (3) Calculate the midspan displacement v(a) using three-dimensional FEA as 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
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 composite uniaxial strengths. The global method yields the global fracture toughness without any regard to participating 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 respective planes (fig. 2) using the following equations u(a + ea) - u(a)
F x
(2)
u(fx)
F - v(a + ea) - v(a) y v(fy) F - w(a + ea) - w( a) z w(fz)
(3)
(4)
(8) Determine the local SERR's from GI = F
x [v(a + ea) - v(a)]/2b ea 3
,,& P
(5)
to^ ., --
i
GII = F x x (u;a + ea) - u(a)1/2bea
G III =
F
x (w(a + ha) - w(a)]/2baa
(6)
(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 displacement 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 step t 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 the Fx, 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 constraint force. It is also conceptually simpler than the local crack closure method and has the added advantage of preserving the characteristic of monotonically increasing displacement under the applied load with crack extension. On the other hand, it is possible to obtain reversal in this displacement when using the local crack closure method. Comparisons of results predicted using these two methods are made in a later section.
FINITE ELEMENT ANALYSIS MODELS The entire specimen was modeled, including the interply layer, using the three-dimensional finite elements available in MSC/NASTRAN. A schematic of the model with the actual dimensions used is shown in figure 3. The specimen modeled is the same as that currently bein g evaluated by the ASTM D30.04 subcommittee for a possible standard test method to determine Mode Ii (using ENF) and mixed Mode I and II (using MMF) fracture toughness. The interply layers and the individual plies are modeled in the vicinity of the crack. The remaining plies ar e grouped as shown schematically in figure 4. 4
-A
A three-dimensional computer plot of the finite element model is shown in figure 5. The specimen was modeled using 1536 solid elements for a total of 6090 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. The superelement contained 360 solid elements, 450 nodes (1350 DOF). The displacement 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
forMMF
2 w=o
at
x=o and t y = o
for ENF
y = t
for MMF
2
(8)
z = b 2 A line load was applied at the specimen midspan (fig. 2). The magnitude of this load was 120 lb. This magnitude corresponds to the experimental load which induced unstable crack propagation as reported in the ASTM D30.02 subcommittee meeting (April 1984). The crack extension propagation was simulated by progressively deleting interply layer elements and repeating the FEA as described in the previous section. The justifications for deleting the element instead 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 relatively little resin residue indicating that the interply layer is destroyed during t!,e fracture process. (3) The crack does not remain at the midplane of the interply layer but meanders 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 summarized in table I assuming room temperature dry conditions. Five different unidirectional 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 were generated 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 the matrix. The three-dimensional composite properties (using MSC/NASTRAN designation) and interply layer thickness predicted by ICAN are summarized in table I1.
5
Even though room temperature dry conditions were assumed in this simulation, hygrothermal environmental effects can readily be simulated using the theory (ref. 6) embedded in ICAN to predict the corresponding composite properties. Other composite systems including (1) intraply hybrids, (2) interply hybrids, (3) intra/inter ply hybrids, (4) composites with perforated interply layers, and (5) composites with different void content can readily be simulated using ICAN.
RESULTS AND DISCUSSION The results obtained together with appropriate discussions, interpretations, and possible implications are summarized below first for the global method and second for the local crack closure methods. The results are presented graphically where midspan displacement and SERR are plotted versus crack propagating length for the five different fiber volume ratios (FVR). In addition, graphical results are presented for the stress field behavior in the vicinity of the crack and also the variation of maximum stress magnitudes versus crack propagating length. The maximum stress magnitudes are assumed to be at the centroid of the interply element in the superelement ahead of the crack tip.
Global Method Results The midspan displacement versus crack propagating length for the five different fiber volume ratios is shown in figure 7 for the ENF specimen.. The midspan displacement decreases with increasing fiber volume ratio. Also, the midspan deflection increases gradually with crack opening length up to about a =1.20 in, and then increases rapidly. The corresponding SERR GII determined using the global method described previously (Eq. (1)) is shown in figure 8. The authors interpret the behavior shown in figure 8 to be associated 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, and therefore rapid crack propagation to fracture. The SERR G II varies approximately inversely with FVR as would be expected since it is calculated from the midspan displacement which also varies inversely with FVR. The corresponding results for MMF are shown in figure 9 for displacement and in figure 10 for SERR G. These curves exhibit the same behavior as those for ENF and, therefore, exhibit similar interlaminar composite fracture characteristics. A comparison of the curves in figures 8 and 10 reveals that the interlaminar fracture characteristics for ENF and MMF are almost identical for 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^
The results in figures 8 and 10 show that the anticipated "global" composite interlaminar fracture strain energy release rate can be predicted by conducting three-dimensional finite element analyses on ENF and MMF specimens and using the global method. In addition, these results show similar characteristics for shear (Mode II) and mixed (Mode I and II) fracture. One conclusion 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 and variable cross sections, and different laminate configurations can be just as easily handled as the two cases already described. The global method generally does not separate the contribution of each mode. However, these contributions can be determined by the local crack closure methods as described in the next section.
