rwvsa NASA Technical Memorandum CHARACTERIZATION OF DELAMINATION ONSET AND GROWTH IN A COMPOSITE LAMINATE T. Kevin O'Brien January 1931

Transcription

1 N81 NASA Technical Memrandum CHARACTERIZATIN F DELAMINATIN NSET AND GRWTH IN A MPSITE LAMINATE T. Kevin 'Brien January ' : ( rq: rwvsa Natinal Aernautics and Space Administratin Langley Research Center Hamptn, Virginia miq QUAldTi lubtwliäi i l

2 DISCLAIMER NTICE THIS DCUMENT IS BEST QUALITY AVAILABLE. THE PY FURNISHED T DTIC NTAINED A SIGNIFICANT NUMBER F PAGES WHICH D NT REPRDUCE LEGIBLY.

3 CHARACTERIZATIN F DELAMINATIN NSET AND GRWTH IN A MPSITE LAMINATE T. Kevin 'Brien Structures Labratry U.S. Army Research and Technlgy Labratries (AVRADM) NASA Langley Research Center Hamptn, Virginia SUMMARY The nset and grwth f delaminatins in unntched [±30/±30/90/90] graphite-epxy laminates is described quantitatively. These laminates, designed t delaminate at the edges under tensile lads, were tested and analyzed. Delaminatin grwth and stiffness lss were mnitred nndestruc- tively. Laminate stiffness decreased linearly with delaminatin size. The strain energy release rate, G, assciated with delaminatin grwth, was calculated frm tw analyses. A critical G fr delaminatin nset was determined, and then was used t predict the nset f delaminatins in [+1 5 /-1+5 /0 /90 1 (n=l,2,3) laminates. A delaminatin resistance curve n n n n s (R-curve) was develped t characterize the bserved stable delaminatin grwth under quasi-static lading. A pwer law crrelatin between G and delaminatin grwth rates in fatigue was established.

4 INTRDUCTIN A cmmnly bserved failure mde in laminated cmpsite materials is delaminatin between the cmpsite layers. Delaminatins may develp during manufacture due t incmplete curing r the intrductin f a freign particle; they may result frm impact damage; r they may result frm the interlaminar stresses that develp at stress-free edges r discntinuities. Furthermre, delaminatins may grw under cyclic lading. Delaminatin grwth redistributes the stresses in the plies f a laminate, and may influence residual stiffness, residual strength, and fatigue life. Hence, a fatigue analysis fr cmpsite materials shuld take int accunt the presence and grwth f delaminatins. A bibligraphy f experimental and analytical wrk n delaminatin is cntained in reference [l]. ne f the mst prmising techniques fr characterizing delaminatin grwth is based n the rate f strain energy released, G, with delaminatin grwth [l]. Previus wrk [2] has shwn that the cyclic grwth rate f debnds between the metal and cmpsite cmpnents f reinfrced panels culd be crrelated with G. Measured critical G values have been used in sphisticated analyses [3,^] t predict the nset f edge delaminatins in unntched cmpsite laminates. In the present study, a simple technique was develped, emplying strain energy release rates t characterize the nset and grwth f delaminatins in a cmpsite laminate. First, the damage that develped in unntched [±30/±30/90/90] graphite-epxy laminates under static tensin lading and tensin-tensin fatigue lading was determined. Next, stress distributins generated frm a finite element analysis were crrelated with the bserved damage. Then, during quasi-static test 2

5 lads, delaminatin grwth and stiffness lss were mnitred nndestructive^ t relate laminate stiffness and delaminatin size. The resulting test data and analysis were used t derive a clsed-frm equatin fr the strain energy release rate, G, assciated with delaminatin grwth. Next, a critical value f G fr delaminatin nset was determined. It was then used t predict the nset f delaminatin in [+^5 n /-^5 n /0 n /90 n ] (n=l,2,3) laminates. A delaminatin resistance curve (R-curve) was develped t characterize the bserved stable delaminatin grwth during quasi-static lading. Finally, a pwer law crrelatin between G and delaminatin grwth rates in fatigue was established. [A] extensinal stiffness matrix SYMBLS A delaminated area A* area f interface cntaining a delaminatin a strip delaminatin size Aa incremental strip delaminatin size da dn delaminatin grwth rate in fatigue [B] cupling stiffness matrix b half-width f laminate crss sectin C,3 empirically determined cefficients [D] bending stiffness matrix 3

6 E axial stiffness f a partially delaminated laminate ETA M axial laminate stiffness calculated frm laminated plate thery E* axial stiffness f a laminate cmpletely delaminated alng ne r mre interfaces E- axial stiffness f the i th sublaminate frmed by a delaminatin E 0 initial tangent mdulus f an undamaged laminate ETHJE?,E lamina mduli ^- rate f stiffness change with delaminatin area da ^- rate f stiffness change with fatigue cycles dn G n' G 12' G 13 lamina shear mduli G strain energy release rate assciated with delaminatin grwth G-pjGjjjGjjj strain energy release rate cmpnents due t pening, in-plane shear, and ut f plane shear fracture mdes G FEM values f Gj, G^, G I1X calculated frm finite element analysis G critical strain energy release rate fr delaminatin nset G delaminatin resistance G max maximum strain energy release rate in cnstant strain amplitude fatigue test

7 h ply thickness K saturatin spacing f cracks in 90 plies gage length used t measure axial displacements N number f fatigue cycles n number f plies in a laminate t laminate thickness tj_ thickness f 1 sublaminate frmed by delaminatin u,v,w displacements in x,y,z directins U,V,W displacement functins in x,y,z directins V material vlume da da da x,y,z rate f strain energy released as flaw extends rate f wrk dne by applied lad as flaw extends cartesian crdinates X,Y,Z ndal frces in x,y,z directins X,-, first element f the inverse extensinal stiffness matrix (A itj _1 ) (i,j = 1,2,3) c nminal axial strain Q unifrm axial strain assumed in finite element analysis

8 nminal axial strain at nset f delaminatin e max maximum cyclic strain level in fatigue V 12> V 13' V 23 l am i- na Pissn's rati a x axial stress in a ply 0 remte axial stress applied at nset f delaminatin a interlaminar nrmal stress between plies SPECIMENS AND APPARATUS Unntched [±30/±30/90/9CT], T graphite-epxy laminates were tested in tensin. This laminate was designed t have relatively high tensile interlaminar nrmal stresses at the edges resulting in the frmatin f a delaminatin [5]. Figure l(a) shws the delaminatin that develped alng the edge. The specimens were 2^k mm (l in.) lng by 38 mm (1.5 in.) wide. These eleven-ply laminates had an average ply thickness f 0.1^1 mm (.005^ in.). Specimens were tested in a clsed-lp hydraulic testing machine. The specimen length between the grips was l80 mm (7-0 in.). Als shwn in figure l(a) is a pair f linear variable differential transducers (LVDT's), that were munted n the specimen t measure displacements ver a 102 mm {k. in.) gage length. T prevent slippage, a fast drying glue was applied t the central 5.6 mm (.22 in.) prtin f the LVDT munts where they tuched the specimen. During "strain-cntrlled" lading, these LVDT's were used as the feedback device in the clsed lp.

