April 2001

NASA/TM-2001-210842

ARL-TR-2432

Fatigue Life Methodology for Bonded

Composite Skin/Stringer Configurations

Ronald Krueger

ICASE

Langley Research Center, Hampton, Virginia

Isabelle L. Paris

Langley Research Center, Hampton, Virginia

T. Kevin O’Brien

U.S. Army Research Laboratory

Vehicle Technology Directorate

Langley Research Center, Hampton, Virginia

Pierre J. Minguet

The Boeing Company

Philadelphia, Pennsylvania
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April 2001

NASA/TM-2001-210842

ARL-TR-2432

Fatigue Life Methodology for Bonded

Composite Skin/Stringer Configurations

Ronald Krueger

ICASE

Langley Research Center, Hampton, Virginia

Isabelle L. Paris

Langley Research Center, Hampton, Virginia

T. Kevin O’Brien

U.S. Army Research Laboratory

Vehicle Technology Directorate

Langley Research Center, Hampton, Virginia

Pierre J. Minguet

The Boeing Company

Philadelphia, Pennsylvania
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National Aeronautics and Space Administration or the U.S. Army.
1

FATIGUE LIFE METHODOLOGY FOR BONDED COMPOSITE

SKIN/STRINGER CONFIGURATIONS

Ronald Krueger1, Isabelle L. Paris2 and T. Kevin O'Brien3

1 ICASE Staff Scientist

2 National Research Council Research Associate

3 U.S. Army Research Laboratory, Vehicle Technology Directorate

NASA Langley Research Center

Hampton, VA 23681-2199

ABSTRACT

A methodology is presented for determining the fatigue life of composite structures based on

fatigue characterization data and geometric nonlinear finite element analyses. To demonstrate the

approach, predicted results were compared to fatigue tests performed on specimens which consisted

of a tapered composite flange, representing a stringer or frame, bonded onto a composite skin. In a

first step, quasi-static tension and fatigue tests were performed to evaluate the debonding

mechanisms between the skin and the bonded stringer. Specimen edges were examined under the

microscope to document the damage occurrence. In a second step, a two-dimensional finite element

model was developed to analyze the tests. To predict matrix cracking onset, the relationship between

the externally applied tension load and the maximum principal stresses transverse to the fiber

direction was determined through geometrically nonlinear analysis. Transverse tension fatigue life

data were used to generate an onset fatigue life P-N curve for matrix cracking. The resulting

prediction was in good agreement with measured data from the fatigue tests. In a third step, a

fracture mechanics approach based on geometrically nonlinear analysis was used to determine the

relationship between the externally applied tension load and the critical energy release rate. Mixed

mode energy release rate fatigue life data from DCB, 4ENF and MMB tests were used to create an

fatigue life onset G-N curve for delamination. The resulting prediction was in good agreement with

data from the fatigue tests. Additionally, the prediction curve for cumulative life to failure was

generated from the matrix onset and delamination onset fatigue life curves. The results were in good

agreement with data from the fatigue tests which demonstrated that the methodology offers a

significant potential to predict cumulative fatigue life of composite structures.
2

KEY WORDS

Composite materials, testing, finite element analysis, fatigue life prediction, fracture mechanics,

skin/flange interface

INTRODUCTION

Many composite components in aerospace structures are made of flat or curved panels with cocured or adhesively bonded frames and stiffeners. Testing of stiffened panels designed for

pressurized aircraft fuselage has shown that bond failure at the tip of the frame flange is an

important and very likely failure mode [1]. Comparatively simple specimens consisting of a stringer

flange bonded onto a skin have been developed to study skin/stiffener debonding. The failure that

initiates at the tip of the flange in these specimens is identical to the failure observed in the full-scale

panels and the frame pull-off specimens [2-6].

The overall objective of this work was to develop a methodology for cumulative life prediction

of bonded composite skin/stringer structures using delamination fatigue characterization data and a

geometric nonlinear finite element analysis similar to the approach used for composite rotor hub

flexbeams [7]. Results were compared to fatigue tests on stringer flange/skin specimens to verify

the methodology.

The damage mechanisms in bonded composite skin/stringer structures under tension fatigue

loading conditions were documented. The specimens consisted of a tapered flange, representing the

stringer bonded onto a skin. Static tension tests were performed to evaluate the debonding

mechanisms between the skin and the bonded flange and yield static failure loads. Then, tension

fatigue tests were performed at load levels corresponding to 40, 50, 60, and 70% of the damage

onset loads. Microscopic investigations of the specimen edges were used to identify typical damage

patterns and to document the onset of matrix cracking and delamination as a function of fatigue

cycles.

Next, an analytical methodology to accurately predict the onset of matrix cracking as well as

delamination was demonstrated. The tension loading was simulated in a geometrically nonlinear

plane-stress finite element model. A stress analysis was used to predict the location and orientation

of the first transverse crack based on the principal transverse tension stress distribution in the flange

tip area. Computed stresses for different load levels were compared to material characterization data

from transverse tensile fatigue tests to generate a curve predicting the onset of matrix cracking. A

fracture mechanics approach was used to determine delamination growth from this transverse crack.

Delaminations of various lengths were discretely modeled by releasing multipoint constraints at the

locations where delaminations were observed during the experiments. Mode I and II strain energy
3

release rate contributions, GI and GII, were calculated for all load cases using the virtual crack

closure technique. Computed peak G values were used with G versus N fatigue characterization

data generated using DCB, ENF and MMB specimens to predict the fatigue life of the skin/stringer

specimens. A cumulative life prediction methodology was developed by combining the results for

fatigue life for matrix crack onset and fatigue life for delamination onset.

EXPERIMENTAL INVESTIGATION

MATERIALS AND SPECIMEN PREPARATION

The specimens consisted of a tapered laminate, representing the stringer, bonded onto a skin as

shown in Figure 1. An IM7/8552 graphite/epoxy system was used for both the skin and flange.

The skin was made of prepreg tape and had a nominal ply thickness of 0.142 mm and a

[45/-45/0/-45/45/90/90/-45/45/0/45/-45] lay-up. The flange was made of a plain-weave fabric of

0.208 mm nominal ply thickness. The flange lay-up was [45/0/45/0/45/0/45/0/45]f, where 0

represents a 0°-90° fabric ply and 45 represents a 0°-90° fabric ply rotated by 45o.

