NASA/CR-2005-213915 

NIA Report No. 2005-06 

 

September 2005 

Skin-Stiffener Debond Prediction Based on 

Computational Fracture Analysis 

Ronald Krueger 

National Institute of Aerospace, Hampton, Virginia 

Pierre J. Minguet 

The Boeing Company, Philadelphia, Pennsylvania 
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NASA/CR-2005-213915 

NIA Report No. 2005-06 

National Aeronautics and 

Space Administration

Langley Research Center Prepared for Langley Research Center 

Hampton, Virginia 23681-2199 under Contract NAS1-02117

 

September 2005 

Skin-Stiffener Debond Prediction Based on 

Computational Fracture Analysis 

Ronald Krueger 

National Institute of Aerospace, Hampton, Virginia 

Pierre J. Minguet 

The Boeing Company, Philadelphia, Pennsylvania 
Available from: 

NASA Center for AeroSpace Information (CASI) National Technical Information Service (NTIS) 

7121 Standard Drive 5285 Port Royal Road 

Hanover, MD 21076-1320 Springfield, VA 22161-2171 

(301) 621-0390 (703) 605-6000 
1

SKIN-STIFFENER DEBOND PREDICTION

BASED ON COMPUTATIONAL FRACTURE ANALYSIS

Ronald Krueger

1

and Pierre J. Minguet

2

ABSTRACT

Interlaminar fracture mechanics has proven useful for characterizing the onset of

delaminations in composites and has been used with limited success primarily to

investigate onset in fracture toughness specimens and laboratory size coupon type

specimens. Future acceptance of the methodology by industry and certification

authorities however, requires the successful demonstration of the methodology on

structural level. For this purpose a panel was selected that is reinforced with stringers.

Shear loading causes the panel to buckle and the resulting out-of-plane deformations

initiate skin/stringer separation at the location of an embedded defect. For finite element

analysis, the panel and surrounding load fixture were modeled with shell elements. A

small section of the stringer foot and the panel in the vicinity of the embedded defect

were modeled with a local 3D solid model. Across the width of the stringer foot the

mixed-mode strain energy release rates were calculated using the virtual crack closure 

technique. A failure index was calculated by correlating the results with the mixed-mode 

failure criterion of the graphite/epoxy material. For small applied loads the failure index

is well below one across the entire width. With increasing load the failure index

approaches one first near the edge of the stringer foot from which delamination is

expected to grow. With increasing delamination lengths the buckling pattern of the panel

changes and the failure index increases which suggests that rapid delamination growth

from the initial defect is to be expected.

1. BACKGROUND

Many composite components in aerospace structures are made of flat or curved panels

with co-cured or adhesively bonded frames and stiffeners. Recent studies focused on the

investigation of the debonding mechanism and included testing of skin/stiffener panels and

failure analysis using shell models [1-4]. Over the last decade a consistent step-wise approach

has been developed which uses experiments to detect the failure mechanism, computational

stress analysis to determine the location of first matrix cracking and computational fracture

mechanics to investigate the potential for delamination growth. Testing of skin gage 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 [5]. Comparatively simple specimens

consisting of a stringer flange bonded onto a skin have been developed to study skin/stiffener

debonding [6-8]. The failure that initiates at the tip of the flange in these specimens is nearly 

identical to the failure observed in the full-scale panels and the frame pull-off specimens [7, 9,

10]. A methodology based on fracture mechanics [11] has proven useful for characterizing the

onset and growth of delaminations in composites and has been used with limited success

primarily to investigate delamination onset and debonding in spimple characterization specimens

 

1 Senior Staff Scientist, National Institute of Aerospace (NIA), 100 Exploration Way, Hampton, VA 23666.

2 The Boeing Company, Philadelphia, Pennsylvania
2

as shown in Figure 1a and laboratory size coupon type specimens such as the skin/stringer

debond specimen shown in Figure 1b,c [9, 10]. Future acceptance of the methodology by

industry and certification authorities however, requires the successful demonstration of the

methodology on structural level.

The objective of this research was to demonstrate the application of the fracture

mechanics based methodology on structural level for which a panel made of IM7/8552

carbon/epoxy tape was selected. The 1,016-mm by 1,016-mm wide panel shown in Figure 1d is

reinforced with three stringers made of IM7/8552 carbon/epoxy plain weave fabric. An artificial

defect was placed at the termination of the center stiffener. The stiffened panel is subjected to 

pure shear loading which causes the panel to buckle. The resulting out-of-plane deformation

causes skin/stringer separation at the location of the initial defect. For finite element analysis the

entire panel was modeled with shell elements. Locally the vicinity of the debonded section is

modeled with solid elements. During a series of nonlinear finite element analyses, strain energy

release rates and mixed mode ratios were computed using the virtual crack closure technique

(VCCT). The analyses were performed for four delamination lengths and results were correlated

to the mixed-mode fracture toughness of the composite material.

2. METHODOLOGY

2.1. Interlaminar Fracture Mechanics

Interlaminar fracture mechanics has proven useful for characterizing the onset and

growth of delaminations [11, 12]. The total strain energy release rate, GT, the mode I component

due to interlaminar tension, GI, the mode II component due to interlaminar sliding shear, GII, and

the mode III component, GIII, due to interlaminar scissoring shear, as shown in Figure 2, need to 

be calculated. In order to predict delamination onset or growth for two-dimensional problems,

these calculated G components are compared to interlaminar fracture toughness properties

measured over a range of mode mixities from pure mode I loading to pure mode II loading [13-

15].

