Compaction Simulation for Prepreg-AutoclaveManufacturing: Improvements and Simplifications of Two Compaction Simulation Methodologies

STOCKHOLM SWEDEN 2019,

Compaction Simulation for Prepreg-Autoclave-

Manufacturing

Improvements and Simplifications of Two Compaction Simulation Methodologies

Developed at Airbus Helicopters Deutschland CHARLOTTE CHAN

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES

Developed at Airbus Helicopters Deutschland

Supervisor: Dr.-Ing. Tobias Weber, Airbus Helicopters Deutschland Examiner: Pr. Malin Åkermo, KTH Royal Institute of Technology

Master’s Thesis 2019

Report number:

Lightweight Structures

Department of Aeronautical and Vehicle Engineering KTH Royal Institute of Technology

SE-Brinellvägen 8, 114 28 Stockholm Telephone +46 87906000

II

In a competitive market such as the aerospace industry, the use of manufacturing process simulation is vital to decrease time and cost of tooling and process development. In the autoclave process, to obtain an uniform part with no void, it is crucial to understand the compaction phenomenon. Through the last decades, compaction simulation methodologies have been developed but only rather simple geometry and/or small parts have been studied. At Airbus Helicopters Deutschland, compaction simulation methodology needs to be able to predict outcomes of rather large and complex helicopter parts such as the final thickness, porosity, wrinkles, thickness deviation, etc. In the two existing Airbus Helicopters Deutschland simulation methodologies, the main problems are the complexity of the simulation process, high computational costs and substantial set-up for rather simple parts. The research presented in this Master thesis aims at providing improvements and optimisations of the two simulations. A comparison of the two methods is also performed in terms of applicability, accuracy, set-up time and computational cost to assess which method should be favoured depending on the problem. Samples previously built at Airbus or during this thesis are used for the simulations’ calibration and validation.

For the first method based on the soil approach, parameters such as the autoclave cycle length, the shear stiffness of the fibres, pore pressure boundary condition, number of contacts, mesh size and radius discretisation are investigated. This method is capable of predicting’ accurately the final thickness and the thickness distribution behaviour for flat and curved parts. However, at lower consolidation pressures, the accuracy decreases. Furthermore, this simulation methodology requires high computational and set-up times. During the calibration of the method, CPU and set- up times are reduced by using smaller model and coarser mesh while still achieving a correct result.

For the second methodology based on membrane elements while neglecting flow effects, the contact modelling is calibrated: the contact stiffness is correctly altered to fit the thickness variation during the manufacturing process. Calibration is done for flat parts. However, wrinkles start to form in the curved part model where no such defect was observed in the samples. This issue needs to be investigated first to continue the simulation calibration. The method shows accurate results for each pressure cycle with lower computational cost and faster set-up than the first method.

In addition, wrinkles can be visualized directly in the simulation and core material such as honeycomb and foam sandwich cores can be taken into account. This method looks quite promising but needs further investigation.

III

Aerospace industrin måste ständigt möta upp mot höga kvalitetskrav samtidigt som den är utsätts för hård konkurrens från andra aktörer. Användningen av processimulering är viktig för ett företags konkurrenskraft genom att det ger minskad uppstartstid tid, skapar robusta tillverkningsmetoder och minskar verktygskostnaderna. I autoklavprocessen, vilken används för tillverkning av avancerade strukturella kompositkomponenter, är det exempelvis av yttersta vikt att med hjälp av modeller förstå och prediktera materialkonsolideringen. Olika metoder har presenterats under de senaste decennierna för att kunna bestämma grad av konsolidering, men de har samtliga varit begränsade till ganska enkla geometrier och/eller studier på små detaljer. Vid Airbus Helicopters Tyskland behöver sådana simuleringar tex kunna förutsäga slutlig materialtjockled, porhalt, veckbildning och tjockleksvariationer vid tillverkning av stora och komplexa geometrier. De två existerande simuleringsmetodiker som används av företaget idag är för komplicerade, kostsamma (kräver mycket datorkraft) och omständliga att sätta igång även för simulering av ganska enkla delar. Forskningen som presenteras i denna avhandling syftar till att förbättra och optimera den existerande simuleringsmetodiken på företaget. En jämförelse mellan de två metoderna är genomförd för att undersöka vilken metod är att föredra för olika typer av problem. Vid jämförelsen studeras metodernas applicerbarhet, noggrannhet, uppstartningstid och beräkningskostnad.

Verkliga komponenter som fanns tillgängliga sedan tidigare eller som har tillverkats vid Airbus Helicopters under tiden för uppsatsen har använts för kalibrering och validering.

Den första metoden är baserad på en soil approach och parametrar så som autoklavens processcykel, fibermaterialets skjuvstyvhet, portryck, antal kontaktpunkter, storlek på beräkningsnätet och beräkningsradiernas diskretisation är undersökta. Metoden gör det möjlig att prediktera slutlig komponenttjocklek samt tjockleksvariationer för plana och krökta delar. Emellertid minskar noggrannheten vid simuleringar av låga processtryck. Dessutom kräver metodiken långa uppstartstider samt simuleringstider. Genom att kalibrera metoden för halverad modell eller grövre beräkningsnät kan dock både CPU-tid och uppstartstid reduceras.

För den andra metoden, som är baserad på skalelement och bortser från matrisflödeseffekter, har arbetet i uppsatsen handlat om att kalibrera kontaktvillkoren.

Kontaktstyvheten har anpassats för att passa de tjockleksvariationerna som uppstår under tillverkning. Dessvärre uppstår veck i den härdade, dubbelkrökta komponenten vilket inte korrelerar med beräkningarna. Detta måste utvärderas vidare genom förbättrad beräkningskalibrering. Metoden visar upp resultat med god noggrannhet för samtliga simulerade tillverkningscykler, samtidigt som detta sker med kortare uppstartstid än den första metoden samt till lägre beräkningskostnad. Dessutom möjliggör metoden att veck kan visualiseras direkt i simuleringarna och att både honeycomb- och skumkärnor kan inkluderas och tas hänsyn till i beräkningarna.

Metoden verkar mycket lovande men kräver vidare utredning.

IV

This Master Thesis was written in the Tooling Innovation department at Airbus Helicopters Deutschland in Donauwörth. It is the conclusion of my double degree in Aerospace Engineering with a specialization in Lightweight Structures at KTH and Arts et Métiers.

I am thankful to Prof. Malin Åkermo for accepting me as a Master thesis student. I would also like to express my gratitude to my supervisor Tobias Weber and to Benjamin Hailer for all their support, comments and remarks during the thesis. Moreover, I would like to thank the Tooling Innovation department for giving me the opportunity to do my Master thesis there and introducing me to the aerospace industry and the production world. I am also grateful to Anna Hellberg Gustafsson (KTH), Pierre Guiol (Arts et Métiers) and the Hauts-de-France region for helping me getting financial support so I can study in Stockholm and do my thesis in Germany. Finally, I am thankful to my family who has supported and encouraged me through my entire studies.

