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1 INTRODUCTION
Simulation tools support the composite design
engineer in the optimisation of the thermoforming
process. Key to a good simulation tool is an
appropriate material model: complex enough to
accurately describe local deformations, but not more
complex than needed. Mechanical behaviour of
textile composites is quite complex during
thermoforming. For instance a woven textile
composite shows non-linear tensile stiffness due to
biaxial coupling between the two yarn families.
Shear stiffness is very low and highly non-linear.
Consequently, shear deformation is the major
deformation mechanism during forming. The
thermoplastic matrix viscous behaviour is dependent
on local temperature and shear rate. A vast amount
of macro-scale material models have been developed
with different degrees of complexity: elastic models
[1,2,3], viscous models [4,5,6], elasto-plastic, and
visco-elastic models (PAMFORM, [5]). Meso-
models of fabric mechanics can produce input data
for the macro-models, as demonstrated in [1,6,7].
Relevant experiments and benchmark exercises [8,9]
may help to validate these material models and
understand their capabilities. It is also useful to
study the sensitivity of thermoforming to material
parameters and to the effect of non-linearity and
interactions as biaxial coupling and shear-tensile
coupling. This way material features required to
obtain desired precision in local deformation
modelling can be deduced. In this work a parameter
sensitivity study was undertaken using a visco-
elastic material model in PAMFORM.
2 MATERIAL MODEL
2.1 Material model 140
This macro-scale material model is composed of
ABSTRACT: Double dome forming simulations are performed on woven textile composites in PAMFORM using a visco-elastic material model, dedicated to reinforced composites. Woven textile composites show very complex behaviour during thermo-forming. Material compliance curves in shear and tension are typically non-linear due to local deformations within the repetitive unit cell of the textile reinforcement, like yarn intertwining, crossover friction, yarn through-the-thickness and lateral compression. Moreover, matrix viscous behaviour is dependent on temperature and local shear rate. The goal of this work is to study the sensitivity of punch force and local fibre deformations on the material parameters. Parameter sensitivity studies can help in determining what the impact is of variability in mechanical test results and the material complexity considered, on the precision of local deformation predictions. Material parameters considered in this work are the non-linearity in uniaxial tensile stiffness, shear stiffness at 200°C and 20°C, bending stiffness (scale factor 0.1 and 0.001 with respect to continuum material), Poisson’s coefficient (0 vs. 0.4) and viscosity. From this simulation case study it can be concluded that shear stiffness and non-linearity in tensile stiffness according to yarn direction have a major impact on local deformations and punch force. In the high shear stiffness model a trade-off has to be made between constant binder force and high ratio of internal energy to hourglass energy. It is felt that viscosity should be studied more in depth, both experimentally - enabling to better define the range of viscosity values - as numerically.
Key words: thermoplastic, woven fabric, thermoforming, double-dome stamping, finite element, parameter sensitivity
Double dome forming simulation of woven textile composites
A. Willems1, S.V. Lomov
2, D. Vandepitte
1, I. Verpoest
2
1Mechanical Engineering Department, Katholieke Universiteit Leuven – Kasteelpark Arenberg 41, B-3001
Heverlee, Belgium URL: www.mech.kuleuven.ac.be e-mail: [email protected]
2Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven – Kasteelpark
Arenberg 44, B-3001 Heverlee, Belgium URL: www.mtm.kuleuven.ac.be e-mail: Stepan.Lomov@ mtm.kuleuven.be
three element layers that are firmly connected:
• Layer 1: Two truss elements account for non-
linear (uniaxial) tensile stiffness in yarn
direction. A bending correction factor and
transverse shear factor enable to downscale
bending and transverse shear stiffness with
respect to the continuum material assumption,
which would highly overestimate bending
stiffness, since fibres can freely slide over one
another. The bending factor is usually estimated
by performing a fabric cantilever test under
gravity load.
• Layer 2: Viscosity is added in a Maxwell model,
wherein viscosity can be dependent on local
shear rate and temperature.
