ISO 4410:2023

INTERNATIONAL ISO
STANDARD 4410
First edition
2023-07
Test methods for the experimental
characterization of in-plane
permeability of fibrous
reinforcements for liquid composite
moulding
Méthodes d'essais pour la caractérisation expérimentale de la
perméabilité dans le plan des renforts fibreux pour le moulage de
composites liquides
Reference number
ISO 4410:2023(E)
© ISO 2023

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ISO 4410:2023(E)
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© ISO 2023
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ISO 4410:2023(E)
Contents Page
Foreword .v
Introduction . vi
1 Scope . 1
2 Normative references . 1
3 Terms, definitions, symbols and abbreviated terms . 1
3.1 Terms and definitions . 1
3.2 Symbols and abbreviated terms . 2
4 Principle . 5
5 Design of experiments . 5
5.1 Selection of injection method . 5
5.2 Number of repeat tests . 5
5.3 Setting the fibre volume fraction . 6
5.4 Selecting the fluid injection pressure . 6
5.5 Temperature conditions . 6
5.6 Plausibility checks . 6
6 Test specimen and specimen preparation . 7
6.1 General information. 7
6.2 Specimen cutting . 7
6.3 Specimen stacking . 7
6.4 Specimen mass measurement . 8
7 Test fluid and fluid injection system preparation . 9
7.1 Test fluid . 9
7.2 Preparing the fluid and the injection system . 9
8 Mould preparation .9
8.1 Specimen thickness control . 9
8.2 Mould height . 9
8.3 Surface roughness of mould . 11
8.4 Alignment of top and bottom part of mould . 11
9 Measurement of fluid pressure, temperature and flow rate .11
9.1 Fluid pressure measurement . 11
9.2 Fluid temperature measurement . 11
9.3 Fluid flow rate measurement . 11
10 Method A: Linear flow experiments .11
10.1 Apparatus design . 11
10.2 Specimen planar dimensions .12
10.3 Injection gate geometry .12
10.4 Vent geometry . 13
10.5 Fluid injection system .13
10.6 Test preparation . 13
10.6.1 Edge sealing .13
10.6.2 Placing the specimen in the mould . 13
10.7 Sensor equipment/Data acquisition . 14
10.7.1 Fluid flow front measurement . 14
10.7.2 Sampling of measurement data . 15
10.8 Data processing. 15
10.8.1 Data segmentation .15
10.8.2 Data evaluation procedure . 15
10.8.3 Calculating the permeability tensor . 17
10.8.4 Validity checks . 18
11 Method B: Radial flow experiments .20
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ISO 4410:2023(E)
11.1 Apparatus design . 20
11.2 Specimen planar dimensions .20
11.3 Injection gate geometry . 21
11.4 Vent geometry . 21
11.5 Fluid injection system . 21
11.6 Test preparation . 22
11.6.1 Inserting the inlet hole in the specimen . 22
11.6.2 Placing the specimen in the mould . 22
11.7 Sensor equipment/Data acquisition . 23
11.7.1 Fluid flow front monitoring . 23
11.7.2 Sampling of measurement data . 23
11.8 Data processing. 23
11.8.1 Data evaluation range . 23
11.8.2 Data segmentation .23
11.8.3 Data processing algorithm . 24
11.8.4 Validity checks .29
12 Result documentation .29
12.1 Single experiment documentation (Mandatory) .29
12.2 Documentation of repeat experiments (Optional) .30
12.3 Documentation of model approximation (Optional) . 31
Bibliography .32
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ISO 4410:2023(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
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electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO document should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use
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This document was prepared by Technical Committee ISO/TC 61, Plastics, Subcommittee SC 13,
Composites and reinforcement fibres.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
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ISO 4410:2023(E)
Introduction
Liquid composite moulding (LCM) processes are employed for the manufacture of fibre reinforced
polymer composites (FRPC). In all LCM processes, dry fibrous reinforcements are impregnated with a
liquid resin system, which is cured following reinforcement impregnation to form the matrix in which
the fibres are embedded. Impregnation is driven by positive applied pressure and/or vacuum. LCM is
widely applied for the manufacture of lightweight components in the automotive, aerospace, marine,
and energy (e.g. blades for wind turbines) industries.
To obtain short cycle times and high component quality in LCM, i.e. fast and complete saturation of the
reinforcement with liquid resin, a suitable process design is required, based on knowledge of material
properties. Darcy’s law relates the phase-averaged flow velocity to the applied pressure gradient,
the dynamic resin viscosity, and the reinforcement permeability for fluid flow. The permeability of
fibrous structures, such as reinforcements, is generally direction-dependent and is described by a
symmetric second-order tensor. Diagonalisation of the tensor leads to three principal permeabilities,
which correspond to the flow oriented along three orthogonal axes, two of which describe the in-plane
permeability.
This document focuses on the experimental characterization of unsaturated in-plane permeability
of reinforcing materials for LCM. As with any kind of experiment, methodological, systematic
and statistical errors may arise. In order to minimize methodological errors caused by different
experimental methods, this document covers the two most common approaches, linear and radial flow
experiments. Systematic errors inherent to these methods are minimized by distinct procedures for
preparing and executing the flow experiments as well as for post-processing the acquired measurement
data as prescribed in this document. Statistical errors are dominated by variations in material
properties, particularly inhomogeneous areal weight and thus, fibre volume fraction of the reinforcing
materials. This document covers well known statistical methods, such as multiple experiments at
repetitive conditions, in order to estimate the uncertainty associated with the results.
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INTERNATIONAL STANDARD ISO 4410:2023(E)
Test methods for the experimental characterization of in-
plane permeability of fibrous reinforcements for liquid
composite moulding
1 Scope
This document specifies test methods for the experimental characterization of in-plane permeability of
fibrous reinforcements for liquid composite moulding. Requirements for test equipment, test methods
and data analysis are detailed, to ensure optimal accuracy and reproducibility of the results.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the cited edition applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 286-1:2010+Cor1: 2013, Geometrical product specifications (GPS) — ISO code system for tolerances on
linear sizes — Part 1: Basis of tolerances, deviations and fits
ISO 2555, Plastics — Resins in the liquid state or as emulsions or dispersions — Determination of apparent
viscosity using a single cylinder type rotational viscometer method
ISO 21920-2, Geometrical product specifications (GPS) — Surface texture: Profile — Part 2: Terms,
definitions and surface texture parameters
ISO 21920-3, Geometrical product specifications (GPS) — Surface texture: Profile — Part 3: Specification
operators
3 Terms, definitions, symbols and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1.1
in-plane permeability
quantitative material parameter of a fibrous reinforcement (a porous medium), relating the phase-
averaged flow velocity of a liquid in the reinforcement to the applied pressure gradient and the dynamic
viscosity of the fluid.
Note 1 to entry: During impregnation of a fibrous reinforcement with a fluid, the permeability of the fibrous
reinforcement, the permeability tensor, K , relates the phase-averaged flow velocity, v , to the applied pressure
gradient, ∇p , and the dynamic resin viscosity, μ , as stated in Darcy’s law.
K
 