V

1 Introduction 1

1.1 Industrial context . . . . 1

1.2 Motivation . . . . 2

1.3 Objective and scope of this master thesis . . . . 3

2 State of the art 4 2.1 Thermal simulation . . . . 4

2.2 Compaction simulations outside AHD . . . . 5

2.3 Compaction simulations at AHD . . . 10

2.3.1 Methodology from T. Weber: Pore pressure simulation . . . 10

2.3.2 Methodology from B. Hailer: Elastic contact simulation . . . 16

2.4 Necessary improvements . . . 17

3 Material Characterization 18 3.1 Viscosity . . . 18

3.2 Permeability . . . 18

3.3 Compaction curve . . . 19

3.4 Interlaminar friction and tool-part interaction . . . 20

4 Experimental procedure 22 4.1 Material . . . 22

4.2 Set-up . . . 22

4.3 Measurements . . . 23

5 Simulation Set-up 25 5.1 Temperature . . . 25

5.2 Friction behaviour . . . 25

6 Results and Discussion 32 6.1 Flat plates . . . 32

6.1.1 Pore pressure simulation . . . 32

6.1.2 Elastic contact simulation . . . 40

6.1.3 Comparison . . . 43

6.2 Small C-profile . . . 44

6.2.1 Pore pressure simulation . . . 45

6.2.2 Elastic contact simulation . . . 49

6.2.3 Comparison . . . 50

6.3 Large C-profile for the pore pressure simulation . . . 51

7 Conclusion and Future Work 59

8 References 62

VI

1.1 Typical autoclave cycle for carbon/epoxy prepreg . . . . 2

2.1 Piston-spring analogy for the compaction . . . . 7

2.2 Fibre volume fraction behaviour depending on the definition . . . 11

2.3 Fibre volume fraction behaviour during saturation and compaction depending on the definition . . . 11

2.4 Modified equations and Carman-Kozeny equation behaviour . . . 12

2.5 Shear locking phenomenon . . . 13

2.6 Hourglass phenomenon . . . 14

2.7 Surface and pore pressure elements: contact description . . . 15

2.8 Pore pressure boundary conditions for open and closed moulds . . . 15

3.1 Viscosity behaviour during an autoclave cycle . . . 19

4.1 Points of measurement for the plate . . . 23

4.2 Experiment values for a quarter model from a full plate . . . 23

4.3 Points of measurement for the small C-profile . . . 24

4.4 Points of measurement for the large C-profile . . . 24

5.1 Cycles tested for the calibration and validation of the simulation of the flat plates samples . . . 25

5.2 Correct friction local tangents for the models used . . . 26

5.3 Orientation definition in the input file . . . 27

5.4 Points a, b and c used for the orientation definition . . . 27

5.5 Orientation example . . . 27

5.6 Interaction definition in the input file . . . 28

5.7 Orientation definition by Abaqus . . . 28

5.8 Different alternatives depending on the choice of the additional rotation axis . . . 29

5.9 Simple geometry - orientation example (in red the coordinate system defined in the input file) . . . 30

5.10 Orientation using option 2 in area A . . . 30

5.11 Orientation using option 2 in area C . . . 31

5.12 C-profile orientation error using option 2 . . . 31

5.13 C-profile orientation using option 1 . . . 32

6.1 Definition of the distances

,

and

on a full plate . . . 32

6.2 Flat plate model . . . 33

6.3 Comparison between quarter and full models . . . 33

6.4 Pore pressure boundary condition: inner nodes selection (full plate model) . . . 34

6.5 Autoclave cycle comparison at an autoclave pressure of 4 bar (quarter model) . . . 35

6.6 Pore pressure boundary conditions comparison at an autoclave pressure of 4 bar (quarter model) . . . 36

6.7 Shear stiffness comparison at an autoclave pressure of 4 bar (quarter model) . . . 38

6.8 Comparison experiment vs simulation (quarter model) . . . 39

6.9 Thickness variations along the plate (full model) . . . 40

VII

6.11 Position of the two honeycomb cores placed in between prepreg layers 42

6.12 Comparison between the two methods . . . 42

6.13 Thickness comparison for different shear stiffness value . . . 46

6.14 Thickness comparison depending on the number of contacts and plies per element . . . 47

6.15 Validation for a consolidation pressure of 0 bar . . . 47

6.16 Validation at 2 bar (autoclave pressure) . . . 48

6.17 Contact areas definition . . . 49

6.18 Thickness comparison . . . 50

6.19 Model comparison . . . 51

6.20 Different models used for the Large C-profile . . . 52

6.21 Strategy regarding the surface element mesh size and the radius discretisation . . . 53

6.22 Thickness distribution for a fine surface element mesh with variable number of element in the radius (Small C-profile) . . . 54

6.23 Thickness comparison for the different options tested . . . 55

6.24 Thickness comparison for the different options tested (position of the points is described in fig. 4.4) . . . 55

6.25 Conclusion on the strategy regarding the surface element mesh size and the radius discretisation . . . 56

6.26 Wrinkles position . . . 56

6.27 Tensile stresses in the fibres due to thermal expansion of the bridging sheet . . . 57

6.28 Thickness comparison between model with improved parameters and Englhard’s model . . . 58

VIII

4.1 Experiment matrix . . . 22 6.1 Absolute errors between simulation and experiment for a consolidation

pressure of 4 bar and for different node spacing (quarter model - for the distances

,

and

see fig.6.1) . . . 37 6.2 Absolute errors between simulation and experiment for a consolidation

pressure of 4 bar and different shear stiffness values (quarter model - for the distances

,

and

see fig.6.1) . . . 37 6.3 Absolute errors between simulation and experiment at different pressures 39 6.4 Errors between simulation and experiment for method 1(quarter model

- for the distances

,

and

see fig.6.1) . . . 41 6.5 Comparison between methods 1 and 2 . . . 42 6.6 Validation for autoclave pressures of 0 and 2 bar for method 1 (quarter

model - for the distances

,

and

see fig.6.1) . . . 43 6.7 Comparison between the two models for a consolidation pressure of 4

bar (quarter model - for the distances

,

and

(see fig.6.1)) . . . 44 6.8 Comparison between the two models for autoclave pressures of 0 and

