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2003 ABAQUS Users’ Conference 1

Progressive Damage Modelling of FML’s. Implementation in a UMAT subroutine

Jan Hol and Valeria Antonelli

Faculty of Aerospace Engineering,

Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands

Abstract: The present paper presents the procedure used to write a user material subroutine UMAT for shell elements to include property degradation of the composite plies of a Fibre Metal Laminate (FML). The Hashim’s three-dimensional piecewise stress-based criteria for in-plane failure has been implemented in the subroutine. The type of failure and its extension in the pre-preg layers can be visualised in ABAQUS-CAE. Case study has been the blunt notch strength of a GLARE plate. The numerical results were in good agreement with the experimental ones.

1. Introduction

Fibre Metal Laminates (FML’s) are hybrid laminates made of polymer matrix composite (PMC) plies interspersed with metal plies. The two materials are assembled by curing the PMC plies and metal foils to form a composite laminate (Figure 1).

Figure 1. Example of a FML.

The benefits of FML’s arise from the ability to tailor material properties so that the attractive aspects of the two constituent materials are utilised and their weaknesses are avoided. The metal

2 2003 ABAQUS Users’ Conference

layers protect the PMC core from environmental effects such as moisture ingress as well as providing improved impact resistance and bearing properties. The composite core has higher strength and stiffness to weight ratio than monolithic metal and is known to be less sensitive to fatigue effects. The combination of the two materials as a hybrid composite could potentially outperform either of the two constituent materials.

To be able to fully exploit the capabilities of FML in a design stage, it is necessary to model with accuracy the type of failure and its location within the laminate. To be able to predict with a better accuracy the blunt notch strength of FML, a user subroutine UMAT has been implemented

2. Material modelling

As fibre metal laminates are normally used in aeronautical applications, to describe the material behaviour of FML structures, laminated shell elements are used in FE-analyses. Two materials are therefore defined to describe the FML: an isotropic metal layer and a 2D-orthotropic one for the composite layer. The isotropic layer is defined as an elastic plastic material using the standard keywords available in ABAQUS.

In general, for the composite ply, the 2D orthotropic material definition is used. In addition to this, failure of the different layers can be verified during post processing with the classical failure criteria as Tsai-Hill, Tsai-Wu, etc. In the present case, the Hashin’s in-plane stress failure [1] has been implemented in a material subroutine.

The state of stress is characterised by the three stress components

[ ]

⋅=

12

22

11

12

22

11

C

γ

εε

τ

σσ

Where [C] is a 3 x 3 stiffness matrix, whose components in terms of the engineering constants are given by:

( ) ( )

( ) ( )12333231

132112

222

2112

21221

132112

12112

2112

111

C ;0C ;0

0C ;1

C ;1

0C ;1

C ;1

GC

EEC

EEC

===

=−

=−

=

=−

=−

=

ννννν

ννν

νν

with 121212 EE νν = . Where E1 is the longitudinal and E2 is the transverse Young’s modulus, ν12 is

the in-plane Poisson’s ratio and G12 is the in-plane shear modulus.

2.1 Failure criteria and degradation modelling

According to Hashin, failure occurs in different modes and cannot therefore be easily represented by one smooth function. The failure modes and their analytical description is given by:


• Tensile fibre mode, σ11≥0:

12

12

2

11 =

+

ct SXσσ

• Tensile fibre mode (fibre buckling), σ11<0:

12

11 =

cXσ

• Tensile matrix mode, σ22≥0:

12

12

2

22 =

+

ct SYτσ

• Compressive matrix mode, σ22<0:

12

12 =

cSτ

where index 1 stands for fibre and 2 for transverse directions, Xt, Xc are the tensile and compressive strength in the fibre direction, Yt and Yc are the tensile and compressive strength in the transverse direction and Sc is the in-plane shear strength of the ply.

The Young’s moduli, Poisson’s ratios and Shear moduli are reduced according to the failure modes of the single ply:

• Fibre breaking / fibre buckling:

12412312222111 12 , ,, νν dGdGEdEEdE dddd ====

• Matrix cracking / matrix failure:

12412612252 12 ; ; νν dGdGEdE ddd ===

Where the coefficients d1 to d6 are degradation factors that can either be derived from tensile testing of the composite, or taken from values found in literature [2].