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 determined using the global method is also plotted for comparison. The range of experimental data reported in the ASTM D30.02 subcommittee meeting is shown by dashed horizontal lines. Three points are worth noting in figure 11: (1) The global method predicts higher GII values than the local crack closure 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 fracture characteristics 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 shown in figure 12 for a composite with 0.6 FVR. The fracture characteristics for each 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 two modes from the local method (short dashed line). The following observations are worth noting in figure 12: (1) Both the local crack closure and the global methods predict similar mixed mode (Mode I and II) fracture characteristics. (2) The local crack closure method predicts lower mixed mode G values than the global method.
o.
(3) Mode II fracture dominates the crack extension during slow and stable crack growth (a < 1.05 in). (4) Mode I dominates the crack extension during unstable crack growth and rapid 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 the local crack closure method. (2) Mode I drives the composite interlaminar delamination in MMF specimens. (3) The local method provides a conservative assessment of mixed mode composite interlaminar fracture characteristics as was the case for Made II. The mixed mode (Mode I and II) composite interlaminar fracture characteristics predicted using the Lewis method (local single point constraints) are shown, in figure 13. The characteristics predicted by using this method are practically the same as those observed in figure 12. One exception is that Mode I is positive for all 'a' and, thus, this method preserves the v displacement 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 coincides with the rapid rise in Mode I (figs. 12 and 13). It is important to note that the contribution of each mode to mixed mode fracture can be jetermined, within acceptable engineering accuracy, by either of the local mF'.hods described herein. The local crack closure method, however, is easier to implement computationally based on the authors' research experience. The composite interlaminar opening mode fracture was also determined by simulating 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 DC specimen becomes unstable at a smaller crack opening compared to the MMF specimen. Apparently the presence of Mode II increases the resistance to Mode I fracture. 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 crack propagation in mixed mode fracture reasonably well.
LOCAL STRESS FIELDS End-Notch-Flexure. - The averaged across-the-width stress field behavior in the interply layer in the ENF is shown in figure 15. Interestingly, all three 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 tip as would be expected from the near-singular stress field. On the other hand, the shear stress exhibits oscillatory behavior near the crack tip, decreases to a relatively constant value and then slowly decays to the value predicted by simple beam theory. At this time the aithors suspect that this oscillatory behavior may be real. Two supporting reasons are: (1) The proper behavior of the two normal stresses gives confidence in the analysis, 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 using the composite micromechanics equations programmed in ICAN. The peak shear stress (axy) reaches relatively high values during the slow crack growth stage and remains practically constant during the stable crack growth stage (fig. 8). The peak shear stress exceeds the corresponding strength for practically the entire extending crack distance. The peak value of the through-the-thickness normal stress (a y) is substantial (comparable to Oxx) and it is compressive throughout she extending crack distance. This compressive normal stress will tend to close the crack and thus e-hance the interlaminar resistance to Mode II type fracture. It appears that the rise in the peak shear stress is associated with an increase 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 the fractured interply layer and, therefore, provide additional credence to simulating the extending crack by deleting the interply layer crack-tip element. The significant conclusion from the above discussion is that interply Mode II fracture occurs when the corresponding shear strength is exceeded. This conclusion can be used to determine critical fracture toughness parameters as will be described later. Mixed-Mode-Flexure. - The corresponding average stress-field behavior in the 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 thereafter. 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 the ENF specimen. (3) The shear stress magnitude beyond the crack tip vicinity is about the same as that in the ENF flexure specimen (fig. 15). The peak stresses in the MMF specimen versus extending crack-tip distance are shown in figure 18. Also shown in this figure are the corresponding interlaminar shear and transverse tensile strengths predicted using ICAN. 9