2 bar with E.C. referring to Elastic Contact (quarter model - for the distances

,

and

(see fig.6.1)) . . . 44 6.9 Mean thicknesses at 2 and 4 bar (autoclave pressure) for the experiment

and the simulation . . . 48

IX

AFP

Automatic Fibre Placement

Central Processing Unit

EC

Elastic Contact

FEA

Finite Element Analysis

MPS Manufacturing Process Simulation SCM Sequential Compaction Model SSM Squeezed Sponge Model UD

Uni-Directional

N OMENCLATURE

a_h

Intra-part shadowing shift factor

Inter-part shadowing shift factor

Waviness ratio

c_h

Longitudinal position shift factor

d₁

Distance value for the pore pressure boundary condition (unchanged)

Distance value for the pore pressure boundary condition (calibrated)

Distance value used for the flat plate simulation comparison

d_h

Distance value used for the flat plate simulation comparison

Distance value used for the flat plate simulation comparison

Void ratio

E_f

Fibre Young modulus

η

Resin viscosity (in the friction behaviour)

F

Force required to generate motion (Friction force)

Acceleration constant

γ˙

Shear rate

h

Heat transfer coefficient

Hydraulic conductivity

k₁₁

Kozeny constant in the fibre direction

Kozeny constant in the thickness direction

Air thermal conductivity

l

Length of the part

Resin viscosity

µc

Coulomb friction model

Friction coefficient

Normal force

Resin pressure

d p_m

dz

Pressure gradient

Normal pressure

Prandtl number

φ

Ratio of fibre contact area to the total contact area

X

r_f

Fibre radius

Resin density

and

Fibre permeability

σ

Applied stress

σ¯

Fibre effective stress

Surface temperature

Air temperature

τ

Acting shear stress between two plies

Resin velocity

v_a

Maximum achievable fibre volume fraction

Fibre volume fraction

v¯_f

Abaqus™fibre volume definition

Initial fibre volume

v_{f a}

Flow limiting fibre volume fraction

XI

1 I NTRODUCTION 1.1 Industrial context

The use of fibre reinforced polymer composite has increased over the last decades in the aeronautical industry. Composites are more and more favoured for structural components in aircrafts and helicopters. For instance, the Boeing 787, Airbus A350 XWB or the Airbus Helicopters H160, all have a structure made at least of

of carbon reinforced polymer [1, 2]. This material offers a lot of advantages for aircraft and helicopter manufacturers: light weight, manufacturing of complex integral parts, excellent fatigue behaviour and high corrosion resistance [3, 4].

The main process used in the aeronautical industry is the autoclave process [1, 5, 6]. Despite its high manufacturing costs, autoclave process provides high quality parts with high fibre volume fraction and complex shapes. Pre-impregnated composites (prepreg) are used with this method in order to stack the plies faster and easier. Prepregs can be in woven or uni-directional (UD) form and are partially cured material. It is possible to use partially impregnated prepreg to reduce the cost of the material. These are called hot melt prepregs. Layers of resin are placed on top and below the surfaces of the fibre layers, thus making it easier to manufacture and reducing the price of the material [7]. Prepreg materials are used in the aeronautical industry since they enable the production of complex integral parts and provide high quality parts with the required fibre volume fraction and a low porosity [8]. They are stacked onto the tooling with the correct orientation. Then, tooling and part are prepared for the autoclave cycle by adding different components such as peel ply, breathers, bleeders and vacuum bag. Vacuum is applied, tooling and part are placed into the autoclave to undergo a pressured cure cycle and therefore achieve higher level of consolidation. Autoclave cycles are divided into three steps [5]:

1. During the first step, the temperature is increased until it reaches an intermediate value which is held for a certain time in order to reduce the resin viscosity and heat part as well as mould evenly.

2. In the second phase, the temperature is increased further to reach the curing temperature of the material. It is held for a certain duration in order to cure the entire part. Pressure is applied to ensure good consolidation - i.e. to achieve the desired fiber volume - and that the laminate conforms properly to the tooling shape.

3. Phase 3 is the cooling step.

These three steps are summarized in fig. 1.1.

This process involves major phenomena such as: heat transfer, curing kinetics,

resin flow and fibre compaction. All these phenomena have a high impact on the final

quality of the part and on process-induced deformations [10, 11]. Typical defects

due to the resin flow and fibre compaction are a non-homogeneous fibre volume

distribution, non-accurate final dimensions, residual deformation (warpage) and void

formation [11]. The first and the latter impact the mechanical properties of the part

and the second and third impact the final assembly process.

Figure 1.1: Typical autoclave cycle for carbon/epoxy prepreg (adapted from [9])

In a competitive market like aerospace, it is essential to use Manufacturing Process Simulation (MPS) in order to decrease the time and cost of tooling development.

In order to be more competitive, changing from experienced based approach to simulation based is vital to avoid lengthy and expensive trial-and-error optimisations [12]. Different tooling, part designs and processes can be compared while avoiding costly and timely testing thus leading to the choice of the most suitable solution. MPS allows to evaluate the manufacturing method and anticipate the part quality long before the tool is produced [12]. Regarding the mould optimisation, using MPS can lead to a decrease in heat-up time and a more homogeneous temperature distribution which results in a shorter manufacturing time while ensuring part quality [13]. MPS can also help adjust the pressure gradient and magnitude which leads to the correct part thickness with adequate fibre volume fraction and minimal porosity. In addition, MPS provides an assessment regarding part design feasibility and producibility [8].

At Airbus Helicopters Deutschland (AHD), a thermo-chemical simulation methodology has already been developed by T. Weber and is used to ensure the part quality and reduce manufacturing costs. Two compaction simulation methodologies, the first one from T. Weber (pore pressure model) [14] and the second one from B.

Hailer (elastic contact model) [15], are currently under development.

1.2 Motivation

Research has been conducted on compaction simulation through the last decades to improve the understanding of this phenomenon and predict manufacturing process outcomes [11, 16, 17, 18, 19] in order to use it in the future on an industrial level.

However, only rather simple geometry and/or small parts have been studied. In

addition, ply-by-ply approach is utilised nowadays [19, 14] which does not allow to

simulate realistic parts in a reasonable time frame [20]. At AHD, the compaction

simulation methodology needs to be able to predict outcomes of rather large and

complex helicopter parts. It is thus essential to upscale the two methodologies which are currently under development. They will be used to predict the final thickness of a part, the final fibre volume distribution and detect all manufacturing defects relevant in helicopter parts such as porosity, wrinkles and thickness deviation. Therefore, they will be quite valuable for part, tooling and process designs during the development phase of new helicopters. Simulation should be available to enable tooling designers to develop and select the right tooling and process design allowing to produce a good part right from the beginning [8]. Tooling design should nowadays change from experience based to simulation assisted which will lead to a decrease in costs [8]. In addition to cost decrease, time should be saved from this change.