9 Dye-penetrant enhanced radigraphy was used t mnitr delaminatin grwth thrugh the specimen width. Diidbutane (DIB), a dye penetrant paque t x-rays, was injected alng the delaminated edge. The film was placed immediately "behind the specimen. While still munted in the test machine, specimens were expsed t x-rays generated fr five secnds at l8 kv frm a prtable pint-surce unit psitined 386 mm (l5»5 in.) away frm the specimen. The radigraphs shwed the lcatin f the delaminatin frnt (fig. 1(b)). The dark utline in the center f the picture is the "shadw" (x-ray image) f the LVDT rds used t measure displacements. DAMAGE DEVELPMENT The same type f damage develped during bth quasi-static tensin and cnstant-amplitude, tensin-tensin fatigue. First, a few islated cracks frmed in the 90 plies. These were fllwed almst immediately by the frmatin f small delaminatins alng the edge, as seen in figure 2(a). When the delaminatins frmed, the number f 90 -ply cracks increased significantly alng the delaminated length f the specimen. Mst f the 90 -ply cracks, which appear as hrizntal lines n the radigraphs in figure 2, extended beynd the delaminatin frnt utlined in the x-ray phtgraph. Many f the ply-cracks immediately extended halfway acrss the specimen width. As lading cntinued, additinal delaminatins frmed and jined with riginal delaminatins. Delaminatins grew much mre rapidly alng the length f the specimen than acrss the width (fig. 2(b)). Eventually, tw delaminatins, ne n each side f the specimen, extended alng the entire specimen length between the grips (fig. 2(c)), after which

10 the delaminatins cntinued t grw acrss the width. Lading was terminated when the delaminatin frnt reached the shadw f the LVDT rds (fig. 2(d)). T illustrate the lcatin f damage thrugh the thickness, a few acetate tape replicas f a delaminated edge were made [6], Figure 3 shws phtgraphs f tw replicas and a prtin f the delaminated edge. As shwn in figure'3(a), ply cracks extended thrugh the thickness f all three interir 90 plies. As shwn in figure 3(h), delaminatins frmed and grew in -30 /90 interfaces, typically shifting frm ne interface, thrugh 90 ply cracks, t its symmetric -30 /90 cunterpart. Hwever, delaminatins did nt shift interfaces at every 90 ply crack encuntered. As shwn in a phtgraph f the delaminated edge, figure 3(c), interface shifting did nt ccur in a regular pattern. Besides frmatin f delaminatins at the -30/90 interfaces and cracks in the 90 plies, an ccasinal angular crack frmed in the innermst -30 ply. The replica f the edge in figure 4(a) shws tw angular cracks in the innermst -30 plies riginating at a 90 ply crack tip and creating delaminatins in the +30/-30 interfaces. As shwn in the radigraph in figure Mb), the delaminatins in the +30/-30 interfaces were small and triangular in shape. These +30/-30 delaminatins ften temprarily arrested initial -30/90 interface delaminatin grwth alng the length f the edge. Hwever, -30/90 interface delaminatins eventually jined up and grew, whereas islated +30/-30 delaminatins usually remained small. STRESS ANALYSIS Tw apprximate analyses were, used t btain quantitative predictins f the nset and grwth f delaminatins. The first was a quasi-threedimensinal stress analysis that yielded stress distributins and strain 8

11 energy release rates. The secnd was a simple rule f mixtures analysis that was used alng with laminated plate thery t calculate stiffness lss and strain energy release rates. Because delaminatins frm in unntched laminates as a result f the interlaminar stresses that develp at the edge, a quasi-three-dimensinal finite element analysis [7] was perfrmed. The finite element analysis was used t calculate stress distributins in the [±30/±30/90/90] s laminate fr a unit axial nminal strain (e = l). Sme details f the analysis are described in Appendix A. Figure 5 shws that the thrugh-thickness distributin f the interlaminar nrmal stress, a, calculated at the edge is cmpressive in the uter 30 plies but reaches a relatively high tensile value at the -30/90 interface and thrughut the 90 plies. Als shwn in figure 5 is the apprximate a z distributin thrugh the thickness calculated frm laminated plate thery and an assumed stress distributin acrss the width [8], This plt als shws the highest tensile 0" z stresses t be at the -3/9 interface and within the 90 plies. Figure 6 shws a distributin f a acrss the specimen width, near the edge, at the -30/90 interface, as well as a distributin f the axial stress, a, in the adjacent 90 ply. Bth a and a have high tensile values at the edge. These stress distributins shwed reasnable crrelatin with the bserved damage that develped. Indeed, examining z and interlaminar shear stress distributins are helpful in identifying likely delaminatin sites. Hwever, interlaminar stress distributins calculated frm finite

12 element analyses vere nt useful fr mdeling damage grwth quantitatively because the magnitude f calculated peak stresses at the edge varied with mesh size. Furthermre, linear elastic analysis suggests that the interlaminar stresses at ply interfaces can becme singular at the edge [7]. This singular behavir wuld preclude the use f a failure criterin based n maximum interlaminar stress values. Therefre, an alternate apprach, based upn strain energy release rates, was adpted t quantitatively describe the nset and grwth f delaminatins. STIFFNESS LSS In many cmpsite laminates, stiffness lss may reflect delaminatin grwth. Furthermre, the rate f stiffness lss with delaminatin grwth can be directly related t strain energy release rates. Therefre, analysis and experiments were perfrmed t crrelate laminate stiffness and delaminatin size. Rule f Mixtures Analysis T analyze stiffness lss due t delaminatin, a simple rule f mixtures analyses, alng with laminated plate thery, was used. First, the stiffness (tangent mdulus) f a balanced, symmetric cmpsite laminate (fig. 7a) was calculated frm laminate thery [9,10] as 1 E LAM = r + x 11 z (1) where X u is the first element f the inverse extensinal stiffness matrix, A^" 1 (i,j = 1,2,3), and t is the laminate thickness. Next, 10

13 assuming a cmplete delaminatin in ne r mre interfaces, and using the rule f mixtures assumptin that the sublaminates frmed underg the same axial strain (but n lnger have the same transverse strains), results in n %*! E*=izl _ (2) where E* - stiffness f a laminate cmpletely delaminated alng ne r mre interfaces E 1 = the laminate stiffness f the i th sublaminate frmed by the delaminatin t^ = the thickness f the i* 11 sublaminate Althugh equatin (2) represents a tw-dimensinal frmulatin, E* will depend upn which interfaces delaminate. This, in turn, determines the stiffness, E is and thickness, t i} f each new sublaminate. Hence, equatin (2) is sensitive t the thrugh-thickness lcatin f the delaminatin. Fr the [±30/±30/90/90] s laminate, assuming a delaminatin in bth -30/90 interfaces (fig. 7b) equatin (2) becmes E# = 8E (±30) 2 + 3E (9Q)3 11 U; Finally an equatin fr the stiffness, E, f a partially delaminated specimen was develped using the rule f mixtures. Equal-sized delaminated 11

