Geometric characterization of polymeric macrofibers

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ABSTRACTThe geometric characteristics of synthetic macrofibers are important because they affect the behavior of fiber-reinforced concrete (FRC). Because there is a lack of specific, relevant publications in Brazil, the European standard EN14889-2:2006 was adopted as a reference to perform the characterization. Thus, an experimental plan was developed to assess the adequacy of testing procedures for the qualification of synthetic macrofibers for use in FRC. Two types of macrofibers were evaluated. The length measurement was performed using two methods: the caliper method, which is a manual measurement, and the digital image analysis method using the ImageJ software for image processing. These aforementioned methods were used to determine the diameter together with the density method, which is an indirect method that uses the developed length obtained by one of the previous methods. The statistical analyses revealed that the length results are similar regardless of the method used. However, the macrofibers must be pre-stretched to maximize the accuracy of caliper measurements. The caliper method for diameter determination has the disadvantage of underestimating the macrofiber cross-section because of the pressure applied by the load claws. In contrast, the digital image analysis method obtains the projected diameter in a single plane, which overestimate the diameter because the macrofibers are oriented with the pressure of the scanner cover. Thus, these techniques may result in false projections of the diameters that will depend on the level of torsion in the macrofibers. It was concluded that both the caliper method using previously stretched macrofibers and the digital imaging method can be used to measure length. The density method presented the best results for the diameter determination because these results were not affected by the method chosen to determine the length.

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# Geometric characterization of polymeric macrofibers _Caracterização geométrica de macrofibras poliméricas_

A. R. E. CÁCERES a

alan.estrada@usp.br

I. GALOBARDES a
Isaac.galobardes@usp.br

M. S. REBMANN a
markusrebmann@usp.br

R. MONTE a
renata.monte@usp.br

A. D. DE FIGUEIREDO a
antonio.figueiredo@usp.br

Abstract

The geometric characteristics of synthetic macrofibers are important because they affect the behavior of fiber-reinforced concrete (FRC). Because
there is a lack of specific, relevant publications in Brazil, the European standard EN14889-2:2006 was adopted as a reference to perform the characterization. Thus, an experimental plan was developed to assess the adequacy of testing procedures for the qualification of synthetic macrofibers
for use in FRC. Two types of macrofibers were evaluated. The length measurement was performed using two methods: the caliper method, which
is a manual measurement, and the digital image analysis method using the ImageJ software for image processing. These aforementioned methods were used to determine the diameter together with the density method, which is an indirect method that uses the developed length obtained
by one of the previous methods. The statistical analyses revealed that the length results are similar regardless of the method used. However, the
macrofibers must be pre-stretched to maximize the accuracy of caliper measurements. The caliper method for diameter determination has the
disadvantage of underestimating the macrofiber cross-section because of the pressure applied by the load claws. In contrast, the digital image
analysis method obtains the projected diameter in a single plane, which overestimate the diameter because the macrofibers are oriented with the
pressure of the scanner cover. Thus, these techniques may result in false projections of the diameters that will depend on the level of torsion in
the macrofibers. It was concluded that both the caliper method using previously stretched macrofibers and the digital imaging method can be used
to measure length. The density method presented the best results for the diameter determination because these results were not affected by the
method chosen to determine the length.

_Keywords_ : fiber-reinforced concrete, synthetic macrofibers, geometric characterization, length measurement, diameter measurement, test method.

Resumo

As características geométricas das macrofibras poliméricas são importantes porque afetam o comportamento do concreto reforçado com fibras
(CRF). Em vista da carência de publicações específicas no Brasil, adotou-se a norma europeia EN14889-2:2006 como parâmetro de referência
para efetuar a caracterização. Assim, foi desenvolvido um plano experimental com o objetivo de avaliar a adequação de procedimentos de ensaio
para a qualificação das macrofibras poliméricas destinadas ao CRF. Foram avaliados dois tipos de macrofibras. As medições do comprimento
se efetuaram por dois métodos: o método do paquímetro, o qual consiste em uma medição manual, e o método de análise de imagens digitais,
empregando o software ImageJ para processamento das imagens. Para a medição do diâmetro, além das metodologias já mencionadas, foi
utilizado ainda o método da densidade, um método indireto que precisa do comprimento desenvolvido obtido por um dos métodos mencionados
anteriormente. Da análise estatística se conclui que ambos os métodos de medição do comprimento são semelhantes e apresentam resultados
equivalentes do ponto de vista estatístico. Porém, salienta-se que as macrofibras precisam ser previamente esticadas para ter maior exatidão nas
medições com o paquímetro. Na determinação do diâmetro, o método do paquímetro tem a desvantagem de subestimar a seção transversal da
macrofibra pela pressão que exercem as garras. Por outra parte, o método de imagens digitais apresenta a projeção do diâmetro em um único
plano, com muita variação dimensional, porque as macrofibras são orientadas com a pressão da tampa do escâner. Assim, podem-se ter falsas
projeções do diâmetro o que também depende do nível de torção das macrofibras. Conclui-se que o método do paquímetro, com o cuidado de
esticar previamente as macrofibras, e o método das imagens digitais podem ser igualmente utilizados para medir o comprimento. Já para determinar o diâmetro da macrofibra, recomenda-se o método da densidade, cujos resultados não são influenciados pelo método escolhido para
determinar o comprimento.