In the existing simulation methodologies, the main issues are the complexity of the simulation process, high computational cost and substantial set up for rather simple parts. Therefore, this paper focuses on improvements and simplifications for the two available methodologies from AHD. Great efforts are given to reduce the complexity of the simulation process and the time needed for set-up and computation.

1.3 Objective and scope of this master thesis

The objective of this Master thesis is to provide improvements and optimisations of the AHD methodologies for the compaction phenomenon. These modifications will help in the future to simulate helicopter parts within a reasonable amount of time.

To do so, the two methodologies from AHD will be compared and further developed using different set-ups, tooling concepts, part geometries as well as optimised model parameters such as mesh and model size, contact parameters, etc. Moreover, the chosen simulation at the end should be able to predict fibre wrinkling, interlaminar ply movement and other manufacturing defects. The two methods will be compared in terms of computational cost, accuracy, applicability, user-friendliness, set-up and computational times. The comparison will result in instructions on which method should be used and for which problem.

Flat plate and small C-profile geometries will be used to optimise simulation parameters and validate simplifications. At last, a large C-profile part will be simulated to verify the previous results and modifications. To calibrate and verify the simulations, experiments from Weber’s PhD [14] will be used. Additional samples will be built during this Master thesis.

After going through the relevant literature (Chapter 2) and the material

characterization (Chapter 3), the experimental procedure is described (Chapter

4). The improvements of the FE-modelling for the compaction phenomenon

(Chapter 5) are then explained followed by the comparison and the analysis of the

experimental and numerical results (Chapter 6). Finally, conclusions are drawn and

recommendations for future work are given (Chapter 7).

2 S TATE OF THE ART

Finite Element Analysis (FEA) is widely used to study composites. However, it requires large computation times. In order to reduce the latter while preserving accuracy, most research has sequenced the manufacturing process into different modules. At AHD, the process is sequenced in the following way [14]:

•

One thermochemical module providing the temperature and degree of cure distributions;

•

One flow-compaction module giving the wall thickness and fibre volume distributions and predicting manufacturing defects.

The focus of this Master thesis is on the flow-compaction module. However, at AHD, the thermal simulation provides the temperature and degree of cure distributions necessary to calculate the material properties required for the compaction simulation [14]. Thus, this module is briefly discussed in the following section.

2.1 Thermal simulation

Thermal simulation is essential in order to calculate the temperature distribution of tooling and part along with the degree of cure of the component. Since material parameters are temperature dependent, it is vital to have accurate predictions from this simulation. Moreover, at AHD, it must be performed before the compaction simulation since parameters such as the resin viscosity or tool-ply and interply friction coefficients, all temperature- and cure-sensitive, are deduced from it. The thermal simulation used in this thesis for the compaction simulation is the one developed by T.

Weber during his PhD thesis and is now used on a daily basis at AHD. [13, 14, 21]

In an autoclave, the heat transfer is mainly ensured by forced convection [13]

which is governed by Newton’s law [22]:

q= h(T_S− T_∞)

(2.1)

With

the heat flux in

,

the heat transfer coefficient (HTC) in

,

the surface temperature and

the air temperature both in

. The main parameters influencing the accuracy of the thermal simulation are [23]:

•

the material characterization

•

the boundary conditions that are directly linked to the HTC on the surfaces.

The material characterization relates to the density, specific heat capacity, the thermal conductivity, the glass transition temperature and the material rate of cure as well as exothermic heat generation. Since it is not in the scope of this paper, it will not be discussed further. Explanations can be found in [14].

Moreover, the effectiveness of the heat transfer depends on the HTC between the circulating air and the tooling surfaces. The HTC depends on the following parameters [22, 24, 25]:

•

the type of flow (laminar or turbulent)

•

geometry of the body heated by the flow

•

the flowing medium (air or nitrogen)

•

the flow velocity

•

the pressure and temperature applied which are given by the chosen autoclave cycle

Weber [13] developed a fast method for setting up the boundary conditions with reasonable accuracy and low simulation and testing costs. Using Abaqus™and film conditions, it enables to reduce CPU and set-up time. Film conditions are a type of interactions in Abaqus™used to define heating or cooling caused by convection [26]. The method, by the use of adjustment factors, can take into account: intra-part shadowing (shadowing effects of the mould on some of its areas due to its design), longitudinal position in the autoclave and inter-part shadowing (influence of moulds onto one another). The method takes also into consideration the variation of HTC due to changes in temperature and pressure in the autoclave [13]. Weber et al. [13]

proved that the inter-part shadowing, intra-part shadowing and the longitudinal position influences are independent from one another. Thus, three independent shift factors:

(intra-part shadowing),

(inter-part shadowing) and

(longitudinal position) can be applied to the basis equation for flow around a cylinder [13, 21]:

h= ahb_hc_h0.193(Re)^0.618(Pr)^0.333

l λai r

(2.2)

With

the heat transfer coefficient in

,

, Reynolds number,

, Prandtl number,

the length of the part and

, the air thermal conductivity in

. By fitting the measured values (obtained by placing a calorimeter at different position in an autoclave and on top of a test mould), to the reference curve and with changing only one shift factor at a time, the values of

,

and

for different set-ups can be obtained. The reference curve is the one for which all the shift factors are equal to 1.

Verifications were then conducted using thermocouples for the different set-ups [13].

Further explanations on AHD thermal simulation can be found in [13, 14, 21].

2.2 Compaction simulations outside AHD

The compaction simulation methodology enables to predict the final thickness and fibre volume in a part. It allows to predict fibre wrinkling and insufficient compaction in the composite. Flow in composites is divided into two main phenomena [27]:

•

Percolation flow

•

Shear flow

In the percolation approach, the applied pressure will cause the resin to flow relative to the fibres: this phenomenon can be compared to a sponge being squeezed.

The resin flow relative to the fibre bed must be coupled to the fibre bed compaction

to obtain the final shape of the part. The resin motion may produce resin-rich and

-poor areas in the composite.

In the shear flow approach, the composite is approximated as a very viscous fluid filled with inextensible and stiff fibres. Resin and fibres are moving together. It will cause inter-ply and intra-ply deformations.

The first approach is typically used for resin flow and fibre compaction of thermoset matrix while the latter for thermoplastic matrix [27]. In this thesis, the focus will be only on the percolation flow model since only thermoset resin is used.

