Composites Advanced AUC04 ALE Airbus

2004 ABAQUS Users’ Conference 421

Modelling and Simulation of Fibre Metal Laminates

Peter Linde1, Jürgen Pleitner1, Henk de Boer2, Clarice Carmone3

1. Airbus Deutschland GmbH, Kreetslag 10, DE-21129 Hamburg, Germany 2. ALE, Advanced Lightweight Engineering, Rotterdamseweg 145, 2628 AL, Delft,

The Netherlands 3. Bishop Aeronautical Engineers GmbH, Oesterleystraße 3, DE-22587 Hamburg, Germany

Abstract: In Aircraft construction, fibre metal laminates (FML) have obtained an increased use as a skin material due to its beneficial characteristics in terms of fatigue and fire resistance. The material, consisting of alternate layers of aluminium and glass fibre reinforced epoxy, is however complicated to model numerically. This paper deals with the modelling of FML and is focused on a detailed simulation of the inter rivet buckling behaviour in a stiffened fuselage shell. The skin material consists of FML and is modelled with solid elements, layer by layer. Each of the constituents are provided with their respective material model. For the glass fibre reinforced epoxy the user subroutine UMAT is employed for description of the failure modes, such as matrix cracking and fibre failure. The behaviour of the delamination between the metal layer and the fibre reinforced epoxy is also described with a user subroutine UINTER, which is an optional contact definition. This subroutine contains a failure criterion for the delamination. The rivets between the stiffener and the skin of a fuselage are modelled by elastic solid elements with a plastic material model, but without any failure criterion. This reflects the design, where no rivet failure is allowed prior to buckling of the skin. A specially designed experimental test, which captures the main characteristics of inter rivet buckling, is modelled and simulated. The numerical results are compared to the experimental data. Finally, conclusions and recommendations are given for future research.

Keywords: Advanced Composite, Aircraft, Crack, Delamination, Epoxy, Experimental Verification, Failure Criterion, Failure Mode, Fuselage, Fiber Metal Laminate (FML), Glass Fibre, Glare®, Inter Rivet Buckling, Layer, Non-linearity, Numerical Modelling, Prepreg, Skin, Static Behaviour, Subroutine.

1. Introduction

In modern aircraft fuselage design advanced composite materials are increasingly utilised. A special family of such materials are the fibre metal laminates or hybrid materials, consisting of

422 2004 ABAQUS Users’ Conference

alternating layers of aluminium and glass fibre reinforced epoxy. This material provides improved fatigue characteristics, considerable fire resistance and provides improved damage behaviour. This paper deals with numerical modelling of the material, focusing on the damage behaviour for the different constituents. Particularly delamination between adjacent layers is modelled and described. An application, the inter rivet buckling problem is presented and used with the developed models. The paper is organized as follows:

first the modelling of fibre metal laminates is presented, containing a description of the damage models. After that inter rivet buckling is introduced and a physical test is presented which is modelled by finite elements. In this model the above mentioned damage models are implemented.

Subsequently, results from numerical simulations are presented and compared with test data.

Finally, a summary and conclusions are presented.

2. Modelling of Fibre Metal Laminate

2.1 General

Fibre metal laminates are increasingly used as skin material in modern aircraft design. FMLs consist of aluminium sheets covering the front and the back and, between them, alternating fibre layers of unidirectional glass fibre reinforced epoxy (prepreg), and aluminium. Typical total skin thickness may vary between 1.6 mm up to around 3.2 mm, corresponding to a thickness of monolithic aluminium skin.

In general, there are three different approaches that can be chosen to model fibre reinforced composite metal laminates: the micro-level approach, in which individual fibre and fibre-matrix interfaces are studied, the meso-level characterization (Vlot, 2001), in which individual plies are modelled and, finally, the macro-level one, in which the effect of the complete homogenised laminate is studied.

Since the aim of this work is to model the failure mechanism on a macroscopic (buckling) level and a microscopic level (delamination growth), the approach applied in this research is the meso-level one (Linde, 2002), (Puck, 2002). This choice also leads to an uniform approach for all FML types possible on the one hand, and on the other hand, to a relatively limited number of elements used. It implies that both the aluminium layer and the prepreg one are considered as homogeneous materials, with given constitutive parameters. In particular, orthotropic material properties are given to the prepreg.

