J

NASA TECHNICAL MEMORANDUM 109052"" /

6z/

Analysis of Local Delaminations Caused by Angle Ply

Matrix Cracks

Satish A. Salpekar, T. Kevin O'Brien and K. N. Shivakumar

November 1993

National Aeronautics and

Space Administration

LANGLEY

Hampton,

RESEARCH CENTER

Virginia 23681-0001

(NASA-TM-IO9052) ANALYSIS OF_ELAMINATIONS CAUSED BY ANGLEMATRIX CRACKS (NASA) 67 p

LOCAL

PLY

N94-24083

Uncl as

G3124 0203596

https://ntrs.nasa.gov/search.jsp?R=19940019610 2020-05-20T18:11:19+00:00Z

SUMMARY

Two different families of graphite/epoxy laminates with similar layups

but different stacking sequences, (0/e/-0)s and (---6/0/0)s, were analyzed using

three-dimensional finite element analysis for 0 =15 and 30 degrees.

Delaminations were modeled In the -0/8 interface, bounded by a matrix crack

and the stress free edge. The total strain energy release rate, G, along the

delamination front was computed using three different techniques: the virtual

crack closure technique (VCCT), the equivalent domain integral (EDI)

technique, and a global energy balance technique. The opening fracture mode

component of the strain energy release rate, Gi, along the delamination front

was also computed for various delamination lengths using VCCT. The effect of

residual thermal and moisture stresses on G was evaluated.

KEYWORDS: Composite Material, Graphite Epoxy, Delamination, Matrix

Crack, Finite Element Analysis

INTRODUCTION

The design of composite structural parts and their life prediction under

service conditions requires the understanding of the details of damage modes

occurring in composites [1]. Some of the important damage modes in laminated

composites are matrix cracking and the local delamination in the region where

a matrix crack meets a stress free edge. Such local delaminations may

contribute to eventual failure of the laminate.

The tests conducted on [0n/-J:l 5]s laminates by Lagace and Brewer [2]

showed that the delamination area in the 15/-15 interface extended between

the transverse ply crack and the free edge. O'Brien & Hooper [3] and O'Brien [4]

found that matrix cracking was detected as the first event, followed by local

delamination, in (02/02/-02)s graphite/epoxy laminates (0=20, 25, 30 degrees)

subjected to tension fatigue loading. This same damage sequence was

observed by O'Brien [5] in (02/-e2/02)s graphite/epoxy laminates (0=15, 30

degrees). The matrix cracks formed near the stress free edge and the local

delaminations formed in the e/-e interface. These local delaminations were

bounded between the free edge and the matrix crack, as shown schematically

in figure 1.

Salpekar and O'Brien [6] analyzed (0/0/---e)s graphite/epoxy laminate

(e=15, 45 degrees) subjected to tension load, using a three-dimensional finite

element analysis. For the e .,15 degree case, the matrix cracking in the -15 ply

was found to create a very large, and possibly singular, interlaminar tension

stress in the 15/-15 interface. This apparent singularity indicated that the

delamination may initiate at the point where the matrix crack intersects the

laminate edge. For the 0 = 45 degree case, the strain energy release rate, G,

2

for a local delamlnatlon was calculated for a delamination in the 45/-45

Interface, growing uniformly away from the matrix crack in the -45 degree ply.

For this case, G was higher near the laminate edge than in the interior of the

laminate. In an experimental and analytical study, Fish and O'Brien [7]

concluded that in (15/90n/-15)s glass/epoxy laminates, the interlaminar tensile

stresses due to cracking in the +15 degree ply plays a significant role in the

onset of local delamination.

The purpose of the present study was to compute the strain energy

release rates associated with local delaminations originating from matrix cracks

in two different families of laminates with similar layups but different stacking

sequences. Both (0/e/-0)s and (-e/0/0)s graphite/epoxy laminates were

analyzed using three-dimensional finite element analysis, for e =15 and 30

degrees. These two cases were chosen because they bound the behavior

observed in experiments on orthotropic laminates with angle ply matrix cracks

[3-5]. The experimentally observed local delaminations that formed in the -e/0

interface and were bounded by the matrix crack and the stress free edge were

modeled using three-dimensional finite elements. The strain energy release

rate, G, along the delamination front was computed using three different

techniques; the virtual crack closure technique (VCCT) [8], the equivalent

domain integral (EDI) technique [9-11], and a global energy balance technique

[12]. The computation of G was performed for three delamination fronts

corresponding to three unique delamination lengths. The effect of residual

thermal and moisture stresses on G was also evaluated.