Darcy’s law can describe the flow through a porous medium. Gebart [28] proved that it was applicable to flow in composite, thus it can be used to model the flow of resin:

v= −S µ

d p_m

dz

(2.3)

With

, the resin velocity in

,

, the fibre permeability in

,

, the resin viscosity in

,

, the pressure gradient in

. Loos and Springer [29], using eq. 2.3, calculated the resin mass loss of a flat laminate. Davé [16] was then able to derive the general flow equation for all kind of composite processes. But in order to predict the part outcome, the resin flow behaviour is not sufficient [27]. Therefore, flow compaction models were developed taking both flow resin and fibre bed compaction behaviours into account. Two different models have been developed to represent the flow-compaction phenomenon [27]:

•

Sequential Compaction Model (SCM)

•

Squeezed Sponge Model (SSM)

In the SCM, Loos and Springer [29] assumed that the applied pressure was only carried by the resin and that the fibre permeability was constant. Gutowski et al.

[30, 31] developed the SSM model in which the applied pressure is shared between resin and fibres. Moreover, they assumed that the compaction was not compelled to be sequential like Loos and Springer [29]. Gutowski applied the effective stress theory in his model [31]:

σ = ¯σ + pm

(2.4)

With

, the applied stress,

, the fibre effective stress and

, the resin pressure. To explain the mechanism, a piston-spring analogy can be taken [16]: the fibres are approximated as a non-linear spring (first uncompressed) placed in a cylinder filled with liquid. The spring analogy takes into account the elastic behaviour of the fibre bed while the fluid approximates the resin. At the initial step, all the applied pressure is borne by the resin. After opening the piston, flow starts and the spring is gradually compressed and thus carries an increasing part of the applied load until it carries the entire applied pressure as seen in fig. 2.1 [27].

It has been demonstrated that the SCM model is actually a special case of the SSM model [32]. The latter is better suited to describe the flow compaction mechanism in a more realistic and accurate way [32].

Using the consolidation theory and flow in a porous medium, Davé et al. [16] built

a 3D SSM model. Young [17] developed further the general 3D consolidation process

by studying multi-directional fibre bed in order to predict the pressure, resin flow

Figure 2.1: Piston-spring analogy for the compaction (adapted from [16])

velocity and laminate thickness for an autoclave process. Young [33] examined also the effect on compacting forces and cure cycles on the degree of consolidation of thick composites. Using a numerical model, Young [33] demonstrates that the compacting pressure is the main parameter influencing the final degree of consolidation while the cure cycle, which controls the thermal response and resin reaction, has little impact.

Thus, a minimum pressure has to be applied to ensure a good degree of compaction while a suitable cure cycle has to be selected to ensure a suitable thermal response.

Moreover, Young [34], using a visco-elastic solid model for the laminate consolidation, took into consideration the variations of permeability and thermal properties due to fibre volume fraction changes during an autoclave cycle.

Hubert et al. [35] developed on COMPRO™a 2D numerical flow compaction model based on effective theory and Darcy’s law for autoclave process and complex shaped laminates. They studied the effect of material properties on the compaction of angle-shaped composites. Their conclusion was that the fibre bed shear modulus has a significant influence on the compaction behaviour in the laminate radii section while the resin viscosity and the fibre bed permeability impact the compaction rate.

Therefore, the influence of the fibre bed shear modulus should not be forgotten when calibrating correctly the AHD simulations. This is not only applicable to C-profiles but to flat plates as well since thermal expansion and tool-part interaction are considered in both Airbus methods and lead to the apparition of shear stress in the thickness direction. Beside, Hubert et al. [35] emphasized that accurate measurement of the fibre bed compaction curve and shear behaviour are essential to obtain accurate prediction of the final thickness. Hubert and Poursartip [36] also proposed a direct method for tape, woven and non-woven fabric prepregs to measure the fibre bed compaction of AS4/3501-6-carbon epoxy prepregs. This method has the advantages of being simple, and not requiring any sample preparation, thus it does not alter the fibre arrangement [36]. It was used at AHD for Weber’s research [14].

Shin and Hahn [37] developed a simulation for heat transfer and compaction for a bleeder and thick composite assembly. They took into account the bleeder plies that were often neglected in previous studies in order to set proper boundary conditions.

They studied two cases: one with variable resin properties and one with constant resin

properties. They demonstrated that the first case gave better through-the-thickness

temperature distribution predictions. However, the model predicted faster compaction

rate due to higher predicted fibre volume fraction for a given effective stress. For

the 228-ply sample, their model had quite good correlations. However, for the 330-

ply sample, some discrepancies were noticed due to inaccurate resin property and compressibility models.

Li et al. [38] developed a numerical model to study the effect of the bleeder flow on the resin flow. Larger resin pressure drops were observed at the laminate-bleeder interface impacting the compaction.

Ganapathi et al. [39] also developed a model, using COMSOL™, for thick laminate with bleeder and vacuum bag to understand the resin flow through the bleeder to find its impact on the local variation in resin volume distribution. According to Ganapathi et al. [39], it is vital to take into consideration the bleeder and its properties because of its impacts on the resin outflow.

In contrast to the previously named sources [18, 37, 38, 39], the simulation methods developed at AHD do not take into account the bleeder explicitly. One reason behind that is the fact that approximately

of the moulds used at AHD are closed moulds [14] which do not require any bleeder. Furthermore, the used prepreg material can be considered as a low or even no-bleed systems. Finally, the calibration and validation of the pore-press-element compaction simulation of Weber [14] showed that accurate results can be achieved without considering the bleeder effects in detail.

Further research was done on flow-compaction model focusing on the effect on interlaminar permeability. Lam et al. [40] studied the fibre bed permeability and compressibility and how they change with the resin volume fraction as the pressure is applied. They found out that the permeability for an aligned fibre sample is up to 4 times higher than for cross-plied samples with an axial flow. Qiao et al. [41] investigated the effect of interlaminar transverse permeability on the flow- compaction behaviour in a thick cross-plied composite. Using COMSOL™, they built a flow compaction model for autoclave process and concluded that a low interlaminar permeability slows down the resin flow and therefore impedes the increase of fibre volume fraction. Thus the thickness of the composite will decrease if the interlaminar permeability increases. In the pore pressure simulation [14], the permeability is used as calibration factor in the compaction simulation.

Other research focused on defect formation during consolidation process. Belnoue et al. [19] investigated the consolidation mechanism for automatic fibre placement (AFP) since it influences fibre path defects and especially out-of-plane wrinkling.

Their goal was to understand the way overlaps and gaps are evolving during the

compaction process since they influence defects and thickness variations. In the paper,

they modelled the gaps and overlaps, introduced by the AFP, in the laminate using

a ply-by-ply approach on Abaqus™. At the end of the compaction, they showed that

gaps are either filled by overlaps falling inside or are filled laterally due to the squeeze

flow. To describe the resin flow behaviour, Belnoue et al. [19] used both shear and

percolation flow which differs from Weber’s approach [14]. Moreover, using Abaqus™,

a thermo-mechanically coupled model was developed to represent the consolidation

process. Belnoue et al. [19] used the Ostwald-de-Waele law (power law fluid) unlike

traditional flow model and Weber’s model where Darcy’s law is applied. Furthermore,

in this model, the effects of introduced defects are estimated and visible on Abaqus™.