14 Strips were assumed t exist at bth edges f the laminate (fig. 7c). Then, by assuming the laminated and delaminated prtins f the specimen act as independent cmpnents laded in parallel, the rule f mixtures yields E = ( E *- E LAM)^+E b 1AM A mre general frm f equatin (k) may be develped by assuming that the relatinship between laminate stiffness lss and delaminatin size can be represented by E E LAM = A_ (5; E* " E L AM A * where A = delaminated area A* = ttal interfacial area Rearranging equatin (5) yields E= ( E * - E LAM) f^+ E LAM (6) Equatin (h) is a special case f equatin (6) where a _ A b A* 12

15 Experiments T verify the linear relatinship between stiffness and delaminatin size implied by equatins (1+) and (6), fur quasi-static tensile tests were cnducted. The specimens were laded in a strain cntrlled mde until a delaminatin frmed. Then, the specimens were unladed t ten percent f the peak nminal strain, DIB was placed n the specimen edges, and an x-ray phtgraph was taken. Next, the specimens were reladed in increments f 250 um/m abve the previus maximum strain level. This prcedure was repeated until the specimen was almst ttally delaminated. During each lading, utput signals f the tw LVDT's were averaged, and lad deflectin curves were pltted n an X-Y pltter. The initial linear prtin f each plt was used t calculate laminate stiffness crrespnding t the damage recrded in the previus x-ray phtgraph (fig. 8). Delaminated areas recrded n the phtgraphs within the 102 mm (k in.) gage length were measured with a planimeter. T minimize data reductin errr, each delaminatin was traced three times and measured areas were averaged. Then, a strip delaminatin size, a, having equal area ver the LVDT gage length as the measured delaminatin, was calculated (fig. 9). Figure 10 shws a plt f nrmalized stiffness, E/E, as a functin f nrmalized delaminatin size a/b. A least-squares regressin line fr the data indicated that E* = 0.7l*2E 9 where E Q is the initial tangent mdulus measured. Hence, a ttal delaminatin in the [±30/±30/90/90] laminate wuld result in a 25.8 percent reductin in laminate stiffness. The data agreed with the linear rule f mixtures equatin (k), nrmalized by ET AM, where E* was calculated frm equatin (3) and sublaminate stiffnesses were calculated using equatin (l) (see appendix B) with material prperties frm reference [ll]. 13

16 Finally, equatins (2) and (1+) were used iteratively t calculate laminate stiffness fr specimens having -30/90 interface delaminatins and cncurrent, althugh small, +30/-30 interface delaminatins (see Appendix C) The cntributin f 90 ply cracks t laminate stiffness lss was als cnsidered (see Appendix C). Hwever, the net effect f bth secndary mechanisms (+30/-30 delaminatins and ply cracks) n stiffness lss was negligible fr the [±30/±30/90/901 laminate. STRAIN ENERGY RELEASE RATE Fr an elastic bdy cntaining a planar flaw f area A, the strain energy release rate, G, is the difference between the rate f wrk dne, dw/da, and the rate at which elastic strain energy is stred, du./da, as the flaw area increases [12], i.e., G _ dw _ da (7) da da Assuming that a nminal strain,, is sufficient t extend the flaw, the wrk term vanishes. Then, if a is expressed as a prduct f the strain- energy-density and vlume f the bdy, I/, substituting Hke's law int equatin (7) yields G=-l/ i^f (8) 2 da where QJü da is the rate f stiffness change as the flaw extends. Ik

17 In this study, the bdy was a tensile-laded, unntched cmpsite laminate, cntaining edge delaminatins. The strain energy release rate assciated with the grwth f edge delaminatins can he calculated byassuming tw strip delaminatins (fig. 9) where V = 2b t A* = 2b A = 2 a (9) da = 2 da Then, substituting equatins (9) int equatin (8) and differentiating equatin (h) yields 2 G = -1 /E - E*\ (l 1 2 I LAM ) UU> Equatin (10) may als be derived fr an arbitrary-shaped delaminatin by substituting equatin (6) int equatin (8), differentiating, and nting that 1/ = A*t. Hence, as indicated in equatin (10), the strain energy release rate assciated with delaminatin grwth is independent f the delaminatin size. The magnitude f G depends nly n the laminate layup and lcatin f the delaminated interface(s) (which determine E LM and E*), the nminal strain, e, and the laminate thickness, t. Furthermre, the strain energy release rate (eq. (l)) may have cn- tributins frm any f the three cmpnents Gj, G r GJJJ, crrespnding t the pening, in-plane shear, and ut-f-plane shear fracture mdes. In additin, near the edge, G may deviate frm the value predicted by 15

18 equatin (l), which was develped using laminated plate thery and the rule f mixtures. Therefre, a virtual crack extensin technique was used with the quasi-three-dimensinal finite element analysis t calculate G-j-, G^, and GJ-Q as a functin f delaminatin size (see Appendix A). As shwn in figure 11, the finite element analysis indicated that the ttal G, represented hy G-j- plus G I]: (djjj was negligible), reached the value predicted frm equatin (l) nce the delaminatin had grwn a very small distance in frm the edge. Because G increased rapidly with "a" near the edge, a small delaminatin that frmed (fr whatever reasn) at the edge wuld be expected t underg rapid initial grwth. This behavir was bserved in the quasi-static tensin tests used t generate stiffness data. As sn as a delaminatin was detected, the lading was stpped. The frmatin and grwth f the delaminatin t sme finite size appeared t be nearly instantaneus. Therefre, G calculated frm equatin (l) at the nminal strain where delaminatin was first detected was cnsidered t be the critical value, G Q, required t frm the delaminatin. This G Q was then used t predict the nset f delaminatin in ther laminates. DELAMINATIN NSET T predict the nset f delaminatin in ther laminates, several things were dne. First, tensin tests f [±30/±30/90/9Ö"] s laminates were run t determine the nminal strain level, e Q, at which delaminatin begins. Next, e was used in equatin (10) t predict a critical G c fr the nset f delaminatin Then, G Q was used t predict the nminal strain at the nset f delaminatin in ther laminates. A mre detailed descriptin f the prcedure fllws. 16