_Palavras-chave:_ concreto reforçado com fibras, macrofibras poliméricas, caracterização geométrica, medição do comprimento, medição do
diâmetro, método de ensaio.

_a_ _Departamento de Engenharia Civil, Escola Politécnica da Universidade de São Paulo, São Paulo, SP, Brasil._

_Received:23 Mar 2015 • Accepted: 25 Jun 2015 • Available Online: 13 Oct 2015_

1. Introduction

The use of fiber-reinforced concrete (FRC) is increasing in the international and Brazilian markets. This technology is associated
with important advantages because the reinforcement is added
to concrete during the mixing process, which reduces the number
of application steps. Moreover, FRC minimizes the technological
limitations of simple concrete, such as brittleness and low deformability when subjected to tensile stresses. However, the fiber-reinforcement efficiency depends on various characteristics, including
geometry (NAAMAN, 2003; PRUDENCIO Jr. et al, 2006; HTUT,
2010; ZĪLE; ZĪLE, 2013). As a result, the geometry of the macrofibers must be parameterized, as is already done for steel fibers in
various international (ASTM A820/A820M:2011; EN14889-1:2006)
and Brazilian standards (ABNT NBR 15575:2007).
The need for parameterization is based on the fact that fiber geometry
affects the reinforcement capacity (NAAMAN, 2003; FIGUEIREDO,
2008). The specific standard for polymeric macrofibers (EN148892:2006) also requires the geometric qualification of such macrofibers
and establishes variation tolerances of the main geometrical characteristics: developed length, equivalent diameter and aspect ratio. However, given the wide variety of potential geometric shapes of polymeric
macrofibers, a number of different procedures can be followed to compare measured values with those reported by the manufacturers. For
this reason, the measurement of the geometric characteristics of the
polymeric macrofibers is much more complex than that of steel fibers,
for which using a caliper is sufficient (FIGUEIREDO et al., 2008).
The European standard EN14889-2:2006 indicates that length must
be measured using a measuring device with a minimum precision of
0.1 mm. Determination of the equivalent diameter is somewhat more
complex. For example, if a manufacturer states that the macrofiber’s
cross-section is circular, the test should be performed using a micrometer with a precision of 0.001 mm if the diameter is greater than 0.3
mm or an “optical measuring device” if the diameter is smaller than 0.3
mm. The omission of the diameter measurement precision in the case
of the optical device is problematic, as are the difficulties encountered
in ensuring the accuracy of measuring the developed length. These
values can be determined with different error levels as a function of
the measurement quality, but the relevant procedure is not completely
established in this standard, although it is the only specific standard
for polymeric macrofibers used in concrete reinforcement.
Because Brazil does not have a specific standard for polymeric
macrofibers and because there are no specific studies focused on
the geometric evaluation of polymeric macrofibers, all these important aspects should be considered for future standardization.
The quality of geometric characterization is also critical for other
important determinations, such as characterization of the mechanical behavior of macrofibers. Therefore, to analyze the reliability of
geometric characterization procedures for the polymeric macrofibers used in FRC, an experimental study was performed with the
objective of identifying reliable methods.

2. Experimental methodology

The experimental study sought to use macrofibers available in Brazil with geometries that are difficult to determine. The macrofibers
employed in the experimental study and the various test methods
used for their characterization are described below.

_2.1 Types of macrofibers_

Two commercially available polymeric macrofibers (denoted A and
B) composed of polypropylene were evaluated in this experiment.
The main characteristics of these macrofibers, according to the information provided by the manufacturers, are shown in Table 1.
Note that the macrofiber aspect ratio is the relationship between
the length (L) and the diameter (D).
Macrofiber A exhibited a cord shape (Figure 1a). These cords may
be broken down into approximately 20 macrofiber bundles (Figure
1b), which present multiple levels of twisting, generating a complicated geometry. Each bundle has one to three filaments bundled
together, so that the bundle is composed of irregular cross-sections along its length. Supplying this macrofiber in the form of bundles coiled in cords is done to facilitate the FRC mixing procedure,
avoiding the macrofiber entanglement associated with a larger aspect ratio (CECCATO, 1998). Thus, the cords may be considered
as fibers with a low aspect ratio that will disperse relatively easily in
the mixture and simultaneously provide the dispersion of filaments
with high aspect ratio. As a result, it is possible to use a macrofiber
with a high final aspect ratio to provide better mechanical performance in the post-cracking behavior of FRC.
Macrofiber B (Figure 1.c) presented an oval cross-section formed
by grouped bundles but with an arrangement unlike that of macrofiber A. Figure 1.d shows the individual bundles of macrofiber
B, which may be composed of one, two, three or more filaments
grouped together. This macrofiber is produced in this way for the
same reason as macrofiber A, i.e., to increase the aspect ratio with
minimal impact on the mixing conditions to ensure homogenization
of the material.

