Over research is to use finite element methods to

Over the last decade, the use of fibre
metal laminates (FMLs), such as glass fibre reinforced aluminum laminate
(GLARE), is increasing in the manufacturing of aerospace structures to
reduce weight and as a result to reduce emissions. In particular, GLARE is a
FML made of several very thin layers of metal (usually aluminum) and interspersed
plies of glass reinforced composite materials, bonded together with a matrix
such as epoxy. FMLs have slow crack propagation and a good damage-tolerance to
fatigue in aerospace structures. Glare is used in fuselage
of Airbus A380 and the leading edge surfaces of the vertical and horizontal
tail planes in the Airbus A380. Due to the nature of the industry, severe
testing of components is required. This is an expensive task, requiring a large
number of tests to achieve certification, and is complicated further by the
nature of anisotropic materials.

 In general, the CAD and Ansys software have
made analysis of FMLs cheaper and attractive for practising engineers in
comparison with experimentation. From a computational point of view, the modelling
of delamination in FMLs involve special features which make the task
challenging as many of the necessary numerical strategies are still in
development. For instance, modelling discontinuities, mixed
damage modes, nonlinear interfaces, initiation and propagation of cracks etc.
These techniques cause often divergence of the numerical procedure.

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The
goal of this research is to use finite element methods to develop computational
models which can accurately replicate behavior to complement physical testing,
in order to reduce the cost and time involved in testing. However, finite
element analyses are very expensive in terms of computational cost if extensive
remeshing is necessary, as in the case of dynamic crack propagation. The
relatively new Extended Finite Element Method (XFEM) solves this problem
however, as no remeshing is necessary.

This
research aims to investigate, by means of the Extended Finite Element Method
(XFEM), the mechanisms of fracture and crack propagation in advanced composite
structures such as fibre metal laminates (FML) used in the aerospace
industries.

 

 

1.     Problem
Statement

Experimental testing of composite
materials is an expensive task and finite element analyses are also very
expensive in terms of computational cost if extensive remeshing is necessary,
as in the case of dynamic crack propagation. Extended Finite Element Method
(XFEM) solves this problem as no remeshing is necessary.

2.     Objectives

The objective of this research are:

a)     
To investigate the stress intensity
factors into a GLARE 3 laminated plate subjected to biaxial loading by means of
XFEM.

b)     
To simulate the initiation and evolution
of a three-dimensional crack. Specific challenges such as the 3D crack
initiation, based on a principal stress criterion, and its front propagation,
in perpendicular to the principal stress direction will be conveniently
addressed.

c)     
To validate the computational outcomes
by means of comparison with theoretical and experimental results.

 

3.     Scope

The
scope of work include the study of complex crack propagation problems like crack
initiation, its evolution path, velocity and the value of applied stress which
produces the failure of the specimen on GLARE 3 laminated plate specimen subjected
to a biaxial loading scenario by means of extended finite element method (XFEM).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.1  Fibre
Metal Laminate (FML)

Fibre
Metal Laminate (FML) is a family of hybrid composite structure formed from the        combination of metal layers sandwiching
a fibre-reinforced plastic layer. The metal currently being used is either
aluminum, magnesium or titanium, and the fibre-reinforced layer is either
glass-reinforced, carbon-reinforced or kevlar-reinforced composite. 1 Typical
classification of FMLs is shown in figure 1.1.

 

 

 

 

 

 

 

 

 

 

                              Figure 1.1       Typical classification of FMLs

In
1978, ARALL has been developed at the Faculty of Aerospace Engineering at the
Delft University of Technology in Netherland. In 1982 the first commercial
product under the trade name ARALL was launched by ALCOA. 

ARALL
laminates are made of high strength aramid fibres embedded in a structural
epoxy adhesive sandwiched between multiple layers of thin aluminium alloy sheets.
A schematic presentation of ARALL is shown in fig. 1.2

               Figure 1.2 Schematic
presentation of Fibre Metal Laminate (ARALL 2)

ARALL
laminates offer many advantages such as high strength and excellent fatigue
properties. Moreover, they retain the advantages of aluminium alloys, namely
lower cost, easy machining, forming, and mechanical fastening abilities, as
well as substantial ductility. Commercially available ARALL laminates are shown
in table 1.1.

 Table 1.1 Commercially available ARALL
laminates

 

Metal
type

Cure
resin

Cure
Temp.

Stretching

Characteristics

ARALL 1

7075-T6

AF-163-2

120 oC

0.4% permanent
stretch

Superior fatigue
resistance
High strength

ARALL2

2024-T3

AF-163-2

120 oC

With or without
0.4% stretch

Excellent fatigue
resistance
Increased formability
Damage tolerant

ARALL3

7475-T76

AF-163-2

120 oC

0.4% permanent
stretch

Superior fatigue
resistance
Controlled toughness

ARALL4

2024-T8

AF-191

175 oC

With or without
0.4% stretch

Excellent fatigue
Resistance
Increased elevated
Temperature properties

GLARE
laminates belong to fibre metal laminates family, they consist of alternating
layers of unidirectional glass fibre reinforced pregregs and high strength
aluminium alloy sheets. Schematic illustration of a cross-ply GLARE laminate is
shown in figure 1.3

 

.               Figure 1.3 Schematic illustration of a
cross-ply GLARE laminates

At
first, they were developed for aeronautical applications as an improvement of
ARALL with advanced glass fibre and introduced at the Technical University of
Delft in Netherlands in 1990. Commercially available GLARE and ARALL laminates
are shown in table 1.12

Table
1.2 Commercially available GLARE laminates

 Both ARALL and GLARE laminates are now being
used as structural materials in aircrafts.

Fibre
Metal Laminates have been successfully introduced into the Airbus A380. ARALL
has                   been developed for
the lower wing skin panels of the former Fokker 27 aircraft and the cargo        door of the Boeing C-17. ARALL 3
material is currently in production and flight test on the C-17 cargo doors and
GLARE is selected for the Boeing 777 impact resistant bulk cargo floor. 2          

 

3.2  Extended
Finite Element Method (XFEM)

                                               

The extended finite element method (XFEM) developed
to alleviate shortcomings of the finite element method and has been used to
model the propagation of various discontinuities: strong (cracks) and weak
(material interfaces). The idea behind XFEM is to retain most advantages of
meshfree methods while alleviating their negative sides.

A
limitation is observed when using FEM for simulating moving cracks throughout a
structure. To accurate represent discontinuities with FEM, it becomes necessary
to conform the discretisation to the discontinuity. Then, in the case of crack
propagation, the mesh is re-generated at each crack-growth increment with a
considerable computational cost. Over the last decades several approaches for
modelling material discontinuities have been proposed based on the partition of
unity concept, as the Generalized Finite Element Method (GFEM) or the XFEM  developed by Belytschko and Black in 1999 and
improved by Moes et al. In particular, XFEM has been a robust numerical
technique for modelling fracture. 3

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