Finite Element Forming Simulation of NCF Considering Natural
Variability of Fiber Direction
W.R. Yu1, P. Harrison2 and A.C. Long2
1
Seoul National University-School of Materials and Engineering, San 56-1, Sillim-dong, Gwank-gu, Seoul,
151-742, Korea
URL: mse.snu.ac.kr
e-mail: woongryu@snu.ac.kr
2
University of Nottingham-School of Mechanical, Materials and Manufacturing Engineering, University
Park, Nottingham NG7 2RD, UK
URL: www.nottingham.ac.uk/~eazwww/composite e-mail:Philip.Harrison@nottingham.ac.uk;
Andrew.Long@nottingham.ac.uk
ABSTRACT: Finite element (FE) forming simulation has received significant attention for designing forming
process of non-crimp fabric (NCF) preform. Difficulty in predicting forming behaviour of NCF preforms
arises due to the lack of knowledge regarding localised buckling and wrinkling during forming. Wrinkling of
NCF with biaxial reinforcement is frequently observed to occur before the shear angle reaches the fiber
locking angle occurring when adjacent tows come into contact, even though it is commonly accepted that
fiber locking determines the onset of wrinkling. In most FE simulations, the tow directions in the entire NCF
are assumed to be initially perfectly orthogonal and uniform within all unit cells, neglecting any variability in
fiber orientation in the unit cells. However, in reality fiber direction can vary across the NCF. This variability
may cause localized buckling and wrinkling of the NCF. As such the current study investigates the effect of
variability of fiber direction on the forming behavior of NCF preform using a non-orthogonal constitutive
equation.
Key words: Fiber orientation variability, Non-orthogonal constitutive equation, NCF, Forming
1 INTRODUCTION
Finite element (FE) forming simulation is becoming
widespread in designing forming processes of noncrimp fabric (NCF) preforms. This is a preliminary
process to the liquid injection stage in liquid transfer
moulding. Difficulty in predicting forming
behaviour of NCF preforms arises due to a lack of
knowledge regarding localised buckling and
wrinkling during forming. Localised buckling and
wrinkling may be related to fiber direction
variability since misalignment of the fiber axis in a
unit cell produces stress discontinuities between
neighbouring unit cells. To the author’s knowledge,
the effects of variability in the fiber direction within
the unit cell across the NCF have not been addressed
in the literature. Recently, the effect of fiber
variability on permeability was simulated using the
Monte Carlo method [1].
In most FE simulations, the tow directions in the
entire NCF are assumed to be initially perfectly
orthogonal and uniform within all unit cells,
neglecting any variability in fiber orientation in the
unit cells. In reality, fiber direction can vary across
the NCF. FE forming simulations that include the
variability of the unit cell geometry, especially fiber
direction, can be used to evaluate these effects
quantitatively. For this purpose, a constitutive
relationship needs to be established. To incorporate
variability in the unit cell, this constitutive equation
should include the unit cell parameters. A nonorthogonal constitutive equation, developed
originally for woven fabric reinforced composites
sheet [2] and utilized recently in the analysis of NCF
forming [3] may be appropriate as it provides a
direct link with the unit cell geometry. With this
non-orthogonal equation, material variability can be
incorporated via two vectors representing fiber
direction in the unit cell. Fiber angle may be
presumed to follow a normal distribution centred on
the average fiber angle. The Monte Carlo method
may be employed to determine the data set for the
fiber angle and direction in each unit cell during a
pre-processing step to FE simulation. The two fiber
2 NATURAL VARIABILITY
2.1 Experimental observation
Fiber angle distribution has been investigated for an
unsheared  45 non-crimp glass fiber fabric,
Formax FGE106 [4]. The angle  between the fiber
direction and the 90  direction of the fabric, which
is expected to be half the fiber angle,  , has been
experimentally determined at various position on
both faces of the fabric using photographic imaging
and digital image analysis. Statistical evaluation of
the data indicates that  can be described by a
normal distribution with a mean of 42.7  and a
standard deviation of 5.6  . Figure 1 compares the
histogram of the observed angle distribution with the
corresponding normal distribution indicating
satisfactory agreement with a correlation
coefficient R 2  0.955 .