_2.2 Assays_

To determine the length of the macrofibers, two basic methods
were considered: the use of a caliper and the analysis of scanned
images of the material. To determine the equivalent diameter of
the macrofibers, three types of assays were performed: the caliper, digital imaging, and density methods. The density method
is a way of determining the diameter that depends on prior measurements of the length of the macrofiber, which can be performed by one of the two methods mentioned above. The measurements of diameter and length were performed on individual
filaments because they, and not the bundles, interfere with the
post-cracking performance of FRC. A total of 60 macrofibers of
each type considered (A and B) were characterized by each of
the assays listed here.

Table 1– Main characteristics of the
macrofibers provided by the manufacturer

Characteristics Macrofiber A Macrofiber B

Density (g/cm 3 ) 0.91 0.90-0.92

Length (mm) 54 58

Aspect ratio 158

- Information not provided by the manufacturer.

IBRACON Structures and Materials Journal • 2015 • vol. 8 • nº 5 645

Figure 1 – Sample of macrofiber A a) and its separate elements

b); Sample of macrofiber B c) and its separate elements d)

A B

C D

2.2.1 Caliper

The use of a caliper was considered because the European standard EN14889-2:2006 indicates the use of this tool to assess the
geometric characteristics of polymeric macrofibers. A digital caliper

(Digimess, model 100_174BL) with a precision of 0.01 mm was
used herein to obtain the diameter and length. Considering the
standard EN14889-2:2006 and given the similarity of their geometrical configurations, both macrofibers were evaluated as Class
II macrofibers.

Figure 2 – Measurement of the length of the undulated macrofiber A a); Measurement of the

length of the stretched macrofiber A b); Measurement of the length of macrofiber B

c); Measurement of the diameter d)

A B C D

646 IBRACON Structures and Materials Journal • 2015 • vol. 8 • nº 5

Regarding length, only one value was obtained in each measurement. The undulating shape presented by macrofiber A
that results from the level of torsion does not allow for accurate determination of the developed length in their natural state (Figure 2.a). Therefore, they were stretched prior to
measurement to obtain a more accurate value (Figure 2.b).
Unlike macrofiber A, undulation did not affect the length measurement of macrofiber B (Figure 2.c). However, regardless
of the measured macrofiber, care must be taken to avoid
applying excessive pressure, which causes bending of the
macrofibers when using the caliper. The measurement of the
diameter of each type of macrofiber was performed at three
points—at both extremities and at the midpoint (Figure 2.d)—
and two orthogonal measurements of the cross-section were
obtained at each point.

2.2.2 Digital imaging

To minimize the influence of human error in determining the dimensions of the macrofibers, which affects the caliper method,
a method based on the analysis of digital images, which has
been widely used in other studies (SHIN; CHO; KIM, 2008;
DENG; KE, 2010; LI; YI; SHANG, 2012; ÖZNERGIZ et al.,
2014), was also considered. This method also has the advantage of measuring the developed length and thus takes into
account macrofiber bending and torsion. The images were obtained using a desktop scanner (HP, model Scanjet 8350).
First, the macrofibers were individually placed on the scanner in a manner that prevented them from touching each other
during scanning. The macrofibers were then carefully covered
with a black plastic sheet, and the room lights were turned off
to ensure the sharpest possible contrast between the macrofibers and the dark background. A resolution of 2400 ppi (pixels

per inch) was used during scanning to obtain a grayscale image, which was saved in the PNG format. An example of the
generated images is shown in Figure 3.a. Images were subsequently processed and analyzed with the ImageJ imaging
software, which is available in the public domain, programmed
in Java and developed by the National Institutes of Health (“ImageJ”, 2015).
The treatment of images was based on the following procedure:
First, the contrast was adjusted with the Threshold tool (Figure
3.b) to define the boundary between the macrofiber and the
image background. Next, the images were transformed into a
binary color system using the ‘Make Binary’ tool, and two types
of colors were defined: black and white. As seen in Figure 3.c,
the black pixels represent the macrofibers, and the white pixels represent the empty space. Next, the ‘Fill Holes’ tool was
used to fill any voids present inside the macrofiber images,
which can occur in some situations due to light reflection or the
presence of translucent parts of the macrofiber.
The contours of the macrofibers were also softened by employing three stages of erosion (deletion of one pixel from the
contour), followed by three dilation stages (addition of one pixel to the contour). This process was implemented with the tools
‘Erode’ and ‘Dilate’ and allowed for the elimination of much of
the image noise and the generation of well-defined contours
without affecting the projected area. In a few cases, small interventions were still needed for minor corrections of the image to eliminate defibrillated filaments, which could cause an
overestimation of the projected area. After this treatment, the
macrofibers were ready for their dimensions to be measured
(Figure 3.c).
To measure the length, the central axis of the scanned projection
was initially determined using the ‘Skeletonize’ tool. Then, with the
aid of the plugin “Analyze Skeleton (2D/3D)” (ARGANDA-CAR

Figure 3 – Scanned images a); with contrast adjustment b); and ready for evaluation c)

A B C

IBRACON Structures and Materials Journal • 2015 • vol. 8 • nº 5 647

Figure 4 – Skeleton of the fiber. Note that at
the extremity, the fiber presents a bifurcation

RERAS, 2014), the longest path of this skeleton was determined
(shown as dark gray section in the enlarged detail of Figure 4).
Note that performing a correction was necessary at both ends of
the longest section because the definition of the central axis results
in a division in the shape of a “Y” at the extremities (Figure 4). Furthermore, it was still necessary to develop a method to smooth the
longest path because the pixel-in-pixel measurements may overestimate the actual length by up to 8%. Finally, the diameter of the
macrofiber was obtained by dividing the total projected area by the
developed length, where the area was determined by the ‘Analyze
Particles...’ tool of the ImageJ software.
The results obtained in the form of pixels were converted to millimeters using a conversion factor of 0.0106 mm/pixel. This value
was determined by scanning a calibrated ruler (Hirox digital microscope ruler, model KH-7700).