This is a major difference to the pore pressure model where Weber can predict wrinkles but these are not visible in the simulation [14].

Belnoue et al. [20] also examined how the properties of a material can influence consolidation-induced wrinkle formation for thick and complex shaped laminates.

They investigated two different geometries relevant to the industry: L-shaped laminate over an external radius and a tapered laminate in a closed mould. The main properties influencing the wrinkle formation are especially the ability or inability of the layers to slip regarding one and another due to the friction coefficient and the applied boundary conditions on the prepreg. However, the ply-by-ply approach in both papers is time consuming and the simulations can’t be applied to big parts.

Sorentino and Bellini [42] studied the relationship between different degrees of compaction and spring-in values. A new sequential approach is presented in this paper considering both compaction (resin flow) and thermo-mechanical behaviour of the part during curing. This is unlike most models for spring-in or for compaction that are developed independently. They used an elastic model for the laminate since they only focus on the laminate behaviour after resin vitrification. However, they highlighted that visco-elastic models are more realistic but too complex and need an extensive material characterization. Moreover, like Weber [14], for the compaction, the soil approach was used: the resin is considered to be the fluid while the fibres are the porous medium. They applied also Darcy’s law for the flow behaviour. They highlighted that a better compaction - i.e. higher value of thickness reduction - leads to a smaller residual stress.

Yoo et al. [43] simulated the cure process of a carbon/epoxy laminate by taking into consideration the phase changes of the resin and thus the laminate material properties variations. Using Abaqus™and user subroutines, they divided the process into 3 phases:

1. Heating (liquid phase) 2. Holding (gelation) 3. Cooling (solidification)

The user subroutine VOIDR, used in this simulation, can calculate the resin flow based on Darcy’s law. Moreover, it is able to give the material state and the variation of the permeability during the liquid phase. [43] The way they divided the simulation is similar to the division done by Weber in his own simulation [14]. They were able to predict process-induced stresses in the laminates. However, even if the FEA performed by Yoo et al. [43] agrees well with the experiments, it is showing important discrepancies compared to the experimental results due to [43]:

•

the use of FEA and linear element (C3D8HT) undervalue the epoxy deformation during phase 1.

•

the use of a simplified model that does not take into account the resin chemical

behaviour and tooling-part interaction. The latest has a great influence on

the compaction behaviour (See 3.4) and is taken into account in both AHD methodologies.

Finally, in this paper, no mention of thickness variations has been made.

On the whole, research has been focusing on a specific aspect of the flow- compaction phenomenon and on rather small parts. The simulation methodologies available are not yet usable on an industrial level. However, many of the aspects investigated so far must be considered, understood and simplified in an adequate way to obtain a methodology that is usable on an industrial scale. A lot of the phenomena explained earlier were already considered and simplified by Weber [14], nevertheless, further improvements are necessary to enable faster simulation of larger parts.

2.3 Compaction simulations at AHD

Two methodologies are under development at AHD. The one developed by Hailer aims at considering sandwich core and is right now the topic of his PhD research project. The one developed by Weber [14] needs optimisation to enable its use for realistic part sizes but can only simulate monolithic part. They both aim to be used on a daily basis and thus still require consequent optimisation to reach a certain maturity.

2.3.1 Methodology from T. Weber: Pore pressure simulation

The compaction simulation built by Weber [14] predicts the final thickness, fibre volume and fibre wrinkling for a part. It takes into consideration several parameters such as the complete part geometry and material, the tool-part interaction and interlaminar friction behaviour as well as cure and temperature progression, permeability and fibre bed stiffness. In the opposite of other methodologies [11, 34], Weber [14] does not use a viscous-elastic model approach but the soil module already implemented in Abaqus™. The soil approach is used by geotechnical engineers to analyse, for instance, the deformation of buildings supported on soil [44]. The specificity of Weber’s simulation is that the saturation phase of hot-melt-prepregs can be considered by simplifying the actual three-phase model of the soil module [14]:

•

porous medium (solid phase) = fibres

•

"wetting" liquid = resin

•

gas = entrapped air

However to simplify the model, Weber [14] only modelled two phases: resin and fibre bed. Therefore, the component appears to be fully saturated but is not. To represent voids in the material containing trapped air at low pressure, permeability is increased in combination with higher initial void ratio. Furthermore, the simulation is done at a macro scale level only in order to be able to simulate large parts relevant for the company in a reasonable amount of time.

The simulation does not consider the filling of the voids with resin, like it would

appear in reality. Instead a virtual resin outflow is used to model the amount of resin

Figure 2.2: Fibre volume fraction behaviour depending on the definition (adapted from [14])

Figure 2.3: Fibre volume fraction behaviour during saturation and compaction depending on the definition (adapted from [14])

that would fill the voids. To achieve an outflow that correlates directly with the filling of voids, an apparent permeability is used which considers the easier flow of the resin when voids are present. In consequence, two definitions of the fibre volume fraction exist [14]:

•

the classic definition of the fibre volume fraction,

(fig. 2.2 - left side)

•

the Abaqus™definition,

(fig. 2.2 - right side)

According to the classic definition, the fibre volume fraction will stay constant until all voids are filled with resin i.e. until saturation as seen in fig. 2.3 [14]. However, the Abaqus™definition will show an increasing fibre volume fraction until saturation and then will follow the same behaviour as the classic approach as seen in fig. 2.3. The first increase represents the virtual resin out flow during the filling of voids [14].

To allow virtual resin outflow, a boundary condition is added in which the pore pressure is set to zero so resin can flow out from the edges and within the part. For small parts, all the edges will have this boundary condition. For bigger parts, some nodes inside the part will also have it. More explanations are given later in this chapter.

In addition, the permeability is adjusted during the saturation process in regards to the air trapped. In reality, the resin can flow more easily during the saturation phase due to the presence of air cavities. The flow encounters less resistance than with a fully saturated material i.e. the fibre permeability is significantly higher for a non-saturated material [45]. In the soil module, the permeability is described using the hydraulic conductivity [26]:

k¯_ii= S_ii(vf)ρmg

µ(T, α)

(2.5)

Figure 2.4: Modified equations and Carman-Kozeny equation behaviour (adapted from [14])

With

the fibre permeability,

the resin density,

the acceleration constant and

the resin viscosity.

is dependent not only on the fibre volume fraction but also on the temperature and degree of cure since the resin viscosity depends on the degree of cure and temperature. In the pore pressure model [14], a degree of cure is assigned to each temperature. This degree of cure was obtained beforehand considering the possible temperature history of a part at different autoclave cycles. Then, for each corresponding temperature and degree of cure, a mean value of the resin viscosity is obtained.