The flange was pre-cured, cut to size, machined with a 25° taper along the edges and co-bonded

with the uncured skin using one ply of grade 5, FM300 adhesive film. A diamond saw was used to

cut the panels into 25.4 mm wide by 177.8 mm long specimens. The average ply thickness obtained

from specimen thickness measurements and micrographs was 0.148 mm for the tape, 0.212 mm for

the fabric and 0.178 mm for the adhesive. The properties of the graphite/epoxy material and the

adhesive were measured at Boeing and are part of the standard design database for the V-22 tiltrotor aircraft. Typical properties are summarized in Table I. The specimen dimensions are shown in

Figure 1.

EXPERIMENTAL PROCEDURE

Quasi-static tension tests were performed in a servohydraulic load frame in displacement

control at a stroke rate of 0.4 mm/min. The specimens were mounted in hydraulic grips with a gage

length of 101.6 mm as shown in Figure 2. A total of 4 specimens were tested. One specimens was

equipped with two strain gages, one located in the center of the flange and the other located on the

skin as close to the flange tip as possible (Figure 1). The remaining three specimens had the gage

on the flange only. In addition to the strain gages, an extensometer with a 25.4 mm gage length was
4

mounted on the backside of the specimen and centered on the flange tip as shown in Figure 2. A

damage onset load was determined at which a small initial load drop was observed prior to flange

debonding. The value of the damage onset load was averaged from four tests and determined to be

17.8 kN which was later designated as P100%. The tests were terminated when the flange debonded

from the skin.

Fatigue tests were performed at a cyclic frequency of 5 Hz, an R-ratio of 0.1 and load levels

corresponding to 70%, 60%, 50% and 40% of the quasi-static damage onset load. Three tests were

performed at 70% and 50% and four tests were performed at 60% and 40%. The damage was

monitored using a Questar digital microscope on one edge and an optical travelling microscope on

the other edge. The specimen edges were painted white to make the cracks and delaminations more

visible. Damage was documented based on location at each of the four corners identified in

Figure 1. The number of cycles at which the first matrix crack appeared was recorded as well as the

number of cycles to delamination onset. After the test, photographs of the polished specimen edges

were taken under a light microscope to document the occurrence of matrix cracking and

delamination. For two specimens, at intervals of damage growth, the test was stopped and the

specimens removed from the grips. Photographs of the polished specimen edges were then taken

under a light microscope to document the progression of the damage.

MICROSCOPIC INVESTIGATION

Typical damage patterns observed from specimens are shown in Figures 3-5. The included

drawings are based on edge observations during the tests and micrographs taken during and after

the tests. All quasi-static and fatigue tests yielded similar damage patterns. Under quasi-static

loading, failure occurred across one flange tip of the specimen only, with no clear preference for

corners 1 and 2 or corners 3 and 4. In fatigue, damage initiated at both flange tips, but not at the

same time.

At corners 2 and 3, a delamination (delamination B) formed in the top 45°/-45° skin ply

interface, as depicted in Figure 3a. In the static tests, the damage was only observed after the test.

Delamination appeared to initiate at the flange tip from a matrix crack in the top 45° skin ply as

shown in Figure 3b. In fatigue, the sequence of events was observed with the Questar microscope.

Micrographs of the polished edge, as shown in Figure 4, were also taken at intervals. The first

matrix crack occurred in the adhesive pocket, then grew through the top 45° skin ply and formed a

delamination in the top 45°/-45° skin ply interface, growing towards the center of the flange.

Sometimes, the delamination grew back towards the grip and coalesced with a matrix crack in the
5

top 45° ply further from the flange.

At corners 1 and 4, a delamination running in the bondline (delamination A1) initiated from a

matrix crack in the adhesive pocket as shown in Figure 5. In some of the quasi-static cases, a

second delamination (A2) was observed below the first, in the top –45°/0° skin ply interface.

Delamination A2 was not observed in fatigue. In the fatigue tests, damage first appeared at corner 2

and 3 (delamination B) for 12 of the 14 specimens.

TEST RESULTS

In Figures 6 to 8, typical results of the four quasi-static tension tests are shown as plots of load

versus displacement or strain versus load. Results from finite element analyses, which are included

in the figures, will be discussed later. As shown in Figure 6, the load-displacement curves were

slightly nonlinear. Possible damage initiation was assumed when a small initial load drop was

observed in two of the tests prior to flange debonding. At this point, a crack in one flange tip or

even a small delamination along one flange corner was observed. In two specimens, no initial load

drop or visible damage could be detected. In general, the initial load drop occurred above 90% of

the maximum sustained load. Figure 7 shows the nonlinear strain-load response up to the point of

flange debonding. Initially, flange strains dropped before rising again with increasing load. In all

specimens, a load drop was also accompanied by a decrease in strain. The same two specimens that

showed a small initial load drop in the load-displacement plots also displayed a drop in flange strain

prior to flange debonding. Skin strains were nearly linear until flange debonding occurred, as

shown in Figure 8.

The tension fatigue failure of the specimens was characterized by plotting the applied tension

load versus the number of load cycles at damage onset. The number of cycles to matrix crack onset

and delamination onset were plotted for each specimen as shown in Figures 9 and 10. The static

strength values obtained from the quasi-static tests were also added to Figure 9 at N=1 to

complement the graph. A noticeable distinction between matrix crack onset and delamination onset

becomes apparent when plotting the mean values only as shown in Figure 11. An almost linear

relationship between Pmax and log N was observed.
6

ANALYTICAL INVESTIGATION

FINITE ELEMENT ANALYSIS

The finite element (FE) method was used to study damage initiation using a stress analysis and

to study the potential for delamination using fracture mechanics. The schematics of the twodimensional model of the specimen, boundary conditions, and loads applied are shown in

Figure 12. FE models for one undamaged and three damaged specimens were developed. Finite

element solutions were obtained using the commercial ABAQUS®/Standard finite element software.

Eight-noded quadrilateral plane-stress (CPS8R) and plane-strain (CPE8R) elements with quadratic

shape functions and a reduced (2x2) integration scheme were utilized for the geometric nonlinear

analyses [8].

For the model of the undamaged specimen, a refined mesh was used in the critical area of the

45° skin ply where cracking was observed during the tests. An outline and two detailed views of the

mesh are shown in Figure 12. Outside the mesh refinement area, all plies were modeled with one

element through the ply thickness. In the refined region, four elements were used per ply thickness

for the first two individual flange plies above the bondline and the top skin ply below the bondline.

Four elements through the thickness were also used to model the adhesive film. Typical ply

properties and adhesive material properties used in this study are summarized in Table I.