• Layer 3: A first order shell element accounts for
non-linear shear resistance and simplified
‘biaxial tensile coupling’ via a constant
Poisson’s coefficient.
2.2 Material parameter values
Linear and non-linear tensile stiffness curves (figure
1) are derived from uniaxial tensile tests while shear
stiffness (figure 2b) is estimated from picture frame
tests. Both tests were performed on the balanced
twill glass-PP fabric in the Woven Benchmark
Exercise [10]. Viscous fabric shear resistance is
composed of an elastic and a viscous component –
the last of which is responsible for shear rate and
temperature dependence. In a purely elastic model,
however – temperature dependency might be taken
into account by performing a thermo-mechanical
simulation with stiffness dependency on
temperature. In this study the shear stiffness at
200°C was increased in one test by a factor 5 in
order to evaluate in a simplified manner for the
temperature dependant stiffening effect as material
cools down after tool contact.
Fig. 1 Linear and non-linear uniaxial tensile stiffness in weft
and warp direction
Viscosity is estimated based on squeeze flow tests
on a UD glass-PP fabric with volume fraction 0.35,
suggesting that mT in the power law (1) for
transversal viscosity, ηT, is 8 to 30 times the matrix
viscosity [11]. The measured transversal viscosity ηT
is used to estimate a Newtonian and power law
viscosity for the isotropic viscous layer (Layer 2).
1. −= n
TT m γη & (1)
Fig. 2 Left: Estimated newtonian viscosity and power law
viscosity (mT-fabric ~ 20*mT-PP) at 180°C, Right: Shear curve at
room temperature, shear curve at 200°C and upscaled shear
curve at 200°C (by factor 5)
3 FORMING SIMULATIONS
3.1 Tools and blank properties
Forming simulations were performed according to
the process conditions in the Double Dome Woven
Benchmark Exercise on the balanced twill fabric
with blankholder (see figure 3). Gap between the
male and female mold is 1 mm. A quarter of the
blank, measuring 270mm x 190mm, is modelled
with first order reduced shell elements of size 4 mm.
The blank has a thickness of 1 mm (according to
fully consolidated material thickness). Warp and
weft yarns lie initially in x- respectively z-direction.
Fig. 3. Double dome forming configuration: male and female
mold, blankholder ring and quarter of the blank
3.2 Punch velocity and blankholder force
Punch velocity history is represented in figure 4.
Punch movement stops when distance between tools
is 4.6 mm. A constant blankholder force of 350 N is
applied on the quarter blank during the whole
forming operation.
0
100
200
0 0.5 1Time [s]
Ve
locity
[mm
/s]
Fig. 4 Punch velocity history
3.3 Parameter sensitivity study
Table 1 gives an overview of the material parameter
combinations used in the parameter sensitivity study. Table 1. Material parameter combinations
1 2 3 4 5 6 7
Linear tensile stiffness X X X
Nonlinear tensile stiffness X X X X
Bending factor = 0.1 X
Bending factor = 0.001 X X X X X X
Shear stiffness at 200 C X X X X X X
Shear stiffness at 200 C * 5 X
No viscosity X X X X X
Const. Viscosity = 2,16E+4 Pa.s X
Power law viscosity (n = 0.25) X
Poisson’s coefficient = 0 X X X X X X
Poisson’s coefficient = 0,4 X
For all material combinations, punch force and local
deformations at the points, indicated in figure 5, are
monitored during the forming operation.
Fig. 5 Positions where local fibre angles are observed
4 RESULTS
4.1 Shear angles
Figure 6 compares fibre angles at final punch
position for all the tests at the specified point
locations (figure 5). The fibre angle is the relative
angle between the two yarn families, which lie
perpendicular to each other in the undeformed state.
Table 2 lists maximum occurring shear angle,
calculated as 90°– fibre angle, and averaged shear
angle difference (over all points considered) with
respect to reference test for linear tensile stiffness
(test 3) and non-linear tensile stiffness (test 4).