3

LAMINATE CONFIGURATIONS AND LOADING

The two graphite/epoxy laminates, (02/02/-02)s and (02/-02/02)s, tested

in references 3-5 were 5 inches long, 1 inch wide, and 12 plies thick, each ply

being .005 Inohes thick. For simplicity in the modeling, these laminates were

assumed to be 6 plies thick, with each ply having a thickness of 0.01 inches.

Furthermore, In order to take advantage of symmetry in boundary conditions,

the second stacking sequence was altered in the modeling so that the -0

degree ply was on the surface. Hence, the two laminates were modeled as

(o/o/-o)s and (-0/0/0)s laminates.

Because the matrix cracks and local delaminations observed in

references 3-5 never extended a distance greater than 5 to 10 times the ply

thickness (h) from the free edge, for reasons of computational efficiency

specimen dimensions were assumed in the model that were much smaller than

the physical dimensions. As shown in fig.2, the model was 75h long by 10h

wide. The coordinate axes were assumed as shown in the fig. 2, with the origin

located at point A. Only half of the laminate thickness was modeled and the

symmetry boundary conditions were applied on the appropriate plane of

symmetry for each _tacking sequence. Thus, the symmetry condition was

applied on the z=0 plane for (0/0/-0)s laminate, and on the z=3h plane for the

(-0/0/0)s laminate.

The matrix crack extended through the thickness of the -0 degree ply,

parallel to the fiber direction in the xy plane. Although the matrix cracks

observed at the free edge in references 3-5 formed at oblique angles to the xy

plane (fig.l), the matrix crack plane was modeled normal to the xy plane for

simplicity and computational efficiency (fig.2).

4

The local delaminatlonwas modeled in the e/-e interface, with the

delamination front inclined at an angle of 20 to the free edge as observed in

references 3-5 (fig. 1). The elastic constants for the graphite/epoxy material

used in the analysis are shown in Table 1. The laminate was subjected to a

uniform displacement by constraining the plane x=0 in the x direction and by

applying an arbitrary uniform displacement of 0.01 inch in the positive x-

direction to the x=75h plane (fig. 2). This displacement corresponded to a

uniform axial strain of 0.0133 in/in. Residual thermal and hygroscopic loads

were applied as described in reference 13.

ANALYSIS

The finite element model of the laminate consisted of 2394 20-noded

hexahedral elements having 11,560 nodes (fig. 3). A fine mesh was used in

the area surrounding the intersection of the -e degree matrix ply crack and the

free edge. For elements at the intersection of the matrix crack and free edge, the

nodes on two edges of the hexahedral elements were consolidated to form

pentahedral elements.

The region of local delamination in the 0/-e interface bounded between

the matrix crack and the free edge was modeled beginning with the first

delamination front at a distance of one ply thickness, h, from the intersection of

the matrix crack with the free edge, followed by elements one third of a ply

thickness, hi3, long at the free edge (fig.4). All elements had a z-direction

thickness of hi3. This mesh was gradually transitioned to a coarser mesh away

from the region of local delamination. Separate finite element models were

generated for e =15 and 0 = 30 degrees cases for the two layups (o/e/-e)s

and (-e/e/O)s.Separate models were needed for each e because the matrix

5

crack in the -e degree ply was parallel '_othe fiber direction and the

delaminatlon front in the xy plane was inclined at 20 to the free edge (fig. 1).

The strain energy release rate associated with the local delamination

was calculated at the delamination front which was inclined at 29 to the free

edge (fig.l). Three different delamination fronts were used for the G calculation.

The length, a, of the delamination front measured along the free edge for the

three cases, was 1.66h, 2.33h, and 3.33h, where h is the ply thickness. The

delamination front was subdivided into six equal length, L, segments as shown

in fig. 4. The magnitude of L for any particular front was a function of the

delamination length, a, and e.

Because the in-plane normal stresses perpendicular to the

fiber direction, o'22, in the -0 degree ply had been previously

determined to be tensile only near the free edge [3], G calculations

were performed for two different damage configurations. In the first

case, the matrix crack was modeled at a distance corresponding to the length at

which the matrix crack faces started to cross into one another. The matrix crack

length, d, was then held fixed and the delaminations were extended to compute

G. The delamination front never reached the matrix crack front in this case. In

the second case, the matrix crack extended only as far as the delamination

front for each increment of delamination growth.

