a new approach to simulating the draping of prepreg
TRANSCRIPT
A new approach to simulating the draping of prepreg
composites manufactured by hand layup
VINCENT
MAYMARD
Master of Science Thesis
Stockholm, Sweden 2017
i
Abstract
Kinematic drape simulations, of applying woven reinforcements to complex geometries, have
to date largely focused on characterising the ply shape and the deformations from fitting it to
the surface of a mould; amongst other manufacturing management outputs. This is increasingly
unsatisfactory: it does not allow for any prediction into the effect of geometry and changes on
the layup; does not realistically simulate the draping process as achieved by operators; instruct
on the process of how to manipulate a ply to achieve the deformations required, or; enable the
information gathered to be exploited in simple useful formats. In essence, drape simulation
tools do not allow for 'Design for Manufacturing' and arguably this is inhibiting manufacturing
growth. Based on recent activity within ACCIS (University of Bristol), which seeks to develop
a Design for Manufacturing in composites solution, this research aims to demonstrate one
available route to answer those previous criticisms. It focuses on developing computationally
efficient virtual tools that allow for a better understanding of the hand layup of prepreg cloths,
as pre- and Post concept routines for existing drape simulation packages. In the Pre-concept
tool (conducted before drape simulation takes place), parts can be automatically simulated and
reviewed. Risks in quality and difficulty to achieve the design-intent can be assessed virtually
by identifying the impact on formability of choices such as ramp angle or pad height. The Post
concept routine intends to collaborate with drape simulation outputs. It models techniques and
grasps used by professional laminators in terms of in-plane shear deformation and attempts to
return the forming process more akin to usual ply handling techniques. This work presents
significant advances in the development of the Pre-concept routine, including the application
of a knowledge base system to record and exploit drape patterns. However the development of
the Post concept routine is by comparison less advanced, due to the modelling of the grip
techniques being unable to sufficiently incorporate boundary conditions and mould interactions
at this time. Further work involves the completion of this Post concept routine followed by
tests in a manufacturing environment.
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Acknowledgement
My appreciation goes to all the people who made this work possible. I would especially like to
thank my supervisor, Dr. Carwyn Ward, for his insightful guidance and patient support
throughout this project. Special thanks also go to Dr. Mike Elkington for sharing his theoretical
and practical expertise of the hand layup forming process and for his continuous feedback.
I wish to express my gratitude to Dr. Dennis Crowley and Dr. James Kratz for broadening my
experience of the ACCIS department of the University of Bristol by involving me in some of
their research activities. Thank you to Dr. Anastasia Koutsomitopoulou and to the lab support
team for the positivity and effervescence that you continuously brought into our office.
Most importantly, I am thankful to my parents for their unconditional care and love throughout
my University years.
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Table of Contents
Abstract .................................................................................................................................................... i
Acknowledgement .................................................................................................................................. ii
Table of Contents ................................................................................................................................... iii
Table of figures ....................................................................................................................................... v
List of Tables .......................................................................................................................................... v
1. Introduction ..................................................................................................................................... 1
2. Literature review ............................................................................................................................. 3
2.1 Hand layup of prepreg materials ............................................................................................. 3
2.2 Design for Manufacture of composite materials ..................................................................... 3
2.3 The composite design process ................................................................................................. 4
2.4 Forming simulations ............................................................................................................... 4
2.5 The PJN model ........................................................................................................................ 5
2.6 The importance of draping order ............................................................................................ 5
2.7 Difficulty metrics .................................................................................................................... 6
2.8 Aim and scope ......................................................................................................................... 6
3. Methodology ................................................................................................................................... 7
4. Draping module .............................................................................................................................. 8
4.1 Model selection ....................................................................................................................... 8
4.2 Mathematical model of an element ......................................................................................... 8
4.2.1 Planar ply ........................................................................................................................ 8
4.2.2 Planar elements ............................................................................................................... 8
4.2.3 Folded elements .............................................................................................................. 9
4.3 Considerations about sets of elements .................................................................................. 10
4.3.1 Planar model ................................................................................................................. 10
4.3.2 Curve glide geometries ................................................................................................. 10
4.3.3 The importance of folding ............................................................................................. 11
4.3.4 Model selection ............................................................................................................. 11
4.4 Techniques ............................................................................................................................ 11
4.4.1 Tension-Tension Shear forming .................................................................................... 12
4.4.2 Tension Secured Shearing (point) ................................................................................. 12
4.4.3 Tension Secured Shearing (edge) ................................................................................. 12
4.4.4 Manual folding (straight) .............................................................................................. 13
4.4.5 Manual folding (curved) ............................................................................................... 13
4.5 Specificities of the technique models .................................................................................... 14
4.6 The virtual draping process ................................................................................................... 14
4.6.1 Structure ........................................................................................................................ 14
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4.6.2 Display .......................................................................................................................... 15
4.6.3 List of operations .......................................................................................................... 15
4.6.4 Node number from coordinates ..................................................................................... 15
4.7 Conclusion ............................................................................................................................ 16
5. The Pre-concept routine ................................................................................................................ 17
5.1 Introduction ........................................................................................................................... 17
5.2 The Knowledge Base and its challenges ............................................................................... 17
5.3 Analysis................................................................................................................................. 18
5.3.1 In-plane shear indicator ................................................................................................. 18
5.3.2 Highly sheared elements ............................................................................................... 18
5.3.3 Shear disparity index ..................................................................................................... 18
5.3.4 Slippage and lifting risk ................................................................................................ 19
5.3.5 Shear along a horizontal tow ......................................................................................... 19
5.4 Case study ............................................................................................................................. 19
5.5 Conclusion ............................................................................................................................ 21
6 Post Concept routine ..................................................................................................................... 22
6.1 Introduction ........................................................................................................................... 22
6.2 Towards draping instructions: visualising techniques .......................................................... 22
6.2.1 Lamination training in the industry ............................................................................... 22
6.2.2 Draping instructions ...................................................................................................... 22
6.3 Sampling VFP features ......................................................................................................... 23
6.4 Case study ............................................................................................................................. 24
6.5 Conclusion ............................................................................................................................ 25
7 Integration of the Pre-concept and Post concept routines into the design process........................ 26
7.1 System diagram ..................................................................................................................... 26
7.2 Case study ............................................................................................................................. 27
7.3 Preconception phase .............................................................................................................. 28
7.4 VFP ....................................................................................................................................... 29
7.5 Post conception phase ........................................................................................................... 29
8. Conclusion .................................................................................................................................... 30
9. Further work .................................................................................................................................. 31
Bibliography ......................................................................................................................................... 32
v
Table of figures
Figure 1. Rise of the use of composite materials in airframes between 1960 and 1990. Taken from [3] 1 Figure 2. Example of an element 5 Figure 3. System diagram of the routines developed in this thesis 7 Figure 4. In-plane and out of plane elements with the same shear angle and one node in common 9 Figure 5. 4 points can be the extremities of 2 different elements in this model 9 Figure 6. Example of the parametrisation of a square zone 10 Figure 7. Warp, weft and bias of a fabric. Taken from [25] 11 Figure 8. Two different features with the same warp and weft (in red) 11 Figure 9. Tension-Tension Shear forming 12 Figure 10. Tension-Tension shear forming (virtual) 12 Figure 11. Tension Secured Shearing (point) 12 Figure 12. Tension Secured Shearing with a point (virtual) 12 Figure 13. Tension Secured Shearing (edge) 13 Figure 14. Tension Secured Shearing with an edge (virtual) 13 Figure 15. Manual Folding (straight) 13 Figure 16. Manual Folding (virtual) 13 Figure 17. Example of curved manual folding 14 Figure 18. A curve-glide geometry obtained by curved manual folding 14 Figure 19. Initial drape pattern 14 Figure 20. Colour scale 15 Figure 21. Display of coordinates in a Figure 16 Figure 22. Outputs of the Pre-concept routine 18 Figure 23. Example of a drape pattern with a low shear disparity index (left) and a high one (right) 19 Figure 24. Shear along a tow 19 Figure 25. Drape pattern for the Pre-concept case study 20 Figure 26. Draping difficulty indicators for the Pre-concept case study 20 Figure 27. Current content of a subfolder of the Pre-concept routine 21 Figure 28. Extract of a .txt report 22 Figure 29. Extract of a Microsoft Word report 23 Figure 30. Sampling model 24 Figure 31. Draping instructions for a ramp with a recess 24 Figure 32. Suggested update to the design process 26 Figure 33. How the routines developed in this thesis support Gandi’s DFM methodology for components manufactured in composite materials. Adapted from [29]. 27 Figure 34. Visualisation of the problem of the case study 27 Figure 35. Drape pattern considered in the case study, shown as displayed in the Pre-concept routine 28 Figure 36. Analysis of the geometries of the case study 28 Figure 37. VFP diagram for “Angle 1: Straight angle” draped top to bottom (left) and bottom to top (right) 29 Figure 38. VFP diagram for “Angle 2: Tapered face” 29 Figure 39. Extract from a Post Conception report on draping instructions 29
List of Tables
Table 1. Classical design process for composite components. Taken from [33]. 4 Table 2. Coordinates of the two cross-overs for the element shown in Figure 5 9
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1. Introduction
In 1966, Watt et al developed a high temperature oxidation process for PAN fibres [1, 2] which
was rapidly put into commercial production. This process became famous as the Royal Aircraft
Establishment (RAE) process and has become the basis for an overwhelming majority of
carbon-fibre production today [3]. Four years later, the Jet Provost, the Vulcan and the Jaguar
already featured carbon-fibre parts. A decade of intense technological development on several
levels followed [4]: fibre properties became more robust, resins were developed, certification
standards were created and aerospace companies tested new processes [5].