and ax ) exceed their corresponding strengths for Both stresses (a practically 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 with the SERR G behavior (fig. 10) and demonstrate that the MMF specimen is subjected 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 axy exceed their corresponding strengths. This is consistent with the conclusion stated previously for the ENF specimen. It has the same significant implications 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 .,er thickness, of the composite. The most obvious ones include interply interlaminar shear strength and transverse tensile strength. These are in addition to the well known critical strain energy release rate (SERR), critical stress intensity factor and crack length. Furthermore, the intrinsic composite properties depend on composite constituent material properties and on fiber volume ratio (FVR) and, as a result, are not independent. Their interdependence can be determined by composite micromechanics (refs. 8 and 9). The effects of fiber volume ratio on the fracture toughness parameters are presented graphically in figure 19 for ENF (Mode II) fracture and for a 120 lb load. The parameters plotted are: interlaminar shear strength, SERR and interply layer thickness for three different crack lengths (ea). The interesting points to be noted are: (1) The SERR decreases with increasing FVR (rapidly at low FVR (about 0.30) and more slowly at high FVR (about 0.70)). (2) Both the interlaminar shear strength and the interply layer thickness decrease with increasing FVR and at a progressively faster rate. Both of these lead to the conclusion that fiber composites with relatively high FVR will have lower fracture toughness compared to those with intermediate (about 0.5) or low FVR. Another, and perhaps by far more important, conclusion is that composite mechanics in conjunction with three-dimensional finite element 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 interlaminar fracture toughness using the End-Notch-Flexure (ENF) and/or Mixed-Mode-Flexure (MMF) methods. In developing this procedure, the critical parameters associated with the fracture toughness of the composite are revealed. This procedure consists of the following steps: 10
(1) Determine t h e r e q u i s i t e p r o p e r t i e s a t t h e deslred ~ 0 n d I t l ~using n~ cornposlte mlcromechanlcs. These requisite p r o p e r t i e s 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 a b l e 11.
( 2 ) Run a three-dlmenslonal f l n l t e element a n a l y s i s 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 h e r e l n ( f l g s . 3 and 4). Note t h a t the superelement I s n o t necessary although it expedl tes t h e computations. ( 3 ) Scaie the a r b i t r a r y load I n step ( 2 ) t o match l n t e r l a m l n a r shear stress a r through-the-thickness normal s t r e s s I n t h e c r a c k - t l p element w l t h the l n t e r l a m l n a r shear s t r e n g t h o r t h e through-the-thickness normal s t r e n g t h o f t h e composlte. Note t h a t t h l s element I s next t o t h e crack t i p . ( 4 ) PUP several f l n l t e element analyses w l t h t h e scaled load and progress i v e l y extsndlng crack l e n g t h (a).
(5) Calculate s t r a l n energy release rates ( 6 ) uslng t h e approprtate equations (eqs. ( I ) , (5), (6). o r ( 7 ) ) . (6) P l o t the curve G c a l c u l a t e d a t step (5) versus s l m l l a r t o those I n f i g u r e s 11 t o 13.
a.
T h l r curve i s
( 7 ) Construct two tangents t o the curve as follows: ( a ) through t h e slowly r l s l n g p o r t l o n o f the s t a b l e crack ~ ; , o w t h reglon (b) through tCc r a p i d l y r l s l n ~p o r t i o n o f t h e unstable crack growth reglon. (8) Select t h e c r ~ t i c a l G ( s t r a i n energy release r a t e ) value and t h e c r l t i c a l crack-length from t h e I n t e r s e c t i o n o f t h e two tangents i n steC ( 7 ) . The steps f o 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 t h a t t h l s procedure has n o t been v e r l f l e d w i t h approprlzte exper:mental data other thaq t h a t descrlbed herein. l h e r e f o r e . 1~ should be used j u d i c i o u s l y u n t i l s u f f i c e n t l y w e l l v a l i d a t e d . 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 s e l e c t those whlch should meet I n t e r l a m i n a r f r a c t u r e toughness deslgn requirements. I t a l s o provldes a d i r e c t means f o r q u a n t t f y l n g values f o r c r l t l c a l s t r a i n energy release r a t e (G) and i t s correspnndlng c r l t l c a l l e n g t h (a) on whlch deslgn c r l t e r l a can be based. I t t s the authors' considered techt.lca1 judgment t h a t proper use o f t h l s computational procedure provldes d e t a l l e d i n f n r m a t i o n whlch can be used t o describe, assess, and p r e d i c t composlte l n t c r i a m l n a r f r a c t u r e toughness. As a r e s u l t , composite s t r u c t u r e s can be designed t o meet t h l s h l t h e r t o e l u s l v e 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 g e n e r a l i t y as was p r e v i o u s l y 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 I n v e s t l g a t t o n of comi;osIte 1nterla;nlnar f r a c t u r e determlned by t h e computatlonal simulation o f 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 conputatlonal method f o r determlning t h e l n t e r larnlnar f r a c t u r e toughness i n u n l d l r e c t l o n a l composites. 2. The s i g n l f i c a n t composite p r o p e r t i e s associated w l t h composlte I n t e r lamlnar f r a c t u r e toughness are: (a) l n t e r l a m l n a r shear strength, (b) transverse t e n s l l e strength, ( c ) l n t e r p l y l a y e r thickness, and (d) f l b e r volume ratio. 3. Three methods a r e s u l t a b l e t o computatlonally determlne t h e l n t e r lamlnar s t r a i n energy release r a t e (SERR): (a) the g l o b a l method. (b) t h e l o c a l crack closure method, ( c ) t h e l o c a l s l n g l e p o l n t constrained f o r c e (Lewls) method. However, o n l y t h e l o c a l methods a r e s u l t a b l e f o r determining the c o n t r i b u t i o n s o f each f r a c t u r e mode.