Three different methods were used to compute G. The first method was

based on the change in the global energy due to the movement of the

delamination front and gives the average G between two delamination fronts

[12]. The other two methods, the Virtual Crack Closure Technique (VCCT) and

the Equivalent Domain Integral (EDI) technique, were used to compute the

distribution of G along the delamination front at each delamination length.

6

The VCCT is well documented in the literature [8]. The VCCT techniques

requires that the elements behind and ahead of the delamination front be

orthogonal to the delamination front. In the present problem, this requirement is

violated because the finite element mesh configuration is dictated by the shape

of the local delamlnation. The local delamination initiates at the intersection of

the matrix crack in the -0 ply and the free edge and the delamination front is

inclined at 20 to the free edge. Thus, the finite element mesh will appear to be

radiating from a corner as shown in figure 3. The EDI technique [9,10,11] does

not have this orthogonality requirement. Therefore, the G computation was

alternatively performed using EDI, and the results of the two methods were

compared.

The EDI method is used to obtain the total J-integral for cracked elastic

and elastic-plastic bodies. For an elastic body, J is equivalent to G. The total

J-integral at any point along the crack front in a 3-D cracked body is defined as

an integral of the energy potential over a closed surface around the crack front.

Recently, the surface integral was extended to a volume integral, called the

equivalent domain integral, for ease of implementation in a finite-element

analysis and accurate evaluation of the integral [9,10,11]. This was done using

Green's divergence theorem and de Lorenzi's s-function [14]. The s-function is

a continuous function defined from the inner surface to the outer surface of the

domain selected for the J-integral calculation. The J-integral is evaluated from

the accumulated stress-work density, stress, total strain, and displacement

fields.

To implement the EDI method, element numbers are input within the user

selected domain, at node numbers on the inner surface at which s is defined to

be 1. The selection of the domain depends on the gradient of the strength of

singularity along the crack front, and the finite element modeling in the crack

7

front region,etc, The guidelines for the selection of the s-function and the

domain are given in reference 11.

TOTAL G RESULTS AND DISCUSSION

The results of the analysis of (0/e/-e)s and (-0/0/0)s graphite/epoxy

laminates for 0 .,15 and 30 degrees are discussed. For each layup, the G

results are presented for a fixed matrix ply crack length ahead of the

delamination front as well as for the case where the matrix ply crack extends

only as far as the delamination front. The effect of delamination growth was

studied by considering three delamination lengths (a/h= 1.66, 2.33, 3.33). The

effect of thermal and moisture residual stresses on the (0/30/-30)s laminate was

also analyzed (see appendix).

Results for (0/15/-15)__

The matrix ply crack in the -15 ply was allowed to grow in hi3 increments

until the crack faces began crossing into one another. This crack length was

found to be d=3.67h. Then, keeping this crack length constant, the

delamination was modeled considering three delamination lengths (a/h= 1.66,

2.33, 3.33).

The strain energy release rate along the delamination front for each

case is shown in figures 5-7, respectively. The results from the VCCT and EDI

methods agree well along the middle of the delamination front but diverge near

the matrix crack and the free edge where the EDI values were always lower

than the VCCT values. The difference in the VCCT and EDI results are limited

to the last element near the matrix crack and the free edge. If a more refined

8

mesh had been used, with more elements along the delamination front, the

difference in the two techniques for calculating G would be insignificant

everywhere except at the matrix crack and free edge. Hence, the VCCT

technique yields accurate G distributions along the delamination front even

though the finite element mesh at the delamination front is not orthogonal.

The VCCT results for all three delamination fronts are shown in figure 8.

The G distribution is relatively uniform along the front at a/h=1.66, but becomes

slightly skewed at a/h=3.33, with a greater G near the free edge than near the

matrix crack. This change in the G distribution indicates that the delamination

may change shape slightly as it grows, deviating from the 2(] angle with the free

edge that was originally assumed.