3. UMAT implementation

In the input file, two materials are given which compose the laminate, the metal layer, described with the *ISOTROPIC and *PLASTIC keywords, with the description of the material properties and the plastic behaviour, and the one defined by the UMAT subroutine which is described by the *USER MATERIAL and *DEPVAR keywords.


The *USER MATERIAL keyword defines the number of constants that describe the material and that are called by the user subroutine. This enables any user to use this subroutine without requiring a background of (Fortran) programming. The *DEPVAR variable defines the number of variables to be stored for post processing. In this case, each failure mechanism is stored as a single variable, to enable visualization of every type of failure.

Figure 2 shows the block diagram for the UMAT subroutine.

Equilibrium iteration

New increment

Failure occurred? No

Use original properties to calculate stiffness matrix

Use degraded properties to calculate stiffness matrix

Update Stresses and strains

Update damage array

Yes

Exit UMAT

Acquire data from input file: mechanical properties, degradation coefficient and damage array size

Compare stresses with failure criteria

Figure 2. Block diagram of the UMAT subroutine.

The subroutine is called for each element in the model. The stresses reached in the previous iteration are referenced by the failure criteria to check if failure has occurred and choose the appropriate properties. In case failure has occurred, the degraded properties are applied and the


element is added to the elements that have failed one of the criteria. In case the element has not failed any of the criteria, the undamaged properties are applied. At this point, the stresses and strains as well as the damage array are updated for the new increment.

Care has been taken, as suggested in [2], to upgrade the damage array so that each damaged element continues having degraded properties. If this was not done, it could happen, in fact, that the stresses in one of the damaged elements are reduced in a following step due to lower mechanical properties, causing the element to be again undamaged at a higher load.

More tips for writing user material subroutines can be found in [4].

4. Analysis procedure

Every analysis has been carried out with ABAQUS, using as much as possible ABAQUS /CAE for pre and post processing.

Advantage of ABAUQS/CAE is that, being a feature-based program, every assignment (material properties, boundary condition, load application) is made on the geometrical model, allowing easy mesh changes.

Small drawback is the difficulty of applying line loads. As ABAQUS does not support “line load” on an edge, this has to be done through point loads, which imp lies the division of the edges in which the load is applied at as many sections as elements on that edge.

Unfortunately the used version of ABAQUS/CAE (Version 6.3-1) does not support layered material yet; the definition of the shell properties has therefore been made by hand, directly in the input file. On the other hand it supports all the keywords needed for the user material subroutine, making the implementation of the needed coefficients very easy. Another advantage is the possibility to view the progression of the damage during post processing, as this output is added to the standard ones through the *DEPVAR keyword, as mentioned before.

5. Case study

Case study is the blunt notch strength of a GLARE3 3/2 0.3 plate, tested in uniaxial tension.

GLARE3 3/2 0.3 is the definition of a FML plate composed by three layers of aluminium of 0.3 mm thickness each, interspersed by two layers of unidirectional glass fibre reinforced epoxy layers of 0.125 mm thickness, placed at 0° and 90°. The laminate is fabricated to be symmetric with respect to the middle aluminium layer [Al/0/90/Al/90/0/Al], and its total thickness is 1.4 mm.

Material properties of the two materials are presented in Table 1 and Table 2.

Table 1. Mechanical characteristic of the aluminium layers.

E (MPa) ν σyield (MPa) σmax (MPa) εmax (%) 71340 0.3 300 400 14


The aluminium layers are defined as an isotropic material with an elastic-plastic behaviour. Each GFRP layer is described via the UMAT subroutine through the definition of its mechanical characteris tics and the degradation coefficients. An orientation is coupled to each layer to define the principal direction of the layer.

Table 2. Mechanical characteristics of the unidirectional glass fibre reinforced plastic layers.

E1 (MPa) E2 (MPa) ν12 G12 (MPa) Xt (MPa) Y t (MPa) Sc (MPa) 54000 9400 0.33 5548 2430 47 40

The degradation coefficients for these calculations are all taken equal to 0.05.

The model geometry is shown in Figure 3. It is a plate of 300 mm length and 50 mm width with a central hole of 5mm diameter.

A tension load has been applied on the two short sides of the plate. To prevent rigid body motion, the x displacement has been fixed along the yz plane as well the y displacement on two point of the xz plane.