Figure 1. Rise of the use of composite materials in airframes between 1960 and 1990. Taken from [3]
The use of composite materials in structural applications has been consistently increasing since
then (Figure 1), especially in the aerospace and naval industries. In the 1980’s, the weight
fraction of composites in the Airbus A310-300 was of 5%. This percentage rose to 53% for the
Airbus A350 XWB produced in 2013 [6]. The composite industry must now adapt to face the
challenges that come with its success. In 2006 it was estimated that 23,385 passenger aeroplanes
would need to be produced between 2006 and 2026 to face the increasing aerial traffic [7].
The exceptional business prospects experienced by big aerospace companies such as Airbus
and Boeing drives the profits of a vast network of subcontractors as production is being
increasingly outsourced [8]. They also lead to an increasing pressure on the aeroplane sector’s
supply chain on several levels [7]:
- Increasing global competition from emerging countries
- Need to adapt to technological changes
- Need to increase production rates
- Shortage of highly skilled engineers and technicians
The above challenges are typically operational. Companies focus has shifted from designing
state-of-the-art aeroplanes to making sure that their designs can be produced effectively and on
time. The Boeing 787 Dreamliner is often used as an example to illustrate manufacturing
difficulties that may occur with composite materials. The sale success of this aircraft put
pressure on its production line to increase its production rate. The production capabilities were
meant to reach 10 aeroplanes per month in 2012 but the actual production rate turned out to be
around 7 aeroplanes per month. Thus, Boeing 787 deliveries were delayed by an average of 27
months [9].Typical composite specific problematics came on top of that. Boeing’s carbon fibre
lay down rate turned out to be much lower than planned, barely reaching 19 lb/hour in 2007
instead of the estimated rate of 100 lb/hour [10]. Some of Boeing’s suppliers also experienced
delays because of their inability to attract competent technicians to their facilities and had to
hire low-wage, trained-on-the-job workers with no previous aerospace experience [9]. These
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workers were unable to produce parts at the expected quality standards which highlights the
need for minimising the complexity of manufacturing composite parts.
Learning from these mistakes, public and private actors are now massively investing in new
equipment and facilities for the composite industry. The United Kingdom opened the National
Composite Centre in 2011 with a £25m investment and extended it three years later with another
investment of £28m [11, 12]. In a report on the “UK Composites Strategy” the Department of
Business Innovation and Skills justifies this investment by the necessity to promote
coordination between companies and by the urgent need for a highly-qualified labour force
[13].
Being a labour-intensive manufacturing method, hand layup should strongly benefit from the
efforts of the UK government to train a highly skilled workforce. It was estimated that the
labour cost associated to hand layup represents around 60% of the manufacturing cost of a part
whereas it usually ranges between 30 and 40% for automated methods [14].
With that in mind, one could question the UK Composites Strategy. Would it not be better to
invest in automated methods? Such methods combine higher production rate with lower labour
cost, addressing simultaneously two challenges that the composite industry is now facing.
While automated methods such as Automated Fibre Placement (AFP) and Automated Tape
Layup (ATL) are very interesting from a cost management point of view they have not yet
reached the capability of producing most aircraft secondary structures due to their complexity.
Secondary structures constitute 85% of an aeroplane’s structure composite volume and it is
only natural that hand layup still dominates other manufacturing methods [15]. The latest
research publications have shown that there is still a long road before automated methods can
be used to drape complex geometries and that, while their development should be pursued,
developing medium term approaches focused towards hand layup manufacturing is an
immediate necessity [16].
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2. Literature review
2.1 Hand layup of prepreg materials
Unlike their metallic counterparts, composite components are manufactured at the same time
than their material meaning that all composite manufacturing methods involve the forming of
an initially planar material into a three-dimensional shape [17, 18]. When the forming process
is performed manually, like in the case of “hand layup”, it is usually referred to as “draping”.
Hand layup draping consists in shaping a ply for it to conform with the three-dimensional shape
of a mould. Although this is mainly done by hand it may involve the use of simple tools such
as “dibbers” [19]. One can drape dry or preimpregnated fibre reinforcements and these
reinforcements can come in several configurations: unidirectional fibres, plain weaves and
Twill weaves [20]. This thesis work will focus exclusively on the hand layup of plain prepreg
weaves.
Although hand layup may intuitively seem to be simple, the reality is that it is a very complex
process that requires years of experience to be mastered. The widely-accepted idea that workers
occupy low-wage jobs that require little skill does not apply to composite laminators. A
laminator can expect a salary between 10£ (early career) per hour and 25£ per hour (late career)
in the current job market (2017). What makes laminators so important to composite
manufacturing companies is the variability in part quality and layup time that comes with
different manufacturing skill levels. Furthermore, hand layup know-how is often transmitted
orally from one laminator to another and the whole composite industry suffers from a severe
lack in qualified labour force [21]. Some authors even consider hand layup to be a “black art”
[22].
Experienced laminators can handle plies to produce high quality parts. They know that unlike
a sheet of paper, a composite ply needs to be sheared. Paper mainly exhibit out-of-plane
deformation whereas the main deformation modes involved in prepregs are intra-ply in-plane
shear and out-of-plane bending. Bending plies is reasonably easy and barely involves more
pressure than folding a sheet of paper. However, applying in-plane shear deformation requires
the use of force due to the high viscosity of the resin impregnating the ply. The force required
to shear an element up to an angle depends on the reinforcement and matrix of the material [23]
and on its temperature. It is not uncommon for laminators to use a heat gun or to heat up a
mould to lower the viscosity of the prepreg plies and to facilitate the draping process [24].