A quasi static mixed-mode fracture criterion is determined by plotting the interlaminar

fracture toughness, Gc, versus the mixed-mode ratio, GII/GT, determined from data generated

using pure Mode I (GII/GT=0) Double Cantilever Beam (DCB) pure Mode II (GII/GT=1) four

point End Notched Flexure (4ENF), and Mixed Mode Bending (MMB) tests of varying ratios as

shown in Figure 3 for IM7/8852 carbon epoxy material. A curve fit to the experimental data is

performed using a failure criterion suggested in [16] to determine a mathematical relationship 

between Gc and GII/GT.

!

Gc= GIc + (GIIc" GIc )#

GII

GT

$

%

&

'

(

)

*

where GIc and GIIc are the fracture toughness data for mode I and II and 

!

"

is a factor

determined by the curve fit. Failure is expected when, for a given mixed mode ratio GII/GT, the

calculated total energy release rate, GT, exceeds the interlaminar fracture toughness, Gc.

Although several test methods have been suggested for the measurement of the mode III
3

interlaminar fracture toughness property [17-19], an interaction criterion incorporating the

scissoring shear, however, has not yet been established. The edge-cracked torsion test (ECT) is

being investigated for standardization of this fracture mode [20, 21].

2.2. Analysis Tools

2.2.1. Virtual Crack Closure Technique

For delaminations in laminated composite materials where the failure criterion is highly

dependent on the mixed-mode ratio and propagation occurs in the laminate plane, the virtual

crack closure technique [22, 23] has been most widely used for computing energy release rates

because fracture mode because fracture mode separation is determined explicitly. The Virtual

Crack Closure Technique requires force and displacement input, which is obtained from

continuum (2-D) and solid (3-D) finite element analyses of the cracked (2-D) or delaminated (3-

D) component.

The mode I, and mode II components of the strain energy release rate, GI and GII are

calculated for four-noded elements as shown in Figure 4a

 

!

GI= "

1

2#a

$ Zi$ wl" wl ( * )

 

!

GII= "

1

2#a

$ Xi$ ul" ul ( * )

where ∆a is the length of the elements at the crack front and Xi and Zi are the forces at the crack

tip (nodal point i). The relative displacements behind the crack tip are calculated from the nodal

displacements at the upper crack face ul and wl (nodal point l) and the nodal displacements ul

and wl at the lower crack face (nodal point l

*

) respectively. The crack surface ∆A created is

calculated as ∆A=∆a1, where it is assumed that the two-dimensional model is of unit thickness

“1”.

For geometric nonlinear analysis where large deformations may occur, both forces and

displacements obtained in the global coordinate system need to be transformed into a local

coordinate system (x', z') which originates at the crack tip as shown in Figure 4b. The local crack

tip system defines the tangential (x', or mode II) and normal (z', or mode I) coordinate directions

at the crack tip in the deformed configuration. The equations to calculate the mixed-mode energy

release rate components remain the same as before, with forces and displacements now

expressed in the local system. For the two-dimensional eight-noded quadrilateral element with

quadratic shape functions this yields

 

!

GI= "

1

2#a

$ Z

i

'

$ wl

'

" wl*

'

( )

 

!

GII= "

1

2#a

$ X

i

'

$ u

l

'

" ul*

'

( )
4

where X’i , Z’i are the forces at the crack tip at nodal point i and u’l, and wl (u’l*, w’l*) are the

displacements at the corresponding nodal points l and l

* behind the crack tip. The total energy

release rate GT is calculated from the individual mode components as

!

GT= GI + GII + GIII

where GIII=0 for the two-dimensional case discussed.

In a finite element model made of three-dimensional solid elements the delamination of

length a is represented as a two-dimensional discontinuity by two surfaces. The additional

dimension allows to calculate the distribution of the energy release rates along the delamination

front and makes it possible to obtain GIII, which is idential to zero for two-dimensional models.

For convenience, only a section of the delaminated area which is modeled with eight-noded

three-dimensional solid elements is illustrated in Figure 5. The mode I, mode II, and mode III

components of the strain energy release rate, GI, GII, and GIII are calculated as

 

!

GI= "

1

2#A

$ ZLi$ wLl" wLl ( * )

 

!

GII= "

1

2#A

$ XLi$ uLl" uLl ( * )

 

!

GIII= "

1

2#A

$YLi$ vLl" vLl ( * )

with ∆A=∆a⋅b as shown in Figure 5. Here ∆A is the area virtually closed, ∆a is the length of the

elements at the delamination front, and b is the width of the elements. For better identification in 

this and the following figures, columns are identified by capital letters and rows by small letters

as illustrated in the top view of the upper surface shown in Figure 4b. Hence, XLi, YLi and ZLi

denote the forces at the delamination front in column L, row i. The corresponding displacements

behind the delamination at the top face node row l are denoted uKl, vKl and wKl and at the lower

face node row l are denoted uKl, vKl and wKl as shown in Figure 5. All forces and displacements

are obtained from the finite element analysis with respect to the global system. A local crack tip 

coordinate system (x’, y’, z’), that defines the normal and tangential coordinate directions at the

delamination front in the deformed configuration, has been added to the illustration. Its use with

respect to geometrically nonlinear analyses was discussed above.

2.2.2. A Global/Local Shell 3D Modeling Technique

Built-up structures are traditionally modeled and analyzed using plate or shell finite

elements as shown in Figure 1d to keep the modeling and computational effort affordable.