19 Critical G c Determinatin First, eighteen [±30/±30/90/90] graphite epxy laminates were laded mntnically in tensin at a rate f UU.5 N/sec (10 lbs/sec) until a delaminatin was detected. The lad level crrespnding t delaminatin nset was recrded and the crrespnding applied stress, a, was calculated. Then, t determine the nminal strain at the nset f delaminatin, e, a was c *- divided by E^^, calculated frm laminated plate thery using the fllwing elastic prperties frm reference [ll] E ll = 138 GPa ^2 ' Msi^ E 22 = 15 GPa (2.1 Msi) G 12 = 5.9 GPa (0.85 M si) V 12 = 0.21 The average e value was 3^70 um/m. In additin, e was determined frm LVDT measurements n the fur tests cnducted t generate stiffness data. In each f these fur tests, the lad deflectin plt was linear until the delaminatin frmed. The average value f e c where the lad-deflectin curve deviated frm linear fr these fur tests was als 3^70 Um/m. Next, was substituted int equatin (10) t determine G. Stiff- ness E and E* were calculated frm equatins (l) and (3), respectively, using elastic prperties frm reference [ll]. The average laminate thick- ness, measured with micrmeters, was 1.51 mm (0.059^ in.). A value f 137 J/m 2 (.78 in-lbs/in 2 ) was calculated fr the critical strain energy release rate. 17

20 Delaminatin nset Predictin T predict the nset f delaminatin in ther laminates, equatin (10) was inverted t yield 2 G e c = t ( E LAM " E *) (111 The critical G determined frm [±30/±30/90/90] laminate data was used c s in equatin (ll) t predict the nminal strain at the nset f delaminatin in [+^5 ri M5 n / n /90 T1 L (n = 1,2,3) T graphite-epxy laminates II LL ll ll having the same stacking sequence but different thicknesses. T evaluate E*, delaminatins were mdeled alng bth 0/90 interfaces where high tensile 0" z stresses were anticipated [3] n the basis f the apprximate analysis f reference [8]. Delaminatins have been bserved in the 0/90 interface f a [±1+5/0/90] laminate in reference [12]. Then, stiffnesses E-^ and E* were calculated frm equatins (l) and (2), respectively, using elastic prperties frm reference [ll]. A ply thickness f 0.15 mm ( in.) was determined in reference [3] fr the 8-ply (n = l), l6-ply (n = 2), and 2l -ply (n = 3) laminates. In figure (12), predictins f e Q were cmpared t e c values calculated by dividing measured a values frm reference [3] by Ejjyyj. Because the data frm reference [3] represents the average f nly tw r three tests fr each stacking sequence, nly preliminary cnclusins can be drawn. Nevertheless, the gd cmparisn indicates that G may be independent f the ply rientatins that make up the delaminating interface. Fr example, G c may be the same fr delaminatin nset in the -30/90 interfaces f 18

21 [±30/±30/90/90] laminates and fr delaminatin nset in the 0/90 inter- faces f the [+1+5 /-45 n / n /90 ] (n = 1,2,3) laminates. In fact, equa- tin (ll) indicates that the dependence f e Q n stacking sequence and the ply rientatins that make up the delaminating interface is accunted fr in the (E^. - E*) term. In additin, bth equatin (ll) and the data indicate that delaminatins will frm at a lwer nminal strain in thicker laminates f identical stacking sequences. Accrding t reference [k] interlaminar stress distributins calculated frm elastic analysis will be identical fr all [+^5 ri /-^5 ri / ri /90 ri ] laminates subjected t the same applied stress. Therefre, the authrs cncluded that a failure criterin, if based n critical interlaminar stresses, wuld nt predict the thickness dependence f delaminatin nset. Hence, the strain energy release rate appears t be the mst useful parameter fr quantitatively predicing the nset f delaminatin after the delaminatinprne interface(s) have been identified frm a stress analysis. DELAMINATIN GRWTH Quasi-Static Tensin Edge delaminatin has been bserved t be a stable fracture prcess in laminates subjected t tensin lading [l,5,lu], Hence, the applied lad must be increased t frce the delaminatin t grw. Tensin tests n the [±30/±30/90/90] laminates cnfirmed this bservatin. Unstable grwth f the delaminatin thrugh the width did nt ccur befre the laminate failed (fractured int tw pieces). In the fur quasi-static tests cnducted t generate stiffness data, delaminatins did nt grw after the mean applied lad exceeded 13,350 N (3000 lbs). The fur laminates eventually 19

22 failed at a mean lad f 20,000 N (1+500 lbs). Therefre, the [±30/±30/90/90] laminate is well suited t studying stable delaminatin grwth. The stable grwth f flaws can be characterized using the crack grwth resistance curve (R-curve) cncept f fracture mechanics [15]. Therefre, a delaminatin resistance curve was cnstructed. Strain energy release rates, G, were calculated frm equatin (l). Because G des nt depend n delaminatin size, it appears as a hrizntal line in figure 13. The three hrizntal lines shwn are G values calculated fr a single specimen at three successive nminal strain levels. In additin, the delaminatin resistance, Gpj, was calculated using the maximum nminal strain in equatin (10). Hwever, G^ was pltted as a pint crrespnding t the size (see fig. 9) f the delaminatin created by the nminal strain. As shwn in figure 13, the curve frmed by all such pints, generated during the fur [±30/±30/90/90] quasi-static tensin tests, cnstitutes the delamina- tin grwth resistance curve (R-curve) fr the graphite epxy specimens tested. The critical G used in the previus sectin t predict the nset f delaminatin represents the first value f G, i.e., the first pint n the R-curve. Hence, the R-curve characterizes the laminates resistance t delaminatin grwth under tensile lading. If the R-curve is independent f the ply rientatins that make up the delaminated interface, like G appears t be (see previus sectin), then equatin (10) and the R-curve can be used t predict the grwth f delaminatins under quasi-static tensin in ther laminates. As the lading is increased, G can be calculated frm equatin (10) and 20

23 cmpared -with, the R-curve t predict delaminatin size. Hence, delaminatin size as a functin f applied lad culd be predicted fr ther laminates. Fatigue Cnstant amplitude, tensin-tensin, strain-cntrlled fatigue tests f [±30/±30/90/90] graphite epxy specimens were cnducted at a frequency s f 10 Hertz and a strain rati f 0.2. Specimens were laded slwly in tensin until a small delaminatin appeared. Laminate stiffness was measured during this initial lading. Then, the specimen was unladed and delamina- tin size was recrded using DIB-enhanced x-ray phtgraphy. Next, the specimen was reladed t the mean strain and the stiffness f the delaminated specimen was recrded. Then, cnstant-strain-amplitude cyclic lading was applied. The cyclic lading was interrupted at specified intervals t measure delaminatin size and static stiffness. Hence, a phtgraphic recrd f delaminatin size and a recrd f static stiffness as a functin f lad cycles were accumulated. Cyclic lading was terminated when the delaminatin had grwn acrss mst f the specimen width and the frnt was bscured by the x-ray image f the LVDT rds (fig. 2(d)). VeJöxmlnatin qtiwth fwjtt mtcu>an.ejmznti> Figure \k shws a typical plt f delaminatin size as a functin f lad cycles. A strip delaminatin size, a, was calculated frm the delaminated area (fig. 9) measured frm x-ray phtgraphs using a planimeter. Three separate planimeter tracings f each delaminated area were perfrmed t minimize data reductin errr. As indicated in figure lu, nce the delaminatin had grwn ver the entire length f the specimen edge, a cnstant grwth 21