2.2.3 Density method

The density method, which is also included in the European standard EN14889-2:2006, is an indirect method and allows the average diameter of the macrofiber to be obtained using Equation 1.
This equation expresses the relationship between different macrofiber parameters: diameter (D), length (L), mass (m) and density (ρ),
where the units of these parameters must be mutually compatible.

## (1)

To estimate the diameter using this method, it is necessary to determine the developed length of the macrofiber with one of the
methods presented above. Determination of the macrofiber mass
was performed individually on an analytical balance with a precision of 0.0001 g (Metler-Toledo, model AB204-S). Finally, the density of the macrofibers was evaluated using a helium gas pycnometer (Multipycnometer Quantachrome MVP 5DC) at 26 °C. Three
samples of chopped macrofibers, each weighing approximately 30
g, were used to evaluate the density of both macrofibers. In addition to geometrical measurements, the density of the macrofibers
is also useful with regard to the amount of macrofibers incorporated in the concrete (NAAMAN, 2003).

3. Experimental results and analysis

The experimental results obtained for the diameters and lengths of
the macrofibers are presented and analyzed according to the dimensional tolerances specified by the standard EN14889-2:2006,
which is specific for polymeric macrofibers. This enables comparison of requirements established for the material. These results are

Table 2 – Results of measurements with the caliper

Macrofiber A

D1 (mm) D2 (mm) De (mm) L (mm) λ

Mean 0.24 0.24 0.24 54.07 249.66

SD 0.07 0.07 0.07 0.63 104.34

CV (%) 28.30 28.00 27.40 1.20 41.80

max 0.36 0.37 0.37 55.49 730.40

min 0.07 0.08 0.08 52.71 146.37

Macrofiber B

D1 (mm) D2 (mm) De (mm) L (mm) λ

Mean 0.28 0.28 0.28 59.10 213.66

SD 0.02 0.02 0.02 0.70 17.91

CV (%) 7.60 8.10 7.10 1.20 8.40

max 0.31 0.32 0.31 60.02 282.86

min 0.22 0.20 0.21 58.09 189.66

648 IBRACON Structures and Materials Journal • 2015 • vol. 8 • nº 5

organized according to the type of test performed (caliper, digital
imaging, and density methods).

_3.1 Caliper_

Table 2 summarizes the results of the geometric characteristics
evaluated with the caliper. Because of the space constraints in this
work, individual determinations obtained in samples of 60 macrofibers were excluded. The results presented for macrofibers A and B
are as follows: the average diameters measured at the extremities
and in the middle section of the macrofibers (D1); the average diameters measured at the same points but on an orthogonal section
(D2); the equivalent diameter (De) calculated as the average of D1
and D2; the length (L); and finally, the aspect ratio (λ) or the ratio
between L and De. In addition to the average results, the standard
deviation (SD), coefficient of variation (CV), maximum value (max)
and minimum value (min) are also shown.
In the case of macrofiber A, the nominal diameter was not provided
by the manufacturer; therefore, this value was calculated from the
nominal values of length (54 mm) and aspect ratio (158), which
were provided. In this case, the nominal diameter was equal to
0.34 mm. For macrofiber B, neither the equivalent diameter nor
the aspect ratio was provided by the manufacturer. Thus, it was
not possible to compare the measurements with a nominal value
or to evaluate the dimensional tolerances relative to the declared
equivalent diameter. It should be noted that this omission does not
satisfy the EN14889-2:2006 standard, which indicates that these
values must be provided by the manufacturer or its sales representative.
As previously mentioned, macrofibers A and B were classified as
Class II according to the European standard EN14889-2:2006.
This standard states that the maximum variation of the individual
diameter and individual aspect ratio in relation to the nominal value
is ±50%. The maximum variations of the mean diameter and mean
aspect ratio compared to the nominal values are ±5% and ±10%,
respectively. For length, the maximum variations of the individual
values and the average in relation to the nominal values must be
±10% and ±5%, respectively.
When applying the dimensional tolerance criteria of the European
standard EN14889-2:2006 for macrofiber A, 15% of the macrofibers were found to have individual diameters differing from the
nominal value by ±50%. The average diameter was within the ±5%
tolerance. Regarding the individual aspect ratio, 37% of the macrofibers presented values exceeding the tolerance of ±50%. The

average aspect ratio also presented a difference greater than the
±5% tolerance. Regarding length, all macrofibers presented values
within the tolerances required for the individual value in relation to
the nominal value. Similarly, the average length presented a variation smaller than the tolerance of ±5%. Thus, macrofiber A can only
be considered to be in accordance with the tolerances of the European standard EN14889-2:2006 with respect to its length.
In the case of macrofiber B, it should be noted that the manufacturer did not provide nominal values of the diameter and aspect
ratio. Therefore, no benchmark was available for applying the dimensional tolerances of the European standard EN14889-2:2006.
As a result, the evaluation was performed only for length, which allowed the conclusion that all macrofibers met the specifications of
the standard regarding both individual and average length values.