The average G along the front calculated using the VCCT and EDI

techniques was obtained for each delamination length. These average G

values are plotted in figure 9. As noted previously, the average EDI values are

lower than the VCCT values, but this discrepancy would diminish if a more

refined mesh was used near the matrix crack and free edge. Also shown in

figure 9 are the average G values between successive delamination fronts,

obtained from the change in global energy, and plotted at the midpoint between

the fronts. The first point from the "global energy" method (a=l.33h)

corresponds to the average energy released from the initial delamination length

modeled at a=l.0h up to the first delamination front at a=1.66h. The average G

increases slightly with increasing a/h and the VCCT and global energy based

methods are in goocl agreement. Although the assumption of orthogonality is

violated in the modeling, VCCT gives fairly accurate results, which are in

agreement with the global energy balance. Therefore, VCCT appears to be a

robust technique for G calculation.

9

The G variations along the delamination front for the three values of aJh

where the matrix crack extends only to the delamination front are shown in

figure 10. The average G calculated using VCCT along the front as a function of

aJh is shown in figure 11. Also shown in figure 11 is the average G calculated

using VCCT along the front vs. a/h from figure 9. The average G where the

matrix crack extends only as far as the delamination front is lower than the

average G where the matrix crack length is held constant at d=3.67h. Hence,

the matrix crack length will influence the magnitude of the strain energy release

rate for local delamination growth. A corresponding G analysis for matrix crack

growth would need to be performed and compared to an appropriate failure

criteria to establish which case is more appropriate. Such an analysis may need

to be performed iteratively with the delamination analysis because any

delamination that initiates may also influence the G for further matrix crack

growth. However, experimental observations for brittle matrix composites [3-5]

indicates that the assumption made in the first case, of a constant matrix crack

length corresponding to the distance to crack closure, may be a reasonable

approximation for analyzing delamination onset and assessing delamination

durability.

Results for !0/30/-30)s_

In the analysis of (0/30/-30)s laminate, the matrix ply crack was grown up

to d=4.33h before the crack faces started crossing into one another. This crack

length was then held constant and the G computation was performed for local

delamination growth. Figures 12-14 show the G variation across the

delamination front, for aJh=1.66, 2.33, 3.33, respectively. As noted previously,

the EDI results agree with the VCCT results along the middle of the

10

delaminatlon front but diverge for the elements near the matrix crack and the

free edge where the EDI values were lower than the VCCT values. However, G

values calculated in the middle of the delamination front using these two

techniques for a/h=1.66 (fig.12) do not agree as closely as was observed for the

longer delamlnation lengths (flgs.13&l 4).

Figure 15 shows the VCCT results for the three values of a/h. The G

distribution are slightly skewed for all three values of a/h, with a greater G near

the free edge than near the matrix crack. The distributions become less uniform

with increasing a/h. This skewness in the G distribution indicates that the

original delamination shape may deviate from the 20 angle originally assumed

and that the delamination may change shape as it grows.

The average G across the front, as calculated by VCCT as a function of

a/h, Is shown in figure 16. The variation in G with increasing a/h is fairly small,

with a only a slight decrease in G up to a/h=3.33. Similar to the e=15 degree

case, the VCCT and the global energy method are in good agreement and the

EDI values are lower due to the lower values in the end segments.

The G variations along the delamination front for the three values of a/h

where the matrix crack extends only to the delamination front are shown in

figure 17. The average G along the front as a function of a/h is shown in figure

18. Also shown in figure 18 is the average G along the front vs. a/h from figure

16. As noted previously for the 0=15 degree case, the average G where the

matrix crack extends only as far as the delamination front is lower than the

average G where the matrix crack length is held constant at d=4.33h. Hence,

the matrix crack length will influence the magnitude of the strain energy release

rate for local delamination growth.

11

Results for _-15/15/0!._ Laminate

For the (-15/15/0)s layup, the matrix crack length in the -15 degree ply

was maintained at d=3.67h; the same length as the (0/15/-15) layup. G was

also computed for the same delamination locations; a/h=1.66, 2.33, 3.33. The G

distributions along the delamination front are shown in figures 19-21. The

comparison between EDI and VCCT is consistent with the previous layup.

However, G values calculated in the middle of the delamination front using

these two techniques for a/h=1.66 (fig.19) do not agree as closely as was

observed in the previous layups or as was observed for the longer delamination

lengths for this layup (figs.20&21).