4. The global method p r e d l c t s hlgher SERR compared t o l o c a l methods d u r l n g slow and s t a b l e crack growth. However, a l l t h r e e methods tend t o converge durlng r a p l d l y lncreaslng s t r a i n energy release r a t e (SERR) u h l c h I n d i c a t e s 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 a c t u r e a r e I n good agreement w i t h l l m l t e d measured data. 6. Mode I 1 (shear) dominates ENF w h i l e Mode I (openlng) dominates t h e unstable crack growth I n MMF.
7. Mode 11 (shear) unstable crack growth occurs I n ENF when t h e 1nte.rlamlnar 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 stress 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 t h e 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 r a c t u r e . REFERENCES 1. Sendeckyj, G.P., Ed., Fracture Mechanics o f Cornposltes, ASTM STP-593, American Society f o r Testlng and Materials. Phi ladelphla, PA. 1975. 2. Relfsnider. K.L., Ed., Damage i n Com~ositeM a t e r i a l s , ASTM STP-775, Amerlcan Soclety f o r Testlng and Materials, Phlladelphia. PA, 1982. 3. Wllkins. D.J., Ed., E f f e c t s o f Defects i n Composite Materials. ASTM STP-836, Amerlcan Society f o r Testlng and Materials. Phlladelphia, PA, 1984.
4. Murthy. P.L.N. and Charnls C.C., 1-3, 1985, pp. 431 -441.
C,.rnouters and Structures, Vol. 20, No.
5. Uurthy. P.L.N. and Chamls, C.C., 'ICAN: I n t e g r a t e d Composites Analyzer,' AIAA Paper 84-0974, American I n s t l t u t e of Aeronautics and Astronautics , New York, Uay 1984. Lark, R.F., and S l n c l a i r , J.H., I n Advanced C m o s i t e 6. Charnls, C.C., M a t e r i a l s - Envlronmental Effects. ASTU STP-658, J.R. Vlnson, Ed., American Soc1et.y f o r Testlng and Materials, Phlladelphla. 1978, pp. 160-192. 7. VL,1derkley, P.S., @ModeI - Mode I1 Delaminatton Fracture Toughness o f a U n l d l r e c t i o n a l Graphlte/Epoxy Composite,' Master o f Science Thesis, Texas A L M Unlverslty, 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, J u l y 1984, pp. 41-55.
TABLE I. - CONSTITUENT MATERIAL PROPERTIES USED IN THE SIMULATION Property
Units
, !Elastic moduli
i x106 psi i
Poisson's ratio' -------- ksi
Strengths
Fiber AS-graphite
Symbol
Value
E fll E f22 Gf12 O f23 v f12 vf23 SfT Sfc
31.00
!
Matrix intermediate-modulus high-strength Symbol Em
{
inch
2.
1. :',
I
df
-
0.5
2.00
0.2 0.25 400 400
!