2.2 Design for Manufacture of composite materials
At an engineering level, facilitating the draping process can be done in various ways. The most
classical ones consist in performing simulations and in designing tools. Simulations involve
specialised programs that study and document the layout process [25] while tools assist
laminators in the forming process [19] or accelerate their training [26]. These efforts belong to
the field of Design for Manufacture (DFM).
Design for Manufacture is defined as the general engineering art of designing products in such
a way that they are easy to manufacture. A product needs to be manufactured to specifications,
be functional and to qualify for a range of certifications. There are many solutions that fulfils
these criteria and companies are looking for the ones that minimise their overall cost [27, 28].
Design for Manufacture means taking into account manufacturing considerations at both part
and assembly level to enable cost reduction.
Many DFM methodologies have already been suggested since 1990 [29]. Their focus may be
layup sequences [30], manufacturing processes [14] or materials [31] for example. These
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methodologies try to incorporate manufacturing considerations into a classical design process
but they seem to struggle to find their way into industrial processes.
2.3 The composite design process
Let us now take a closer look at a classical design process with the aim of understanding why
it is unsatisfying from a DFM point of view and why upgrading it poses a challenge. The design
process of a part made in composite materials follows the below steps (Table 1) [32]:
a. Material selection
b. CAD model: sizing
c. Layup breakdown
d. FE analysis: static loads, vibroacoustic performance, thermal properties, buckling
behaviour, joints and fasteners, point load, fatigue etc.
e. Manufacturing process development: forming, distortions, moulding.
Table 1. Classical design process for composite components. Taken from [33].
These steps are iterated throughout the development process, leading to several prototypes.
Manufacturing considerations come last in a classical design process which is problematic
knowing that most of the cost of a product is committed during the concept phase and the early
stages of the first design iteration [34, 35]. Some design for manufacture methodologies have
therefore suggested to shift them towards earlier stages to enable cost savings [29] but they
appear to lack simple tools to ease their complex implementation. There is a clear interest in
combining simple simulation tools with an earlier integration of manufacturing considerations
into the design process [30].
2.4 Forming simulations
Many simulation packages attempt to simulate the behaviour of a woven cloth during forming.
These packages usually focus on ply deformation (shear, deflection) and on residual stresses.
However, their most important output is clearly fibre orientation as it is a key input for FE
simulations. Forming simulations are therefore essential to stiffness predictions, flow modelling
and thermal behaviour and are a keystone in industrial design processes. This literature review
provides a short introduction to the 2 dominant categories of forming algorithms: FEM schemes
and fishnet models.
Commercially available forming simulation packages such as PlySim, Aniform, CATIA
Composites Fibre Modeler and FibreSim typically use FEM schemes. Finite Elements
Modelling (FEM) schemes can be based on energetic balance or force equilibrium. Energetic
models usually require higher computational resources which explains why their force-based
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counterparts are preferred in commercially available simulation packages. Due to the multiscale
nature of composite materials, FEM simulation models may opt for several types of approaches:
discrete [36], semi-discrete [37] or mesoscopic [38]. They may be based on elastic models,
derived from shell theory, or on viscous models, derived from fluid dynamics [39].
Unlike FEM models, fishnet models focus on ensuring a low computational time at the expense
of an accurate representation of materials properties or processing conditions during draping.
As early as in 1956 Mack and Taylor proposed a model based on a pinned joint-net (PJN)
description of a plain weave [40]. This model gave birth to the mapping approach, a simulation
strategy that consists in mapping a mesh of quadrilateral cells onto a surface. Defects, such as
wrinkling, can be predicted based on the “shear locking angle” of a fabric (see 2.5). This
material characteristics is typically measured experimentally using a bias-extension or a
picture-frame test [41, 42]. In 1996, however, Prodromou showed in his study on the
relationship between in-plane shear and wrinkling that the “shear locking angle” can also be
estimated theoretically based on tow parameters [43].
2.5 The PJN model
The PJN model [40] assumes that a net is made of straight and inextensible fibres rotating
around tow cross overs. The net is described in terms of quadrilateral elements that are not
necessarily planar. In the context of draping simulations, it is common practice to refer to the
net as a “drape pattern”. This term emphasises the importance of in-plane shear deformation by
suggesting that a net is a patchwork of elements with a specific shear. The “shear angle” of an
element can be defined as the complementary angle of one of its acute angles (Figure 2).
Figure 2. Example of an element
In practice, the shear angle of an element has an upper bound called “shear locking angle” [25].
This material characteristic comes from the inability of two orthogonal tows to coincide with
each other without colliding. The shear locking angle cannot be calculated from the PJN model
alone because tows are modelled in it by zero-thickness geometries, lines. Draping simulation
programs based on the PJN model usually require the user to input the shear locking angle of
each weave.
The software “Virtual Fabric Placement” (VFP) developed by Hancock [25] implements a
mapping simulation scheme based on the PJN model. It calculates and displays the drape pattern
of a ply once the user sets the position of an initial set of nodes. These nodes must be chosen in
such a way that they fully define the ply. Locking a ply in warp and weft fully defines all its
elements for example. Generally speaking, this is only true if elements are planar or if they are
constrained by some kind of contact modelling.
2.6 The importance of draping order
The same component can be formed in many ways and each VFP simulation can only provide
one possible solution. The drape pattern of the component is determined by the initial set of
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elements that are stuck to the node, hence the importance of draping process on fibre
orientation.
Furthermore, fibre orientation determines the mechanical properties of a component which
means that a suboptimal drape pattern may result in a non-conformity in the context of an
industrial production line. Flow and heat simulations are also known to be heavily dependent
on fibre orientation [44].
It follows that draping order heavily impacts the quality of a finished part. It also determines
the layup time and the formation of defects during the forming process, although VFP does not
directly capture these two variables.
2.7 Difficulty metrics
One axis for DFM research work has been to discriminate drape patterns to determine which
one is the easiest to drape. This is clearly useful in the process development phase, when it
comes to providing instructions for an optimal drape pattern, but not only. Having the capability
to discriminate components based on their drapability would be very valuable at the early stages
of the development process.
Draping difficulty indicators based on VFP output have been suggested by previous researchers
and showed a good correlation with experimental data on a set of similar geometrical features.
Bloom [23] introduced a model that can predict the layup time required to drape a part by hand
layup using prepreg materials. Time predictions were formulated using a linear combination of
shear, tackiness and flexural rigidity. This model is remarkable in its ability to link material
properties with geometrical considerations but it only captures the drape pattern through one
global indicator, the shear force applied on the prepreg. Prita [45] addressed this criticism by
suggesting another time-predictive model capable of assessing each part feature individually
for a simple set of parts. This model takes shear distribution into account through the
introduction of connection coefficients between features. Prita’s model is based on the shear
force required to form a feature, its distance to the free edge, its distance to the starting point of
the draping process and on connection types between features. However, none of these models
capture the draping difficulty that arises from the techniques that are required to achieve a drape
pattern.
2.8 Aim and scope
The author strongly believes that the focus of DFM research in the area of hand layup draping
of prepreg needs to shift to enable a better understanding of the draping process itself and that
this understanding must be communicated through simple simulation tools. Currently available
simulation programs describe finished components but do not investigate the draping process
itself and this is increasingly unsatisfying. It does not allow for any early stage prediction into
the effect of geometrical changes on layup difficulty, does not realistically simulate the draping
process as achieved by operators and does not instruct on the process of manipulating a ply to
achieve the required deformations.
A six-month project was carried out in the ACCIS research group of the University of Bristol
to develop virtual tools based on existing descriptions of the draping techniques used by
professional laminators in the draping process of preimpregnated reinforcements by hand layup.