As shown in figure 1, the fiber orientation may
deviate from the orthogonal position by up to 10 
when a 95% probability is considered. This variation
is significant, resulting in variable mechanical
properties, such as shear stiffness. Regarding the
effect of fiber direction variability, it is reported that
the application of pre-tension helps to improve
reproducibility of picture-frame shear test [5]. This
is possibly caused by the pre-tension aligning the
tows straightly in the preform and thus removing
fiber directional variability.
0.4
0.35
Normal distribution
Experimental data
0.3
Probability
vectors are then used in calculating the stiffness
matrix and updated to create a new matrix as
deformation proceeds due to stamping.
Besides fiber directional properties, shear properties
also need to be varied according to the variability of
the fiber direction. Shear properties are characterized
by either picture frame or bias extension tests that
record shear force vs. shear angle. For such tests, the
shear angle is defined as an angle sheared from the
original fiber angle. Thus, because of the variability
in the fiber direction, the pre-shear stiffness inherent
in the un-deformed NCF sheet will vary between
elements. This initial variation in element stiffness is
determined from the shear force versus angle
experiments. In this way, effects of variation in the
fiber direction within unit cells are investigated
virtually.
0.25
0.2
0.15
0.1
0.05
0
22.5
27.5
32.5
37.5
42.5
47.5
52.5
57.5
62.5
Fibre Angle (degrees)
Fig. 1. Half fiber angle of a NCF preform: histogram of
experimental data and corresponding normal distribution [4].
2.2 Incorporation of variability into simulation
The aim of the current study is to investigate the
effect of fiber direction variability on the forming
behavior of NCF preforms. The variability results
from the fabric attribute. It is referred to here as
‘natural’ variability because the variability is
introduced
naturally
during
production,
manipulation, storing, and handling of the preform.
Since it is difficult to predict precisely where fiber
angle variation occurs in the preform, we employed
a statistical method to impose fiber direction
variability in the NCF specimen. The statistical
method is based on the assignment of fiber angle to
each material point using a random variable as
follows.
   2erf 1 (2D  1)   0
(1)
Here,  is fiber angle determined from normal
distribution of mean fiber angle (  0 ) and standard
deviation (  ) through uniformly distributed random
values D on the interval (0, 1). Using equation (1),
fiber angle can be assigned to any material point, i.e.
to the Gaussian integration points of the finite
elements that are used to approximate the fabric
preform. Once the fiber angle is given, the fiber
orientation for the two tows needs to be determined.
For a given fiber angle, the fiber orientations are
described by two vectors e warp and e weft . Naturally
the fiber direction, e.g., e warp , can be misaligned
from global fiber direction which represents
 45 fiber axis in NCF preform when not
considering variability. The misalignment has been
constrained to lie within  (90   ) / 2 from the
global fiber direction. The actual misalignment (  )
can be determined using equation (2) as with the
fiber angle case in equation (1).
  (2D  1)(90   ) / 2
(2)
As a result, a fiber direction ( e warp ) can be placed
randomly between  (90    ) / 2 to  (90    ) / 2
from global fiber direction. The weft direction ( e weft )
is then obtained by rotating the warp direction
through the given fiber angle. Since, in this approach,
the fiber directions and angle are randomly assigned
to the material point of the preform, the continuity of
the fiber path is not preserved between adjacent
elements. More study should be focused on the
compatibility of the fiber orientation between
adjacent elements to avoid unrealistic fiber paths.
This will be discussed in a future study.
The fiber orientation is crucial to determining the
constitutive equation. Since fiber orientation is not
initially orthogonal when variability is considered, a
non-orthogonal
constitutive
equation
is
indispensable to simulating the forming behavior of
NCF. Material properties for the non-orthogonal
equation consist of structural parameters, including
fiber orientation and mechanical properties such as
shear stiffness. Considering fiber direction
variability, the structural parameters remain
unchanged except the fiber direction vector. As for
shear resistance, the question of whether the
misalignment of the fiber direction invokes preshear stress must be decided. In this study, fiber
angle variation is regarded as a pre-sheared fiber
angle, thus the material point has a pre-shear stress.
The size of this stress can be determined from shear
force - shear angle data using the shear constitutive
equation. Details about this pre-stress treatment are
omitted here.
3 RESULTS AND DISCUSSION
Prior to evaluating the effect of natural variability,
mesh sensitivity needs to be investigated because the
current approach to considering fiber direction
variability relies on the assignment of fiber angle to
material points using random variable, i.e., as the
number of elements increase, the fiber angle
variation follows a normal distribution more closely.