6m
.1852
vm
.35
SmT Smc Sms
,Fiber diameter
Value
15 35 113
0.0003
'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
Elastic constants in the stress/strain relationship for unidirectional AS/E composite
1
x106 lb/in2 G11 G21 = G12 G31 = 013 G41 = G14 G51 - G15 G61 = G16 G22 G32 = G23 G42 - G24 G52 - G25 G62 = G26 G33 I G43 = 534 G35 IG53 G63 = G36 G44 654 = G45 G64 = G46 G55 ^G65 = G56 G66
I
0.55
12.420 20.023 0.734 0.629 .734 .629 .000 .000 .000000 .000 .000 1.412 1.511 .863 .7?1 .000 .000 .000 .000 .000 .000 1.544 1.620 .000 000 .000 .000 .000 .000 I .368 .5b6 .000 .000 .000 .000 .245 .336 .000 .000 .368 .566
j
I
0.60
0.65
0.75
21.478 0.615 .615 .000 .000 .000 1.549 .710 .000 .000 .000 1.654 .000 .000 .000 .623 .000 .000 .362 000 .623
22.921 0.602 .602 .000 .000 .000 1.593 .691 .000 .000 .000 1.694 .000 .000 .000 .690 LOU .000 .394 .000 .690
25.782 0.583 .583 .000 .000 .000 1.704 .654 .000 .000 .000 1.800 .000 .000 .000 .865 .000 .000 .476 .000 .865
I
I
Interply Byer
properties moduli Thickness
x101 lb/in 2 ` _
incn
E v 6
5 .35 0.1854x10-3
.5 .35 0.5850x10 -4
.5 .35 0.4323x10 -4
.5 .3 0.2977x10 -4
.5 .35 0.6998x10-5
1
II
I
1 EDGE -DELAMINATI ON MIXED MODE II & III
DOUBLE CANTILEVER OPENING MODE (I)
CRACK-LAP-SHEAR SHEAR MODE III)
Figure 1. - Schematics of test methods for measuring interlaminar fracture toughness.
A
a --+
Y,v
l END-NOTCH-FLEXURE (ENF)--SHEAR MODE (I1)
ORIGIN X, u
p
Z, w
r —aMIXED-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
1 "/A
2
X
Z 0.5" 1---
-{ 0. 5" 1---
V
Figure 3. - Model geometry and F. F. schematic.
INTER PLY LAYERS
Figure 4 - Schematic of F. L model through-the-thickness ietails.
y,
tl
CS )ELEMENTS HEDRANS AND WEDRANSI 6090 DOF SUPER ELEMENT IN CRACK REGION 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.
. .V
1.0"r
120 Ib ti
^a
12'
FVR
^MIDSPAN
.30
c zi O
U
55 60
W
65
z aN cm
75
1.0
1.05
1.10 1.15 CRACK LENGTH, a, in
1.20
1.25
Figure 7. - Fiber volume ratio effects on midspan deflection. End-notchflexure (AS1E).
120 Ib
0T 17.7
^MIDSPAN DEFLECTION (W) FVR 4 0^ —__^ 0.30
6.0
c a 48
0.55 0.60
j,43.6 W
\
2.4
0.75
>
0.65
W 1,2 z W
0 1,00
1.05
1.10 1.15 CRACK LENGTH, a, in
1.20
Figure 8. - Fiber volume ratio effects on Mode II energy release rate, End-notch-flexure (ASIE).
1.25
.._7117
120 lb 2"
FVR L wnf DAKI
20
0.30
c .16
0. 55 0.60 0.65 0.75
^ .12 rc.>
o
z o0 f
.08
.04
0 1 1.0
1
1
1
1.15 1.10 CRACK LENGTH, a, in
1.05
1
1
1.20
1.25
Figure 9. - Fiber volume ratio effects on midspan deflection, Mixed-modeflexure (ASIE).
120 lb
a^
017 2" i
MIDSPAN
17,7
DEFLECTION IWI 6.0
c
6
4,8
1,
V 3.6 W tJ 2.4 c^
1.2 i z D 1 —
I
1.00
1.05
I
1
1.10 1.15 CRACK LENGTH, a, in
1
1
1.20
1.25
Figure 10, - Fiber volume ratio effects on mixed mode ( I & III. Mixed-mode-
flexure (ASIE).
I
1.0"^
120 Ib
^ ate{
0:r2I T
^MIDSPAN r DEFLECTION lWl }`-- — 4.0" — — •^
4
1 1
1
MODE (II)
1
—"'--^---'—"— t---^ MEASURED 3
Q cle
------
2
/'—^\ --- Jt-----
RANGE
/
W N
/ GLOBAL
}
1
---- LOCAL
w
W Z
1.0
I 1.3
I 1.1 1.2 CRACK LENGTH, a, in
D
Figure 1L - End-notch flexure energy release rate-comparison,
17.7
5
17.1 }14.6 o 11
4
3
1.0"^
120 lb I
^• a—^
r
I
,:
s> 2
sf
MIDSPAN DEFLECTION IW1
i
f I (
o"c 1
; /
-----
GLOBAL
MIXED lI & III
LOCAL
MIXED 41 & 11)
LOCAL
I
/' — -- LOCAL 11
1.0
1.1
1,2 CRACK LENGTH, a, in
1.3
Figure 12. - Mixed-made-flexure energy release rate and components (ASIE). Local closure method,
-C
17.0
5 .