24 rate, da/dn, was eventually achieved. Table 1 lists the grwth rates, da/dn, determined frm least squares linear regressin analysis f the data fr each fatigue test. Figure 15 shws a typical plt f static stiffness lss as a functin f lad cycles. This plt als became fairly linear nce the delaminatin had grwn away frm the edge. Stiffness degradatin rates, de/dn, were calculated frm least squares linear regressin analysis f the data ver the same cyclic range used t fit da/dn data. Because stiffness was fund t be linearly related t delaminatin size, differentiating bth sides f equatin (h) with respect t number f cycles (W) allwed an alternate determinatin f delaminatin grwth rates, da/dn, frm measured stiffness degradatin rates, de/dn, i.e., da cln / b \ cle \S*-E LAM JdN 12 Therefre, delaminatin grwth rates fr the edge delaminatin specimens culd be estimated withut measuring the delaminatin size directly (Table l), Hence, the [±30/±30/90/9Ö"] specimens used in this investigatin shuld be useful fr generating baseline delaminatin grwth data. Data an/lzlcutln utith anali/a-u Fur fatigue tests were cnducted at each f three maximum cyclic strain levels. The maximum cyclic strain levels, max, chsen were 3000, 3250, and 3500 jim/m. The maximum strain energy release rate, G max» was calculated frm equatin (l) using e. Therefre, a cnstant max test ULclX was als a cnstant G,_ test. The mean f the fur delaminatin grwth 22

25 rates, da/dl, was determined fr each f the three G levels. A pwer curve f the frm ^ = cg max ß was fit t the three mean values f da/dw and the three values f G^ using a least squares rutine. An excellent crrelatin was achieved fr bth delaminatin grwth rate measurement tech- niques. Figure l6 shws ^ as a functin f G^^ fr grwth rates estimated directly frm measured delaminated areas. The grwth rates fr all fur tests at each G max level are shwn alng with the mean grwth rate. Figure 17 cmpares the least-squares pwer law fits using direct area measurements and indirect stiffness estimates f delaminatin grwth rates. Because bth da/dn and G can be calculated withut direct measurement f delaminatin size, the stiffness technique presents a relatively simple means f generating data t determine the dependence f empirical parameters c and 3 n differences in lad histry, frequency, temperature, etc. With the parameters c and 3 determined, the pwer law might be applied t ther laminates. The calculated strain energy release rates culd be used with c and 3 measured frm edge-delaminatin baseline tests t determine delaminatin grwth rates. NCLUDING REMARKS Methdlgy Summary A methdlgy fr analyzing the nset and grwth f delaminatins in cmpsite materials was frmulated based n findings in the current wrk and in the literature. The methdlgy is as fllws. First, a stress analysis f the particular material, cnfiguratin, and lading must be perfrmed. The analysis shuld establish where 23

26 delaminatins will be lcated. Fr unntched laminates, the apprximate analyses discussed in this paper [8,l6] might be adequate. After the lcatin is established, the delaminatin nset and grwth can be characterized quantitatively using strain energy release rates. Such a characterizatin incrprates the influence f material vlume. Furthermre, determinatin f the singular stress field at the delaminatin frnt is nt required. The current wrk indicates that a ttal strain energy release rate may be sufficient t characterize the nset and grwth f edge delaminatins in tensile-laded cupns. Mre wrk is required t determine if this is true fr ther cnfiguratins and ladings. Hwever, if strain energy release rates must be separated int G J3 G^ and G m cmpnents using a numerical analysis, then the dependence f these calculated cmpnents n grid size shuld be carefully checked and dcumented. Immediate Results A simple rule f mixtures analysis, using laminated plate thery, indicated that laminate stiffness was a linear functin f delaminatin size. The analysis accurately predicted stiffness lss due t edge delaminatins in [±30/±30/90/90] s graphite epxy laminates. The linear stiffness relatinship was used t derive a clsed-frm equatin fr the strain energy release rate, G, assciated with delaminatin grwth in unntched laminates. The simple G equatin was used t predict delamina- tin nset in [+^5 n M5 n / n /90 n ] s (n = 1,2,3) laminates using a critical G determined frm [±30/±30/90/9Ö~] s laminates. Stable c delaminatin grwth in the [±30/±30/90/9Ö"] 3 laminates was characterized 2k

27 by develping a delaminatin resistance curve (R-curve). Delaminatin grwth in [±30/±30/90/9Ö~] laminates in fatigue was characterized by develping a pwer law crrelatin between G and delaminatin grwth rates Ptential Applicatins Preliminary predictins f delaminatin nset in [ +^5 n / n / n /90 ri ] s laminates using a critical G c determined frm tests n [±30/±30/90/90] s laminates indicated that G Q may be independent f the ply rientatins that make up the delaminating interface. If this is true fr stable delaminatin grwth with increased tensile lad and delaminatin grwth in fatigue, then the delaminatin resistance curve (R-curve) and pwer law develped n [±30/±30/90/90] laminates can be used t predict delaminatin grwth in ther laminates. 25

28 APPENDIX A FINITE ELEMENT ANALYSIS Frmulatin The quasi-three-dimensinal finite element analysis was develped in reference [7]. A displacement field f the frm u = e 0 x + U(y,z) v = V(y,z) (Al) w = W(y,z) was assumed, where e was a prescribed unifrm axial strain. Eight-nded quadrilateral, isparametric elements with three degrees f freedm per nde were used t mdel a crss sectin alng the specimen length (fig. 18). nly ne quarter f the crss sectin was mdeled due t symmetry cnditins. Each ply was mdeled with ne element thrugh its thickness except fr the central 90 ply, which was mdeled with ne element thrugh its half-thickness. The graphite epxy unidirectinal prperties [ll] used in the analysis were E ll = 138 GPa ( 20 - Msi ) E 22 = E 33 = 15 GPa (2-1 Msi ) G 12 = G 13 = G 23 = 5.9 GPa (.85 Msi) (A2) v 12 = v 13 = v 23 = ' 21 26

29 APPENDIX A Virtual Crack Extensin Technique Previusly, a virtual crack extensin technique has been applied t finite element analysis f delaminatins [l,u]. In this technique, the wrk required t clse the delaminatin, expressed in terms f ndal frces and displacements, is assumed t be equivalent t the strain energy released as the delaminatin extends due t a cnstant nminal strain. This technique greatly simplifies the cmputatin f Gj, GTT» and Gj TT because knwledge f the singular stress field near the crack tip is nt required. Figure 19 illustrates the technique as it was used with the quasi-threedimensinal finite element analysis. First, the ndal frces were calculated fr an initial delaminatin f size a. Then, the delaminatin was extended an amunt Aa and the resulting ndal displacements at the same lcatin were calculated. The expressins fr Gj, GJ-J-, and GJJJ in terms f ndal frces and displacements were 1 2Aa Z l + Z b)k " W c) + Z dk - W e II 2AE Y 1 + Y 2 Vv b h \ b V p + Y'V, - V c.' d\ cl e (A3) T 2A X 1 + X 2 VlI - u ) + X 2 (IL, - u where, fr example, Z represents the frce in the z directin at nde b b calculated frm element 1. Figure 11 shws Gj and G-j-,. as functins f delaminatin size. G TTT was negligible fr this case. Strain energy release rates, G xx± -"' ' FEM 27

