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: An.Willems@mech.kuleuven.be

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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