In his simulation, Weber [14] used the Carman-Kozeny equations, adapted by Gutowski et al. [30, 31], for the phase after saturation. For the phase prior to saturation, these equations have been modified. Figure 2.4 shows the behaviour of the modified equations compared to Carman-Kozeny equations. The Kozeny factor of the Carman-Kozeny equations was used to calibrate the permeability keeping the relations between 1-, 2- and 3-direction as well as the relation between UD and fabric intact [14].

To be noted is that the hydraulic conductivity is a function of the fibre volume fraction. However, the latter is not a degree of freedom in Abaqus™but the void ratio is. Hubert [11] provides the relationship between the void ratio and the fibre volume fraction:

e= 1− vf

v_f

(2.6)

Interlaminar friction and tool-part interaction have a large influence on defects and final thickness. Weber [46] determined the coefficients of friction for different material pairings using two different methods in order to implement them in the flow-compaction model. This topic will be further discussed in Chapter 3.

The simulation approach used by Weber [14] is phenomenological: the validation

and verification of the simulation are therefore vital. However, it can not be easily

transferred to another application using for instance different materials without a

certain effort. Validation will be needed again. Weber [14] was able to predict results

with a rather good accuracy but there are still possible improvements to optimise the

simulation in terms of CPU time and model set-up, especially for the model size and

mesh.

Figure 2.5: Shear locking phenomenon

Simulation set-up

Elements used

Various types of elements are necessary to model a part depending on the part geometry, the loading conditions, the type of analysis and the computer capacity for instance. In the pore pressure simulation [14], pore fluid/stress elements (C3D8RP) are used to model the composite layers. In addition to the three degrees of freedom per node that can normally be found on solid elements, they offer an additional degree: pore pressure [26]. For the tooling, two types of solid elements are used depending on the geometry: 3D stress hexahedral element (C3D8) or 3D stress tetrahedral element (C3D4). To improve the contact interaction, surface elements (SFM3D4R) can be added between the layers. These elements have no stiffness or

thickness. Their role will be discussed in detail later in this chapter.

Reduced integration elements have to be selected to avoid shear locking phenomenon in the composite part. The phenomenon is described in fig. 2.5.

Fully integrated elements are more stiff than reduced integration elements due to the elements definition [26]. This in turn hinders shear deformation which occurs excessively in curved parts during compaction [14]. However, when using reduced integration elements, a phenomenon called hourglassing must be avoided.

Hourglassing is a purely numerical deformation mode due to the use of only one integration point for the stress and strain calculations. It is described in fig. 2.6. Setting the correct hourglassing stiffness can prevent this phenomenon from occurring. Since the simulation uses a UMAT subroutine, this additional element stiffness can not be automatically calculated by Abaqus™. A fixed value is thus given by the user. As stated before, shear deformation happens mainly in curved components. For flat plates, the hourglassing and shear stiffnesses have a smaller influence on the final results. They will impact the edge effect meaning that a higher hourglassing and shear stiffnesses will result in thicker edges since the pore pressure method considers tool-part interaction as well as tooling expansion. By considering these phenomena, development of shear stress

between the part and tooling will happen. This shear stress also has a component in thickness direction leading to a decrease of the thickness [14]. The values for the hourglassing stiffness and shear one were determined by Weber during his PhD project [14].

Regarding the aspect ratio of the elements for the layers, Weber[14] recommands

an aspect ratio below 15.

Figure 2.6: Hourglass phenomenon

Contact and friction

In Abaqus™, the contact is defined by setting tangential and normal behaviours. The normal behaviour is set as "hard" [14, 47] while the tangential is set using the friction measurements performed at AHD [14]. Due to high computational costs, contacts are set only every second or fourth ply depending on the part size [14].

Standard contact (surface to surface) and tie contact are compatible with pore pressure: they are capable to transfer the pore pressure between the contact surfaces [26]. But the use of friction contacts between the pore pressure elements causes problems in pore pressure calculations in the model. These are due to the anisotropy of the permeability and the boundary conditions used for the pore pressure. Resulting pore pressure fluctuations impact directly the contact pressure and the frictional forces and thus increase convergence issues. Adding contact stabilization in the model is not enough to overcome these convergence problems. A solution found by Weber [14] is to use the previously named surface elements which have no stiffness and only three degrees of freedom related to movement.

The surface elements are tied to the underlying elements and have a standard contact with the surface above as shown in fig. 2.7. However, these elements can not transmit the pore pressure degree of freedom which makes it impossible for the resin to flow between the laminate layers separated by contact. This reduces the difficulties and fluctuations in pore pressure calculations which in turn stabilises the simulation. For a composite material with anisotropic permeability, the permeability in the thickness direction is often by 10 to 25 times lower than the in-plane permeability [31, 48]

which results in only minimal through thickness flow. With closed moulds, there is also no resin flow in the thickness direction. In addition, Münch [49] investigated the compression behaviour of M18/1 and highlighted that stiffness and flow behaviour of individual plies can be considered independent of each other. Thus, the surface elements can be used in this model with minimal impact on accuracy [14].

Pore pressure set-up

All the fibre nodes have an initial pore pressure set to zero at the

beginning of the simulation (predefined field). In reality, resin can flow out from the

edges thus in the simulation, the pore pressure at the edges is set to zero (boundary

condition that allows resin outflow). In contrast to the real process, the size of the

part in the simulation influences the compaction process and thus the final thickness

because of the chosen boundary condition. When resin can only flow out along the

edges, the size of the part will influence the pore pressure gradient which in turn will

Figure 2.7: Surface and pore pressure elements: contact description

Figure 2.8: Pore pressure boundary conditions for open and closed moulds (adapted from [14])

impact the resin flow [14]. In addition, the virtual resin outflow necessary during saturation can not be achieved for large parts when resin can only leave the parts through the edges [14]. To achieve a correct saturation phase, avoid inaccuracies for larger parts and enable differentiation between open and closed moulds, an additional boundary condition must be set. Nodes inside the part reaching through the complete thickness are selected to form additional flow out points for the resin (see fig. 2.8) [14]. When the saturation is completed at the end of the first holding phase, the boundary condition on those nodes is switched off for closed mould. Therefore, resin can only flow out through the edges during the second heating phase. For an open mould, this boundary condition is kept during the entire simulation to mimic the function of the bleeder foil on top of the part. This is illustrated in fig. 2.8.

The use of this boundary condition has a disadvantage which is the modification of the resin pressure. Setting some of the part inner nodes to a pore pressure of zero to achieve outflow will result in an unrealistic pressure distribution [14]. Consequently, the resin pressure is not used for further analysis such as to determine porosity formation.