30 APPENDIX A calculated using equatins (A3), where nrmalized by the cnstant value predicted frm equatin (10). The ttal G, represented by Gj plus G^, reached the value* predicted by equatin (10) nce the delaminatin had grwn a very small distance in frm the edge. Furthermre, the ttal G calculated was nt sensitive t mesh refinement. Hwever, the values f G-j- and G-J-J calculated were sensitive t mesh refinement. Figure 11 shws the ndal discretizatin used in the finite element analysis. Fur different initial delaminatin sizes, a, were mdeled. Fr each a, the delaminatin was grwn in ten increments, Aa, equal t ne tenth ^Because the finite element analysis mdels nly ne quarter f the laminate crss sectin due t symmetry, the analysis assumes fur delaminatins grw simultaneusly, tw n each side, lcated in the -30/90 interfaces. Hwever, in the derivatin f equatin (10), nly a single delaminatin was cnsidered n either edge t be cnsistant with the physically bserved behavir shwn in figure 3(c) and illustrated in figure 20(a). Making the same assumptins as the finite element analysis wuld have yielded 1/ = 2b t A* = khl A = hla da = hi da which wuld result in G = * (E-^ - E*J. Hence, the values calculated frm the finite element analysis using equatins (A3) were dubled t be cnsistent with equatin (l) and the bserved physical behavir. 28

31 APPENDIX A f the initial delaminatin size. As a was increased, the mesh refinement changed accrdingly. Fr the smallest delaminatin size, G cntinually increased as the delaminatin grew, but G- was cnstant fr all ten increments f grwth. The ten values f Gj fr the smallest a are represented by a hrizntal line segment. Fr the next three delaminatin sizes, bth G and GJJ were cnstant fr all ten increments f grwth, but the ratis GJ/GJJ changed. Fr the largest delaminatin size mdeled, Gj and GJJ were identical, bth equal t ne-half the ttal G. Hence, calculatins f Gj and GJJ varied with mesh size. 29

32 APPENDIX B EFFECT F UPLING N STIFFNESS LSS The stiffness f an arbitrary cmpsite laminate may be calculated frm laminate thery [9? 10] as J LAM [A -]t 11 (Bl) where [A'] = [A] -1 + [ArtBUB^r^BHAr 1 [D*] = [D] - [B][A] _1 [B]. and [A], [B], [D] are the extensinal, cupling, and bending stiffness matrices, respectively, defined in reference [9]. If the laminate is symmetric, the [B] matrix vanishes, and equatin (Bl) reduces t equatin (l). Fr an arbitrary laminate cntaining delaminatins in ne r mre interfaces, equatin (Bl) may be used in equatin (2) t calculate the stiffnesses, E^, f the sublaminates that are frmed. Fr the [±30/±30/90/9Ö~] laminate, with delaminatins mdeled in bth -30/90 interfaces, equatin (2) becmes equatin (3) 8E (±30) p + 3E (90). E* =

33 APPENDIX B If the :(±30) 2 sublaminate stiffnesses are calculated using equatin (Bl) and material prperties frm reference [ll], then E* = 0.69 Erj M, which exceeds the value f E* extraplated frm a least-squares regressin line fr the stiffness data. Hwever, bth -30/90 interfaces did nt delaminate cmplete (fig. 3). As shwn in figure 20(a), delaminatins shifted frm ne -30/90 interface t anther thrugh varius 90 ply cracks. Delaminatins were believed t grw in this manner t reduce the effect f bending-extensin cupling that wuld have been present had nly ne interface been cleanly delaminated r had bth interfaces delaminated at the same time. Therefre, delaminatins were mdeled ver bth -30/90 interfaces (fig. 20(b)) but the bending-extensin cupling in the (±30) 2 sublaminates was neglected. Hence, the stiffness f each sublaminate was evaluated using equatin (l). This resulted in E* = E LAM which agreed with the value f E* extraplated frm a least-squres regressin line fr the stiffness data (fig. 10). In additin, stiffness lss fr delaminatins f varius s,ize was calculated frm the finite element analysis. Cncurrent strip delaminatins were assumed in bth -30/90 interfaces. Unifrm axial extensin was als assumed and, hence, bending-extensin cupling was ignred. The stiffness crrespnding t a particular delaminatin size was calculated using the technique utlined in reference [l6]. Figure 21 shws the stiffness lss predicted by the linear rule f mixutes (R..M.) equatin withut cupling (E i calculated frm eq. (l)) and with cupling (E i calculated frm eq. (Bl)). The finite element predictins agreed with the rule f mixtures equatin that neglected bending-extensin cupling. Hence, the finite element results als agreed with the data pltted in figure

34 APPENDIX C STIFFNESS CHANGE FRM SENDARY MECHANISMS Ninety Degree Ply Cracks The spacings f 90 ply cracks in the laminated prtin f partially delaminated [±30/±30/90/90] laminates were measured directly frm enlarged x-ray phtgraphs. The mean spacing is pltted in figure 22 as a functin f delaminatin size (see fig. 9) fr three quasi-static test specimens. As the delaminatins grew, the crack spacings decreased t within values predicted by a simple ne-dimensinal mdel [6]. Near the 90 ply cracks, lad was assumed t be transferred t the neighbring plies and then back int the 90 plies t frm the next crack. The mdel predicted that 90 ply cracks wuld reach a characteristic saturatin spacing, K, determined by the laminate stacking sequence, ply thickness, and ply stiffness, but independent f lad histry. Fr the [±30/±30/90/90] s laminate, the mdel predicted a saturatin spacing f.838 mm (0.033 in.). Fr a [±30/±30/90 3 ] sublaminate, representative f the delaminated prtin f the [±30/±30/90/90L laminate, the mdel predicted a saturatin spacing f mm (.367 in.). Stiffness change due t 90 ply cracking in the partially delaminated specimen was estimated by reducing the maximum axial stress in the 90 plies based n the density f cracks present. As shwn in figure 23, the transverse utiffness f the 90 plies, E 2 2, "was reduced by the percentage difference in the maximum axial stress, calculated frm the ne dimensinal mdel, at the predicted crack spacing K and at ne half the spacing K/2. This difference represents the reductin in lad carried by the 90 ply nce the saturatin crack pattern has frmed. 32