Computed mixed mode strain energy release rate components, however, depend on many

variables such as element order and shear deformation assumptions, kinematic constraints in the

neighborhood of the delamination front, and continuity of material properties and section 

stiffness in the vicinity of the debond when delaminations or debonds are modeled with plate or

shell finite elements [24-26]. These problems may be avoided by using three-dimensional

models as shown in Figures 1a and b. Since many layers of brick elements through the thickness
5

are often necessary to model the individual plies, however, the number of degrees of freedom in

a finite element model may become prohibitively large.

For detailed modeling and analysis of the delaminations, the shell/3D modeling technique

will reduce the modeling time since existing plate or shell models may be modified to shell/3D

models. This is a considerable advantage compared to the creation of an entirely new threedimensional finite element model. The technique will also reduce computational time because

only a relatively small section of interest needs to modeled with solid elements reducing the

number of unknowns. The technique combines the accuracy of the full three-dimensional

solution with the computational efficiency of a plate or shell finite element model and has been 

demonstrated for various applications such as fracture toughness characterization specimens and

on coupon level for the skin/stringer separation specimen as as shown in Figures 1c [13, 27-29].

3. FINITE ELEMENT MODELING

For the demonstration of the methodology on structural level the stringer stiffened panel

as shown in Figure 6 was selected. The 1,016 mm by 1,016 mm wide panel made of IM7/8552

carbon/epoxy tape is reinforced with three stringers made of IM7/8552 carbon/epoxy plain

weave fabric. The stiffened panel is bolted to a steel picture frame as shown in Figure 6a. Shear

is induced in the panel through the frame reaction to the externally applied tensile load. During

manufacturing an artificial defect had been placed at the termination of the center stiffener as

shown in the sketch of Figure 6b. The shear loading leads the panel to buckle as visible in the

photograph of Figure 6a. The resulting out-of-plane deformation causes skin/stringer separation

at the location of the initial defect.

3.1. Global Shell Model of Stringer Stiffened Panel

The global model includes the steel load frame and attachments, the panel made of

graphite/epoxy prepreg tape and the stringers made of graphite/epoxy fabric as shown in

Figure 7. The outer steel load frame and the attachment bolts were modeled with beam elements

available in the finite element software ABAQUS® as shown in Figure 7a. The inner steel load

frame which overlaps the panel edge was modeled with standard shell S4 elements. Shell

elements were also used to model the panel bay, the reinforced panel bay and the reinforced 

panel perimeter as shown in Figure 7a. The stiffener components, such as foot, web and hat as

shown in Figure 7b, were also modeled with S4 shell elements.

A detail of the global finite element model in the vicinity of the stringer termination is

shown in Figure 8a. The stacking sequence for the different skin/stringer components are shown 

in Figure 8b. In the detail it is clearly visible that the panel skin and the stiffener foot are

modeled as separate offset entities. The S4 shell elements are located at the panel skin and

stiffener foot respective mid-planes. The shell elements are connected by beam elements

designed to enforce plate theory constraints [30]. In the sections containing the arificial defects

the beam elements were replaced by gap elements. The gap elements allow the modeling of the

skin/stringer separation but also prevent element interpenetration in case the surfaces get into

contact.

In preparation for the global/local modeling approach shell elements representing the foot

of the stiffener and the panel were removed from the original shell model around the center
6

stringer termination as shown in Figure 9. The shell elements used to model the stiffener web

and hat were kept in place. At the boundaries shell edges in ABAQUS®were defined as shown 

which were used to connect the shell model with the local 3D insert model using the shell to

solid coupling option in ABAQUS®which allows the connection between non-conforming shell

and solid models.

3.2. Local 3D Insert Model for Solid Modeling of the Stringer Foot and Panel Skin

The local 3D insert model was generated using C3D8I solid brick elements and consisted

of an intact section and a delaminated section with a fine mesh around the delamination front as

shown in Figure 10a. Surfaces were defined in ABAQUS on the outer faces of the insert model

to provide a connection with the global shell model using the shell to solid coupling option in

ABAQUS®. The initial defect is located at the bondline between stringer foot and the panel. This

defect was treated as a delamination and modeled as a discrete discontinuity using two

unconnected nodes with identical coordinates one on each side of the delamination. A refined

mesh was used along the stringer boundary in order to capture edge effects as shown in

Figure 10b. Using the finite sliding option available in ABAQUS® contact was modeled between

the delaminated surfaces to avoid interpenetration during analysis. Four elements over the

thickness were used to model the foot of the stiffener made of carbon/epoxy fabric as shown in 

Figure10b. The -45° skin ply made carbon/epoxy tape which is adjacent to the plane of

delamination was modeled with one element. The remaining 10 plies of carbon/epoxy tape were

modeled with three elements over the thickness a shown in Figure 10b.

3.3. Combined Global/Local Shell/3D Model of Stringer Stiffned Panel

For modeling the experiment, which was performed under constant displacement control,

as closely as possible uniform displacements u,v were applied at one corner node to introduce

shear as shown in Figure 11a. The inplane displacements u,v were suppressed at the diagonally

opposite corner and the out of plane displacements w were suppressed along all four edges across

the entire width of the inner and outer steel load frame. The local 3D insert model containing a

straight delamination front was inserted into the global shell model as shown in the detail of

Figure 11b. The local 3D insert model consisted of an intact section and a delaminated section of

length a with a fine mesh around the delamination front as discussed above. The global shell

model was connected to the local 3D insert model using the shell to solid coupling option in

ABAQUS®which allows the connection between non-conforming shell and solid models. For

the entire analyses the non-linear solution option was used in ABAQUS®.