Based upon examinations of tested specimens, the critical damage was assumed to start at

corners 2 and 3 in the form of a matrix crack in the top 45° skin ply that developed into a

delamination in the 45°/-45° interface as shown in Figure 3. Therefore, damage was modeled at one

flange tip only as shown in Figure 13a. At the opposite taper, the original mesh created for the

model of the undamaged specimen was used. Damage was modeled as discrete discontinuities as

shown in Figure 13. Based on the experimental observations shown in Figure 4, three different

locations were selected for the origin of the matrix crack in the models. This was done to determine

how the matrix crack origin influenced the energy release rate computed as a function of

delamination length for a delamination growing in the 45°/-45° interface.

It is inherent to a two dimensional FE model that the geometry, boundary conditions and other

properties are constant across the entire width of the model. This may not always capture the true

nature of the problem. As shown in Figures 3 and 5, the delamination pattern changed from

corner 3 to corner 4 from a delamination running in the 45°/-45° interface to a delamination

propagating in the bondline. These three-dimensional patterns of matrix cracks and delaminations,

which vary across the width of the specimen, can not be accounted for in any two-dimensional FE

model. In addition, the plane-stress model imposes szz=txz= tyz=0 at the free edge of each ply and

allows the displacement to be the free parameter. The plane-strain model, on the other hand,
7

imposes ezz=gxz= gyz=0 at the free edge, which excessively constrains the plies. An alternative to a

full three-dimensional simulation might be a generalized plane-strain model, which requires about

the same modeling effort as a simple two-dimensional model [9]. The generalized plane-strain case

may be regarded as an intermediate state, and it is assumed that ezz=-nLexx and gxz= gyz=0 where nL

is the laminate Poisson’s ratio. The current study, however, was restricted to the use of twodimensional models to demonstrate the methodology.

The Virtual Crack Closure Technique (VCCT) described in references [10] and [11] was used

to calculate strain energy release rates for the delaminations. The mode I and mode II components

of the strain energy release rate, GI and GII, were calculated as

 

G

a I i Yv v Yv v = - m m* * j ¢ ¢ ( ) - ¢ + ¢ ¢ ( ) - ¢ [ ] 1

2D l l (1)

and

 

G

a II i Xu u Xu u = - m m* * j ¢ ¢ ( ) - ¢ + ¢ ¢ ( ) - ¢ [ ] 1

2D l l (2)

where Da is the length of the elements at the crack tip, Xi

' and Yi' are the forces at the delamination

tip at node i, and um' and vm' are the relative displacements at the corresponding node m behind the

delamination tip as shown in Figure 14. Similar definitions are applicable for the forces at node j

and displacements at node l. Both forces and displacements were transformed into a local

coordinate system (x', y'), that defined the normal and tangential coordinate directions at the

delamination tip in the deformed configuration. The mode III component is identically zero for all

the two-dimensional cases evaluated. Therefore, the total strain energy release rate, GT, was obtained

by summing the individual mode components as

 

G GG T I II = + (3)

The data required to perform the VCCT in equations (1) to (3) were accessed directly from the

ABAQUS® binary result file to get better accuracy. The calculations were performed in a separate

post-processing step using nodal displacements and nodal forces at the local elements in the vicinity

of the delamination front. Details are given in the appendix.

Care must be exercised in interpreting the values for GI and GII obtained using the virtual crack

closure technique for interfacial delaminations between two orthotropic solids as the observed

oscillatory singularity at the crack tip becomes an issue for small element lengths [12, 13]. Hence, it

had been suggested to use element lengths Da at the crack tip in such a manner that the computed

results are insensitive to the variation of Da. For practical applications, the element size (length and

height) should not be less than 1/10 of a ply thickness, which corresponds to the diameter of two
8

carbon tows in the carbon/epoxy material modeled. For smaller element sizes the assumption of

modeling each ply as an orthotropic continuous layer is no longer valid. For the current

investigation, therefore, the element length Da was chosen to be about 1/3 of the ply thickness,

h=0.148 mm, for the delamination in the 45°/-45° flange ply interface. Note that for the FE models

shown in Figure 13 c and d Da/h =0.169 for the first element in the delaminated zone and

Da/h =0.338 for the following elements. Consequently, the technique suggested in reference [10]

was used to estimate the forces Xi' and Yi' for the case of unequal element lengths at the

delamination tip. For all subsequent delamination growth, a value of Da/h =0.338 was used.

GLOBAL RESPONSE

First, the global response of the specimens was computed at the mean quasi-static damage onset

load (P100%=17.8 kN) determined from experiments. The load-displacement and the load-strain

behavior computed were compared to the corresponding experimental results. This global response

was used to examine whether the FE model, the boundary conditions, the loads and the material

properties used in the model were accurate. Calculated displacements are reported for the locations

where they were measured in the quasi-static experiments. Strains were averaged from computed

nodal point values over a length corresponding to the dimensions of the strain gages.

A schematic of the deformed geometry, the boundary conditions, and the load applied in the

simulations are shown in Figure 15. In the schematic, the elongation of the specimen caused by the

applied tensile load is shown. Also visible is the bending effect caused by the load eccentricity in

the flange region, the asymmetric layup with respect to the neutral axis, and the membrane stiffening

effect. The extensometer displacement plots in Figure 6 show that there is good agreement between

the analyses and the experiments; the models therefore captured the global response. As expected,

the specimen shows a stiffer behavior than the experiments when modeled with plane-strain

elements. The plane-stress model, on the other hand, is more compliant. A comparison of measured

strains at the surface of the flange and computed results is shown in Figure 7. The nonlinear

analysis yielded results that were in close agreement with the experiments. Again, the plane-strain

models were stiffer, and the plane-stress models more compliant compared to the tested specimens.

The linear analysis for both cases, however, was not able to capture the transition from compressive

flange strains at the beginning to tension flange strains at the end of the loading. Hence, a

geometrically nonlinear FE analysis is necessary to account for the effects due to the load

eccentricity in the flange region, the asymmetric layup with respect to the neutral axis, and the

membrane stiffening effect. In Figure 8, measured strains at the surface of the top 45o skin ply near
9

the flange tip (see Figure 1) and computed surface strains were compared. As mentioned above, the

plane-strain models showed a stiffer behavior and the plane-stress models a more compliant

behavior compared to the tested specimens. The strain-load responses obtained from the nonlinear

plane-stress analysis are in better agreement with the experiments compared to the values obtained

from the other analyses. This result is of particular interest as the failure observed in the

experiments occurred in top 45o skin ply where the strain gage was mounted near the tip of the

flange as shown in Figures 3 to 5. Hence, the geometrically nonlinear plane-stress FE analysis was

used for the remainder of this study as it produced the most accurate results in the area of interest.