Fig. 6 Fibre angles at maximum punch depth on different point
locations for all material combinations
Shear angles are typically quite small, max. 37.3° -
38° for material with linear tensile stiffness and low
shear stiffness (test 1 to 3) and about 32° for
material with non-linear tensile stiffness (test 4 to 7).
Shear locking is likely to happen around 40°, and
thus wrinkling is not expected to occur for these test
cases. Figure 6 and table 2 show clearly that
maximum shear angle was influenced the most by
change in non-linearity of the tensile curves (test 3
vs. 4). Fibre angle distributions for test cases 1, 3
and 4 are shown in figure 7. One can observe that
fibre angle distribution is affected the most by
change in shear stiffness and change of non-linearity
in tensile curve. Some wrinkling could be observed
in the high shear stiffness test (test 1). Table 2. Shear angle and punch force values at maximum
punch depth
1 2 3 4 5 6 7
Max. shear angle γ 38.07 37.29 37.34 31.88 31.62 32.08 31.90
Average ∆γ with test 3 2.10 0.50 0.83
Average ∆γ with test 4 0.83 0.07 0.10 0.12
Punch force F [N] 1053.0 527.0 464.6 389.7 409.0 389.7 432.2
Relative ∆F [%] from test 3 126.7 13.4 -16.1
Relative ∆F [%] from test 4 19.2 4.9 5.1 10.9
Fig. 7 Relative fibre angles for (left to right) test 1, test 3
and test 4
4.2 Fibre strains
Figure 8 shows typical strain distribution in fibre
warp (left) and weft (right) directions.
Fig. 8 Strain in warp (left) and weft (right) for test 1, 3 and 4
(upper to lower)
Warp strains are typically higher than weft strains
due to the mold shape, which requires more draw-in
in x-direction than in z-direction. Significant local
compressive strains occur as well. As compressive
stiffness of the shells equals initial stiffness at zero
deformation, this causes high local compressive
stresses (in the order of 20 MPa) for the material
with linear tensile stiffness and high shear stiffness
(test 1). Numerical values for local strains in fibre
warp direction are visualized in figure 9. As
expected, strains increase most significantly between
linear and non-linear tensile stiffness tests (test 3 vs.
4). Only minor local fibre strain redistributions can
be observed when Poisson’s coefficient is changed
(test 4 vs. 5) or viscosity added (test 4 vs. 6).
Fig. 9 Fibre strains in warp direction
4.3 Punch force
Figure 10a shows that punch force histories are very
similar for all test cases, except for high shear
stiffness test, where final punch force is about two
times higher with respect to other tests. Forces at
maximum punch depth are compared in figure 10b
and table 2. Compared to reference test 3 and test 4,
punch force was influenced as well by increasing
bending factor (+13%), adding non-linearity to
tensile curve (-16%), increasing Poisson’s
coefficient (+5%) and adding viscosity (+5 to
+11%).
5 CONCLUSIONS
The conclusions of this preliminary sensitivity study
are that non-linearity of the tensile stiffness curve
and shear stiffness have most influence on local
deformations and punch force. Poisson’s coefficient,
bending stiffness and viscosity had negligible impact
on local deformations, but changed punch force with
5 to 13,5%. Real viscosity values might, however,
be higher than those used in the simulations, since
values were derived from squeeze flow experiments,
but P. Harrison observed alarming dependency of
fabric viscosity on test method and sample size [10].
It is felt that viscosity should be studied more in
depth, both experimentally - enabling to define a
more reliable range of viscosity values - as
numerically. It would be interesting to look at the
influence of localized material cooling by tool
contact and conductivity by a thermo-mechanical
coupled analysis when more experimental data is
available.
Fig. 10 Left: Punch force history, Right: Punch force [N] at
maximum punch depth
ACKNOWLEDGEMENTS
This research is funded by the Fund for Scientific Research
Flanders (FWO Vlaanderen). Saint-Gobain Vetrotex is kindly
acknowledged for supplying the Twintex® fabrics.
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