Figure 22 compares VCCT G distributions along the delamination front

for all three delamination lengths. The G distributions are skewed for all three

values of a/h. Unlike the previous cases, however, the distributions are more

non-uniform at the smaller delamination lengths, indicating that the original

delamination shape may deviate significantly from the 20 angle originally

assumed but may approach this shape as the delamination grows.

The average G across the delamination front, as a function of a/h, is

shown in figure 23. Tho variation is fairly small, with a slight decrease in G, up

to a/h=3.33. As noted previously, the VCCT and the global energy method are

in good agreement and the EDI values are lower due to the lower values in the

end segments.

plesults for {- 30/30/0__

For the (-30/30/0)s layup, the matrix crack length in the -30 ply was

maintained at d=4.33h; the same length as the (0/30/-30) layup. Figures 24 and

12

25 show the G distribution along the delamination front for the _,-30/30/0)s

layup containing a matrix crack in the -30 ply, for a/h=1.66 and 3.33,

respectively. The comparison between EDI and VCCT is consistent with the

previous layup. As noted in that case, G values calculated in the middle of the

delaminatlon front using these two techniques for a/h=1.66 (fig.24) do not agree

as closely they did for the longer delamination length of a/h=4.33 (fig.25).

Figure 26 compares VCCT G distributions along the delamination front

for all three delamination lengths. The G distributions are skewed for all three

values of a/h. The distribution at the intermediate delamination length

(a.h=2.33) is the most uniform, indicating that the original delamination shape

may deviate from the 29 angle originally assumed, but the delamination

approaches this shape before deviating once again with further growth.

The average G across the delamination front, as a function of a/h, is

shown in figure 27. There is a slight decrease in G with delamination length up

to a/h=3.33. As noted previously, the VCCT and the global energy method are

in good agreement and the EDI values are lower due to the lower values in the

end segments.

Comoarison of 15 and 30 dearee layu0s

Figures 28 and 29 compare the average G along the delamination front

for the 15 and 30 degree layups for the two unique stacking sequences,

respectively. For both stacking sequences, the 30 degree layup had a greater

average total G than the 15 degree layup.

13

GI RESULTS AND DISCUSSION

Recent studies have indicated that G components due to the three

unique fracture modes I, II, and III (corresponding to opening, sliding shear,

and tearing shear, respectively), as calculated using the VCCT technique in

finite element analyses, are depended on the mesh refinement at the

delamination front [15-17]. This mesh size dependence has been attributed to

the oscillatory nature of the singularity associated with a crack growing at a

bimaterial interface [16]. Two techniques have been proposed to overcome this

limitation. The first involves modeling the resin rich layer between delaminating

plies as a thin adhesive film and simulating the delamination growth within this

thin resin layer. Although this technique yields G components that are

independent of mesh refinement, it requires a very fine mesh near the

delamination front, and greatly increases the number of degrees of freedom

required in the model. The second technique involves modifying specific

material properties in the elements at the delamination front such that the

oscillatory term in the singularity vanishes [17]. This technique has only recently

been proposed, and to date, has not been attempted in fully 3D analyses.

These techniques are needed if a quantitative comparison of calculated

fractures modes are required to compare to delamination failure criteria for

predicting experimentally observed delamination failures. However, if a

reasonable mesh refinement is used at the delamination front, where element

dimensions are no larger than the ply thickness, h, and no smaller than the fiber

tow dimensions (typically h/20 for graphite fiber reinforced composites),

qualitative conclusions may be drawn as to the presence and distribution of the

three fracture modes for delamination in a particular laminate configuration and

loading. This is the approach that was taken in the present study.

14

The opening fracture mode component of the strain energy release rate,

Gi, was determined using the VCCT technique for the cases where the

matrix crack length was held constant. However, because of the non-

orthogonality of the finite element mesh, the two independent shear

fracture mode components, GII and Gill could not be isolated.

However, the sum of these two modes must equal the difference in

the total G and the mode one component, G l. In addition, for brittle

epoxy matrix composites, the mode I interlaminar fracture

toughness, GIc, is typically much lower than either the mode II or

mode III interlaminar fracture toughness, GIIc and GIIIc, respectively

[3-5]. Hence, The presence of mode I, and its relative contribution to

total G, is often of primary concern.