Two simulations have been performed for bias
extension and picture-frame shear tests. For pure
shear deformation, as in the picture-frame shear test,
mesh sensitivity seems negligible. However, the
simulations of bias extension test show mesh
sensitive behavior due to the combination of both
pure shear and tensile deformation. Thus, for the
forming simulation of NCF including fiber direction
variability, mesh sensitivity should be investigated
also. However we discuss simulation results in this
paper without presenting such mesh sensitivity
studies.
To investigate the effect of fiber direction variability,
a forming example is chosen from a collaborative
benchmark forum for woven composite forming [6].
The forming tools are constructed to stamp textile
preform or prepreg into a half cylindrical shell with
double dome ends. Tool geometry and forming
condition are detailed in [6]. The NCF preform used
for this simulation is a tricot-stitched biaxial fabric.
Its material properties, including shear resistance,
can be found in [3].
Fig. 2. Fiber angle variation applied to material points of a
NCF preform for double dome forming simulation.
Figure 2 shows the fiber angle distribution of a NCF
preform, determined using equation (1) by assuming
a normal distribution with a mean of 90  and a
standard deviation of 1 . The fiber angle variability is
incorporated into the non-orthogonal constitutive
equation using a user material subroutine in
ABAQUS/Explicit. Shell elements (S3) are used to
approximate the NCF preform. To compare the
effect of fiber angle variation on the forming
behavior, the first simulation was performed for a
zero-variability case. Figure 3 (a) shows a formed
shape when the global fiber orientation is placed on
the 1 and 3 axes. In this simulation a blank holder
force was not applied but instead clearance between
the blank holder and die was maintained during the
simulation in order to maintain a preform thickness.
In the simulation, wrinkling is observed at six parts
in both fiber directions on the flange part of the
preform. When fiber angle variability is incorporated,
the formed shape shows wrinkling behavior similar
to the zero-variability case but more localized
wrinkling was propagated along the line where the
major wrinkling occurs as shown in Figure 3(b).
More theoretical analysis should be performed to
conclude the main causes of such localized
wrinkling; however tentatively it can be thought that
the localized buckling may be caused by
incompatible material properties through thickness
due to the fiber angle variation.
variability is an important factor in determining the
onset of localized wrinkling, however, systematic
research for incorporating fiber angle variability in
NCF preforms needs to be performed in order to
support the findings.
(a)
(a)
(b)
Fig. 4. The effect of fiber direction variability on the fiber
angle distribution: (a) zero-variability (b) variability
(  0  90,   1 )
REFERENCES
1.
(b)
Fig. 3. The effect of fiber direction variability on the formed
shape: (a) no variability (b) variability (  0  90,   1 )
Fiber angle distribution is also compared for the two
cases to investigate its role in wrinkling. As shown
in figure 4(a), the fiber locking angle may not be the
crucial factor in determining wrinkling behavior
because wrinkling is not observed in locations of
severe shear deformation. It is clear from figure 4(b)
that even though fiber locking is not an absolute
factor for the wrinkling, fiber direction variability
plays a role in the localized wrinkling.
4 CONCLUSION
Fiber angle and direction variability are incorporated
into forming simulations using a statistical method.
From forming simulations it is shown that fiber
2.
3.
4.
5.
6.
A. Endruweit, A.C.Long, F.Robitaille, C.D.Rudd,
Dependence of permeability variations on the textile
structure. In: Proc. ECCM'11 From nano-scale
interaction to Engineering structures, Rhodes in Greece
(2004).
W.R. Yu, F. Pourboghrat, K. Chung , M. Zampaloni and
T.J. Kang, Non-orthogonal constitutive equation for
woven fabric reinforced thermoplastic composites, Comp
Part A-App S, 33, (2002), 1095-1105
W.R.Yu, P. Harrison and A.C. Long, Finite Element
Forming Simulation for Non-crimp Fabrics using a NonOrthogonal Constitutive Equation, Comp Part A-App S,
accepted, (2004)
R.A. Andrews, Real life process simulation-Predicting
the range of outcomes during composites manufacturing,
BEng Individual Project Report, University of
Nottingham (2003).
A.C.Long, B.J.Souter, F.Robitaille, C.D.Rudd, Effect of
fiber architecture on reinforcement fabric deformation,
Plast Rubber Compos, 2/31, (2002), 87-97.
http://www.gtwebsolutions.com/nwbenchmark/index.php