LOCAL RESPONSE

A stress analysis was used to study the initial damage in the form of matrix cracks from which

delaminations may start to grow. As shown in Figures 3 to 5, the matrix crack always occurred in

the top 45° skin ply near the flange tip. Earlier investigations [2, 3] indicated that the matrix

cracking occurred when the maximum principal transverse tensile stress, stt, normal to the fiber

direction, as calculated by

 

s

ss ss

t tt = ++ æ -

è

ç ö

ø

÷ + 22 33 22 33

2

23

2

2 2 (4)

reached the transverse tension strength of the material (Figure 16). The computed maximum

principal tensile stress was calculated for the static failure load using plane-stress and plane-strain

models. The stress distribution in the top 45o skin ply is plotted in the immediate vicinity of the

flange tip in Figure 17. In the graph, x=0 corresponds to left grip as shown in Figures 12 and 15,

and x=26.4 corresponds to the left flange tip. The transverse tensile strength for IM7/8552

obtained from three-point bending test of 90° lamina was included in the plot for comparison.

Stresses at the static failure load computed from the plane-stress analysis correspond well with the

transverse tensile strength. Stresses from the plane-strain analysis are excessively high. This is

caused by the constraints inherent to the plane-strain model, particularly in the ±45° plies. These

findings support the conclusions drawn from the comparison of computed and measured skin

strains in the previous paragraph. Hence, the geometrically nonlinear plane-stress FE analysis was

used for the remainder of this study as it appeared to produced the most accurate results in the area

of interest. The computed maximum principal tensile stress calculated from plane-stress analyses

for all fatigue load levels are plotted in Figure 18. During the fatigue tests, first matrix cracking was

observed at locations right next to the flange tip (Figure 5) which corresponds to the location where
10

peak stresses were calculated.

A fracture mechanics approach was used to investigate delamination onset once the initial crack

had formed. The Virtual Crack Closure Technique (VCCT) was used to calculate the mode I and II

components of the strain energy release rates for the delamination. The initial crack was modeled at

a location as suggested by the microscopic investigation and the stress analysis described in the

previous paragraph. Recall that the models of the discrete matrix cracks and delaminations are

shown in Figure 13. For this investigation, the delamination growing between the skin top 45o and

–45o plies was extended by releasing multi-point constraints at the crack tip and in front of the

crack tip. During a series of nonlinear finite element analyses, strain energy release rates were

computed at each tip location for the loads applied in the experiments. A critical energy release rate,

Gc, needs to be determined to predict delamination onset. This critical G is generally identified

based on the shape of the total energy release rate versus delamination length curve, which is

determined through analysis as shown in Figure 19. The GT versus x curve reached a peak at some

virtual delamination length and then decreased. The delamination was extended to a total simulated

length of 2.2 mm to ascertain that the peak value had been captured. The total energy release rates

computed for all load levels are plotted in Figure 19. To determine the influence of the initial matrix

crack location corresponding to the models shown in Figure 13, the total energy release rates and

the corresponding mixed mode ratios GII/GT at P100% were plotted in Figures 20 and 21. The results

demonstrated that the computed energy release rates and corresponding mixed mode ratios did not

depend on the location of the matrix crack that initiated the delamination. A slight discrepancy was

only noticeable up to the first four increments of delamination growth. For longer delamination

lengths the results for all three cracked models were identical. Hence, the maximum total energy

release rate, GT, was chosen as the critical value to be used for the fatigue life prediction. This peak

in GT also corresponded to the maximum mode I percentage, i.e., minimum value of GII/GT in

Figure 21.
11

METHODOLOGY FOR FATIGUE LIFE PREDICTION

For a particular structural component and loading of interest, the cumulative life to failure, NT,

may involve the onset and growth of several cracks and delaminations. For example, NT may be

predicted by summing the lives for onset of matrix cracking, NM, delamination onset from this

matrix crack, ND, and stable delamination growth to a finite acceptable delamination size, NG. Hence,

 

N NNN T MDG = ++ . (5)

The current study focussed on the prediction of damage onset only. Hence, stable delamination

growth to a finite acceptable delamination size was not considered and the total cumulative life to

failure was

 

NNN T MD = + . (6)

MATRIX CRACKING ONSET FATIGUE LIFE PREDICTION

Matrix cracking was the first damage mechanism to occur in the specimen and was followed by

delamination. In order to predict the onset of matrix cracking, the following steps were taken.

In Figure 22, the relationship between the externally applied tensile load, P, and the principal

transverse tensile stresses, stt, in the top 45° skin ply was determined by plotting the loads versus

the peak stresses from Figure 18. To account for residual stresses after cooldown and moisture

absorption, a simple analysis was performed using classical laminate theory. Since the flange had

already been cured before it was adhesively bonded to the skin it was not included in the calculation

of the residual stresses. Coefficients of hygrothermal expansion were not available for IM7/8552.

Therefore, data from similar types of carbon/epoxy prepreg were taken from the literature [14]. The

values used in the calculation were: ax= 0.6 x 106

 1/K, ay= 28.6 x 106 1/K for the coefficients of

thermal expansion in parallel and transverse direction of the fibers and bx= 0.0, by= 0.664

(dimensionless) for the coefficients of moisture expansion. The temperature difference between

curing and room temperature was assumed to be DT=157 K. The moisture content of the specimens

was measured by drying five specimens and comparing the mass before and after drying. The

average moisture content was determined to be 0.0042 of the specimen mass. It was assumed that

the residual stresses existed prior to testing and were not altered during the fatigue tests. This

means that the tests were performed at frequencies which did not result in a temperature increase
12

and therefore did not relax the stresses. Hence, the calculated residual stress was simply added to

the transverse tensile stresses obtained from finite element analysis. These results were also

included in Figure 22.

The transverse tension fatigue life of IM7/8552 carbon-epoxy was characterized using flexure

tests of 90° laminates loaded in three point bending. A fatigue onset life characterization curve was

generated using data from three-point bending tests performed at a frequency of 10 Hz and a load

ratio of R=0.1. The transverse tensile stress sttmax, (where "max" refers to the maximum stress

resulting from the sinusoidal cyclic load applied) was determined from beam theory as

 

smax

max = ×

×

3

2 2

P s

b t

(7)

and was plotted versus the number of cycles to failure, N as shown in Figure 23. Here Pmax is the

maximum of the sinusoidal cyclic load applied, s is the span between the supports, b is the average

specimen width and t is the average thickness of the three point bending specimen. The fatigue life

curve in Figure 23 was obtained by curve fit of the mean life data. Additionally, scatter was

addressed by constructing curves with plus and minus one standard deviation, which were included

in Figure 23.