A Pre-concept routine was developed to guide inexperienced designers in the process of
selecting features that are easy-to-manufacture, introducing manufacturing considerations at an
early stage of the design process. Work was also conducted towards the development of a Post
concept routine with the capability to break down a drape pattern into a draping process and to
use the latest to automatically generate technique-based draping instructions.
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3. Methodology
The keystone of this research project is a numerical model of the grasps and techniques used
by professional laminators. Section 4 describes the choices that were made in terms of
modelling strategy and the resulting technique models. These techniques were integrated into a
draping module, a program that makes it possible to combine them to generate drape patterns.
Functions were developed to assist the virtual draping process by providing a variety of displays
and assisting the user with input definitions.
Section 5 describes a first application of the draping module, the “Pre-concept routine”. It is an
independent program that manages a Knowledge Base of drape patterns to provide data to
designers on their drapability. The drape patterns in the Knowledge Base must have been draped
beforehand using the draping module described in Section 4 or using an external draping
software. This thesis work only guaranteed the compatibility between the Pre-concept routine
and VFP files.
The Pre-concept routine is meant to be used by designers prior to the design of a CAD model
whereas the “Post concept routine” describes an application that comes in at the Process
Development stage and that targets operators (Section 6). The Post concept routine is an effort
to generate draping instructions that detail the techniques to use at every stage of the draping
process. The goal of the Post concept routine will ultimately be to link drape patterns generated
using commercial software to the technique models described in Section 4 to induce a draping
process from the fibre orientation in a finished part. This evolution is outside the scope of this
Master thesis project.
The case study in section 7 illustrates how the Pre-concept and Post concept routines can be
integrated into a simple DFM methodology (Figure 1). Details are given regarding its potential
industrial impact and the evolutions that are required for it to achieve its full capability.
Figure 3. System diagram of the routines developed in this thesis
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4. Draping module
4.1 Model selection
The literature review conducted in Section 2 showed that there are two main types of modelling
strategies: FEM and fishnet models. The choice of a model has major implications in terms of
computational time and complexity. The decision was taken to implement a fishnet model
scheme in both the Pre-concept and Post concept routines for several reasons.
The first one is the need for the Post concept routine to import drape patterns from VFP. This
has implications in terms of data types. VFP implements a mapping strategy based on the PJN
model and implementing a similar approach ensures that its outputs will be compatible with the
Post concept routine.
Another argument comes from the practical use that will be made of the Pre-concept routine.
The Pre-concept routine is meant to generate many drape patterns in one run and to analyse
them. This process must be performed with a low computational time, ideally within seconds –
or less. FEM models typically require too much resources to meet this requirement.
Finally, the PJN model is a basic model that is easier to implement than its FE counterparts,
making it particularly suited for a Master thesis project.
There are several variants of the PJN model and attention should be paid to which one is the
most suited to the applications that are suggested in this project. This subsection will
successively focus on assumptions that may rule mapping schemes and on their implications in
terms of degrees of freedom. This is critical as degrees of freedom will translate into user input
and strongly impact the usability of the program. In other words, for a given model, how many
angles and coordinates does the user need to key in for the program to understand the design
intend?
4.2 Mathematical model of an element
4.2.1 Planar ply
The assumption is made in this paragraph that the ply does not undergo any out-of-plane
deformation and stays perfectly planar. In that case, an element is fully constrained if one of
the below sets of geometrical entities is fixed:
- 3 adjacent nodes
- 2 diagonally opposite nodes
- 2 intersecting edges
- 1 edge is fixed and the shear of the element is set
- 1 point is fixed and the shear and yaw of the element are set
4.2.2 Planar elements
In this second model, each individual element stays planar but two different elements do not
necessarily belong to the same plane. In this case, the first 3 conditions listed in the previous
paragraph still fully constrain an element but fixing an edge and the shear of the element leaves
2 nodes under-constrained. The pitch becomes an additional degree of freedom (Figure 4).
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Figure 4. In-plane and out of plane elements with the same shear angle and one node in common
The parameters that must be set to fully define an element with one fixed point are:
- The shear angle
- The pitch of the diagonal
- The yawing angle
- The rolling angle
4.2.3 Folded elements
Elements can be folded along either one of their two diagonals in this third and last model. A
first observation is that a set of 4 points can sometimes correspond to two valid elements. An
example is given by the set of points in Table 2, illustrated in Figure 5.
Coordinates (x,y,z)
A [0 0 0]
B [1 0 0]
C [0.836 0.836 0.5]
D [0 1 0]
Table 2. Coordinates of the two cross-overs for the element shown in Figure 5
Figure 5. 4 points can be the extremities of 2 different elements in this model
The parameters that must be set to fully define an element with one fixed point that does not
belong to the folding axis (left in Figure 5) are:
- The shear angle
- The pitch of the first half of the element
- The pitch of the second half of the element
- The yawing angle
- The rolling angle
10
However, the parameters that must be set to fully define an element with one fixed point that
belongs to the folding axis (right in Figure 5) become:
- The shear angle
- The roll of the first half of the element
- The roll of the second half of the element
- The pitching angle
- The yawing angle
4.3 Considerations about sets of elements
The draping module faces the challenge of preserving a good usability while being able to
generate a varied range of geometries. A user should ideally be able to generate any geometry
after keying in as few angles and coordinates as possible. The program should also run within
seconds. The below subsection will explore how the 3 types of element models translate into
mapping models and will evaluate their suitability with respect to capability and usability.
4.3.1 Planar model
In the planar model, the only deformation mode is in-plane shear. One should notice that the
drape pattern of a square zone of the ply can be fully defined by setting the shear and the yaw
of each node in the bias direction (See subsection 2.4.1). The choice was made in Figure 6 to
set the yawing angle to 0° for all the diagonal elements of the square zone. It follows that the
shear of the diagonal elements of the ply is the only degree of freedom.
Figure 6. Example of the parametrisation of a square zone
The planar model is very simplistic. It cannot be used in a module that aims at draping
components, that are naturally 3 dimensional entities, and its main use is to serve as a basic test
case to study how a local deformation propagates through the ply.
4.3.2 Curve glide geometries
Curve glide geometries belong to a set of geometries that was identified by Hancock when
carrying out reverse draping simulation [46]. This set of geometries is of interest when working
under the PJN assumption. It comprises all geometries that can be generated in this model and
is obtained by constraining the position of control points in warp and weft (Figure 7).
11
Figure 7. Warp, weft and bias of a fabric. Taken from [25]
4.3.3 The importance of folding
An important thing to notice in PJN models is that locking the ply in warp and weft uniquely
defines their drape pattern [46]. This is a clear limitation of the model as many features share
identical boundaries (Figure 8).
Figure 8. Two different features with the same warp and weft (in red)
4.3.4 Model selection
A model that allows elements to fold along one of their diagonals can generate a much wider
range of geometries than curve glide geometries. This model was selected and implemented in
a draping module because of its ability to drape corners.
The high number of parameters required to fully define each element in this model (six, see
4.2.3) was deemed to be high enough to allow for most techniques to be modelled. Each
technique automatically constrains some degrees of freedom by setting implicitly some key
parameters. These constraints were defined to match the user’s intuition of the techniques they
are incorporated in. This strategy allows the user to set boundary conditions intuitively to
maintain a good level of usability of the program. Boundary conditions derive from the grasps
that are used by professional laminators.