_3.2 Digital imaging_

Table 3 shows the geometric characteristics of the macrofibers
evaluated by digital imaging. For macrofibers A and B, the results
presented are as follows: the measured average diameter of the
macrofiber on a single plane according to the projection of the
scanned image (D), the developed length (L), and finally, the aspect ratio (λ) considering the ratio between L and D. For all average
results, the standard deviation (SD), coefficient of variation (CV),
maximum (max) and minimum (min) values are also presented.
Only the projected macrofiber image on a single plane was considered when calculating the diameter by the digital imaging method.
Therefore, it was not possible to obtain a more accurate assessment because the macrofibers had variable cross-sections along
their lengths. This is especially true for macrofiber A, which is thinner in some parts and thicker in other parts, according to the exhibited torsion (Figure 5).
According to the dimensional tolerance criteria of the European
standard EN14889-2:2006, it was found that 3% of the macrofiber
A presented individual diameters that did not meet the tolerance
of ±50% in relation to the nominal value. Additionally, the mean diameter falls outside the tolerance of ±5% in relation to the nominal
value. Regarding the individual aspect ratio, all macrofibers are
within the maximum tolerance of ± 50%. The mean aspect ratio
also lies within the maximum permitted tolerance of ±10%. All individual values of the length are within the tolerance of ±10%. The
average length is also within the tolerance of ±5% in relation to the
nominal value. Therefore, macrofiber A is within the tolerances of
European standard EN14889-2:2006 only with respect to length.

Table 3 – Results of measurements with digital imaging

Macrofiber A Macrofiber A

L (mm) D (mm) λ L (mm) D (mm) λ

Average 54.03 0.37 149.70 59.65 0.32 189.71

SD 0.76 0.07 26.05 0.80 0.03 15.28

CV (%) 1.40 17.90 17.40 1.30 10.00 8.10

max 55.66 0.56 234.11 60.88 0.43 215.69

min 52.57 0.23 96.25 58.29 0.27 141.21

IBRACON Structures and Materials Journal • 2015 • vol. 8 • nº 5 649

Figure 5 – Variation of the diameter along

the length of macrofiber A due to torsion

In the case of macrofiber B, because no information was provided by
the manufacturer regarding either the diameter or aspect ratio, only
the length was evaluated according to standard EN14889-2:2006.
All macrofibers were found to comply with the requirements of the
standard with regards to both the individual and average lengths.

_3.3 Density method_

The results obtained for the macrofiber density using the helium
gas pycnometer assay are shown in Table 4. This table presents

Table 4 – Density of the macrofibers according

to the helium gas pycnometer

ρ i
Macrofiber Sample
(g/cm 3 )

ρ
(g/cm 3 )

A 1 0.937 0.930

A 2 0.934 0.930

A 3 0.921 0.930

B 1 0.939 0.935

B 2 0.934 0.935

B 3 0.933 0.935

the density of each sample (ρi) and the average density for each
of the macrofibers (ρ). These results are essential for determining
the geometric characteristics of the macrofibers using the density
method.
Table 5 lists the geometric characteristic results of macrofibers A
and B evaluated by the density method: the mass, the developed
length by the digital imaging method (Li), the length by the caliper
method (LP), the equivalent diameter (De) calculated using Equation 1, and the aspect ratios (λ) calculated considering both Li and
Lp. For all average results, the standard deviation (SD), coefficient
of variation (CV), maximum (max) and minimum (min) values are
also presented.
The average mass values for each macrofiber are an order of
magnitude larger than the precision of the scale (0.0001 g). The
masses of macrofiber A ranged from 0.0017 g to 0.0103 g, with

Table 5 – Results of measurements with the density method

Macrofiber A Macrofiber A

Mass

(g)

Li
(mm)

De λ LP
(mm) (mm)

De
λ
(mm)

Average 0.0043 54.03 0.33 171.34 54.07 0.33 171.67

SD 0.0015 0.76 0.06 31.56 0.63 0.06 32.65

CV (%) 35.3 1.40 17.50 18.40 1.20 17.60 19.00

max 0.0103 55.66 0.51 254.40 55.49 0.51 265.76

min 0.0017 52.57 0.21 105.36 52.71 0.21 104.70

Macrofiber B Macrofiber B

Mass

(g)

Li
(mm)

De λ LP
(mm) (mm)

De
λ
(mm)