A total of eight delamination lengths were modeled (a=81.9 mm, 88.9 mm, 94.9 mm,

101.6 mm, 127.0 mm, 203.2 mm, 279.4 mm and 355.6 mm). The initial length corresponds to 

the length of insert used to create an initial defect at the termination of the center stringer as

shown in Figure 6. Additional lengths were chosen to study the change in energy release rate

distribution across the width (b) of the stringer with increasing delamination length (a). A short

local 3D insert as shown in Figures 12a - where c=116.7 mm of the stringer foot and panel skin 

were modeled with CD8I solid brick elements - was used to model a total of four delamination

lengths (a=81.9 mm, 88.9 mm, 94.6 mm, and 101.6 mm). A longer local 3D insert - where

c=431.2 mm of the stringer foot and panel skin were modeled with CD8I solid brick elements -
7

was used to model the delamination lengths from a=127.0 mm to a=355.6 mm as shown in

Figure 12b.

4. ANALYSIS RESULTS

4.1. Deformed Panel

The deformed finite element models of the stiffened panel are shown in Figures 13 and

14. The color contour plots illustrate the out-of-plane deformation w designated u3.in ABAQUS.

The color limits were set for the last analysis increment after the entire external displacement

u=v=6.35 mm had been applied during the analysis of the panel with a simulated delamination 

length a=81.9mm. The limits were kept unchanged for all plots ranging from dark blue for the

trough to bright red for the peak. For the panel with a short local insert and a simulated

delamination length a=81.9mm three peaks and one trough can be observed in the panel bays

adjacent to the center stiffener as shown in Figure 13a. For longer delaminations modeled the

buckling pattern changed as shown in Figure 13b for a simulated delamination length

a=101.6 mm. The longer delamination caused a change in the stiffness which resulted in an 

altered buckling pattern. In one panel bay one peak disappeared and the trough became more

pronounced. Out-of-plane displacements which exceeded the previously set color limits are

shown in black for the trough and white for the peak. The buckling pattern remained unchanged 

for the panel with a long local insert and a simulated delamination length a=127.0 mm as shown

in Figure 14a. Another change in the global buckling pattern was observed for a simulated

delamination length a=355.6 mm as shown in Figure 14b. The analysis terminated prematurely 

due to convergence problems after only 83% of the external displacement had been applied. The

new pattern only had one prounced peak. Additionally another trough formed and the original

trough extended to both bays adjacent to the center stringer.

The detail of the deformed local models are shown in Figures 15-18. For a delamination 

length a=81.9mm details of the deformed local models are shown in Figure 15 for different

analysis increments. Early in the analysis (increment 5) a mode I opening was observed only

near one edge as shown in Figure15a. With increasing applied external displacement the

deformation changed locally and for increment 15 mode I disappeared completely and the

delamination appeared closed over the entire delaminated length. A small scissoring shear (mode

III) could be observed as shown in Figure 15b. Further increasing the external displacement

resulted in a small mode I opening across the entire width of the stringer as observed for

increment 20 as shown in Figure 15c. For the last step of the analysis (increment 41) after the

entire external displacement u=v=6.35 mm had been applied mode I opening was observed

across the entire width of the stringer over the entire delaminated length as shown in Figures 15d

and e. The same opening is also observed for modeled delamination lengths a= 88.9 mm and

94.9 mm as shown in Figures 16a and b. The detail of the deformed local model for a

delamination length a=101.6 mm is shown in Figure 16c for the last analysis increment. The

figure reveals that not the entire delaminated section opens under mode I. After initial opening,

the section below the web termination closes and the delaminated surfaces contact. This closing

is caused by a change in the local buckling pattern, due to stiffness changes caused by the longer

delamination, as discussed above. It was observed that the local buckling pattern in the

immediate surrounding of the delaminated stringer is dependent on the delamination length 

modeled, which made convergence difficult.
8

The detail of the deformed long local 3D insert model for a delamination length

a=127.0 mm is show in Figure 17a also for the last analysis increment after the entire external

displacement u=v=6.35 mm had been applied. Although opening of the entire delaminated

section is observed, the deformed shape is similar to the deformation shown in Figure 16c for a

delamination length a=101.6 mm. For both cases the closing at the web termination is caused by

a change in the local buckling pattern. The detail of the deformed local model for a delamination

length a=203.2 mm is show in Figure 17b after only 83% of the external displacement had been 

applied. The analysis terminated prematurely due to convergence problems. For the model

representing a delamination length of a=279.4 mm an opening of the delaminated section is

observed for the entire delamination length modeled as shown in Figure 18a. Partial closure of

the delaminated surfaces which result in local contact is observed for the analysis of the

a=355.6 mm delamination as shown in Figure 18b.

4.2. Calculation of Mixed-Mode Strain Energy Release Rates and Failure Indices

The virtual crack closure technique (VCCT) – discussed earlier - was used to calculate

the mode contributions GI, GII and GIII the total energy release rate GT=GI+GII+GIII, as well as

the mixed mode ratios GS/GT along the delamination front across the width b of the stringer for

all delamination lengths modeled. Here GS denotes the sum of the in-plane shearing components

GII+GIII. For two-dimensional analyses, where GIII=0, this definition is equal to the commonly

used definition of the mixed mode ratio, GII /GT. For three-dimensional analysis, which also

yields results for the scissoring mode GIII, the modified definition of GS is introduced since a

mixed-mode failure criterion, which accounts for all three modes is currently not available.