Once these calculations and characterizations were available, it was possible to determine for an

arbitrary maximum cyclic load, (Pi

 in Figure 22), the maximum transverse tensile stress (si in

Figure 22) as well as the associated fatigue life (Ni in Figure 23). Plotting the relationship between

the externally applied load, P, and the fatigue life for onset of matrix cracking, NM, yielded the

prediction onset curve as shown in Figure 24. This procedure was repeated using the curves with

plus and minus one standard deviation in Figure 23 to obtain the set of curves in Figure 24. The

prediction for matrix cracking onset in the skin/stiffener specimens agreed reasonably well with

measured P-N data from the fatigue tests which were included in Figure 24. However, significant

deviation was noted between measured and predicted onset loads under monotonically increasing

(quasi-static) loads. Alternate characterization test methods may ultimately prove more useful than

three-point-bending test of 90° laminates. However, only this method was used in this study to

demonstrate the methodology.
13

DELAMINATION ONSET FATIGUE LIFE PREDICTION

Delaminations originated from the matrix cracks as shown in Figures 3 to 5. In order to predict

delamination onset, a quasi static mixed-mode fracture criterion had to be determined first [15].

This was accomplished by plotting Gc versus the mixed-mode ratio, GII/GT, determined from data

generated using pure Mode I DCB (GII/GT=0), pure Mode II 4ENF (GII/GT=1), and mixed-mode

MMB tests of varying ratios, as shown in Figure 25 for IM7/8552 [16]. A curve fit of these data

was performed to determine a mathematical relationship between Gc and GII/GT. Based on this type

of fracture criterion, the following steps were taken to determine the delamination onset life.

First, the relationship between the externally applied load, P, and the total energy release rate, GT,

was determined by plotting P versus peak GT (from Figure 19) as shown in Figure 26 for several

load cases and fitting a curve to these results. Additionally, the corresponding mixed-mode ratio,

GII/GT, was calculated at each load step, and the results were also curve fit and plotted in Figure 26.

Due to a minimal variation in the mixed mode ratio, an average constant GII/GT=0.18 was assumed

for the following step.

Second, a failure surface as shown in Figure 27, relating the total energy release rate, Gmax, to

the mixed mode ratio, GII/GT, and the number of cycles to delamination onset, N, was created. The

surface was fit through data from fatigue experiments using DCB, 4ENF, and MMB tests [16]. The

quasi-static mixed mode failure criterion, as shown in Figure 25, is represented in Figure 27 by the

plane at log N=0 (N=1). From the failure surface an appropriate fatigue life curve (shown in

Figure 28) was extracted for GII/GT =0.18, which corresponds to the calculated average mixed mode

ratio from above.

Then, with this information available, for an arbitrary maximum cyclic load, Pi

, the total energy

release rate, Gi

, was determined as illustrated in Figure 26. The associated fatigue life, Ni, was

obtained as shown in Figure 28.

Finally, plotting the relationship between the externally applied load, P, and the fatigue life for

delamination onset, ND, yielded the prediction onset curve as shown in Figure 29. The measured P-N

data from the fatigue tests, corresponding to the total life to delamination onset (Figure 10) minus

the life to matrix cracking onset (Figure 9), were included in Figure 29 for verification. The

prediction for delamination onset is in good agreement with the experimental observations.
14

CUMULATIVE LIFE PREDICTION

The prediction curve for cumulative life to onset of failure

 

NNN T MD = + (8)

is plotted in Figure 30. For verification the measured P-N data from the fatigue tests, corresponding

to the total life to delamination onset in Figure 10, were included in the plot of Figure 30. For

higher number of cycles (NT>102

) the prediction for delamination onset is in good agreement with

the experimental observations. However, agreement was not as good for low load cycles (NT<102

),

primarily reflecting the poor agreement noted earlier for the matrix cracking onset.

CONCLUDING REMARKS

A composite bonded skin/stringer specimen was used to demonstrate a methodology for

determining the fatigue life based on matrix cracking and delamination fatigue onset

characterization data along with geometric nonlinear finite element analyses. A consistent step-wise

approach was used to investigate the damage mechanism in composite specimens which consisted

of a tapered composite flange, representing a stringer or frame, bonded onto a composite skin. The

approach used experiments to detect the failure mechanism, computational stress analysis to

determine the location and onset of first matrix cracking, and computational fracture mechanics to

investigate the potential for subsequent delamination growth.

In a first step, quasi-static tension and fatigue tests were performed to evaluate the debonding

mechanisms between the skin and the bonded stringer. Specimen edges were examined on the

microscope to document the damage occurrence. Observed failures initiated in the top 45° skin ply

near the flange tip causing the flange to almost fully debond from the skin.

Based upon the experimental findings, a two-dimensional nonlinear plane-stress finite element

(FE) analysis was performed using the ABAQUS® FE code in a second step. To predict matrix

cracking onset, the relationship between the externally applied tension load and the maximum

principal stresses was determined through geometrically nonlinear analysis. Transverse tension

fatigue life data from flexure tests of 90° laminates loaded in three-point bending were used to

generate an onset fatigue life P-N curve for matrix cracking. The resulting prediction agreed

reasonably well with measured data from the skin/stringer specimen fatigue tests at higher cycles.

A fracture mechanics approach was used to determine when a delamination would grow from

the transverse matrix cracks. Delaminations of various lengths were simulated as starting in
15

locations where matrix cracks had been observed during the tests. Mixed mode energy release rates

were computed using the virtual crack closure technique. It was demonstrated that the energy

release rates and the corresponding mixed mode ratios, computed as a function of delamination

length, were insensitive to small changes in the location used to start the initial matrix crack in the

finite element model. Using the peak values in the mixed mode energy release rate versus

delamination length plot, the relationship between the externally applied tension load and the critical

energy release rate was created. Further, a failure surface relating the total energy release rate to the

mixed mode ratio and the numbers of cycles to delamination onset was generated. The fit surface

was used to create an onset fatigue life P-N curve for delamination at the computed mixed mode

ratio. The resulting prediction was in good agreement with data from the skin/stringer specimen

fatigue tests.

Additionally, the prediction curve for cumulative life to failure was generated from the matrix

onset and delamination onset fatigue life curves. The results were in good agreement with data from

the skin/stringer specimen fatigue tests which demonstrated that the methodology offers a

significant potential to predict the cumulative fatigue life of composite structures.