35 APPENDIX C Fr the [±30/±30/90/9Ö] s laminate, a twelve percent reductin in the axial stress in the 90 plies was predicted. Reducing, the transverse stiffness, E 22, f the 90 plies by twelve.percent resulted in a 0.7 percent reductin in [±30/±30/90/9Ö] s laminate stiffness. Similarly fr the [±30/±30/902] sub-laminate, a lit percent reductin in the axial stress in the 90- plies was predicted. Reducing the transverse stiffness, E 2 2» f the 90 plies by ik percent resulted in a 2.2 percent reductin in the [±30/±30/90 3 ] sublaminate stiffness. Because the estimated cntributins f 90 ply cracks t stiffness reductin in the [±30/±30/90/9Ö"] s delaminatin specimen were s small, they were neglected in calculating E*. Hwever, fr ther laminates and materials, ply cracking may have a greater effect n axial stiffness and ther stiffness parameters [lt,l8]. +30/-30 delaminatins The largest +30/-30 interface delaminatins, a, recrded during the fur quasi-static tensin tests were measured and tabulated in table 2. nly specimen E20 had a +30/-30 delaminatin f significant size. Als shwn in table 2 are predicted stiffness values fr the [±30/±30/90/90] S laminate, cntaining bth -30/90 and +30/-30 interface delaminatins. The stiffness was predicted using equatins (2) and (k) first fr the +30/-30 delaminatin, and then fr the -30/90 delaminatin. The stiffness predicted fr specimen E20 was three percent less than the stiffness predicted assuming nly -30/90 delaminatin. Hwever, the data agreed best with the predictin that mitted the +30/-30 delaminatin. Hence, the effect f +30/-30 interface delaminatins n measured [±30/±30/90/9Ö"] stiffness lss was neglected in calculating E*. J s 33

36 REFERENCES 1. E. F. Rybicki, D. W. Schmueser and J. Fx, "An Energy Release Rate Apprach fr Stable Crack Grwth, in the Free-Edge Delaminatin Prblem," J. Cmpsite Materials, Vl. II (1977), P- ^ G. L. Rderick, R. A. Everett, and J. H. Crews, Jr., "Debnd Prpagatin in Cmpsite-Reinfrced Metals," Fatigue f Cmpsite Materials, ASTM STP 569, American Sciety fr Testing and Materials, 1975, PP B. T. Rdini, Jr. and J. R. Eisenmann, An Analytical and Experimental Investigatin f Edge Delaminatin in Cmpsite Laminates, *rth Cnf. n Fibrus Cmpsites in Structural Design, San Dieg, Calif., Nv. lu-17, h. A. S. D. Wang, F.. Crssman, and G. E. Law, "Interlaminar Failure in Epxy-Based Cmpsite Laminates," Prc. 29th Symp. Failure Mdes in Cmpsites, Natinal Bureau f Standards, L. M. Lackman and N. J. Pagan, "n the Preventin f Delaminatin in Cmpsite Laminates," AIAA/ASME SAE 15th Structures, Structural Dynamics and Materials Cnference, *, Paper N. 7^ K. L. Reifsnider, E. G. Henneke, and.. Stinchcmb, "Defect Prperty Relatinships in Cmpsite Materials, AFML-TR-76-81, Final Reprt, June I. S. Raju and J. H. Crews, "Interlaminar Stress Singularities at a Straight Free Edge in Cmpsite Laminates," NASA TM-81876, August N. J. Pagan and R. B. Pipes, "Sme bservatins n the Interlaminar Strength f Cmpsite Laminates," Internatinal Jurnal f Mechanical Science, Vl. 15 (1973), pp R. M. Jnes, Mechanics f Cmpsite Materials, Scripta (1975). 10. T. K. 'Brien and K. L. Reifsnider, "Fatigue Damage: Stiffness/ Strength Cmparisns fr Cmpsite Materials," Jurnal f Testing and Evaluatin, Vl. 5, N. 5, 1977, pp. 38U A c S D. Wang and F. W. Grssman, "Sme New Results n Edge Effect in Symmetric Cmpsite Laminates," J. Cmpsite Materials, Vl. II (1977), p G. R. Irwin, "Fracture," Handbuch der Physik, Vl. 6 (1958), p J. G. Bjeletich, F.. Crssman, and W. T. Warren, "The Influence f Stacking Sequence n Failure Mdes in Quasi-Istrpic Graphite Epxy Laminates," Failure Mdes in Cmpsites - IV, AIME, H

37 Ik. K. L. Reifsnider, E. G. Henneke, II, and W. W. Stinchcmb, "Delaminatin in Quasi-Istrpic Graphite-Epxy Laminates," Cmpsite Materials: Testing and Design (Jlth Cnference), ASTM STP 6l7 (1977), P Fracture Tughness Evaluatin by R-Curve Methds, ASTM STP 527, American Sciety fr Testing and Materials, Philadelphia, Pennsylvania, T. K. 'Brien, "An Apprximate Stress Analysis fr Delaminatin Grwth in Unntched Cmpsite Laminates," Prceedings f the Sixth Annual Mechanics f Cmpsites Review,. Daytn, hi, ctber, A. L. Highsmith and K. L. Reifsnider, "The Effect f Tensile Fatigue Damage n Tensile, Cmpressive, and Bending Stiffness f Cmpsite Laminates," Cmpsites Technlgy Review, Vl. 2, N. 1, Winter W. S. Jhnsn and G. J. Dvrak, "Mechanisms f Fatigue Damage in Brn/Aluminum Cmpsites," Presented at ASTM Sympsium n Damage in Cmpsite Materials, Bal Harbur, Flrida, Nvember 10-14, 1980, (will appear in ASTM STP). 35

38 TABLE 1.- FATIGUE GRWTH RATE MEASUREMENTS max (ym/m) G max (J/m 2 ) Spec. # da dn' Area measure mm cycle Stiffness measure P a de dn' cycle Cycle r ange f linea r fit (cycles x 10 3 ) C ^5-120 Fl F2k 2U CI ^0-115 i f ' f MEAN 2k A7 la.8 k - 80 F k Ik - 50 El k - 70 Cl k > r 1 ' MEAN 38.2, D B ^ k D22 6k B21 V r ' f MEAN

39 TABLE 2.- EFFECT F +30/-30 DELAMINATIN N STIFFNESS PREDICTIN Specimen # -30/90 +30/-30 E / E IAM predictin a.' b b E/E Q measured With ä i Withut ä i F E C D6,

40 c. ri ' 2 UJj_ «se- l~j es 5fe z < UJ i CL. a cr. cu '.).... c. :> : UJ. a.] t t/1 '2 IS +i T <:z Q. C71

41 IBSk +1 :*S' : Sf q :;M:', BM - $ <-* «a : i f; I«:" p;, : "'f 1 S?:. \ c_;- 22 < < >- 2: «-J «\_ «: < j.j.,1 Cr- WHJ MMV'' ; % : " - liiil

42 \ < "J *~^S* wmk^ y»*»*0, "" tu - 1 i * ^ ; 25 H """"** 3 < LLi CC </> : -< \ : ~3 \J C\J