For each nodal point along the delamination front the critical energy release rate Gc was

calculated from the mixed mode failure criterion for IM7/8552 graphite/epoxy (Figure 3)

!

Gc= 207.7 +1126.8"

GS

GT

#

$

%

&

'

(

4.46

.

for the computed mixed-mode ratio GS/GT at each point. Subsequently the failure index 

GT/Gc was determined with the assumption that delamination propagation occurs for

!

GT

Gc

"1.

For all delamination lengths modeled, the computed failure indices were calculated for

every fifth increment plus the final increment of the analysis and plotted versus the

dimensionless coordinate s across the width of the stringer b

 

!

s(y) =

y " y0

b ; 0.0 # s #1.0.

At the left edge of the stringer the nodal point coordinates are equal to y=y0 which yields

s=0.0 and the right edge nodal point coordinates are equal to y=yb which results in s=1.0 as

depicted in Figure 11.
9

Shown as example are the mode contributions GI, GII and GIII and the total energy release

rate GT=GI+GII+GIII for increment 5 (Figure 19) and the last increment 41 (Figure 20) for a

modeled delamination length of a=81.9 mm. The results indicated that the distribution across the

width changes during the analysis. The analysis also revealed a significant mode III contribution 

for the problem investigated. The computed total energy release rates GT for all increments are

plotted in Figure 21. The total energy release rates peaks at the edges (s=0.0 and s=1.0) with and

additional peak around the center (s~0.5) underneath the stringer web. Selected mixed mode ratio

GII/GT distributions are shown in Figure 22 and appear to be dependent on the applied load. Early

in the analysis (increment 5) mode I opening is observed near one edge and in the center on

stringer. The other delamination at the other edge does not open and ratio GII/GT =1. For

increment 20 mode I disappears completely which indicates that the delamination is closed

almost along the entire front. For the last step of the analysis (increment 41) mode I opening is

observed over almost the entire width of specimen except for one small region near one one

edge. The change in the distributions is caused by the change in local buckling pattern with 

increasing load.

For all delamination lengths modeled, the calculated failure indices are shown in

Figures 23 to 30 for selected increments only. For delamination lengths up a=94.9 mm the

failure index peaks at the edges (s=0.0 and s=1.0) with an additional peak around the center

(s~0.5) underneath the stringer web, as shown in Figures 23 to 25. Early in the analysis (small

increment numbers), which corresponds to small applied displacements, the failure index GT/Gc

is well below one across the entire width. This result indicates that the delamination is not going

to grow. With increasing load the failure index approaches one first near one edge where failure

is expected to initiate. Generally, for the next load increment, the index is well above one across

the entire width. For the longer delaminations (a=101.6 mm and a=355.6 mm) which are

associated with a different global buckling pattern, the distribution across the width changes, the

failure index peaks in the center underneath the stringer web and is reduced toward the edges as

shown in Figures 26 and 30. As before, the failure index GT/Gc remains well below one across

the entire width for small increment numbers, which corresponds to small applied displacements.

With increasing load, the failure index first approaches one near the center of specimen.

Generally, for the next load increment, the index is well above one across the entire width.

In Figure 31 the failure index in the center of the specimen (s=0.5) is plotted versus the

applied displacement u for all delamination lengths modeled. The failure index for delamination

lengths of a=81.9 mm, 88.9 mm, and 94.9 mm, were almost identical. For the longer

delaminations modeled (a=101.6 mm up to 355.6 mm), which are associated with a different

global buckling pattern, the index is significantly higher. A different way to visualize the results

is to plot the critical displacement, i.e. the applied displacement for GT/Gc=1.0, at the center of

the specimen (s=0.5) versus the delamination length as shown in Figure 32. The critical

displacements for delamination lengths of a=81.9 mm, 88.9 mm, and 94.9 mm, were almost

identical. For the longer delaminations modeled (a=101.6 mm up to 355.6 mm), which are

associated with a different global buckling pattern, the critical displacements are significantly 

lower, which suggests that rapid delamination progress is to be expected once the delamination

starts to propagate for a critical applied displacement.
10

5. SUMMARY AND CONCLUDING REMARKS

The skin/stringer separation of a graphite/epoxy composite panel reinforced with three

stringers and subjected to pure shear loading was studied using computational fracture analysis.

The shear loading causes the panel to buckle and the resulting out-of-plane deformation initiates

skin/stringer separation at the location of an embedded defect. The panel and surrounding load 

fixture were modeled with shell elements. A small section of the stringer foot and the panel in 

the vicinity of the embedded defect were modeled with a local 3D solid model. A total of eight

delamination lengths were modeled. Across the width of the stringer foot the mixed-mode strain

energy release rates were calculated using the virtual crack closure technique. A failure index 

was calculated by correlating the results with the mixed-mode failure criterion of the

graphite/epoxy material.

Initially - for applied loads less than 25% maximum load - the computed failure index is

well below one across the entire width of the straight front, which represented the edge of the

embedded insert. With loads reaching 35% of the maximum load the failure index approaches

one first near one edge of the stringer foot from which the delamination is expected to grow.

