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The use of lightweight components

stands or falls by the choice of

materials. The product value,

product costs, production costs,

development costs and risks are,

however, difficult to estimate when

talking about less well-known

materials such as composites.

This is why the SLC-Lab and

the department dealing with

sustainability at Sirris, as well as their

partners in the CompositeBoost

project, want to pass on the

essential tools and methodologies

to help designers and OEMs make

the right choices. This fifth white

paper shows how a lay-up of fibre

reinforced layers can be defined

from given load cases by calculating

stiffness matrices.

SirrisLeuven-GentCompositesApplication Lab

WHITE PAPER

COMPOSITE LAMINATE DESIGN IS NOT COMPLICATED WITH THE RIGHT TOOLS

In the white paper ‘Do Composites and their anisotropic behaviour

only lead to advantages?’ we have shown the importance of the

stacking sequence of several fibre reinforced layers, not only in

terms of stiffness, but also in terms of unexpected behaviour.

For example, an unexpected out-of-plane bending deformation

was demonstrated even though an in-plane loading scenario was

used. In view of the importance of the lay-up sequence, this white

paper shows how a lay-up can be defined from given load cases

by calculating stiffness matrices. The classical laminate theory is a

fast and easy method to be used for relatively simple geometries,

avoiding complex finite element simulations. Different commercial

and free tools are described and illustrated by a case study.

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THE STACKING SEQUENCE OF A LAMINATE

A composite laminate consisting of N-layers with different orientations, definition of the applicable coordinate systems.

When we look at the stacking sequence of the laminate, three

coordinate systems are defined: the global structural coordinate

system (x, y, z), the local coordinate system of orthotropy (1, 2, 3)

within each layer and the fibre direction θ of each layer with respect

to the global structural coordinate system (x, y, z).

The mechanical behaviour of such a fibre reinforced composite

is already quite complex if one considers a single layer, without

considering the combination of different layers.

layer k

layer N

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THE CLASSICAL LAMINATE THEORY Classical laminate theory (CLT) describes the relation between the

loadings (in-plane forces, out-of-plane bending moments and, by

extension, temperature) and the deformations (in-plane strain and

out-of-plane curvatures) of the laminate.

The relation is typically called the ABD matrix, in which A represents

the membrane stiffness of the laminate, B the coupling stiffness and

D the bending stiffness. In short, this relation is also defined as

Though simple, it is good to define the boundaries of the theoretical

model:

• Note that the laminate theory is not able to describe three

dimensional stresses and strains. Everything that occurs in the

z-direction is omitted.

• The zero in refers to the mid-plane of the laminate.

• The forces and moments are defined in the equation as ‘per unit

length’. Forces are in N/m and Moments are in N.

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DOES THE STACKING AFFECT THE ABD MATRIX?The coefficients of the ABD compliance matrix are strongly affected by:

• Material choice (reinforcements/resin combination): stiffness

difference of e.g. glass or carbon

• The thickness of each layer

• The number of layers and the stacking sequence: two laminates

with the same number of plies but with a different stacking

sequence will have a similar membrane stiffness (A) but different

coupling stiffness (B) and bending stiffness (D).

In a number of cases, certain coefficients of the ABD matrix can be

reduced to zero:

• The decoupling of membrane and bending responses leads to

. This decoupling prevents in-plane loads from leading

to out-of-plane deformations (e.g. bending) and vice versa.

• The reduction of anisotropic laminates to orthotropic laminates

leads to . As

defined in the white paper ‘Do Composites and their anisotropic

behaviour only lead to advantages?’, orthotropic materials display

three planes of symmetry.

For unidirectional laminates - a laminate with all the fibre

reinforcements in the same direction - the two reductions above

are valid.

For symmetrical laminates, which are laminates with a plane of

symmetry within their stacking sequence, is typically 0.

In cross-ply laminates, the layers are stacked in an alternating

sequence of 0 degree and 90 degree layers. This is an example of

an orthotropic laminate.

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IS IT POSSIBLE TO PREDICT THE STRENGTH OF A LAMINATE? The analysis of the strength of a composite is more complicated

than that of the stiffness, for the following reasons:

• Failure of one layer leads to progressive degeneration of the

laminate and not to catastrophic failure of the whole composite.

When a single ply fails, the stresses are re-distributed to the

remaining ‘healthy’ layers.

• Failure of adjacent layers (delamination) should be taken into

account.

• The potential influence of cracks of one layer on adjacent layers

Laminate theory is not able to predict the onset of delaminations in

laminates because it omits interlaminar stresses .

Consequently, the strength analysis should be based on a single-layer

failure criterion. Frequently used failure criteria include those of Tsai-

Wu, Tsai-Hill and Puck.