43 M

44 ) - er N M a M t = r 1 r 1 TU. M h E a i i 1 1 ]"-> Icn c s cu en Z \ Ai h» 1 +1 xr s M 1 N^ x: en i±j Z3 l_ XI 1 L M LC CU i_ r3 en 1+2

45 D": >^ L CM M L >- 1 «^. m i ^ t < X M G > CM v ' ja CM N b CJ c: X cz JQ -i i a -c +j a r-h l.c 031 Z3 r3 CM CM ITN LPi I Q_ I t L_ Z3 i+3

46 «4- i i I i c: a i_ 13 +-> X i «rj r i i_ CJ) ^

47 ^'' ' ' ' ' TlTffifY-TlViV'"*.,v'-I-!-l-l-,v,v,vl-M mmmimamaan"' "wmfflwhw" <r\ CM ^H*M*MliiMiMÜrii^ Öl 11 1 i-h a +-> c t a X a. ** Mill ilimmj i* f VlWliliiiiiHiiiiii^ LU c a X Q- < f " a t c CU g N 1 1 c: V 1 00 U5

48 3T s: <r i -> i < J ^ < g <r UJ i INI UJ Q n " Q UJ Q 1 i 1 1 l/> < < s_ Q. Q. a a i < < i ^ UJ Di Q < C/5 a s_ M n uj UJ DU U_ c/1 i± < - ^ (13 I cn cn 1*6

49 i i It m 5 (>r) ft n % >- T < <c 7 Aw d i 2: LU T b Stiffness as a functin f delaminatin size. u_ - CNJ i < C I 1 1 ID ^ Q U_ 1_ Z3 P -1 1 LL l 1 ^ «=3- CVl i i LU LU * UT

50 a C/5 t ~ S ffl Fft CX> cz a cz <U E cu cu II _i < ( I V 1 II 1 <n / < ZJ 1 =7. T El v CM r - cu E Nl -1 1 J^ n cz M -f 1 c +-> cu c: cz I 1 Q. irr. fc: a i cu a cu 4-J 4- a i_ cz cu i ( a +-J cu t i cr cu rj i_ 4 >. ) i_ cu c: a> cz -f 4 a L_ 4-J G 1 l_ LPv cu s_ Z3 ai 1+8

51 m CM II C\J I Q_ U_ LU ID ^ d) L_ a E u - a c: +-> I 1 +-> <_> * N i i i^> a % CM i_ ^ ci i 1 4-> II a> c c: c: ^^ c: ( 1 Z I 1 4-J en a \ cr c i i E \ cz r 4 m cu =r T3 i \ <D c: Dl L T3 a- LU.+, -vt CM CSI Z3 1+9

52 00 CM LA I _ 1 I CJ) \ +1 "v. +1, v X 31 1 ' n < nr, +1 CNJ «+1 ' i ' * a> +- > a $_ c 3 i i 1 E (Ul-Q i a I Cd i >. X > «vt i_ a * i +-» 1 1 c XT a Q. 4-» L_ -i i en a> i_ CXJ Z I rh i_ CNJ 50

53 i I X 0 M. 1 0 r 1 +-» v amina ycles 2: * " TD c/> a UJ H- *$ 1 «0 >- -M M 0 r 1 a. c: 0 1! 1 a -t-» CJ 0 CNJ. rs >> M- l i ir\ u\ E E u ZJ en 1 i «7 51

54 t a cu V C\i ii 4-. irh M cu 1 1 a >. r-h +-> a a +-j a,_ » C 1 Q J r 1 <_) c: u Z a. >» h- L 1-H Lf\ LT\ CU L_ LU <3 ) 52

55 l. X 03 <2: CV X S E "d- LT\ i i i i X 1 1 X E lj ( ) E >- i X x CP t_> cz t 2? lncj > 2: D_ I td ih ) 53

56 LA vt i i i X I i i X >- CM E LC\ LA i i X r > CJ <u ex c: E c E i_ t cu er c: cu CÜ 1 cu i_ r3 i i U_ 5U

57 <v c i_ E -r * <_> Q. H s 0) -IT-I i I 00 55

58 1 r H ^ ZJ LJJ H- i X LU ct: LU 4-> f u- a < a> Z3 ^^ X3 " ' - => cr a) "-H 4-» c a sz s- a) cu +-> a c: <u.--t i- cr cu >. 4-» Ü) X s- CÜ S ± a c c/> i_ «- 2 a X c a: 1 > u_ LJJ 1 - cr> ^~~ ' r-i i_ rs en 56

59 e a. -a Q a> 4-> a x L_ Q. I CNI i_ en 57

60 -I I c vd Q LU < rl -Q l/) 1 m +1 n +1 Q UJ < U- CNJ Q. m i I I I CNI cu C\J 58

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63 1. Reprt N. NASA TM-819^0 4. Title and Subtitle 2. Gvernment Accessin N. CHARACTERIZATIN F DELAMINATIN NSET AND GRWTH IN A MPSITE LAMINATE 7. Authr(s) T. Kevin 'Brien 9. Perfrming rganizatin Name and Address NASA Langley Research Center Hamptn, VA Spnsring Agency Name and Address Natinal Aernautics and Space Administratin Washingtn, DC 205^6 3. Recipient's Catalg N. 5. Reprt Date January 198l 6. Perfrming rganizatin Cde 8. Perfrming rganizatin Reprt N. 10. Wrk Unit N Cntract r Grant N. 13. Type f Reprt and Perid Cvered Technical Memrandum 14. Army Prject N. 15. Supplementary Ntes Presented at the ASTM Sympsium n Damage in Cmpsite Materials: Basic Mechanisms, Accumulatin, Tlerance, and Characterizatin, Bal Harbur, Flrida, Nvember 10-lH, 1980., _ 16. Abstract The nset and grwth f delaminatins in unntched [±30/±30/90/90] s graphite-epxy laminates is described quantitatively. These laminates, designed^ t delaminate at the edges under tensile lads, were tested and analyzed. Delaminatin grwth and stiffness lss were mnitred nndestructively. Laminate stiffness decreased linearly with delaminatin size. The strain energy release rate, G, assciated with delaminatin grwth, was calculated frm tw analyses. A critical G fr delaminatin nset was determined, and then was used t predict the nset f delaminatins in [+U5 n /-^5 n / n /90 n ] s (n=l,2,3) laminates. A delaminatin resistance curve (R-curve) was develped t characterize the bserved stable delaminatin grwth under quasi-static lading. A pwer law crrelatin between G and delaminatin grwth rates in fatigue was established. 17. Key Wrds (Suggested by Authr(s)) Graphite-epxy Stiffness lss Delaminatin R-curve Ply cracking Fatigue Rule f mixtures Grwth law Strain energy release rate 18. Distributin Statement Unclassified - Unlimited Subject Categry 2k 19. Security Classif. (f this reprt) Unclassified 20. Security Classif. (f this page) Unclassified 21. N. f Pages Price* A04 Fr sale by the Natinal Technical Infrmatin Service, Springfield, Virginia 22161