With increasing modeled delamination length a change in the buckling pattern of the panel of is

observed locally and globally. The change in the local buckling pattern is believed to be due to 

stiffness changes caused by the longer delaminations. The different buckling pattern for the

longer delaminations caused a change in the distribution of computed failure index across the

width of the stringer. For longer delaminations, the failure index was found to be significantly

higher which suggests that rapid delamination progress is to be expected once the delamination

starts to propagate for a critical applied load.

ACKNOWLEDGEMENTS.

This research was supported by The Boeing Company and the Aviation Applied

Technology Directorate under Technology Investment Agreement No. DAAH10-02-2-0001 as

part of the Survivable, Affordable, Repairable, Airframe Program (SARAP).

The authors gratefully acknowledge Dr. Dale Berry of ABAQUS® Central for providing

guidance and help when problems with ABAQUS® Standard were encountered during the

analyses.

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Structural Dynamics and Materials Conference, Long Beach, California, AIAA 98-2022,

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2001.
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425-435, 2002.

[5] 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.

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

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

[7] 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, pp. 105-124, 1996

[8] 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, pp. 2783-2790, 1997

[9] 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.

[10] R. Krueger, I.L. Paris, T.K. O'Brien, and P.J. Minguet, Fatigue Life Methodology for

Bonded Composite Skin/Stringer Configurations, Journal of Composites Technology and 

Research, vol. 24, pp. 56-79, 2002.

[11] T.K. O'Brien, Fracture Mechanics of Composite Delamination, in ASM Handbook,

Volume 21, Composites: ASM International, pp. 241-245, 2001.

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

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

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

[13] R. Krueger and T.K. O'Brien, A Shell/3D Modeling Technique for the Analysis of

Delaminated Composite Laminates, NASA/TM-2000-210287, ARL-TR-2207, 2000.

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of Unidirectional Fiber-Reinforced Polymer Matrix Composites, in Annual Book of

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406, 1999.

[16] M.L. Benzeggagh and M. Kenane, Measurement of mixed-mode delamination fracture

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243-266, 1991.

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12

[20] J. Li, S.M. Lee, E.W. Lee, and T.K. O'Brien, Evaluation of the Edge Crack Torsion ECT

Test for Mode III Interlaminar Fracture Toughness of Laminated Composites, Journal of

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Applied Mechanics Reviews, vol. 57, pp. 109-143, 2004.

[24] E.H. Glaessgen, W.T. Riddell, and I.S. Raju, Effect of Shear Deformation and Continuity

on Delamination Modeling with Plate Elements, in The 39th

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials

Conference, 1998.

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Continuity Effects Related to the Modeling of Debonding of Laminates, Using Plate

Elements, CMES, vol. 3, pp. 103-116, 2002.

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modeled with plate elements, Engineering Fracture Mechanics, vol. 54, pp. 211-228,

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[27] R. Krueger and T.K. O'Brien, A Shell/3D Modeling Technique for the Analysis of

Delaminated Composite Laminates, Composites Part A: Applied Science and

Manufacturing, vol. 32, pp. 25-44, 2001.

[28] R. Krueger and P.J. Minguet, Analysis of Composite Skin-Stiffener Debond Specimens

Using a Shell/3D Modeling Technique and Submodeling, Hampton, VA, NIA Report No.

2004-04, NASA/CR-2004-212684, 2004.

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Using Volume Elements and a Shell/3D Modeling Technique, NASA/CR-2002-211947,

ICASE Report No. 2002-38, 2002.

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13

Table 1.

Material Properties

IM7/8552 Unidirectional Graphite/Epoxy Prepreg

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

ν12 = 0.32 ν13 = 0.32 ν23 = 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

ν12 = 0.04 ν13 = 0.35 ν23 = 0.35

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

Grade 5 FM300 Adhesive

E = 1.72 GPa ν = 0.3 (assumed isotropic)

The material properties are given with reference to the ply coordinate axes where index 11 denotes

the ply principal axis that coincides with the direction of maximum in-plane Young’s modulus

(fiber direction). Index 22 denotes the direction transverse to the fiber in the plane of the lamina

and index 33 the direction perpendicular to the plane of the lamina.
Figure 1. Finite element analyses of different complexity.

local 3D model of 

delaminated section

(c) Deformed shell/3D model of a skin/stringer specimen (101.6 mm x 25.4 mm) [28,29].

x,u

z,w

y,v global shell element model of 

unfractured section

local 3D model of 

delaminated section

(b) Deformed 3D model of a skin/stringer 

specimen (101.6 mm x 25.4 mm) [28,29].

(a) Deformed 3D model of half a DCB 

specimen (250 mm x 12.5 mm).

(d) Deformed shell model of stringer stiffened panel under shear loading (1016 mm x 1016 mm).

P

P

P

P

14
Figure 2: Fracture Modes. 

Interlaminar sliding shear

Mode II

Interlaminar scissoring shear

Mode II

Interlaminar tension

Mode I

Q

P

P

Figure 3: Mixed-mode fracture criterion for IM7/8552 . 