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LAMINATE THEORY CALCULATOR TOOLS THAT DO THE JOB A short list of available tools (free and commercially available) is

given below. This list is certainly not exhaustive and many people

have their ‘homemade’ tools which run as ‘spread sheet’ versions.

FREE TOOLS:

• Efunda ABD calculator:

http://www.efunda.com/formulae/solid_mechanics/composites/

calc_ufrp_abd_layout.cfm, which is an internet based application.

• eLaminate© :

http://www.espcomposites.com/software/software.html, not free if

you need more advanced functionalities.

• Exelcalcs, Laminate Tool.xls:

https://www.excelcalcs.com/repository/strength/plates/laminate-

tool.xls/, Excel-based version.

• eLamX²:

https://tu-dresden.de/ing/maschinenwesen/ilr/lft/elamx2/

elamx, extended stand-alone version with graphical interface.

Visualisation of deformations, loads, stresses and strains

throughout the thickness of the laminate.

COMMERCIAL TOOLS:

• Esacomp:

http://www.esacomp.com/overview/what-is-esacomp, extended

stand-alone version with graphical interface. Visualization

of deformations, loads, stresses and strains throughout the

thickness of the laminate. Link with existing finite element

software.

• LAP:

http://www.anaglyph.co.uk/lap.htm, standalone version with

graphical interface. Visualisation of stresses and strains

throughout the thickness of the laminate.

Luckily, many tools exist to calculate the ABD matrix and use it to

estimate the deformations your laminate will experience under load.

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WHAT IS THE DIFFERENCE WITH FINITE-ELEMENT SOFTWARE? One of the most frequently asked questions is the link between

classical laminate theory and finite element analysis software. In

short, every design phase has its tools. Finite elements are not the

most efficient tool (in terms of time and cost) to deal with lay-up

design (or study at laminate level). CLT software tools are not the

best in terms of detailed modelling. Nevertheless, it is important not

to forget that most calculations can be done using a low-cost CLT

software tool.

A few examples:

• No complete geometric model is needed for laminate calculators.

However, the loads acting locally on the laminate should be known.

This is not the case for FE calculators. For example, a structure

can be loaded outside the laminate zone (e.g. a hinge, a lever or

another component) that you are trying to design.

Comparing the possible geometric complexity of eLamX² and FE software

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• A trade-off between solid laminates, sandwich structures and

laminates with stiffeners can already be made using CLT software

tools. An example will be given later.

• No specific knowledge or background in CLT is needed to interpret

the results. The graphical user interface (not supplied with all

software tools) allows non-experts to instinctively understand the

design and for experts to optimise it. An example of the graphical

user interface of eLamX2 is shown below and will be used in a

further example.

Graphical interface of the eLamX² laminate calculator tool

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• Micro-mechanical modelling is integrated in most CLT software

tools. It uses the ‘rules of mixtures’ to calculate the mechanical

properties of a laminate based on the mechanical properties of the

individual components (fibre reinforcement and matrix material).

• For a detailed study, however, FEA software tools are needed.

Examples of details include stress concentrations around holes,

inserts, connections, etc. In most cases, composites are modelled

in FEA using a certain amount of homogenisation (mechanical

properties homogeneous over one layer). If more detail is needed,

a meso-scale FEA model can help to visualise stress distribution

between reinforcement bundles and the matrix.

• If interlaminar stresses need to be visualised, FEA software tools

are recommended. As mentioned before, CLT omits these stresses.

A meso-scale model in FE-software

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EXAMPLE THE WHEEL-CHAIR RAMP ‘ROLLO’ In the CompositeBoost project, tools for and knowledge of

composite design and production are transferred from SLC-Lab

(Sirris Leuven-Gent Application Lab) to the Flemish composite

industry. Two demonstrator cases come under the spotlight in this

project: the side table ‘Lina’ (cost and surface finish-driven design)

and the wheel-chair ramp ‘Rollo’ (stiffness/weight-driven design).

In this white paper a preliminary design (composite lay-up) is created

using the CLT software tool eLamX² for ‘Rollo’. A market survey

provided the weight properties of existing ramps as shown in the

graph below. Our design aim is represented by the star, with a target

weight of 6 kg for a length of 1.5 m. The maximum deflection in the

middle of the ramp for a loading of 300 kg should be around 10

mm. Three different options are considered: a monolithic structure,

a monolithic structure with stiffeners, and monolithic shells in

combination with a sandwich core material. The designs shown

below are definitely not yet optimised, but they do give a good idea

of the potential of a CLT software tool.

Market survey provided the weight properties of existing ramp as function of their length

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Option 1 - Monolithic

The monolithic design consists of a carbon fibre reinforced (medium

modulus) lay-up with a combination of 0° , 90° and ±45° oriented

layers. The 0° layers are at the outer surfaces to increase the bending

stiffness of the ramp, 90° layers are added to give the strength in the

perpendicular direction and the ±45° layers give a torsional stiffness

to the design if (part of) the load comes on one side of the ramp.