14.5
117,73 i
1.0" ^`
120 lb
4 _ iS
► ' 0 1 ► i ' '^ Z-' ►
3
^ MIDSPAN DEFLECTION W
I
I ►
oc
MODE
1
GLOBAL MIXED lI & III MIXED Q& III — LOCAL
0
^
--- LOCAL I LOCAL
-1.0 1.0
II
1.3
1.2 1.1 CRACK LENGTH, a, in
Figure 13. - Mixed-made flexure energy release rate and components (ASIEI. Single point constrained (Lewis) method.
1000
c
n 100
a W N W Q' d' W -L W
10
1.0 1 1.0
1 1
1
1
1.2 1.1 CRACK LENGTH, a, in
Figure 14, - Double-cantilever energy release rate-comparisons (AS IE).
NNW
,
1.3
a
C4
15
O°x7 X7 ' °Yz ' °zz ' 0
12
y
9
^^LAYER x
6
z
oxy
CRACK
TIP Y
3
z N
W 1
o yy 0
N
3°xx
-6
acyy -12 15 .050
0
.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 TIP
r o xy
ELEMENT
z 12.0 W
3.0 °xx -6.0
ayy 0
.05
.10
i
J
.15
.20
.25
EXTENDING CRACK-TIP DISTANCE, in Figure 16.- Peak stress behavior in interply layer with crack extension. End-
notch-flexure (AS/E).
-3
; 0
.lo0 .150 DISTANCE FRW CRACK-TIP. i n
.05
.2M
.200
Figure 17. - Stress field Ir! interply layer near cradt tip. Mixed-mcde-flexure MSIEI,
\
.05
-
-
L'
.lo IS EXTENDING CRACK-TIP DISTANCE. in
ELEMENT
.n
.a
Figure 18 Peak s t r m behavior at crack tip with crack extension. Mixed-modefracture MSIEI.
0 INTERLAMINAR SHEAR STRENGTH A INTERPLY LAYER THICKNESS 000 MODC ;:EiGRGY RELEASE RATE
-
20-
10-3
-
k
6-o l l - l 5 0.0
a30 a% a70 FIBER VOLUME RATIO
-
aw
Figure 19. Flber volume ratio effect on lnterlamlnar fraclure 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 SELECT C.RITICAL "G" AND CRITICAL "a"
I_
G
-- -----
METHOD HAS VERSATIUNIGENERALITY
-
,-
I
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 ,.,.
3. Reclplent'a cataIoO No.
2. Oo¥emment Acceulon No.
NASA TM-81138 5. ~Det•
• . TItle and Subtitle
InterlaM1nar Fracture Toughness: Three-01mens1onal F1n1te Element Mode11ng For End-Notch and M1xedMode Flexure 7. Aut!tof(a,
•. Perfonnlng 0fgM1zal1on Code
505-33-18 • . Perfonnlng 0fgM1zal1on Aepoft No.
P.L.N. Murthy and C.C. Cham1s
E-2626 10. Wotk Unit No.
I . PerformIng OrgMlUlion NMIe and Add.....
Nat10nal Aeronaut1cs and Space Adm1n1strat1on Lew1s Research Center Cleve~and, Oh10 44135
11. Contraet or Orant No.
13. Type 01 Report and '-loci eo-.d
Techn1cal Memorandum
12. 8poneorIng Agency NMIe and Add .....
Nat10nal Aeronaut1cs and Space Adm1n1strat1on wash1ngton, D.C. 20546
1•. Sponeoring Aeency Code
15. Supplementary Not"
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.
18. Dlltrlbullon Statement
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 11. Security Cle..lI. (01t1111 report,
Unc lass H 1ed
20. Security CI..III. (01 tl111
Unclass1f1ed - un11m1ted STAR category 24
page,
21 . No. 01 paget
Unc las s H1 ed
·For sale by the National Technical Information Service. Springfield. Virginia 22,6,
22. PrIce·