4.4 Techniques
The next steps of the development of a draping module were to identify and select techniques
to model and to simulate them virtually using the selected mapping strategy. The only accurate
description of hand layup draping techniques that could be found in the literature was performed
by Elkington in 2013 [33] and it is only natural that this thesis work makes use of his
terminology, with some minor modifications to differentiate between variants of the same
techniques. Five techniques were selected and modelled successively using a fishnet description
of the weave.
12
4.4.1 Tension-Tension Shear forming
The Tension-Tension shear forming operation consists in grabbing the ply in two points to apply
tension on the area comprised between those points (Figure 9).
Figure 9. Tension-Tension Shear forming
Figure 10. Tension-Tension shear forming (virtual)
In the numerical model, this is done by setting a uniform shear and inclination in between the
points where tension is applied. Figure 10 shows the result of a virtual Tension-Tension shear
forming operation with a shear of 25° and an inclination of 45° starting from a flat ply.
4.4.2 Tension Secured Shearing (point)
When performing a punctual Tension Secured Shearing operation the operator applies pressure
with the left hand on two perpendicular edges to prevent them from lifting from the tool and
grasps a small area of the ply using the right hand. Tension is then applied on the zone of the
ply comprised in between the operator’s hands (Figure 11).
Figure 11. Tension Secured Shearing (point)
Figure 12. Tension Secured Shearing with a point
(virtual)
The virtual equivalent of this operation sets the inclination of diagonally aligned points while
preserving two edges. This operation is mainly used to form corners (Figure 12).
4.4.3 Tension Secured Shearing (edge)
Tension Secured Shearing with an edge consists in applying pressure on one edge of the ply
with one hand to keep it stuck to the mould surface while grasping a parallel edge and pulling
it to shear the band of the ply comprised between both hands (Figure 13).
13
Figure 13. Tension Secured Shearing (edge)
Figure 14. Tension Secured Shearing with an edge (virtual)
This operation provides a simple way for the user to shear an element while keeping one of its
edges fixed (Figure 14). It can also be used to align the edge of the ply with a contour. This
operation requires two input: the shear angle and the inclination.
4.4.4 Manual folding (straight)
Manual folding was defined by Elkington as the action of “actively folding the material out of
plane” [33]. The operation described in this subsection is limited to straight folds: the ply is
only folded along a tow or in the bias direction and no curvature is applied other than the
curvature that was already in the drape pattern induced by previous operations (Figure 15).
Figure 15. Manual Folding (straight)
Figure 16. Manual Folding (virtual)
The straight manual folding operation is usually used to form ramps (Figure 16). The user can
define this operation by keying in the desired ramp angle and the axis along which the ply
should be folded.
4.4.5 Manual folding (curved)
The curved manual folding operation is the exact equivalent of a Manual Folding as defined by
Elkington [33]. The need for a distinction between straight and curved manual folding arose
from the difference in complexity between those operations both on the user side (input) and
on the computational side (range of output). The curved Manual folding operation allows the
user to generate geometries that have a constant curvature by folding the ply along parallel tows
(cylinders) or along diagonally aligned lines of nodes (Figure 17). It can also be used to set the
warp and weft of the ply and to generate a curve-glide geometry (
Figure 18). In that case, unlike in the manual folding (straight) operation, shear is induced in the
ply.
14
Figure 17. Example of curved manual folding
Figure 18. A curve-glide geometry obtained by
curved manual folding
4.5 Specificities of the technique models
Operators’ techniques were modelled using a kinematic description of the weave: tow
crossovers are assimilated as points who are connected to each other by inextensible bars. The
hypothesis was therefore implicitly made that no variation in crimp percentage occurs when
tension is applied which is questionable. Because of the inextensibility of the fibres, and since
no correlation between in-plane and out-of-plane deformation was modelled, it is also apparent
that any variation in fibre orientation propagates indefinitely. This same phenomenon can be
observed in VFP but does not match the experimental tendency of shear deformation to decay
in the weave.
4.6 The virtual draping process
4.6.1 Structure
Techniques need to be combined to perform draping simulations. The draping module starts by
displaying a flat 0/90 ply weave (Figure 19) and a list of operations. The user can select an
operation and set the parameters that are needed to perform it, guided by prompts. If inputs are
valid, the program performs the corresponding operation. The above steps are then iterated until
the user decides to exit the program.
In practice, an operator needs to stick an edge to the mould before draping it feature by feature.
The requirement was therefore added that, for a virtual draping process to be valid, the same
rectangular area of the ply must never exhibit any shear deformation. This area must be located
along one of the four edges of the weave and corresponds to the part of the weave that is initially
stuck to the mould in an experimental setup.
Figure 19. Initial drape pattern
15
4.6.2 Display
A colour scale allows the user to quickly identify
the shear of the elements after each operation:
- 0° to 10°: Dark blue
- 10° to 20°: Cyan
- 20° to 30°: Green
- 30° to 40°: Yellow
- 40° to 50°: Orange
- 50° and above: Red Figure 20. Colour scale
4.6.3 List of operations
The draping module cannot be limited to featuring virtual techniques. It also needs to include
operations to assist the user in the input and validation processes. These operations were
implemented but will not be detailed in this thesis report because they are well-known and
mainly focus on displaying the ply in a variety of ways.
The operations that are available in the draping module can be divided into 4 categories:
I. Manipulating the ply
a. Tension-Tension Shear forming
b. Tension Secured Shearing (point)
c. Tension Secured Shearing (edge)
d. Manual folding (straight)
e. Manual folding (curved)
f. Undo
II. Orientation within the ply
a. Highlight a node
b. Node number from coordinates
c. Displays the operation log
III. Display the ply
a. Displays the ply
b. Displays the ply using a relative colour scale
c. Highlight the elements whose shear was modified by the previous technique
IV. Others
a. Saves the simulation
b. Exit
The algorithm simply asks the user which operation it should execute until the forming process
is finished. The ply is displayed after every step and user inputs are documented.
4.6.4 Node number from coordinates
The draping module features several operations whose goal is to assist the user in the draping
process. This paragraph focuses on one of them: “Node number from coordinates”.
The program displays the coordinates of a node when the user clicks on it in a display window
but does not display its node number (Figure 21). However, every geometrical operation
requests a node number from the user to determine the position of the zone in which the
corresponding technique should be applied. A practical problem that users face when using the
tool is that they need to determine the node number of an element whose coordinates are known
16
before keying in the next geometrical operation. The operation “Node number from
coordinates” allows them to do that.
Figure 21. Display of coordinates in a Figure
4.7 Conclusion
The draping module can translate five draping techniques and grasps into virtual operations. By
doing so, this program contributes to a better understanding of the deformations induced by
real-life draping techniques. Support features have been implemented to assist the user in the
virtual forming process: variety of displays, highlights of relevant nodes, documentation…
The draping module has significant advantages over existing draping simulation programs.
First, it can generate a high number of drape patterns with varying parameters within seconds
because it enables the user to parametrise its designs and to generate them on a loop. Second, it
generates drape patterns and draping processes simultaneously whereas other simulation
programs cannot compute draping processes. However, the draping module can only generate
a small range of drape patterns because it does not involve any kind of contact modelling.
A typical forming process involves some tool interaction. The set of five techniques that was
implemented does not involve any contact modelling and this is restricting the range of
geometries that can be modelled.
Moreover, performing a virtual technique may change the drape pattern in various areas of the
ply, including areas in which the ply has already been formed as per the mould geometry. In
practice, a laminator sticks the ply to the mould surface and progressively works on each feature
of the part. The need may arise to lift the ply to drape another feature but the draping process
stays mainly progressive. The existing virtual techniques need to be modified to be compatible
with boundary conditions to prevent them from shearing the ply in areas where it is already in
contact with the (virtual) mould.