Usually, the adhesive bonding between the aluminium and the prepreg surfaces is of excellent quality. Indeed, the ultimate interface strength is much higher than the strength in the transition zone between fibre rich and resin rich zones of the prepreg (Vlot, 2001). Therefore a delamination crack can be expected in those areas. Moreover, experimental observations have shown that delamination may grow in the resin rich zone between two plies. It follows that particular attention must be paid in modelling the interface between mated plies. One method to accurately


model that area is by means of an additional layer (Figure 1) made of continuum elements. However, since

Figure 1. Modelling of FML’s resin-rich interface.

the layer is very thin, the number of elements needed would be very large and, as consequence, this method is scarcely used in finite element analyses. Another method, which is frequently used, is by lumping the behaviour of the layer in zero-thickness interface elements (Allix, 1992), (Hashagen, 1998), (Schipperen, 2001). In these elements only the aspect ratio between the length and the width of the element has to be taken into account, so the number of elements is defined by the element size in the individual plies and not by the thickness of the resin-rich interface layer. A disadvantage however, is that the FE meshes of two adjacent plies have to comply so that the interface elements can be placed in between. This disadvantage can be removed by modelling the delamination behaviour using an interaction law between two adjacent plies. This can be accomplished with the ABAQUS FE program. In this method no elements have to be generated between matching layers by the user. The program itself finds the displacements between two adjacent points on the surfaces of the layers and these displacements can be evaluated by a user defined interaction law.

The present work deals with the development of proper damage models for damages that can occur in the Fibre Metal Laminate Glare®. Two main failure modes for FML are numerically modelled: fibre/matrix failure and interlaminar delamination.

2.2 Damage modelling

Damage in fibre metal laminates can be distinguished between damage in the aluminium, damage in the prepreg, and delamination, see Figure 2.

plyResin rich layer

Continuum elements

Interface layer

Interface elements

plyInteraction surfaces

pl

resin rich

continuum

interface

interface

pl

Interaction surfaces


In the aluminium layers, the damage typically consists of plasticity in compression, but it can also consist of cracking under tension.

For damage in the prepreg, a distinction must be made between the epoxy matrix failure and the fibre failure. In the first case the damage will typically occur under tension by cracking. In the

Figure 2. Modelling of damage in Fibre Metal Laminates.

second case, the fibre may fail under tensile loading. Some further forms of failure exist, which involve both matrix and fibre; however since not relevant for this study they are not described here. The matrix failure and the fibre failure are implemented in the models by means of the user subroutine UMAT.

Between two layers, delamination may take place when a failure criterion has been exceeded. A failure criterion is described below. The delamination between two layers is implemented by means of the user subroutine UINTER. The failure criterion for delamination is described subsequently.

a) undamaged fibre metal laminate

b) matrix failure c) delamination


3. Fibre/matrix failure

Fibre or matrix failure only occurs inside a glass/epoxy layer of the FML. Matrix failure is a non-fatal failure mode, since the layers can still carry an increasing load after matrix failure.

A laminate will show stress redistributions after first ply cracking and additional loading of the laminate will still be possible (Alessandrini, 2003). Therefore, for a correct description of a laminate structure also the effects of crack propagation have to be described. Crack propagation influences the material properties of the cracking ply. For a finite element modelling on a meso-level, the degradation of the properties at a ply level is needed. In papers dealing with numerical modelling three different options are mentioned for the material degradation:

1. instantaneous unloading;

2. gradual unloading;

3. constant stress at ply failure.

The failure criterion used here is based on a strain-based continuum damage formulation with different failure criteria for matrix and fibre failure. A gradual degradation of the material properties is assumed. This gradual degradation is controlled by the individual fracture energies of matrix and fibre, respectively.

The user-subroutine UMAT has been used for implementation of the damage model. For matrix failure the following failure criterion is used

212

2

12

2222

22

222

222

2222

22 )()(

)( εεεε

εεεε

εε

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−+= s

t

c

tt

c

t

mf ,

where t22ε and c

22ε are the failure strains perpendicular to the fibre direction in tension and

compression, respectively. The failure strain for shear is s12ε . Failure occurs when mf exceeds its

threshold value t22ε .

In case of damage, a damage parameter is calculated as follows

( )mt

mt GfC

m

t

m ef

d /)(22 2222221 εεε −−−= .