Average 0.0046 59.65 0.32 185.74 59.10 0.32 183.18

SD 0.0004 0.80 0.01 6.16 0.70 0.01 6.49

CV (%) 8.8 1.30 4.00 3.30 1.20 4.10 3.50

max 0.0057 60.88 0.36 200.09 60.02 0.36 196.39

min 0.0038 58.29 0.30 167.74 58.09 0.30 165.98

650 IBRACON Structures and Materials Journal • 2015 • vol. 8 • nº 5

a coefficient of variation of 35.3%, which demonstrates that
when separating the individual filaments of the bundles, the
filaments present variable sections with great mass variation
between individual macrofibers. In the case of macrofiber B,
the masses vary from 0.0038 g to 0.0057 g, with a coefficient
of variation of 8.8%, corresponding to a relatively small variation in the mass.
Using the density method, the average equivalent diameter of
each macrofiber was calculated directly. The ranges of variation
of this diameter were similar when using the length obtained
by either the digital imaging method (Li) or caliper method (LP):
from 0.21 mm to 0.51 mm with a mean value of 0.33 mm for
macrofiber A and from 0.30 mm to 0.36 mm with a mean value
of 0.32 mm for macrofiber B. This similarity was confirmed by
applying the paired t-test for both macrofiber A and B, in which
the difference between the values of the average diameter is
essentially zero at a 95% confidence level. When the developed length obtained by the digital imaging method was used,
the values of the aspect ratio were 171.34 and 185.74 for macrofibers A and B, respectively. However, when the length measurements obtained via the caliper method were used, a slight
variation in the aspect ratio was observed, resulting values of
171.67 and 183.18 for macrofibers A and B, respectively.
Considering the tolerances of the standard EN14889-2:2006,
all individual diameters of macrofiber A are within the tolerance
of ±50% when compared with the nominal value. Similarly, the
average diameter value is within the tolerance of ±5%. Regarding the individual aspect ratio, 8% of the macrofibers are
outside the ±50% tolerance, and the average aspect ratio is
within the tolerance of ±10% compared to the nominal value.
Therefore, macrofiber A does not comply with the European
standard because 8% of the macrofibers were not within the
tolerance level for the individual aspect ratio.
For macrofiber B, it was not possible to determine whether the
diameter obtained by the density method satisfies the dimensional tolerances established by European standard EN148892:2006 because the nominal diameter was not reported by the
manufacturer. This value is important and should be provided
by the manufacturer.

4. Comparative analysis of the methods

A comparative analysis of the diameter and length values of
the macrofibers obtained by the different test methods is presented here. Additionally, the experimental results are compared with the data provided by the manufacturers. The length
results determined with the caliper and digital imaging methods reported first, followed by the experimental results for the
diameters obtained using the three methods applied (caliper,
digital imaging and density).
Statistical analysis was performed using the software MINITAB
17. To evaluate whether the results had a normal distribution,
the Anderson-Darling normality test was applied at a 95% confidence level. The results were also analyzed for their degree
of distortion with respect to a symmetric distribution by calculating the skewness coefficient. When this coefficient is close
to zero, the distribution can be considered symmetrical. For
positive or negative skewness coefficients, the distribution is

considered asymmetrical to the right or to the left, respectively.
A box plot was used as a criterion for the detection of spurious
values. In this method, the spurious values are those included
outside the upper and lower limits of the box (MONTGOMERY;
RUNGER, 2004).

_4.1 Comparison of the lengths_

The distribution curves of the length results obtained for each
type of macrofiber are presented below (Figure 6) for both the
caliper method and the digital imaging method.
The descriptive analysis of the length data revealed that for
macrofiber A, the distribution results obtained using both methods follow a normal distribution and that the existence of spurious values was not observed. At a 95% confidence level, the
average length of the caliper method was between 53.09 mm
and 54.02 mm and that of the digital imaging method was between 53.83 mm and 54.22 mm. Both ranges also include the
length declared by the manufacturer: 54 mm.
When performing the data distribution analysis, the results for
macrofiber B indicated non-normality, clearly revealing two distinct populations regardless of the method used (Figure 7.a
and 7.b). The existence of two distinct populations was attributed to the method used to collect the samples. The macrofibers were provided by the manufacturer in the form of large
billets (group of macrofilaments, Figure 7.c), and sampling
consisted of random selection of two of these billets from a total of approximately 100 billets, which usually come in a single
package. The final sampling consisted of randomly selecting
thirty macrofibers from the first billet and another thirty from
the second billet. The confirmed existence of two populations
demonstrates the variability in production, specifically in the
cutting of the billet.
Thus, sampling performed as described above is inappropriate, and therefore, opening all billets contained in a package,
mixing the loose macrofibers, and then randomly collecting
the macrofibers for analysis is recommended. Nevertheless,
it could be concluded that the lengths of both groups exceed