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5. The Pre-concept routine
5.1 Introduction
The Pre-concept routine is an independent module whose purpose is to provide designers with
an early stage difficulty assessment of common features. The main difficulty to overcome when
designing the architecture of this routine was that there is no CAD model to analyse at the Pre-
conception stage. Certainly, a simulation program needs accurate inputs. It cannot work based
on a vague idea. On the other hand, the Pre-concept routine needs to have an excellent usability
and to require little time. It would not make sense to design an early stage routine that requires
more effort than the existing forming simulation process. In brief, the Pre-concept routine must
work with little or no input and produce reasonable forming assessment estimations. This is
atypical for a simulation program as most programs typically have both very accurate inputs
and outputs. One last point to keep in mind is that a drapability assessment is not only dependant
on a geometry but also on the strategy that is used to drape it. The Pre-concept routine
consequently needs accurate input. A succinct formulation of the above problem is that “The
Pre-concept routine needs accurate inputs to run but its users should not bear the task of
designing them”.
This thesis work suggests to solve this problem by implementing a “Knowledge Base” system.
The Knowledge Base can be built when developing the program and exploited by its users after
its release. VFP and the draping module provide two independent ways of building the
Knowledge Base. Users can import draping processes from the Knowledge Base for the Pre-
Concept routine to assess their forming characteristics. This is achieved thanks to difficulty
indicators designed to capture complementary characteristics of a draping process.
5.2 The Knowledge Base and its challenges
A Knowledge Base was built using draping processes from the draping module and drape
patterns from VFP. Specific functions had to be coded for this matter to save and load several
data types without any data loss. They not only save the shape of the finished component but
also the parameters corresponding to each technique required to drape it.
However, the main challenge that came with the Knowledge Base is how representative it is of
typical design features. In other words, the Knowledge Base must contain enough geometries
to be relevant. What’s more, the process of adding files to the Knowledge Base using VFP is
time consuming which means that the range of geometries available in the Knowledge Base
strongly depends on the capability of the draping module. The latest implies that improving the
Pre-Concept routine goes through modelling additional techniques in the draping module and
making sure that these techniques can be used effectively and intuitively thanks to a user-
friendly graphical interface.
The focus of this work was to add a small set of simple features in the Knowledge Base for
them to serve for testing and validation purpose rather than to build a Knowledge Base large
enough for the routines to be used in an industrial environment. Therefore, the Knowledge Base
is currently limited to 8 features available with varying parameters (58 files in total): convex
and concave corners draped bottom to top, convex and concave corners draped top to bottom,
tapered corners draped bottom to top, hemispheres, ramps with a constant inclination, ramps
with a constant curvature, bumps and a loft.
18
5.3 Analysis
Although the one-time process of building the Knowledge Base is time consuming, indicators
that assess the drapability of a set of parts are on the other hand generated within seconds,
allowing for a smooth user-experience.
These indicators are plotted using bar diagrams (Figure 22). The x-axis of the bar diagrams
displays the part number or, in the case of a set of similar parts, the parameter that varies in the
current simulation run. There is one bar per indicator per part.
The “View” window on the top-left displays by default the drape pattern of the latest part that
was analysed by the Pre-concept routine. However, the user can decide to display any of the
parts analysed during the last simulation run.
Figure 22. Outputs of the Pre-concept routine
5.3.1 In-plane shear indicator
The Pre-concept routine sums up the force that is required to shear each node of the ply for each
imported feature and displays the results in a bar diagram (in red in Figure 22). This force is
calculated based on the Force versus Shear curve established experimentally by Bloom [23] on
a MTM44-1 carbon fibre 2x2 Twill produced by Umeco. The main purpose of this indicator is
to assess the physical effort that is involved when applying in-plane deformation during the
draping process.
5.3.2 Highly sheared elements
The “Number of high shear elements” indicator (green bar diagram in Figure 22) counts the
number of elements whose shear exceeds a threshold that is hard coded in the MATLAB code.
The purpose of this indicator is to determine to what extend the draping process of a part
involves high level of physical effort.
5.3.3 Shear disparity index
Some parts contain features that can only be draped in VFP. In that case, the techniques required
to perform the draping process are unavailable and can only be estimated. The higher the Shear
disparity index, the more techniques are required to form a part and the more complex it is. This
19
heuristic is defined as the number of sets of adjacent elements of a ply that share the same shear.
The Shear disparity index is equal to 9 on the left figure in Figure 23 and to 55 on the right one.
Figure 23. Example of a drape pattern with a low shear disparity index (left) and a high one (right)
5.3.4 Slippage and lifting risk
Each time that the Pre-concept routine computes formability indicators for a feature it also
computes the displacement of the elements that surround that feature assuming that they are not
stuck to the ply and can move freely. This assumption does not hold in practice as the draping
process is mainly progressive but it does provide a heuristic with regards to potential lifting and
slippage (pink and black diagrams in Figure 22). The slippage risk and the lifting risk are
respectively calculated as the average in-plane and out-of-plane displacement of the nodes that
surround the feature that is assessed in the Pre-concept routine. It is scaled by dividing it by the
length of the edge of an element.
5.3.5 Shear along a horizontal tow
Tracking the shear along a tow (Figure 24) provides an indication on the shear disparity in a
zone of the ply which links to the ply tendency to go out of plane since out-of-plane deformation
usually accompanies variations in in-plane deformation. The hypothesis is that this indicator
could relate to the risk that the ply may locally lift from the mould if the prepreg is not tacky
enough. This hypothesis has not been investigated experimentally in this thesis work.
Figure 24. Shear along a tow
5.4 Case study
Figure 25 exhibits a set of drape patterns. Layup trials carried out in the lab on similar
components show that the draping difficulty associated to the forming process of these
geometries varies significantly, along with the risk of defects that may arise when forming them.
This case study illustrates and justifies the above using the Pre-concept routine.
20
Figure 25. Drape pattern for the Pre-concept case study
The drape patterns shown in Figure 25 are selected in the Pre-concept routine and the program
automatically runs a draping difficulty analysis. Indicators are then displayed in the form of bar
diagrams (Figure 26).
It is immediate that “Bumps” are very difficult to drape: an operator needs to use many
techniques to drape them (high “Shear disparity index”), to apply a lot of force (high “Force to
apply to shear the ply”) and some areas of the drape pattern are sheared with an excessively
high angle (high “Number of high shear nodes”). However, draping the bumps does not involve
a high risk of slippage in the surrounding area of the ply (low “Slippage indicator”).
The “Loft” is also difficult to drape for the same reason than the bump, although it is much less
complex because it can be draped using fewer techniques. It is therefore faster to drape on its
own. However, this loft has a very high slippage risk which means that an operator will
consistently have to make sure that defects do not arise in the surrounding features when
draping this geometry. In practice, the loft will therefore be the most time-consuming feature
to drape if it is integrated in a component (a propeller blade for example).
Unlike the “Loft”, the “Convex corner” and the “Concave corner” will not induce any slippage
in the surrounding ply. These geometries require both little force and few techniques to be
formed, making them the easiest to drape in the considered panel.
Finally, the “Ramp” is interesting because it can obviously be formed using only one technique
(“Shear Disparity index” equal to 1), does not involve any deformation in any area of the ply
but draping it is very likely to cause surrounding geometries to lift from the mould and can
therefore be troublesome.
Figure 26. Draping difficulty indicators for the Pre-concept case study
21
5.5 Conclusion
The Pre-concept routine relies on a database of features that have been draped using its own
draping module or using Virtual Fabric Placement (VFP). It can import drape patterns and can
assess them in terms of several forming indicators. Moreover, the Pre-concept routine provides
a heuristic for assessing the risk of defects in the rest of the ply that may occur during the
draping process of the imported feature.