The glass/epoxy layer shows transverse isotropy. Therefore, the modulus stiffnesses read

aEC TTL )1( 2

11ν−= ;

aEC TLLTT )1(

22νν−= ;

aEC TLLTT )1(

33νν−=


aEC TTLTLTT )(

12ννν −= ;

aEC TTLTLTT )(

13ννν −= ;

aEC TLLTTTT )(

23ννν −=

TTGC =33 ; LTGC =55 ; LTGC =44 ,

with

TTTLLTTTTLLTa νννννν 221 2 −−−= .

The failure criterion for fibre failure is given by

1111

211

112

1111

11 )()( εεεεε

εε

⎟⎟⎠

⎞⎜⎜⎝

⎛−+= c

tt

c

t

ff .

Here t11ε and c

11ε are the failure strains in fibre direction in tension and compression, respectively.

Failure occurs when ff exceeds its threshold value 11ε .

A second damage parameter for fibre damage is introduced

( )ft

ft GfC

f

t

f ef

d /)(11 1111111 εεε −−−= .

The modulus matrix of the glass/epoxy layer will be reduced according to

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

−−

−−−−−−−

=

66

55

44

33

2322

131211

0

00)1)(1(000000)1)(1()1(000)1()1)(1()1(

CC

Cdd

sym

CCddCd

CdCddCd

Cmf

mfm

fmff

The stresses are computed by

εσ ⋅= C .


4. Delamination

Interlaminar delamination might occur at any interface of the FML, i.e. at the interface between aluminium and glass/epoxy or at the interface between two glass/epoxy layers. Experimental observations have shown that a delamination may grow at the resin rich layer between two layers. Its initiation, however, might be due to matrix failure inside the glass/epoxy layer.

An orthotropic delamination model, describing mixed mode delamination, is applied.

If an initial delamination exists this delamination may close under the applied load. To prevent the two adjacent plies from penetrating, a simple contact model is utilised. In this contact model the normal stiffness of the interface is given a penalty value if the relative normal displacement between two adjacent plies is negative. The normal stiffness is zero if opening of the initial delamination occurs. The shear stiffness of the initial delamination zone is always taken equal to zero, so no friction is modelled.

The delamination model has been implemented in the ABAQUS FE program, using the surface-to-surface contact option. In case of surface-to-surface contact, the FE meshes of adjacent plies do not need to be identical. The contact algorithm of ABAQUS will determine which node of the so-called master surface is in contact with a given node on the slave surface. The relative displacement between these two nodes is given in a local coordinate system. The first component of the relative displacement 1u corresponds to the normal direction of the master surface. The

other two components ( 2u and 3u ) are the two out-of-plane shear components. The user-subroutine UINTER can be used to specify a dedicated relation between the relative displacement and the corresponding traction forces. Hence, the user can define the interaction between the two surfaces.

Failure in this model is related to the equivalent relative displacement, κ , defined by

23

2

22

2

21 u

uu

uuu

ufs

ft

fs

ft

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛+=κ ,

where ftu is the gap opening displacement leading to failure and fsu denotes the maximum shear

displacement. Failure will occur when ftu>κ . Notice that the failure function is based on

relative displacements. The stiffness of the interface is taken equal to the stiffness of the matrix material. The strength of the interface is taken from experimental results. This leads to

tEu t

ft ⋅= max,σ

, and tG

u fs ⋅= maxτ

.

Here t denotes the thickness of the resin rich layer, E , G and maximum stresses relate to the matrix material.


In case of damage the elastic properties of the interface will reduce. The damage parameters are defined as

( )Icftft GuuCft eu

d ,11 /)(1 1 −−−= κ

κ,

( ))/()(2

,2

221 ftIIcftfs uGuuCft eu

d ⋅−−−= κ

κ,

( ))/()(3

,2

331 ftIIcftfs uGuuCft eu

d ⋅−−−= κ

κ,

where IcG , and IIcG , denote the fracture energy per unit area for mode I and mode II in [MPa],

respectively.

The modulus stiffnesses read

τEC =11 ,

τGC =22 ,

τGC =33 .

Notice that damage parameters are equal to zero if ftu>κ . The relation between relative

displacements and tractions is given by

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−

−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

333

222

111

3

2

1

)1(000)1(000)1(

uuu

CdCd

Cd

ttt

.

Notice that the failure function κ and the damage parameters id cannot be chosen independently, since

∫∞

=

=uftu

IcGdut1

,11

must hold true. A similar relation applies for Gc,II.