0

400

800

1200

1600

0 0.2 0.4 0.6 0.8 1

Mixed Mode Ratio GII/GT

GC, 

J/m2

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

Gc = G

Ic

 + (GIIc-GIc)(GII/GT)

Gc = GIc + (GIIc-GIc)(GII/GT)

n

GIc 207.7

GIIc 1334.5

4.46

15
(b): Virtual Crack Closure Technique (VCCT) for geometrically nonlinear analysis.

x',u',X'

x,u,X

z,w,Z

global system

z',w',Z'

local crack tip system

undeformed state

(outline)

deformed state

Z'i

X'i

u' *

u' 

w' i

k

a

crack closed

a

a

 *

 w' *

GI = - Z'i ( w'l - w'l * ) / ( 2 a )

GII = - X'i ( u'l - u'l * ) / ( 2 a ) 

X,Y,Z: forces

u,v,w: displacements

Figure 4: Virtual Crack Closure Technique for two-dimensional analysis

(a): Virtual Crack Closure Technique (VCCT) for four-noded element.

a a

x,u,X

a

z,w,Z crack closed

i

Zi

Xi

u *

 w *

u 

w 

GI = - Zi ( w - w * ) / ( 2 a )

GII = - Xi ( u - u * ) / ( 2 a ) 

k

 *

element

thickness=1

X,Y,Z: forces

u,v,w: displacements

16
i

*

L

 b

a

 ZLi

x',u',X'

z',w',Z'

x,u,X

y,v,Y z,w,Z

global

system

local crack tip 

system

a

 XLi

 YLi

(a). 3D view

Figure 5. Virtual Crack Closure Technique for eight noded solid elements.

(b). Top view of upper surface (lower surface terms are omitted for clarity)

 XLi ΔA

x,u,X

global system

y,v,Y

a

b/2

i

delamination front 

delaminated

 area 

intact area 

a

x',u',X'

y',v',Y'

 i 

 YLi

 L 

b/2

b

b

 uL *

 wL *

 uL 

 vL wL 

 uL 

 vL 

a

a

17
b. Outline of composite panel and steel load frame

x,u

z,w

y,v

inner steel load 

frame and panel 

overlaped and 

joined with bolts

outer steel load 

frame

panel made of 

carbon/epoxy 

prepreg tape

stringer made of carbon/epoxy fabric

Figure 6. Stringer stiffened composite panel (1016 mm x 1016 mm)

a. Buckled composite panel under shear loading with picture frame

stringer made of 

carbon/epoxy fabric

outer steel load frame

panel made of 

carbon/epoxy 

prepreg tape

attachment steel 

bolts

inner steel load frame 

with attchment bolts

initial defect

initial defect

18
b. Stiffener components

x,u

z,w

y,v

stiffener foot

stiffener hat

Figure 7. Finite element model of stringer stiffened composite panel and load frame

a. Composite panel and load frame components

reinforced panel 

perimeter

outer steel load 

frame modled with 

beam elements

panel edge

stiffener web

inner steel load 

frame modled with 

shell elements

reinforced 

panel bay

panel bay

x,u

z,w

y,v

attachment steel bolts 

modeled with beam elements

overlap

19
x,u

z,w

y,v

stiffener foot

[0/45/45/0]

stiffener hat

[0/45/45/0]

reinforced panel 

perimeter

stiffener web 

[0/45/45/0]

reinforced 

panel bay

skin/stringer connection in delaminated 

section modeled with gap elements

skin/stringer connection 

in intact section 

modeled with beam 

elements

delamination 

front

panel made of carbon/epoxy prepreg tape

stiffener made of carbon/epoxy fabric

panel edge

-45

+45

+45

-45

+45

-45

-45

+45

-45

+45

+45

-45

0

0

0

+45

-45

-45

+45

-45

+45

+45

+45

-45

-45

0

0

0

+45

+45

-45

-45

-45

+45

45

45

45

45

-45

+45

+45

+45

-45

-45

0

0

0

+45

+45

-45

-45

-45

+45

Figure 8. Detail of finite element model at stringer termination

panel bay

fabric

fabric

fabric

fabric

20
x,u

z,w

y,v

STRBOT

Figure 9. Detail of global shell model with edges for shell to solid coupling

PNLFRNT

STRFOOT PNLRGHT

PNLEND shell elements PNLLEFT

removed for local 

3D insert

21
a. Local 3D insert model and surfaces for shell to solid coupling

Figure 10: Local insert model 

b. Detail of local 3D insert model around delamination front

x,u

z,w

y,v

REAR1

REAR2

REAR1

REAR2

RIGHT1

RIGHT2

SOLTOP

LEFT1

LEFT2

SOLBOT

delamination

delamination front

delaminated section

intact section

stringer foot made of 

IM7/8552 fabric [0/45/45/0] 

modeled with four solid 

elements

skin made of IM7/8552 tape 

ply at interface modeled 

with one solid [-45]

layered solid [-45/45/45]

layered solid [0/0/0]

layered solid [45/-45/-45/45]

22
Figure 11: Shell model of stiffened panel with detail of local 3D insert 

b. Detail of center stringer with local 3D insert

a. Global shell model of panel (1016 mm x 1016 mm) and load frame

w=0 w=0

u=v= 6.35 mm

z,w

y,v

x,u

intact section

delaminated section 

refined mesh used to model straight delamination front across the width

 b 

y=yb

s=1.0

steel load frame panel made of carbon/epoxy prepreg tape

stringer made of 

carbon/epoxy frabric

u,v,w: displacements

z,w

y,v

x,u

shell to solid coupling in ABAQUS 

y=y0 s 

s=0.0

 a 

u=v= 0

 d 

23
a. Short local 3D insert (c=116.7 mm) with a=101.6 mm delamination length

Figure 12: Local 3D insert models

b. Long local 3D insert (c=431.2 mm) with a=355.6 mm delamination length 

24
Figure 13: Out of plane deformation of stiffened panel with short insert

a. Deformed panel for 81.9 mm delamination

b. Deformed panel for 101.6 mm delamination

25
Figure 14: Out of plane deformation of stiffened panel with long insert

b. Deformed panel for 355.6 mm delamination

a. Deformed panel for 127.0 mm delamination

26
Figure 15: Detail of deformed center stringer with short local 3D 

insert for 81.9 mm delamination

e. Increment 41 (true scale)

a. Increment 5 (displacement enlarged) b. Increment 15 (displacement enlarged)

c. Increment 20 (displacement enlarged) d. Increment 41 (true scale)