Figure 3. Geometry of the Finite Element Model.

In order to check the mesh sensitivity, three different meshes have been considered in an area of 20 mm x 20 mm around the cut-out, while the mesh seed on the edges of the plate has a typical length of 3 mm and has remained unchanged for all four calculations. The different meshes are shown in Figure 4.


Figure 4. Different mesh densities.

All meshes gave the same load at which fibre and resin failure occurred, although the shape of the fibre failure for the most refined meshes was different from the previous two (Figure 5). This difference seems to be due to the shape of the elements more than an improvement of the results. As it has already been pointed out in [2], the “triangular” mesh around a cut-out is not the best type for this type of problem. As failure occurs at adjacent element, being the elements very small in the critical area, failure increases in an unusual way, following the shape of the elements. Since it is known that the delamination is triangular at cut-outs, and the mesh is becoming straighter in the first two meshes closer to the cut-out, the second mesh has been used for further calculations.

Figure 5. Area in which fibre failure has occurred for different mesh densities.

The type of element used is S4R5 elements. These are four node elements used for the analysis of thin shells and have 5 degrees of freedom per node. The same analysis has been carried out also with S4R elements, which are four nodes elements for general purpose. Although resin and fibre


failure prediction were quite accurate, the S4R, failed to converge quite early in the calculation, giving a poor prediction of the blunt notch strength.

Figure 6 and Figure 7 show the progression of matrix and fibre failure respectively for the blunt notch of GLARE 3 3/2 0.3. Matrix failure occurs at first in the layers where the fibres are placed at 90° with respect to the load, while fibre failure occurs in the layers with fibres parallel to the load.

Figure 6. Matrix failure progression for specimens tested at 0° off-axis angle from starting of matrix failure up to maximum load.

Figure 7. Fibre failure progression for specimens tested at 0° off-axis angle from starting of fibre failure up to maximum load.

Three more calculations have been carried out for uniaxial tension of GLARE3 3/2 0.3, at off-axis angles, as uniaxial tests for this configurations were available. In the present work those results are useful to check whether the subroutine works well also in the case when different fibre angles are considered. The results obtained with the user material subroutine are compared with the test result in Table 3.


Table 3. Test versus FEM results.

Off axis angle Test results (average f our results)

(MPa)

ABAQUS with umat (MPa)

Difference

0° 472 431 9 % 15° 435 392 10 % 30° 357 328 8 % 45° 346 316 9 %

Although the degradation coefficients are not verified with test results, the results are well in agreement with the experimental results.

Figure 8 shows the stress-strain diagram for a notched specimen at an off-axis angle of 45° under uniaxial tension, while Figure 9 and Figure 10 show the fibre and resin failure extension at maximum load for the same specimen.

The stiffness of the plate is not influenced by matrix failure of the composite layers, while the fibre failure deeply influences its stiffness. The plate will fail when the aluminium layers have failed.

0

50

100

150

200

250

300

350

0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0%

strain

net b

lunt

not

ch s

tres

s (M

Pa)

First resin failure

First fiber failure

Figure 8. Simulated stress-strain curve for a test at an off-axis angle of 45°.


Figure 9. Fibre damage extension at maximum load (red part has failed).

Figure 10. Resin damage extension at maximum load (red part has failed).


6. Conclusions

A user material subroutine for shell elements allows the prediction of the damage and failure mechanisms within the composite layers of a fibre metal laminate. ABAQUS/CAE allows the visualization of the different failure modes and their progression in the structure at increasing load. The user subroutine is created in such a way to be easily used by an inexperienced user, although attention has to be paid in the choice of element type and size.

The use of more appropriate degradation coefficient could improve the results.

7. References

1. Hashin, Z, “Failure Criteria for Unidirectional Fibre Composites,” Journal of Applied Mechanics, June 1980

2. Feih, S, Shercliff H.R, McGrath G, “3-D progressive damage modelling for adhesively bonded composite peel joints: implementation in a UMAT and related computational issues”, Conference proceedings of UK ABAQUS user conference, 2000

3. Chang, F, and Chang, K, “A progressive damage model for laminated composites containing stress concentrations. Journal of Composite Materials”, 21:834-855, 1987

4. “Writing user Subroutines with ABAQUS”, Hibbit, Karsson & Sorensen, Inc., 2001

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