5. Inter Rivet Buckling simulation

The developed models described above are applied in the simulation of the static behaviour of fuselage structures. If tested statically until failure these structures typically eventually fail by column buckling. Among the different types of instability of a stiffened fuselage, the inter rivet buckling is particularly challenging since physical and geometrical non-linearity needs to be modelled together with rivet contact behaviour in order to obtain realistic results.

In general, two types of inter-rivet buckling are distinguished:

1. the classical type of a skin riveted on a stringer;

2. the skin riveted to a stringer at the crossing of the frame attachment and the stringer. This crossing causes locally a larger distance between the last rivet in a frame clip and the rivet in the crossing stringer, as shown in Figure 3.

Figure 3. Inter rivet buckling: larger rivet pitch where stringer pass between clips.

The physical test of the inter rivet buckling problem is shown in Figure 4. The width of the specimen is equal to 25 or 32 mm, respectively without and with initial delamination, while the total length is 226 mm. The specimen consists of either Glare® 3-5/4-0.41 or Glare® 4B-5/4-0.4 with a total thickness of 3.0 mm and 3.5 mm, respectively. Three layers of aluminium stiffener tabs are added. Rivet Type I is ASNA 2026-T3A, and rivet type II is DAN5-8-8.

1 According to the laminate coding system (Vlot, 2001), the following definitions are used: Glare®3 and Glare®4B are the Standard Glare grades, 5/4 represent the number of aluminium and fibre layers respectively and 0.4 is the aluminium layer thickness in mm.


Figure 4. Inter rivet buckling test.

The loading at the right hand side of the specimen is applied as a uniform horizontal displacement. The C3D8I incompatible modes solid elements are used for the Glare® material and the aluminium 2024-T3 tabs.

Delamination and prepreg damage modelling is obtained by using UINTER and UMAT subroutines.

The behaviour of the aluminium layers in the Glare® is modelled by an orthotropic plasticity model. It accounts for orthotropic hardening by using the *POTENTIAL option in ABAQUS. Table 1 gives the plasticity data for Aluminium 2024-T3, which is used in Glare®. Isotropic elastic properties are: Young’s modulus 73800 MPa and Poisson’s ratio 0.33.

Table1. Plasticity data for aluminium 2024-T3.

Yield stress [MPa]

300 320 340 355 375 390 410 430 450 470 484

Plastic strain [%]

0.00 0.016 0.047 0.119 0.449 1.036 2.130 3.439 5.133 8.00 14.71

The UD glass-epoxy prepreg shows a transversely isotropic behaviour. The corresponding elastic properties are listed in Table 2.


Table2. Elastic properties and ultimate stresses of UD prepreg.

EL [MPa]

ET [MPa]

GLT [MPa]

GTT [MPa]

νLT νTT σLu,t

[MPa] σL

u,c [MPa]

σTu,t

[MPa] σT

u,c [MPa]

τLTu

[MPa] τTT

u [MPa]

53980 9412 5548 3000 0.33 0.33 2430 2000 50 160 50 50

The rivets between the stiffener and the skin of a fuselage are modelled by a plastic material model, but without any failure criterion. This reflects the intention of the design, according to which no rivet failure is allowed prior to buckling of the skin.

Figure 5. Numerical model of the inter rivet buckling problem.


Figure 6. Delamination modelling.

Due to symmetry reasons, only a quarter of the specimen is modelled. The different interfaces and their numbering are depicted in Figure 5.

A section is shown through a model in Figure 6, and an initial delamination is seen at interface 5 (see Figure 5) placed at the most critical location at the edge of the stiffener plate.

Tests on samples with initial defects were carried out on specimens having a width of 32 mm instead of the 25 mm. The increased width is required to be able to add an initial circular delamination with a diameter of 12 mm. Firstly an analysis has been carried out on a 32 mm specimen without an initial delamination. Subsequently, a specimen having an initial delamination as described above has been analysed. As a reference, also the modelling of a 25 mm wide specimen without initial delamination is considered.

6. Results

In this section results are presented in form of axial average stress at the center of the specimen versus axial displacement from numerical simulations of the inter rivet buckling problem described in the previous section. Moreover a comparison between the numerical results obtained and experimental results is shown.

The experimental results refer to inter-rivet buckling tests that were carried out on both Glare® 3-5/4-0.4 and Glare® 4A-5/4-0.4 specimens having a width of 25 mm. Additional tests were carried out on the effect of a circular initial delamination, using a specimen width of 32 mm.