Results for e = 15 dearee Laminates

Figures 30 and 31 show the distribution of Gi across the delamination

front for the (0/15#15)s and (-15/15/0)s laminates, respectively. For all three

delamination lengths modeled, the mode I component was greatest near the

matrix crack and vanished near the free edge. In addition, the mode I

component decreased with increasing delamination length. Fig. 32 shows the

dependence of Gi on delamination length using the value calculated

next to the matrix crack for both laminates. Fig. 33 shows the ratio of Gi

to the total G as a function of delamination length using the values

calculated next to the matrix crack for both laminates. Comparison

of the (0/15/-15)s and (-15/15/0)s laminates in figures 32 and 33 illustrate the

influence of stacking sequence on local delamination. The GI/G ratio for the

(-15115/0)s laminate with a matrix crack in the surface -15 degree ply is greater

15

than the GI/G ratio for the (0/15/-15)s laminate with a matrix crack in the -15

degree ply in the interior of the specimen thickness.

Results for 0 = 30 degree Laminate

Figures 34 and 35 show the distribution of GI across the delamination

front for the (0/30/-30)s and (-30/30/0)s laminates, respectively. For

all three delamination lengths modeled, the mode I component was greatest

near the matrix crack and decreased near the free edge. In addition, the mode I

component decreased with increasing delamination length. Fig. 36 shows the

dependence of Gi on delamination length using the value calculated

next to the matrix crack for both laminates. Fig. 37 shows the ratio of Gi

to the total G as a function of detamination length using the values

calculated next to the matrix crack for both laminates. Comparison

of the (0/30/-30)s and (-30/30/0)s laminates in figures 36 and 37

illustrate the influence of stacking sequence on local delamination. The Gi/G

ratio for the (-30/30/0)s laminate with a matrix crack in the surface -30

degree ply is greater than the GI/G ratio for the (0/30/-30)s laminate with

a matrix crack in the -30 degree ply in the interior of the specimen thickness.

Comoarison of 15 and 30 degree layuos

Figures 38 and 39 compare the Gi/G ratios for the 15 and 30 degree

layups for the two unique stacking sequences, respectively. For both stacking

sequences, the 30 degree layup had a greater GI/G ratio than the 15

degree layup.

16

CONCLUSIONS

Two different families of graphite/epoxy laminates with similar layups

but different stacking sequences, (0/0/-0)s and (-8/e/O)s, were analyzed using

three-dimensional finite element analysis for 0 =15 and 30 degrees.

Delaminations were modeled in the -e/e interface, bounded by a matrix crack

and the stress free edge. The total strain energy release rate, G, along the

delamination front was computed using three different techniques: the virtual

crack closure technique (VCCT), the equivalent domain integral (EDI)

technique, and a global energy balance technique. The opening fracture mode

component of the strain energy release rate, Gi, along the delamination front

was also computed for various delamination lengths using VCCT. The effect of

residual thermal and moisture stresses on G was evaluated. From these

analyses, the following conclusions were drawn:

(1) The variation of average G along the delamination front as a function of

delamination length was relatively small, with the VCCT and global energy

based methods showing good agreement.

(2) The G distributions along the delamination front calculated from the VCCT

and EDI methods agree well in the interior but diverge at the end segments

near the matrix crack and the free edge. The EDI values at the end segments

were always lower than the VCCT values. The average EDI values were lower

than the values obtained by the other two methods due to the significantly lower

G values at the end segments.

17

(3) Although the assumption of orthogonality is violated in the finite element

model, VCCT gives fairly accurate results, which are in agreement with the

global energy balance and EDI techniques. Therefore, VCCT appears to be a

robust technique for G calculation.

(4) The matrix crack length influences the magnitude of the G for delamination.

For both layups analyzed, the average G along the delamination front for the

case where the matrix crack extends with the delamination front was lower than

the average G for the case where the matrix crack was a constant length

beyond the delamination front.

(5) For both layups modeled, the opening mode, GI, was greatest near the

matrix crack and decreased near the free edge. In addition, GI decreased with

increasing delamination length. The Laminates that had a matrix crack in the

surface ply had a greater Gt/G ratio than the laminates that had a matrix

crack in the interior of the specimen thickness.

(6) The addition of the contribution of thermal residual stresses, resulting from

the cool down after cure, to the strain energy released as the delamination

grows results in a G M+T value that is greater than G M for mechanical

loading only. The subsequent addition of moisture relaxes these residual

thermal stresses, and hence, decreases GM+T+H.