v =− ⋅∇p
 
μ
 
1
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ISO 4410:2023(E)
2
As per this definition, the permeability is given in units of square metres (m ). Importantly, the permeability of a
reinforcement depends on the fibre volume fraction and the geometrical fibre arrangement. Because of the
directionality of the fibre arrangement in a reinforcement, the permeability is generally anisotropic. The
principal components of the tensor K , in its diagonal form are referred to as k and k , representing the highest
1 2
and lowest values of the in-plane permeability, respectively.
Note 2 to entry: Permeability is an equivalent parameter defined at the level of an equivalent homogeneous
medium representing an intrinsically heterogeneous material. Darcy’s law has been extended to unsaturated
flow or transient flow, neglecting the effect of dynamic wetting.
3.1.2
unsaturated flow
dynamic flow of a fluid in a porous medium where initially empty (vacuum) pore spaces are filled or an
initially present fluid (e.g. air) is displaced
3.1.3
in-plane anisotropy ratio
characteristic of a material showing different properties in different directions
Note 1 to entry: The in-plane anisotropy ratio, α , is defined here as the ratio of lowest to highest in-plane
k
2
permeability, i.e. α = .
k
1
3.1.4
linear injection
injection of fluid into a porous medium along one short edge of a rectangular geometry, resulting in a
flow along the long edge, with velocity vectors oriented primarily in one direction
3.1.5
radial injection
injection of fluid into a porous medium through a central injection gate, resulting in a flow with velocity
vectors extending radially outward from the gate, in all in-plane directions
3.1.6
race-tracking
locally increased flow velocity in gaps between specimen and mould
3.1.7
slowtracking
locally decreased flow velocity caused by over-compaction of the specimen along the mould edges
3.1.8
orientation angle
angle, β, between the direction of highest flow velocity, k , and a reference direction, which is commonly
1
the production direction of the material
Note 1 to entry: See Figure 2.
3.2 Symbols and abbreviated terms
Symbol Unit Meaning
2
m
A Specimen area (i.e. l multiplied with w for rectangular specimens)
s s s
2
m Constants for the calculation of the principal permeabilities
C
14…
% Coefficient of variation
CV