It is important to highlight that the edge to volume ratio has a great impact on

the final thickness in the simulation which is not the case in reality. If the edge to

volume ratio is high, the part will get thinner in the simulation.

Loads and boundary conditions

The vacuum and autoclave pressure are applied to the right surfaces. Boundary conditions are also applied to prevent displacement of the mould in the necessary directions. These boundary conditions must not prevent the thermal expansion of the mould. Symmetry boundary conditions are applied for half and quarter model. Pore pressure boundary condition is applied at the free edges and inner nodes (if necessary).

2.3.2 Methodology from B. Hailer: Elastic contact simulation

The second methodology currently in development at AHD takes into account honeycomb and foam sandwich cores present in helicopter parts. When core crush and foam shrinkage are included in the simulation, the use of pore pressure elements brings a problem regarding the convergence of the model. To get rid of this issue, Hailer uses membrane elements in combination with a contact formulation that allows overclosure in order to model the thickness reduction. This approach has several advantages. First of all no complex resin flow calculation has to be performed on a complete solid mesh (the soil module does not allow the use of shell elements). In addition, the contacts used to model the compaction include already interlaminar friction and tool-part interaction. Finally, the membrane elements allow the visualization of wrinkles since no bending stiffness is allotted to those elements. Besides, the simulation is capable of predicting core crush and foam shrinkage. However, resin flow effects are neglected completely in this methodology. For this model, the correct contact modelling must be developed: the contact stiffness in the thickness direction is altered to fit the the thickness variations during the manufacturing process. Thus, as soon as pressure is applied in the autoclave, the layers will start to compact according to the contact definition and the part thickness will decrease. [15]

Simulation set-up

Elements used

This simulation uses shell elements (S4R) for the tooling and membrane elements (M3D4) for the plies. These elements have the advantage to reduce the CPU time quite drastically.

Contact formulation

In this method, contacts are defined by the use of pressure- overclosure values set in the normal behaviour of the interaction properties. Depending on the pressure on the part, the contact will be more or less stiff thus leading to areas with different thicknesses. This method needs to be calibrated in terms of overclosure parameters for closed mould parts. For the tangential behaviour, it is set using the friction measurements performed at AHD [14].

Loads and boundary conditions

The vacuum and autoclave pressures are applied

to the right surfaces. In addition, boundary conditions are applied to prevent

displacement of the mould in the necessary directions. These boundary conditions

must not prevent the thermal expansion of the mould. Symmetry boundary conditions

are applied for half, quarter and strip model.

2.4 Necessary improvements

Following the literature review, several improvements will be tested during the thesis.

Bleeder effects

As stated before, the bleeder is not taken into account explicitly in the pore pressure simulation. Nevertheless, its effects are considered: by selecting the pore pressure nodes where resin outflow can happen, the effects are included.

However, here the selection of the inner nodes will only be refined for parts built with closed moulds: calibration is done on the flat plate built with a compaction pressure of 4 bar, and verification will be performed on the flat plate (0 and 2 bar for the autoclave pressure) and the large C-profile (4 bar for the compaction pressure). Thus, the bleeder effects are not investigated here since only parts built with closed moulds are used to correctly set the pore pressure boundary conditions on inner nodes.

Elastic contact simulation improvements

It has been shown that the pore pressure simulation is capable of giving accurate results [14, 49, 50]. After calibration and verification of the elastic contact methodology, it will be investigated if it is able to predict the thickness distribution better or as accurately as the pore pressure simulation without any flow effects considered.

Modelling improvements

As opposed to the ply-by-ply approach commonly used [19, 20], focus will be given on increasing the number of plies per element to reduce the size of the model. The use of half, quarter and strip models will also be studied in order to reduce the CPU time. This will be a step further in the direction of realistic parts modelling.

Shear stiffness and hourglassing stiffness

It was highlighted by Hubert [35] that the shear stiffness influences the compaction of curved regions. This will also be investigated for flat parts since Weber [14] takes into account in his methodology tooling thermal expansion and tool-part interaction. Thus shear stress will appear at the edges that might influence the thickness distribution.

Friction behaviour in Abaqus™

In both methodologies, tool-part-interaction is included. In this thesis, it will be highlighted that Abaqus™does not properly set the friction behaviour. Thus, a solution will be researched.

In order to study all these improvements, the use of experiments to calibrate and

validate the methodologies is required. At AHD, parts are built with a compaction

pressure of 2 or 4 bar. Simulations are calibrated at an autoclave pressure of 4 bar and

verification is performed at a compaction pressure of 0 and 2 bar. To do so, samples

built during Weber’s PhD [14] will be used in addition to samples built during this

thesis.

3 M ATERIAL C HARACTERIZATION

All material characterizations were performed by T. Weber and B. Hailer during their PhD research project [14, 15]. The following shows a summary of their selected material models.

3.1 Viscosity

One major parameter impacting the compaction process is the resin viscosity. It describes the liquid resistance against movement and deformation. This resistance is due to the fact that by moving or deforming the liquid, one changes the fluid molecules arrangement [5]. Thermoset matrices are assumed to behave like a Newtonian fluid, i.e. the viscosity is independent of the shear rate [27]. This assumption can be used especially for autoclave production, since the resin flow during an autoclave cycle may be considered quasi-static with low shear rates [11, 27]. For thermoset matrices, the viscosity is dependent of the temperature and the degree of cure [5].

At the beginning of the autoclave cycle, the resin viscosity decreases while the temperature is increasing. At high temperatures, the molecular chains are becoming longer due to the cross-linking and therefore the viscosity is increasing until gelation [5].

Different viscosity models can be found in the literature. One of the most used is the one developed by Dusi et al. [51]:

µ = µ_∞e x p(κα)ex p( U

RT)

(3.1)

In his simulation, Weber [14] used the model developed by Lynam and Arafath [52] and calibrated it for the use with Hexply M18/1:

µ =

¨ µ01e x p(_RT^E1) + µ02e x p(_RT^E2)_α^αg

g−α

if

µma x

if

The values of the constants were obtained through experiments using a rheometer with parallel plate configuration. This is further explained in [14]. Figure 3.1 shows the differences between the models during a rheometer test with temperature ramp from 25 to 160°C.

3.2 Permeability

The fibre bed permeability is another parameter essential during compaction. It

defines the ease with which the fluid flows through the porous medium. In order to

predict the flow behaviour and the resin pressure, through Darcy’s law, it is vital to

have the permeability values. First, Loos and Springer [29] assumed that the fibre

permeability perpendicular to the fibres was constant. In reality, the fibre permeability

is a function of the fibre architecture but more importantly of the fibre volume which

varies during compaction.