Figure 6 – Distribution curves of length

for macrofibers A and B

IBRACON Structures and Materials Journal • 2015 • vol. 8 • nº 5 651

the length specified by the manufacturer: 58 mm. At a 95%
confidence level, the average value is between 58.92 mm and
59.28 mm by the caliper method and between 59.44 mm and
59.86 mm by the digital imaging method.
According to the paired t-test, comparing the length of macrofiber A
measured by the caliper method with that measured by the digital
imaging method did not reveal a significant difference. The average value of the difference was found to be essentially zero with a
95% confidence interval of -0.11 mm to 0.18 mm, confirming that
these methods can be considered equivalent. This similarity occurred because the individual macrofibers of macrofiber A were
stretched prior to being measured with the calipers (Figure 2.b).
For macrofiber B, the same comparative analysis via the paired
t-test revealed a slight variation between the methods. The difference in the means was found to range from -0.62 mm to -0.48 mm.
The fact that both values are negative confirms that the length of
macrofiber B determined by the caliper method was always smaller
than that of the digital imaging method. As a result, the averages
were found to be significantly different at a 95% confidence level. It
is possible that this difference arises from the fact that these macrofibers were measured directly (without stretching) with the cali

pers, which led to a slight decrease in the length despite applying
the smallest possible pressure between the caliper ends (Figure
2.c). Because these macrofibers did not exhibit undulation similar
to that of macrofiber A, it was not necessary to stretch them prior
to performing the measurement. However, the smaller difference
observed in the caliper results indicates that stretching is a good
practice, even when the macrofiber presents no tortuosity.

_4.2 Comparison of the diameters_

The statistical analysis based on the paired t-test is first presented
for the diameter obtained using the density method. This method
was performed to allow for comparison with the diameter values
found using the length obtained by the caliper and digital image
analysis methods. For macrofiber A, the results do not differ significantly. It was observed that the difference in averages was practically zero with a 95% confidence interval of between -0.000382
mm and 0.000457 mm, confirming that both methods for determining the length may be used to calculate the diameter.
When the same analysis was applied to the results of macrofiber B, a slight variation in the diameter determined by the

Figure 7 – Histograms of the length distribution of macrofiber B by the caliper
method a) and by the digital imaging method b); Billet or group of macrofibers B c)

A B

652 IBRACON Structures and Materials Journal • 2015 • vol. 8 • nº 5

Figure 8 – Distribution curves of the diameters

of macrofibers A and B according

to the three methods

density method was observed. The difference in averages was also
close to zero but exhibited a 95% confidence interval of -0.001706
mm to -0.001318 mm. The average diameter obtained when using the caliper-determined length was slightly greater than that
obtained using the digital imaging method, although these values
were statistically equivalent. As previously discussed, this verification is due to the fact that the lengths of the macrofiber B were
slightly shortened during the measurement because they were not
stretched beforehand. Again, it can be concluded that stretching
the macrofiber when measuring its length using calipers is a very
important practice, even when the macrofibers do not exhibit undulation. Based on this information and the present comparative
analysis, the diameter obtained by the density method was used
as a function of the developed length according to the digital imaging method for both macrofibers.
The distribution curves for the diameter results of the different macrofiber types (Figure 8) determined using the different methods
(caliper, digital imaging and density) are presented below.
When performing the descriptive analysis of the distribution of
the caliper-determined diameters of macrofiber A, asymmetry
was verified, which did not confirm a normal distribution. However, no spurious values were present, and the average values
were very low compared to the other two methods. For the digital imaging method, a normal distribution was confirmed, with a
single spurious value. For the density method, no normal distribution was found and five spurious values were present because this method depends on measurement of the macrofiber
mass, which in itself is an additional source of variability. This
variation may also be ascribed to the possible variation in the
macrofiber sections; some may have been thicker than others,
which might have skewed the distribution obtained when the
bundles were separated.
For macrofiber B (Figure 8), the diameter distributions of all three
methods did not present normality, indicated skewness and included spurious values. This indicates that macrofiber B also
present irregular cross-sections and that the differences between
two macrofibers may be substantial. The fact that there are two

well-defined populations also has influenced the various analytical
methods used in this study.
For macrofiber A, at a confidence level of 95%, the average diameter obtained using the caliper method was between 0.22 mm and
0.26 mm, that of the digital imaging method was between 0.35 mm
and 0.39 mm, and that of the density method was between 0.31
mm and 0.34 mm. The nominal diameter of 0.34 mm is only within
the mean diameter variation of the density method. For macrofiber
B, with a confidence level of 95%, the average diameter obtained
using the caliper method was between 0.27 mm and 0.28 mm,
that of the digital imaging method was between 0.31 mm and 0.33
mm, and that of the density method was between 0.3153 mm and
0.3218 mm. However, it was not possible to compare these values
with a nominal diameter because no value was reported by the
manufacturer.
Comparing the diameter distributions of the three methods for both
macrofibers (Figure 8), the results obtained by the caliper method
were found to be smaller than those acquired by the other two
methods. This difference can be attributed in part to the decrease
in diameter resulting from the pressure exerted by the caliper
load claws because the operator may squeeze the sample when
performing the measurement. Furthermore, the caliper has a tendency to measure the smaller cross-section when the macrofiber
has an elliptical shape, as illustrated in Figure 9. As a result, the
average diameter of the macrofiber may be underestimated when
determined using this method. Although high-precision equipment
is required to be used in the measurement (a micrometer with precision of 0.001 mm is recommended by the European standard
EN14889-2:2006), this method will always underestimate the
cross-section because of the preferred point of measurement on
the macrofiber.
For macrofiber B, the digital imaging and density methods returned
almost the same average value, although the results exhibited different degrees of dispersion. Thus, another difference between
these methods is the degree of dispersion. The digital imaging