18

APPENDIX

EFFECTSOF THERMALAND MOISTURESTRESSES

The effect of residual thermal stresses, due to the difference in cure and

room temperature, and hygroscopic stresses, due to moisture weight gain, on

the value of G wu also analyzed for the [0/30/-30]s laminate. In addition to the

uniform mechanical axial strain (_), the laminate was subjected to a temperature

drop (AT) and an increase in humidity (AH). The coefficients of thermal

expansion and moisture absorption used in the analysis are shown in Table 1.

Figures 40-42 show the G along the delamination front due to the combined

mechanical, thermal, and hygroscopic Ioadings for a matrix crack length of

4.33h and a delamination length of 3.33h. Results are shown for: (1) the same

mechanical loading, _, applied previously, but with AT= -280°F and

AH=0.0% (fig.40); this same _ but with AT = -280°F and AH=0.6% (fig.41);

and this same E but with AT = -280°F and AH=l.2% (fig.42). As in the

previous cases, the EDI and VCCT agree well in the middle of the delamination

front but diverge at the ends, with the agreement being best for the longer

delamination lengths. Figure 43 shows the effect of the different Ioadings on G

calculated from the elements closest to the free edge. G M corresponds to

mechanical load only, whereas G M+T corresponds to mechanical plus thermal

loading only. The additional contribution of the thermal residual stresses

(resulting from the cool down after cure) to the strain energy released as the

delamination grows results in a G M+T value that is greater than G M for

mechanical loading only. The subsequent additional moisture contribution

relaxes these residual thermal stresses, and hence, decreases G as shown by

the two other loading cases designated G M+T+H.

19

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20

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21

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22

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REPORT DOCUMENTATION PAGE I Form ,%3proveci

! OME, No 070z:-C7,S_

I. AGENCY CS_. ONlY _eave o,anK) i 2 REPORT _)/-.TE

I November 1993

4. TITLE AND SUBTITLE

AnalysisofLocal DelaminationsCaused byAngle Ply MatrixCracks

6. AUTHOR{S)

SatishA. Salpekar,T. Kevin O'Brienand K. N. Shivakumar

7. PERFORMING ORGAN;Z_-.TIOI_ NAM'ICS_ ANS, ADD.KE_._r.S;

NASA Langley Research Center

>Iampton, VA 23681-0001

National Aeronautics and Space AdministrationWashington, DC 20546-0001

3. RZP_;_,T TY:'Z _r_. DATES COVZRZDTechnical Memorandum

5. FUNDING NUMBERS

WU 538-02-10-01

_-. P-R=ORMING OKGAN:ZA'_iDN

REPORT NUMBER

NASA TM 109052

' :; ._.J'=;_£1.C.',,_::_ t. CT_.-_

Salpekar: Analytical Services & Materials, Inc., Hampton, VA; O'Brien: US Army Research Laboratory, VehicleStructures Directorate, Langley Research Center, Hampton, VA; Shivakumar: North Carolina A & T State3niversity, Greensboro, NC.

Unclassified -Unlimited

Subject Category - 24

Two different families of graphite/epoxy laminates with similar layups but different stacking sequences, (0/O/-O)s and(-0/0/0)s were analyzed using three-dimensional finite element analysis for 0=15 and 30 degrees. Delaminations were

modeled in the -0/0 interface, bounded by a matrix crack and the stress free edge. The total strain energy release rate, G,along the delamination front was computed using three different techniques: the virtual crack closure technique (VCCT),the equivalent domain integral (EDI) technique, and a global energy balance technique. The opening fracture modecomponent of the strain energy release rate, GI, along the delamination front was also computed for various delaminationlengths using VCCT. The effect of residual thermal and moisture stresses on G was evaluated.

14, SL/E.;ECT TERMS

Composite material; Graphite epoxy; Delaminadon; Matrix Crack;Finite element analysis

17. oFSECURiTYREPORTunclassifiedCLASSIFICATIOM118. oFSECOR;TYTHISPAGECLASSIFICATIONunclassified[_9.

NSN 7540-0_-280-5500

15 _MBER OF PAGES

SECURITY CLASSIFICATION 20. LIM:TA_ION OF Af.._TRAC.OF ABSTRACT

Stanaarri Form 298 (Rev 2-89)P,e_Cfll:_C Oy ANS_ SIo Z39-18

298-13;.