ACKNOWLEDGMENTS

This work was performed as part of a Cooperative Research and Development Agreement

(CRDA) between the U.S. Army Research Laboratory, Vehicle Technology Directorate, located at

NASA Langley Research Center, and The Boeing Company, Philadelphia, PA.
16

REFERENCES

[1] P. J. Minguet, M. J. Fedro, T. K. O'Brien, R. H. Martin, and L. B. Ilcewicz, "Development

of a Structural Test Simulating Pressure Pillowing Effects in Bonded Skin/Stringer/Frame

Configuration," in Proceedings of the Fourth NASA/DoD Advanced Composite Technology

Conference, Salt Lake City, Utah, 1993.

[2] P. J. Minguet and T. K. O'Brien, "Analysis of Test Methods for Characterizing

Skin/Stringer Debonding Failures in Reinforced Composite Panels," in Composite

Materials: Testing and Design (Twelfth Volume), ASTM STP 1274, 1996, pp. 105--124.

[3] P. J. Minguet and T. K. O'Brien, "Analysis of Composite Skin/Stringer Bond Failures

Using a Strain Energy Release Rate Approach," in The Tenth International Conference on

Composite Materials, vol. I, A. Poursartip and K. Street, Eds., 1995, pp. 245--252.

[4] P. J. Minguet, "Analysis of the Strength of the Interface Between Frame and Skin in a

Bonded Composite Fuselage Panel," in The 38rd AIAA/ASME/ASCE/AHS/ASC Structures,

Structural Dynamics and Materials Conference, 1997, pp. 2783--2790.

[5] M. K. Cvitkovich, T. K. O'Brien, and P. J. Minguet, "Fatigue Debonding Characterization in

Composite Skin/Stringer Configurations," in Composite Materials: Fatigue and Fracture,

Seventh Volume, ASTM STP 1330: American Society for Testing and Materials, 1998,

pp. 97-121.

[6] R. Krueger, M. K. Cvitkovich, T. K. O'Brien, and P. J. Minguet, "Testing and Analysis of

Composite Skin/Stringer Debonding Under Multi-Axial Loading," Journal of Composite

Materials, vol. 34, pp. 1263-1300, 2000.

[7] G. B. Murri, T. K. O'Brien, and C. Q. Rousseau, "Fatigue Life Methodology for Tapered

Composite Flexbeam Laminates," Journal of the American Helicopter Society, vol. 43,

pp. 146--155, 1998.

[8] ABAQUS/Standard - User's Manual - Version 5.6, vol. II: Hibbitt, Karlsson & Sorensen,

Inc., 1996.

[9] D. M. Hoyt, S. H. Ward, and P. J. Minguet, "Strength and Fatigue Life Modeling of

Bonded Joints in Composite Structure," in Proceedings of the American Society for

Composites - 15th Annual Technical Conference on Composite Materials: Technomic

Publishing, 2000, pp. 729-736.

[10] E. F. Rybicki and M. F. Kanninen, "A Finite Element Calculation of Stress Intensity

Factors by a Modified Crack Closure Integral," Eng. Fracture Mech., vol. 9, pp. 931--938,

1977.
17

[11] I. S. Raju, "Calculation Of Strain-Energy Release Rates With Higher Order And Singular 

Finite Elements," Eng. Fracture Mech., vol. 28, pp. 251--274, 1987.

[12] I. S. Raju, J. H. Crews, and M. A. Aminpour, "Convergence of Strain Energy Release Rate

Components for Edge-Delaminated Composite Laminates," Eng. Fracture Mech., vol. 30,

pp. 383--396, 1988.

[13] C. T. Sun and M. G. Manoharan, "Strain Energy Release Rates of an Interfacial Crack

Between Two Orthotropic Solids," J. Composite Materials, vol. 23, pp. 460--478, 1989.

[14] A. A. Johnston, "An Integrated Model of the Development of Process-Induced Deformation

in Autoclave Processing of Composite Structures," Ph.D. Thesis, The University of British

Columbia, Vancouver, B.C., Canada, 1997.

[15] R. H. Martin, "Incorporating interlaminar fracture mechanics into design," in International

Conference on Designing Cost-Effective Composites: IMechE Conference Transactions,

London, U.K., 1998, pp. 83-92.

[16] P. Hansen and R. Martin, "DCB, 4ENF and MMB Delamination Characterisation of

S2/8552 and IM7/8552," Materials Engineering Research Laboratory Ltd. (MERL),

Hertford, U.K., N68171-98-M-5177, 1999.
18

TABLE 1. MATERIAL PROPERTIES

IM7/8552 Unidirectional Graphite/Epoxy Prepreg

E11 = 161.0 GPa E22 = 11.38 GPa E33 = 11.38 GPa

n12 = 0.32 n13 = 0.32 n23 = 0.45

G12 = 5.17 GPa G13 = 5.17 GPa G23 = 3.92 GPa

IM7/8552 Graphite/Epoxy Plain Weave Fabric

E11 = 71.7 GPa E22 = 71.7 GPa E33 = 10.3 GPa

n12 = 0.04 n13 = 0.35 n23 = 0.35

G12 = 4.48 GPa G13 = 4.14 GPa G23 = 4.14 GPa

Grade 5 FM300 Adhesive

E = 1.72 GPa n = 0.3 (assumed isotropic)
19

APPENDIX

Currently, the large commercial finite element codes do not offer the choice for calculating

the mixed mode energy release rates using the virtual crack closure technique (VCCT) as described

in the main text. Therefore, the energy release rate components GI and GII were computed in an

separate post-processing step. The element forces at nodes, the nodal point displacements and the

nodal point coordinates required as input were extracted directly from the ABAQUS® binary result

file using a user written FORTRAN routine (extract.f) the flow chart of which is depicted in

Figure 31.
Figure 1. Specimen Configuration.

177.8 mm

25.4 mm

42 mm

25°

Strain Gages

(quasi-static tests only)

Figure 2. Tension Test Set-Up.

Upper Grip

Lower Grip

Extensometer

(quasi-static tests only)

25.4 mm

101.6 mm

 50.8 mm 

0°

Corner 4

Corner 3 Corner 1

Corner 2

20
(a) Typical damage pattern

45°

0°

45°

45°

-45°

0°

Adhesive Pocket

Matrix Crack Delamination B

(b) Micrograph of the edge of a failed specimen.

Figure 3. Damage patterns at corners 2 and 3.

200 μm

21
Figure 4. Evolution of matrix cracks and delamination growth in fatigue, corners 2 and 3.

Matrix crack in

top 45o ply

200 mm

Initial delamination

in 45o/-45o interface Initial matrix

crack closed

Second

matrix crack

200 mm

Initial crack in adhesive layer

Adhesive layer

Flange tip 200 mm

22
(a) Typical damage pattern.