27
Figure 16: Detail of deformed center stringer with short local 3D insert.

c. Local 3D insert for 101.6 mm delamination

a. Local 3D insert for 88.9 mm delamination

b. Local 3D insert for 94.9 mm delamination

28
Figure 17: Detail of deformed center stringer with long local 3D insert.

a. Local 3D insert for 127.0 mm delamination length with detail

b. Local 3D insert for 203.2 mm mm delamination length with detail

29
a. Local 3D insert for 279.4 mm delamination length with detail

Figure 18: Detail of deformed center stringer with long local 3D insert. 

b. Local 3D insert for 355.6 mm delamination length with detail

30
0

2000

4000

6000

8000

10000

0 0.2 0.4 0.6 0.8 1

G

I

G

II

G

III

G

T

G,

J/m2

coordinate s, -

Figure 20. Computed energy release rate across the width of the stringer 

at increment 41 for delamination length a=81.9mm.

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1

G

I

G

II

G

III

G

T

G,

J/m2

coordinate s, -

Figure 19. Computed energy release rate across the width of the

stringer at increment 5 for delamination length a=81.9 mm.

31
0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

5

20

41

GII/GT

coordinate s, -

Figure 22. Computed mixed mode ratio across the width of the stringer 

for selected increments for delamination length a=81.9 mm.

0

2000

4000

6000

8000

10000

0 0.2 0.4 0.6 0.8 1

5

10

15

20

25

30

35

40

41

GT,

J/m2

Figure 21. Computed total energy release rate across the width of the stringer 

for all increments for delamination length a=81.9 mm.

coordinate s, -

32
0

1

2

3

4

5

0.0 0.2 0.4 0.6 0.8 1.0

25/0.054

30/0.059

35/0.085

40/0.102

GT/Gc

coordinate s, -

increment / appl. displ.

Figure 24. Computed failure index across the width of the stringer 

for selected increments for delamination length a=88.9 mm.

increment / appl. displ.

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1.0

20/0.052

25/0.061

30/0.095

35/0.157

GT/Gc

coordinate s, -

Figure 23. Computed failure index across the width of the stringer 

for selected increments for delamination length a=81.9 mm.

33
0

1

2

3

4

5

0.0 0.2 0.4 0.6 0.8 1.0

10/0.012

15/0.030

20/ 0.053

GT/Gc

coordinate s, -

Figure 26. Computed failure index across the width of the stringer 

for selected increments for delamination length a=101.6 mm.

increment / appl. displ.

0

1

2

3

4

5

0.0 0.2 0.4 0.6 0.8 1.0

30/0.056

35/0.059

40/0.073

45/0.095

50/0.105

GT/Gc

coordinate s, -

Figure 25. Computed failure index across the width of the stringer 

for selected increments for delamination length a=94.6 mm.

increment / appl. displ.

34
0

1

2

3

4

5

1 0.8 0.6 0.4 0.2 0

25/0.0126

30/0.0196

35/0.0344

40/0.0944

GT/Gc

coordinate s, -

Figure 28. Computed failure index across the width of the stringer 

for selected increments for delamination length a=203.2 mm.

increment / appl. displ.

0

1

2

3

4

5

0.0 0.2 0.4 0.6 0.8 1.0

5/0.0104

10/0.021

15/0.043

GT/Gc

coordinate s, -

Figure 27. Computed failure index across the width of the stringer 

for selected increments for delamination length a=127.0 mm.

increment / appl. displ.

35
0

1

2

3

4

5

1 0.8 0.6 0.4 0.2 0

30/0.0252

35/0.032

40/0.039

45/0.042

50/0.053

55/0.074

GT/Gc

coordinate s, -

Figure 30. Computed failure index across the width of the stringer 

for selected increments for delamination length a=355.6 mm.

increment / appl. displ.

0

1

2

3

4

5

1 0.8 0.6 0.4 0.2 0

35/0.0239

40/0.0281

45/0.0368

50/0.045

GT/Gc

coordinate s, -

Figure 29. Computed failure index across the width of the stringer 

for selected increments for delamination length a=279.4 mm.

increment / appl. displ.

36
0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0

G

T

/Gc=1.0

Applied 

displacement 

u, mm

Delamination length a, mm

Figure 32. Applied external displacement at delamination onset 

for different delamination lengths modeled.

a=81.9 mm

a=88.9 mm

a=94.6 mm

a=127.0 mm

a=101.6 mm

a=203.2 mm

a=279.4 mm

a=355.6 mm

0.0

1.0

2.0

3.0

4.0

5.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

a=81.9 mm

a=88.9 mm

a=94.6 mm

a=101.6 mm

a=127.0 mm

a=203.2 mm

a=279.4 mm

a=355.6 mm

GT/Gc

Applied displacement u, mm

Figure 31. Failure index at the center of the stringer for different delamination lengths modeled.

37
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