In practice, a designer could use the Pre-concept routine to interrogate a database of parts. Parts
and their corresponding draping difficulty assessments could be searched for in the database.
Based on these pieces of information, the designer could then move to designing a 3D model
using a CAD software. This effectively introduces forming considerations as an additional type
of considerations to keep in mind when designing a part.
The Pre-concept routine constitutes a first step towards a selection package similar to existing
solutions developed for material selection [30, 47, 48] but it is still missing a search engine and
its graphical interface can be improved.
Designers should be able to search for features in the database based on their formability
assessment. Examples of features include corners, ribs, hemispheres and common lofts. It
should also be possible to refine the search to discriminate features based on the techniques that
are required to form them. One could exclusively display corners that can be draped using only
Tension-Tension Secured shearing and Manual Folding for example. Experiments could also
be designed to assess the respective difficulty of each technique and their conclusions could be
used to formulate additional draping indicators.
When considering the existing content of some subfolders of the Pre-concept routine (Figure
27), one may think that turning this tool into a selection package is not that big of a leap. It is
easy to imagine that the space in grey in Figure 27 could be used to display a detailed view of
the selected feature, a table showing its formability indicators and a form in which the user
could key in the parameters of the feature that is being investigated. An advanced search engine
would also be needed and further work is required to extend and structure the database.
These additional features do not require any innovation. They are textbook software
engineering features and have been implemented by Ashby in the material selection software
CES [47, 49, 48]. These features were not implemented in this thesis project because of time
limitations and because MATLAB was not an ideal choice of programming language for this
application.
Figure 27. Current content of a subfolder of the Pre-concept routine
22
6 Post Concept routine
6.1 Introduction
Currently available forming simulation programs can calculate the drape pattern of a part.
However, they do not provide any draping instructions nor inform about the draping process
that is carried out to layup the finished part. There is value in reverse draping simulations
capable of assigning techniques to an existing drape pattern because such simulations would be
able to capture more accurately the complexity of the draping process than current simulations
do. The Post concept routine is an attempt at interpreting drape patterns in terms of the
techniques used during the draping process. In other words, this routine aims at providing
draping instructions based on the deformation of the finished part.
The development of the Post concept routine can be divided into two activities. The first one
consists in displaying the techniques that correspond to a draping process. The program starts
from a list of techniques and their parameters and needs to produce visual documents that
operators can use when draping a part, draping instructions. The second activity is to convert
drape patterns into draping processes. Indeed, the draping module can simultaneously generate
drape patterns and draping processes but commercial programs can only generate drape
patterns. There is still a need to import drape patterns obtained using commercial programs to
expand the Post concept routine capability because the draping module is not yet capable of
draping complex features. The second activity was deemed to go outside the scope of this thesis
project.
6.2 Towards draping instructions: visualising techniques
6.2.1 Lamination training in the industry
There are currently no standardised draping instructions used in the aerospace industry.
Operators are being trained by master laminators with years of experience through internal
training programmes or in specialised training centres (Dark Matter, NCC) [21]. For each part,
they are given drawings specifying the part dimensions, its layup, its stack-up sequence and the
orientation of each ply. Laminators can then drape the same part in various ways which would
result in different drape patterns between laminators and introduce some variability in the
mechanical properties of the final part. Because of this variability, composite parts must be
designed with high safety factors, typically comprised between 1.5 and 2.0 [14].
6.2.2 Draping instructions
The Post concept routine generates 2 reports to describe how a drape pattern was obtained:
- A technical report in a .txt file contains an exhaustive description of the techniques used to
generate the drape pattern and lists their parameters.
Figure 28. Extract of a .txt report
23
- A more user-friendly report in a Microsoft Word file contains the name of the techniques used
to generate the drape pattern and shows corresponding pictures but does not specify every
parameter.
Figure 29. Extract of a Microsoft Word report
These reports are respectively generated by calling functions that can read and write in a text
file and by sending requests to an external application that communicates with Microsoft Word.
6.3 Sampling VFP features
A first step towards giving the Pre-concept routine the capability of assigning a draping process
to a drape pattern was made by coding a simple sampling algorithm that allows it to import
VFP files. Importing VFP files comes with specific problematics such as import format, data
integrity and sampling. The focus of this thesis report being on materials the choice was made
not to detail two out of these three operations. Sampling was deemed to be more relevant
because of the limitations in usability that may arise from the way it was implemented.
VFP outputs typically contain several thousands of nodes while the Pre-concept routine prefers
working with one thousand nodes. It is therefore preferable to sample the VFP point cloud
before inserting it into the existing drape pattern. The import code makes the approximation
that each element is planar. It first generates the surface of the VFP output and then samples it
by dividing it into a new grid. In the below explanation, it is assumed that the VFP output is
imported as 3 m by m coordinate matrices that must be sampled down to 3 n by n matrices (n <
m). The first step of the sampling algorithm is a Euclidean division that calculates the
proportionality parameters 𝑡𝑖 and 𝑡𝑗 of node 𝐴𝑖,𝑗(𝑥𝑠𝑖,𝑗, 𝑦𝑠𝑖,𝑗 , 𝑧𝑠𝑖,𝑗):
𝑖
𝑛=
𝑎
𝑚+ 𝑡𝑖 𝑤𝑖𝑡ℎ 0 ≤ 𝑡𝑖 <
1
𝑚 𝑎𝑛𝑑 𝑎 ∈ ℕ
(1)
𝑗
𝑛=
𝑏
𝑚+ 𝑡𝑗 𝑤𝑖𝑡ℎ 0 ≤ 𝑡𝑗 <
1
𝑚 𝑎𝑛𝑑 𝑏 ∈ ℕ
(2)
The parameters a and b convey information on the element of the VFP solution where the
sample node will fall and the parameters 𝑡𝑖 and 𝑡𝑗 describe the percentage of the length of each
edge where this node will be placed. The coordinates of point A are then calculated in the
general case as follow:
24
𝑥𝑠𝑖,𝑗 = 𝑥𝑎,𝑏 + 𝑚𝑡𝑖(𝑥𝑎+1,𝑏 − 𝑥𝑎,𝑏) + 𝑚𝑡𝑗(𝑥𝑎,𝑏+1 − 𝑥𝑎,𝑏) (3)
𝑦𝑠𝑖,𝑗 = 𝑦𝑎,𝑏 + 𝑚𝑡𝑖(𝑦𝑎+1,𝑏 − 𝑦𝑎,𝑏) + 𝑚𝑡𝑗(𝑦𝑎,𝑏+1 − 𝑦𝑎,𝑏) (4)
𝑧𝑠𝑖,𝑗 = 𝑧𝑎,𝑏 + 𝑚𝑡𝑖(𝑧𝑎+1,𝑏 − 𝑧𝑎,𝑏) + 𝑚𝑡𝑗(𝑧𝑎,𝑏+1 − 𝑧𝑎,𝑏) (5)
Figure 30. Sampling model
The sampling code may generate inconsistencies in element length depending on the ratio
between m and n. Sampling VFP files using a low number of data points should be avoided.
6.4 Case study
Figure 31 illustrates how the Post-concept routine generates draping instructions for a ramp
with a recess. The figures and captions had to be rearranged to fit in this report but their
orientation and content were not changed in any way. It is also possible to display images on
the point of application of each technique directly on the figures (see Figure 29) but this option
was disabled in Figure 31 for the purpose of readability.