A Glare® 3-5/4-0.4 specimen having a width of 25 mm is analysed. Initially, the clamped part of the specimen (50 mm) is not modelled. Instead, it is assumed that the edge of the specimen remains

initial delamination


Figure 7. Simplified boundary conditions.

straight and the specimen is loaded by a uniform prescribed displacement of 2 mm at this edge, see Figure 7. Finally, the clamping conditions were modelled in an improved manner, more realistic, leading to the boundary conditions as depicted in Figure 8.

Results are shown in Figure 9. Tests (Ypma, 2001), in a batch of 4, are shown with thin lines, numerical simulations are shown with thick lines. For the simplified boundary conditions it can be noticed that the FE curve shows a too stiff behaviour and the gross strength is roughly 15%-20% too high. For the improved modelling of the boundary conditions, both the stiffness and the gross strength are in good agreement with the experimental results. It should be noticed that these test conditions are more severe than the conditions in a real aircraft fuselage, and thus conservative.

The numerical simulation showed that damage develops in the specimen during loading. Around the rivets and at the buckled area matrix cracks are found. No fibre damage occurs during the

u = 2 mmu = 2 mm


Figure 8. Improved model of boundary conditions.

p = 10 MPa

z = 0

u = 2 mm

p = 10 MPap = 10 MPa

z = 0z = 0

u = 2 mmu = 2 mm


Figure 9. Boundary conditions results.

analysis. At interface 5, in the middle of the specimen delamination takes place upon ultimate load. Also, there is some delamination around the rivet and just in front of it. However, the main delamination is found to be a free edge delamination crack. This failure mode was also observed in the experiments. Moreover, experimental results show that the location of the delamination at interface 5 at the free edge is also correctly predicted by the numerical simulation, see Figure 10.

0

25

50

75

100

125

150

175

200

225

250

275

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25

G3-1

G3-2

G3-3

G3-4

Glare 3-5/4-0.4 L, simplified BC

Glare 3-5/4-0.4 L

[MPa]

[mm]


Figure 10. Inter rivet buckling tests.


Figure 11. Delamination results.

Figure 11 (all numerical) shows that the initial delamination has hardly any influence on the ultimate load. The initial delamination did not grow until ultimate load upon which a slight growth took place.

0

25

50

75

100

125

150

175

200

225

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

width 25mm

width 32mm

width 32mm + initial delamination[MPa]

[mm]


7. Summary and conclusions

Based on the results presented, it can be concluded that:

• The damage models for FML developed during the present research are capable of accurately predicting the inter rivet buckling behaviour both qualitatively and quantitatively.

• Proper modelling of the boundary conditions for the clamping is important. Improper boundary conditions can overestimate the gross stress by approximately 20%.

• Upon inter rivet buckling, delaminations occurred at the free edge of the test specimen which are not relevant in aircraft conditions and in design.

• In these simulations, the circular initial delamination did not grow until ultimate load.

• The initial delamination was not found to have an influence on the gross stress at failure.


8. References

1. Alessandrini, A., “Delamination Behaviour of Z-pinned Laminates under Shear Loading”, M.Sc. Thesis, Cranfield University, 2003.

2. Allix, O., Ladeveze, P., “Modelling and Computation of Delamination for Composite Laminates”, Arch. Mech, vol. 44, pp. 5-13, 1992.

3. Hashagen, F., “Numerical Analysis of Failure Mechanisms in Fibre Metal Laminates”, Dissertation, Delft University of Technology, Delft, 1998.

4. Linde, P., “Fibre Metal Laminate Simulation”, Outline Proposal of Research and Technology Project, Internal report, Airbus Deutschland GmbH, 2002

5. Puck, et al., “Guidelines for the Determination of the Parameters in Puck’s Action Plane Strength Criterion”, Composites Science and Technology, vol. 62, pp. 371-378, 2002.

6. Schipperen, J. H. A., “Computational Modelling of Failure in Fibre Rinforced Plastic”, Dissertation, Delft University of Technology, Delft, 2001.

7. Vlot, A., Gunnink, J. W., “Fibre Metal Laminates - An introduction”, Kluwer Academic Publishers, 2001.

8. “Writing user Subroutines with ABAQUS”, Hibbitt, Karlsson & Sorensen, Inc., 2001. 9. Ypma, M.S., Exploratory compression strength tests on skin detail (IRB frame clip), Report

B2V-00-59, Delft University of technology, 2001

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