The previous white paper on anisotropy of composites taught us to

keep the lay-up balanced and symmetric if a flat plate is desired, so

unexpected coupling effects should be avoided. The end result is a

48 layer composite laminate with an overall weight of 11.9 kg and a

maximum bending of 11.2 mm in the middle. Our target of 6 kg was

therefore not reached.

Monolithic design of the ‘Rollo’

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Option 2 - Monolithic with stiffeners

The monolithic design with stiffeners consists of a carbon fibre

reinforced (medium modulus) lay-up with a combination of 0°, 90°

and ±45° oriented layers, and incorporating two stiffeners on the

side where the load is acting. The same remark as for the first option

applies to the combination of 0, 90 and ±45° layers. The end result

is a 16 layer composite laminate with an overall weight of 5.4 kg and

a maximum bending of 3.7 mm in the middle. Our target of 6 kg and

minimum deflection was easily reached.

Monolithic design with stiffeners of the ‘Rollo’

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Option 3 - Monolithic shells and a sandwich core material

The monolithic shell design in combination with a sandwich core

material consists of a carbon fibre reinforced (medium modulus)

lay-up with a combination of 0°, 90° and ±45° oriented layers, but

this time an Airex core material has been used on the inside. As

core materials are not yet defined in eLamx2, this was approximated

by modelling the core material as one of the laminate layers. The

end result is a 16 layer composite laminate with an overall weight of

5.3 kg and a maximum deflection of 10 mm in the middle. Our aim of

6 kg and a minimum deflection was achieved! Compared to option

2, a sandwich core is more straightforward to produce than adding

stiffeners.

The ‘Monolithic shell and a sandwich core’ design of the ‘Rollo’

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SUMMARY

This white paper describes the basic principles of classical laminate

theory. This theory describes the behaviour under load (deformation,

stresses and strain) of a laminate consisting of different reinforced

layers with different orientations and a particular stacking sequence

(in-plane loads and out-of-plane bending). The differences in

capabilities between laminate theory calculating tools and FE

software are listed. A list of freeware and commercially available

tools is given. As an example, the eLamX² software has been used

to calculate the stacking sequence of a wheelchair ramp for different

composite types.

AUTHORGeert Luyckx, PhD (UGent)

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‘CompositeBoost’ is a collaborative project involving the Sirris

SLC-Lab, UGent and KU Leuven. Based on six highly relevant

issues, the project partners want to use these essential tools and

methodologies to allow designers and OEMs to make the right

choices. Masterclasses, demonstrations and exploratory case

studies will help transform the composites processor into a reliable

production company and partner. This means that our companies

will retain their competitiveness over foreign competitors.

COMPOSITEBOOST

Markus Kaufmann, PhD (Sirris)

is the program manager of the composites division of Sirris and has

been head of the SLC-Lab since April 2012. Before that he acquired

experience in design and cost estimation of composite structures.

Markus is responsible for coordinating CompositeBoost.

Linde De Vriese (Sirris)

is the SLC-Lab’s team member specialising in material characterisation,

press forming of thermoplastic composites, and bio-composites. Linde

received her Master’s in Materials Engineering at KU Leuven in 2010,

specialising in polymers and composite materials.

This white paper was written within the scope

of the project “CompositeBoost”.

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Bart Waeyenbergh (Sirris)

works at SLC-Lab on prototyping, product development, mould

design and processing of thermoset composites. He graduated

with a Master’s in industrial sciences at Group T in Leuven in 2008,

specialising in advanced manufacturing.

Tom Martens (Sirris)

is the senior technician at SLC-Lab, with 18 years of experience

in the plastics industry. He is responsible for the production

of prototypes and demonstrators in both thermoplastics and

thermoset composites.

Katleen Vallons, PhD (KU Leuven)

is a post-doctoral researcher at SLC-Lab. She has worked with the

Composite Materials Group at KU Leuven since 2005, mostly on

projects in collaboration with industrial partners. Her expertise is in

the material behaviour of composites.

Geert Luyckx, PhD (UGent)

is a post-doctoral researcher at SLC-Lab. He has worked at

UGent, Mechanics of Materials and Structures, since 2003 and is

involved in the experimental validation of new optical measuring

technologies for measuring shape distortion in composite

components.

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PARTNERS

SIRRIS LEUVEN-GENT COMPOSITES APPLICATION LABCelestijnenlaan 300C 3001 Heverlee +32 498 91 94 91www.sirris.beinfo@sirris.beblog.sirris.be

SirrisLeuven-GentCompositesApplication Lab