Figure 31. Draping instructions for a ramp with a recess
25
6.5 Conclusion
The Post concept routine can automatically generate draping instructions in both a technical
and a non-technical format. These instructions provide indications on the forming process itself,
rather than being limited to describing the finished part. However, their display could be
significantly improved with the proper visuals and experimental trials have not been conducted
to validate them.
The compatibility between VFP files and the Post concept routine was also verified by
implementing a code that can import drape patterns from VFP. There is no theoretical barrier
to the use of files from other commercial programs in the Post-Concept routine, including FEM
schemes based software, but no work has yet been conducted in that direction. However, an
algorithm with the capability of interpreting a drape pattern into a sequence of techniques needs
to be developed before the Post concept routine can be used effectively in the industry. Once
this has been done, the Post concept routine will be able to determine how parts can be draped
by hand layup, unlike existing simulation tools that only describe the fibre orientation of laid
up parts.
A suggestion for this algorithm is given below:
1. The user imports a drape pattern
2. The user sticks the ply to the surface of the drape pattern
3. The user selects a node, an edge or a combination of edges of the ply to fix
4. The user sets a moving node
5. The user selects a point of the drape pattern
6. The program determines a list of techniques and their parameters that can displace the
moving node to the selected location without moving the fixed node, edge or
combination of edges.
7. The program decides on one of these techniques based on forming indicators
8. The program applies the relevant technique
9. The program displays the ply geometry
10. Repeat operations 3 to 9 until the part is fully draped
11. The program generates draping instructions
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7 Integration of the Pre-concept and Post concept routines into the
design process
7.1 System diagram
Figure 32. Suggested update to the design process
The Pre-concept and Post concept routines can be used in combination with existing
commercial software to shift the focus of the current design process towards manufacturability.
The Pre-concept routine assists designers prior to the design of the first CAD model to help
them assess the impact that a design choice has on manufacturability. Commercial programs
can be used to calculate the fibre orientation in the finished parts. FEM analyses can then be
carried out to assess the mechanical properties of the part. The whole design process should
then be iterated. At the process development stage, the Post concept routine provides
standardised draping instructions for operators.
This methodology is very similar to the one designed by Gandi in 1990 [29]. Both
methodologies require a back and forth between manufacturing process considerations and the
design of the successive 3D models for each design iteration (Figure 33). However, Gandi’s
methodology is applicable to any composite-specific manufacturing process while this thesis
work focuses on the hand layup of prepreg materials using plain weaves. It also goes one step
further by implementing virtual tools that effectively lower the skill level required to take hand
layup process requirements into account. These tools could allow access to some composite
conception positions to inexperienced designers, facilitating their insertion into the industry and
contributing to the training of a highly skilled labour force.
27
Figure 33. How the routines developed in this thesis support Gandi’s DFM methodology for components
manufactured in composite materials. Adapted from [29].
7.2 Case study
The above methodology will now be illustrated with a short case study. A part is composed of
two flat bases positioned such that they can only be connected through a feature with double-
curvature. The designer considers two ways of connecting these bases, illustrated in Figure 34.
Figure 34. Visualisation of the problem of the case study
28
Draping order influences the drape pattern of the finished part. Three drape patterns will be
considered in this case study:
- Feature 1: Draped from bottom to top (drape pattern 1)
- Feature 2: Draped from top to bottom (drape pattern 2)
- Feature 2: Draped from bottom to top (drape pattern 3)
The designer wants to determine which one of these drape patterns is the easiest to drape before
selecting one (Preconception). The fibre orientation of the ply will then be calculated and
handed in to the company’s FEM team for it to perform various calculations. Finally, the
designer will define draping instructions based on the techniques required to form the ply (Post
conception).
7.3 Preconception phase
The designer searches the knowledge base for these 3 geometries, inserts them into a specific
folder and runs the Preconception tool. The Preconception tool displays each drape pattern
(Figure 35) together with the indicators described in subsection 5.3 (Figure 36).
Figure 35. Drape pattern considered in the case study, shown as displayed in the Pre-concept routine
Figure 36 shows that all geometries can likely be draped using the same number of techniques
because they have the same Shear disparity index. Shearing drape patterns 1 and 3 involves
more force than shearing drape pattern 2 but no element in any drape pattern needs to be sheared
by more than 30°. The slippage indicator shows that the ply may lift from the mould when
draping drape patterns 1 and 3.
With that information in mind, using feature 2 should be preferred. The laminator should drape
it from top to bottom (drape pattern 2) as this can be achieved using very few techniques and
would require the least shear of all drape patterns. On top of that, there is little or no risk that
the ply slips from surrounding features with this draping strategy.
Figure 36. Analysis of the geometries of the case study
29
7.4 VFP
Having selected feature 2 and drape pattern 2, the designer can move to building a CAD model
that incorporates this feature, keeping in mind that it should be draped from top to bottom. This
CAD model is then converted into an STL file and exported into a layup program such as VFP.
Figure 37 and Figure 38 are shown here to illustrate that the drape pattern obtained
independently in the draping module of the Pre-concept routine matches the one from VFP.
However, the designer only needs to drape one feature at this stage of the design process, shown
on the left side of Figure 37.
Figure 37. VFP diagram for “Angle 1: Straight angle” draped top to
bottom (left) and bottom to top (right)
Figure 38. VFP diagram for
“Angle 2: Tapered face”
7.5 Post conception phase
The drape pattern obtained using VFP is then interpreted in terms of features to generate
instructions for the draping process (Figure 39). This is currently done manually by starting
from a flat ply and applying techniques to form it into the desired shape. The parameters needed
to define these techniques are extracted from the VFP output. However, research is being
carried out to give the Post Conception tool the capability of semi-automatically breaking down
an imported VFP drape pattern into a sequence of techniques.
Step 1/1
Technique 2: Tension-Secured-Shearing
Grip: Form a corner by grasping one point and applying pressure on 2 perpendicular edges
Figure 39. Extract from a Post Conception report on draping instructions
30
8. Conclusion
The deformations associated to several techniques were modelled numerically and combined
into a draping module using various practical features (reporting, draping instructions). The
Pre-concept routine makes use of this model to edit and manage a database of features and
produce drapability indicators. It enables designers to consider the manufacturing implications
of design choices before building a CAD model. Using the Pre-concept routine is easy, fast and
does not require any specialised training other than a basic sensitisation to composite materials.
The Pre-concept routine can also be used as a training tool for designers who are not familiar
with process development considerations, promoting more collaboration between the design
and the manufacturing departments of a company.
Work was also conducted to contribute to the development of a Post concept routine. The Post
concept routine automatically generates accurate technique-based draping instructions. Further
work is needed to improve the display of these instructions and to validate them in a lab
environment. That being done, the Post-concept tool would shorten laminators training period
and lower the skill level that is required to drape components with composite weaves. It would
also increase the reliability of composite components by promoting a standardised draping
process which could ultimately lead to material cost savings thanks to lower safety ratios.
31
9. Further work
The draping module is limited by its inability to model defects such as wrinkling or bridging
which is a typical problem for simulation codes that rely on a fishnet model. It would also
benefit from the implementation of additional techniques that involve some kind of contact
modelling. These techniques would expand the range of geometries that can be draped using
the draping module and facilitate the creation of the Knowledge Base of the Pre-concept
routine.
Both the Pre and Post concept routines have been coded in MATLAB and their interface should
be updated to make them visually more attractive. Most input are currently being keyed in, node
coordinates for example, although it would be much more intuitive to select them on the screen
by clicking on the ply. Finally, further work is required to turn the Post-concept routine into a
reverse simulation package capable of importing draping patterns from VFP and breaking them
down into draping processes. The Post-concept routine could also benefit from a Knowledge
Base system allowing it to save and load manufacturing instructions.
32
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