Initial Matrix Crack

Delamination A1

Delamination A2

45°

0°

45°

45°

-45°

0°

(b) Micrograph of the edge of a failed specimen.

Figure 5. Damage patterns at corner 1 and 4.

200 μm

23 
-2000

-1000

0

1000

2000

0 5 10 15 20

experiments

nonlinear plane strain analysis

linear plane strain analysis

nonlinear plane stress analysis

linear plane stress analysis

Figure 7. Flange strain-load plots for quasi-static tests.

Load, kN

μ Strain

Flange

debonding

Flange tip cracking or

delamination formation

0 0.2 0.4 0.6 0.8 1 1.2 1.4

0

5

10

15

20

25

nonlinear plane strain analysis

nonlinear plane stress analysis

Load, kN

Displacement, mm

Figure 6. Load-displacement plots for quasi-static tests.

Flange

debonding

Actuator stroke

Extensometer

Flange

debonding

Damage

 onset

Damage

 onset

24
0

5

10

15

20

25

100101102103104105106107108

fatigue data

quasi-static data

quasi-static data, mean

fatigue data, mean

Applied

Load, 

P, kN

Number of Cycles, N

Figure 9. Matrix crack onset fatigue life for composite skin/flange debonding

f = 5 Hz

R = 0.1

0

2000

4000

6000

8000

10000

12000

0 5 10 15 20

experiments

nonlinear plane strain analysis

linear plane strain analysis

nonlinear plane stress analysis

linear plane stress analysis

Figure 8. Typical skin strain-load plot for quasi-static tests.

Load, kN

μ Strain

Flange

debonding

25
0

5

10

15

20

25

100101102103104105106107108

mean static strength

mean matrix crack onset life

mean delamination onset life

Applied

Load, 

P, kN

Number of Cycles, N

f = 5 Hz

R = 0.1

Figure 11. Fatigue life for composite skin/flange debonding.

0

5

10

15

20

25

100101102103104105106107108

fatigue data

fatigue data, mean

Applied

Load, 

P, kN

Number of Cycles, N

Figure 10. Delamination onset fatigue life following matrix 

cracking for composite skin/flange debonding

f = 5 Hz

R = 0.1

26
detail

u=v=0 at x=0

y

x

Static failure load: P =17.8 kN

Fatigue loading:

P =12.46 kN

100%

70% P =8.9 kN

P =10.68 kN P =7.12 kN 50%

60% 40%

101.6 mm

Figure 12. Finite element model of skin/flange specimen

detail

45°

0°

45°

0°

adhesive

45°

-45°

0°

-45°

45°

-45°

90°

x= 24.9 mm 25.4 25.9 26.9 26.4 27.4 27.9 28.4

27
y

x

Figure 13. Finite element model of damaged zone around flange tip

45°

adhesive

45°

-45°

0°

x= 26.1 26.2 26.4 26.6 26.8 27.0 27.2

(a) Model used to simulate different damage onset locations

second matrix crack

as shown in Fig. 4

(b) Delamination B growing from second matrix crack

(d) Delamination B growing from initial

first matrix crack

modeled intermediate

location

initial matrix crack

as shown in Fig. 4

(c) Delamination B growing from

intermediate location of matrix crack

28
Figure 14. Virtual Crack Closure Technique (VCCT).

GI = -[ Y'i ( v'm - v'm* ) + Y'j ( v' - v' * ) ] / ( 2 a )

GII = -[ X'i ( u'm - u'm* ) + X'j ( u' - u' * ) ] / ( 2 a ) 

y',v',Y'

a

x',u',X'

a

x,u,X

y,v,Y

global system

local crack tip system

undeformed state

(outline)

m

m*

*

i

j

k

X'i

X'j

Y'i

Y'j

deformed

state

29
u=v=0 at x=0

y

x

Figure 15. Deformed outline of modeled skin/flange specimen

undeformed outline

deformed outline

v=0 at x≥101.6

30
33

23

22

tt

x (laminate axis)

z,3

33 1 (fiber direction)

12

23

22

Figure 16. Definition of ply transverse tensile stress. 

31
0

50

100

150

200

25.5 26 26.5 27

1.0 x static failure load

0.7 x static failure load

0.6 x static failure load

0.5 x static failure load

0.4 x static failure load

Transverse

Tensile

Stress,

tt

, N/mm2

x coordinate, mm

flange tip

Figure 18. Computed transverse tensile stress results in top 45° skin ply for fatigue loads.

location of

maximum 

tt

0

100

200

300

400

500

600

25.5 26 26.5 27

plane-strain elements

plane-stress elements

Transverse

Tensile

Stress,

tt

, N/mm2

x coordinate, mm

flange tip

Figure 17. Computed transverse tensile stress results in top 45° skin ply for static failure load.

transverse tensile 

strength 127 MPa

32
500

1000

1500

2000

26 26.5 27 27.5 28 28.5

FE model from Fig. 13b

FE model from Fig. 13c

FE model from Fig. 13d

G

T

,

J/m2

 x coordinate, mm

flange tip

a

Figure 20. Computed total strain energy release rate for 

delamination between top 45°/-45° skin plies.

location of

maximum G

T

0

500

1000

1500

2000

26 26.5 27 27.5 28 28.5

1.0 x static failure load

0.7 x static failure load

0.6 x static failure load

0.5 x static failure load

G 0.4 x static failure load

T

,

J/m2

 x coordinate, mm

flange tip

a

location of

maximum G

T

Figure 19. Computed total strain energy release rate for 

delamination between top 45°/-45° skin plies.

FE model from Fig. 13b

33
0

5

10

15

20

25

0 50 100 150 200

peak stress from Fig. 18

peak stress from Fig. 18 + hygrothermal prestress

Applied

External 

Load 

P, kN

Transverse Tensile Stress tt, MPa

Pi

i

Figure 22. External load versus calculated ply transverse tensile stress.

0

0.2

0.4

0.6

0.8

1

26 26.5 27 27.5 28 28.5

FE model from Fig. 13b

FE model from Fig. 13c

FE model from Fig. 13d

GII/G

T

,

J/m2

 x coordinate, mm

flange tip

a

Figure 21. Computed mixed mode ratio for delamination between top 45°/-45° skin plies.

location of

maximum G

T

34
0

5

10

15

20

25

100101102103104105106107108

fatigue data

quasi-static data

quasi-static data, mean

fatigue data, mean

Applied

Load, 

P, kN

Number of Cycles, N

M

, to Matrix Cracking Onset

predicted onset curve

± standard deviation

Figure 24. Comparison of matrix cracking onset prediction and experimental results.