Figure 9 – High-probability position a),
low-probability position b), and improbable

position c) for the measurement of the

equivalent diameter of a macrofiber

with an elliptical cross-section

A B C

IBRACON Structures and Materials Journal • 2015 • vol. 8 • nº 5 653

Figure 10 – Variation of the projected
diameter of the macrofiber by the digital

imaging method a); Cross-section of a
macrofiber with branching, which may result

in an overestimation of the diameter b)

A B

method was observed to have the highest dispersion and the highest average values. This relatively high average value may be explained by the fact that the macrofibers have an oval cross-section
and may thus be subject to overestimation of the mean diameter
during the image scanning process. Because the macrofibers are
compressed by the scanner cover, it is possible that orientation
may occur because of the oval shape. Thus, unlike the caliper
method, which underestimates the average diameter, this method
may result in an overestimation. Together with the macrofiber torsion level, this orientation causes in projections with variable diameters (Figure 10.a).
Furthermore, regions with low contrast along the edges of the macrofiber could be interpreted as part of the projection. When the contrast between the macrofiber and the background is not sharp, the
image-treatment process can amplify the diameter. The fact that
some macrofibers present regions of branching along their structure (Figure 10.b), which can be interpreted as a closed macrofiber
in the projection area during image treatment, can also lead to an
overestimation of the diameter.
The equality of variance test for macrofiber A revealed that the variances can be considered statistically equivalent with a confidence
level of 95% by the ‘t’ test for all three methods used. For macrofiber B, the equality of variance test showed that the caliper and
digital imaging methods have wide ranges of variation, unlike the
density method, which has less variation. The three methodologies
are slightly different in terms of variance and were considered statistically different by the ‘t’ test.

5. Conclusions

The following conclusions can be drawn from the results of
this study:

n Regarding length, the criteria of standard EN14889-2:2006

may be utilized to evaluate polymeric macrofibers. The variation of this parameter is very low because of the level of control

in macrofiber production, which guarantees a homogeneous
cut and maintains a uniform length. However, a good sampling
procedure is necessary to avoid variation in the results, which
can occur as a function of the selected billet. The uniformity
of the length is important because fiber length should be compatible with the maximum aggregate diameter to provide good
reinforcement performance in FRC (FIGUEIREDO, 2011). To
evaluate dimensional tolerances, it is essential that the manufacturer provides the nominal length, diameter and aspect ratio
values, which does not always happen.

n For the determination of the length for macrofiber A, the cali

per and digital imaging methods produced statistically similar
results at a 95% confidence level. To obtain these results, it
was necessary to stretch the macrofibers prior to measuring
them with the caliper, which did not allow them to bend when
exposed to the pressure applied by the instrument and ensured
that the final results were similar. For macrofiber B, which was
not subjected to the same stretching procedure of A, a small
but significant difference was found, and the values obtained by
the digital imaging method were larger than those of the caliper.
This difference demonstrates the independence of the digital
imaging method of the manual procedures of the operator.

n In light of the results presented above, the macrofibers were

carefully measured via the caliper method, and both of the
methods for determining the length studied here can be considered equally valid. Although the method of digital imaging
analysis is currently relatively labor intensive, in the future,
automated high-speed analysis for continuous sampling systems may be possible. However, this method will be difficult
to use when there is a need for individualized control of the
macrofibers.

n Calculating the diameter by the density method is the most rec

ommended method to determine the average diameter. This
method is not affected by the methods used to obtain or process
the images, as is the digital imaging method, nor is it affected by
the pressure exerted by the caliper load claws, as in the case of
manual measurement with calipers. However, the density method requires an appropriate analytical balance to determine the
mass of the macrofibers and a helium gas pycnometer to determine the density. Regardless of whether the lengths obtained
by either the caliper or the digital imaging method were used,
the resulting diameters were statistically equivalent at the 95%
confidence level, demonstrating the robustness of this method.
It should be noted that the determination of the diameter or the
associated average cross-sectional area is extremely important
because of the effect that this parameter has on the mechanical
behavior of the macrofiber.

n It is important to establish geometric characterization methods

for polymer macrofibers that can be applied in everyday quality control because the information provided by manufacturers
may be insufficient or even incorrect and the user should not
be forced to rely only on this information. It should be noted
that not all results were consistent, i.e., a fiber may be considered to be in conformance by one method and to be in nonconformance when using a different method. This variability
clearly demonstrates the importance of establishing reliable
measurement methods in future standards that are specific for
polymeric macrofibers.

654 IBRACON Structures and Materials Journal • 2015 • vol. 8 • nº 5

6. Acknowledgements

The authors would like to thank the São Paulo Research Foundation (Fundação de Amparo à Pesquisa do Estado de São
Paulo – FAPESP) for the financial support provided via the postdoctoral fellowship to the second author (process 2014/24410-6)
and the doctoral scholarship provided to the third author (process
2012/21134-2).
The authors also thank the Foundation for Technological Development of Engineering (Fundação para o Desenvolvimento Tecnológico da Engenharia) project (USP/BRASKEM) module 1: Mechanical characterization of polypropylene macrofibers.

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