D
Matrix containing the ()xy,,z data sets of an experiment
e
Eigenvector
Auxiliary functional terms
ff,
12
FS Full scale
2
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ISO 4410:2023(E)
Symbol Unit Meaning
h m Height of the reinforcement specimen
i Counting variable indicating the time step
J Counting variable for experimental configurations of mould height and number
of layers
k Counting variable indicating the measurement data set
2
m Kozeny constants
k and k
C,1 C,2
2
m Average of experimentally measured permeability
k
e
2
m Experimentally determined permeability
k
e
2
0 m Experimentally determined permeability in the defined reference direction
k
e
2
45 m Experimentally determined permeability orientated at an angle of 45° to the
k
e
defined reference direction
2
90 m Experimentally determined permeability perpendicular to the defined refer-
k
e
ence direction
2
−45 m Experimentally determined permeability orientated at an angle of -45° to the
k
e
defined reference direction
2
m Permeability in flow direction
k
x
2
m Permeability perpendicular (in-plane) to flow direction
k
y
2
m Highest in-plane permeability
k
1
2
m Lowest in-plane permeability
k
2
2
m Out-of-plane permeability
k
3
2
m Highest in-plane permeability, adjusted according to the actual fibre volume
k
1,a
fraction
2
m Lowest in-plane permeability, adjusted according to the actual fibre volume
k
2, a
fraction
2
m Permeability tensor
K
m Specimen length
l
s
LCM Liquid composite moulding
2

m
Slope of the trend line correlating x and t
mid
kg Specimen mass (dry)
M
s
n Number of measurement data sets in an experiment
Number of layers of a fibrous reinforcement in a specimen
n
L
Number of sampled data sets in a linear injection experiment
n
T
Number of experiments in a set
N
p
Pa Array of experimental pressure values
∇p Pa Pressure gradient applied across the specimen, i.e. the gauge pressure applied
Pa Pressure drop
ΔP
Pa Time-averaged pressure drop
ΔP
eff
q
Coefficient in paraboloid matrix
q
Array of coefficients from paraboloid matrix
 Coefficient in rotated matrix
q
3
Q m /s Volume flow rate
Q Matrix of paraboloid coefficients
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ISO 4410:2023(E)
Symbol Unit Meaning
3x3 Submatrix of paraboloid coefficients
Q
33
 Matrix of rotated paraboloid coefficients
Q
m Specimen radius
r
s
m Major radial extension of flow ellipse
r
1
m Minor radial extension of flow ellipse
r
2
m Root mean square error of fitting the elliptic paraboloid
E
RMS
f
Pa Root mean square error of the pressure
E
RMS
p
2
m Permeability standard deviation
s
N−1
S Scatter matrix
SVD Singular value decomposition
t
s Time
t
s Array of experimental timestamp values
°C Time-averaged temperature
T
eff
v
m/s Darcy velocity vector
V Coefficient of variation
% Fibre volume fraction
V
f
m Specimen width
w
s
x
m Spatial coordinate in the reference direction of the coordinate frame of the test
rig
m Shortest distance between the inlet region and the flow front position at the
x
mid
midpoint along the specimen width
m Shortest distance between the inlet region and the flow front position along
x
M1
the upper edge of the specimen in linear injection
m Shortest distance between the inlet region and the flow front position along
x
M2
the bottom edge of the specimen in linear injection
y
m Spatial coordinate perpendicular (in-plane) to the reference direction of the
coordinate frame of the test rig
z
s Experimental time
α
Anisotropy ratio ( kk/ )
21
β degrees Angle indicating orientation of K with respect to the defined reference direc-
1
tion of the considered fibrous reinforcement
° Relative angle between the long cutting edge of a specimen for linear flow ex-
δ
periments reinforcement and the defined reference direction of the considered
fibrous reinforcement
2
ε
m Root mean square error of the flow front location x
Critical threshold for the race-tracking error
ε
crit
2
m Measurement error
ε
K
Race-tracking error
ε
R
μ
Pa∙s Dynamic viscosity of fluid
Eigenvalue
λ
Auxiliary quantities
ξ
02…
3
kg/m Material density
ρ
f
φ % Porosity of reinforcement
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ISO 4410:2023(E)
Symbol Unit Meaning
2
kg/m Areal density of a fibrous reinforcement layer (grammage)
w
A
ω
°
Smallest of the three relative angles δ selected for testing
4 Principle
A specimen of the fibrous reinforcement is compressed between two impermeable, parallel plates
at a defined and uniform thickness. Then, a test fluid with known viscosity is injected at constant
injection pressure through a defined inlet region, either a linear injection gate along one specimen edge
or a radial injection gate in the centre of the specimen. This results in a one- or two-dimensional (i.e.
linear or elliptical) flow pattern. While the reinforcement is impregnated, the flow front propagation
is tracked to determine the directional flow front velocity. Data reduction schemes based on Darcy’s
law are applied to calculate in-plane permeability from the flow front velocity, the applied pressure
gradient, the fluid viscosity, and the reinforcement porosity.
5 Design of experiments
5.1 Selection of injection method
The linear and radial test methods are equally applicable to the majority of reinforcements.
NOTE In special cases, each of the methods provides relevant specific advantages and disadvantages
resulting from the different injection strategies:
— In the linear flow method, resin flows along the spe
...