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

100101102103104105106107108

3 pt. bending test data

Failure

 Stress,

tt max, 

MPa

Fatigue Life, N, Cycles

R = 0.1

f = 10 Hz

mean ± 1 standard deviation

Figure 23. Fatigue life characterization data for matrix cracking onset .

Ni

i

35
0

5

10

15

20

25

30

35

0

0.05

0.1

0.15

0.2

0.25

0.3

0 500 1000 1500 2000

total energy release rate, GT

mixed mode ratio, GII/GT

External

Load

P, kN

Mixed

Mode

Ratio,

GII / GT

Total Energy Release Rate GT, J / m2

Pi

Gi

(GII/GT)

i

Figure 26. External load and mixed mode ratio plotted versus calculated G

T

0

400

800

1200

1600

0 0.2 0.4 0.6 0.8 1

Figure 25. Mixed-mode delamination criterion for IM7/8552

Mixed Mode Ratio GII/GT

GC, 

J/m2

DCB, Mode I MMB, Mode I and II 4ENF, Mode II

Gc = G

Ic

 + a*(GII/G

T

) + b*(GII/GT)

2

 + c*(GII/GT)

3

 + ...

36
0

500

1000

1500

0

0.5

1

0

1

2

3

4

5

6

7

logN

G /GII T

Gmax

DCB, 4ENF, MMB test data

quasi-static

mixed-mode criterion

Figure 27. Delamination onset surface for IM7/8552 mixed mode I/II fatigue failure

G /G =0.18 II T

37
0

5

10

15

20

25

100101102103104105106107108

onset life = total - crack onset

mean

Applied

Load 

P, kN

Number of Cycles, N

D

, to Delamination Onset

predicted mean onset curve

Figure 29. Comparison of delamination onset prediction and experimental results.

0

50

100

150

200

250

300

350

100101102103104105106107108

Critical

Energy

Relase

Rate

GT max, 

J/m2

Fatigue Life, N, Cycles

GII/GT=0.18

Ni

Gi

Figure 28. Delamination onset curve for constant mixed mode ratio GII/GT

38
0

5

10

15

20

25

100101102103104105106107108

fatigue data

quasi-static data

quasi-static data, mean

fatigue data, mean

Applied

Load, 

P, kN

Number of Cycles, N

T

, to Damage Onset

predicted onset curve

Figure 30. Comparison of cumulative life prediction and experimental results

39
 output file

grate.out

contains echo input

and results

Figure 31. Flow chart of routine extract.f to calculate strain energy release rates.

40

program grate

start program

LRUNIT(1,1)=8

...

CALL INITPF(FNAME,NRU,...

CALL DBRNU(JUNIT)

ABAQUS result file initialization

user specified

input file

extract.data

contains parameters

to chose options

and input/output

file names

read(nunit,*)word,b1,...

read data from user input file

call gstart(kunit,output)

open file for output

ABAQUS result file

binary format

specimen.fil

INCLUDE ‘aba_param.inc’

enable access to ABAQUS files

CALL DBFILE(LOP,ARRAY,JRCD)

read each record of the ABAQUS result file

...

IF(KEY.EQ.15)THEN

call datin(head,1,nnum,...)

...

identify forces at element nodes, nodal

displacements and nodal point coordinates

record and store data in arrays for later use

call gend(iunit)

end

close output file and terminate program

...

call varea(iunit,ntype,...)

call local(iunit,ntype,...)

call trans(iunit,ntype)

call grate(ntype,iunit,...)

calculate area and local coordinate system,

transform forces and displacements,

compute mixed mode energy release rate
REPORT DOCUMENTATION PAGE Form Approved

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE

April 2001

3. REPORT TYPE AND DATES COVERED

Technical Memorandum

4. TITLE AND SUBTITLE

Fatigue Life Methodology for Bonded Composite Skin/Stringer

Configurations

5. FUNDING NUMBERS

WU 712-10-21-01

6. AUTHOR(S)

Ronald Krueger, Isabelle L. Paris, T. Kevin O'Brien and Pierre J. Minguet 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center U.S. Army Research Laboratory

Hampton, VA 23681-2199 Vehicle Technology Directorate

 NASA Langley Research Center

 Hampton, VA 23681-2199

8. PERFORMING ORGANIZATION

REPORT NUMBER

 L-18067

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

 National Aeronautics and Space Administration

Washington, DC 20546-0001

 and

 U.S. Army Research Laboratory

 Adelphi, MD 20783-1145

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA/TM-2001-210842

ARL-TR-2432

11. SUPPLEMENTARY NOTES

Krueger: ICASE Staff Scientist, NASA Langley Research Center

Paris: National Research Council Research Associate, NASA Langley Research Center

Minguet: The Boeing Company, Philadelphia, Pennsylvania

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12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

A methodology is presented for determining the fatigue life of composite structures based on fatigue

characterization data and geometric nonlinear finite element (FE) analyses. To demonstrate the approach,

predicted results were compared to fatigue tests performed on specimens which represented a tapered composite

flange bonded onto a composite skin. In a first step, tension tests were performed to evaluate the debonding

mechanisms between the flange and the skin. In a second step, a 2D FE model was developed to analyze the

tests. To predict matrix cracking onset, the relationship between the tension load and the maximum principal

stresses transverse to the fiber direction was determined through FE analysis. Transverse tension fatigue life data

were used to generate an onset fatigue life P-N curve for matrix cracking. The resulting prediction was in good

agreement with data from the fatigue tests. In a third step, a fracture mechanics approach based on FE analysis

was used to determine the relationship between the tension load and the critical energy release rate. Mixed mode

energy release rate fatigue life data were used to create a fatigue life onset G-N curve for delamination. The

resulting prediction was in good agreement with data from the fatigue tests. Further, the prediction curve for

cumulative life to failure was generated from the previous onset fatigue life curves. The results showed that the

methodology offers a significant potential to predict cumulative fatigue life of composite structures.

14. SUBJECT TERMS

Composite materials; Testing, Finite Element Analysis, Fatigue Life Prediction

15. NUMBER OF PAGES

45

Fracture mechanics; Skin/Flange Interface 16. PRICE CODE

A03

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18. SEC U RITY CL ASSIF IC AT ION 

O F TH IS PA GE

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 OF ABSTRACT

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20. LIMITATION

 OF ABSTRACT

 UL

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z-39-18

298-102