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Transition points in steel fibre pull-out tests from magnesium
phosphate and accelerated calcium aluminate binders
P. Frantzis
a,*
, R. Baggott
b
a
Composites Technology Consultant, 5/25 Sefton Park Road, Liverpool L8 3SL, UK
b
Department of Surveying, University of Salford, Salford M5 4WT, UK
Received 3 November 2000; accepted 11 July 2001
Abstract
Results are reported on the pull-out characteristics of two distinct types of steel fibre from two different rapid strengthening
matrices, magnesia phosphate and accelerated calcium aluminate. The procedure incorporated a novel method of identifying the force
necessary to initiate whole fibre movement relative to the matrix, one of the key transition points in the force/displacement rela-
tionship. Significantly different force/displacement relationships were obtained with each fibre/matrix combination. The two types of
fibre were of similar length and section diameter but one type was of regular circular cross-section and smooth surface finish whereas
the other type was of irregular kidney shaped cross-section and rough surface finish. The two different matrices had similar strengths
but were completely different chemically. The results are discussed in the context of transition points of fibre/matrix interaction.
2002 Elsevier Science Ltd. All rights reserved.
Keywords: Rapid strengthening cementitious binders; Transition points; Adhesional (chemical) debonding; Frictional bonding; Initiation of fibre
movement; Fibre pull-out; Dynamic friction
1. Introduction
The mechanical property benefits achieved by fibre
reinforcing cementitious matrices are determined to a
large extent by the pull-out behaviour of fibres once the
matrix has cracked. In practical application of com-
posites this behaviour is complex and the starting point
in developing micromechanical models is the charac-
terisation of the simplest pull-out situation: that of a
single fibre aligned and pulled out perpendicular to a
matrix surface. This characterisation has been the sub-
ject of considerable research [1–10] which has now
advanced sufficiently to allow theoretical treatment en-
abling the individual fibre pull-out stress/displacement
relationships to be incorporated in composite behaviour
models.
The processes occurring between the transition points
are envisaged as follows:
•Fibre/matrix adhesional debonding comprises grad-
ual fibre matrix separation starting at the entrance
point of the embedded fibre into the matrix.
•The partially de-adhered zone (often referred to as
the debonded zone in the literature) is subjected to
frictional resistance to local relative movement be-
tween fibre and matrix.
•The completion of adhesional debonding corre-
sponds to the elimination of any chemical bonding
along the length of the fibre.
•At this stage pull-out forces may be resisted by static
friction and probably mechanical interlocking (fric-
tional bonding) sufficient to prevent any fibre move-
ment.
•When sufficient force is applied the subsequent initia-
tion of fibre movement is resisted by dynamic fric-
tion. This could be made up of several components
(such as micro and macro matrix shearing and fibre
deformation).
However, there are still details of the simple pull-out
condition that have not been resolved completely.
These particularly concern the location on pull-out
*
Corresponding author. Tel.: +44-151-733-0470; fax: +55-151-733-
0470.
0958-9465/03/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.
PII: S0 9 5 8 - 9 4 6 5 ( 0 1 ) 0 0 0 5 3 - 1
Cement & Concrete Composites 25 (2003) 11–17
www.elsevier.com/locate/cemconcomp
force/displacement curves of the initiation of fibre/
matrix adhesional debonding, the completion of ad-
hesional debonding and subsequent initiation of fric-
tional bonding. Also the initiation of fibre movement
and the maximum pull-out force, otherwise known as
the basic phenomenological transition points. The in-
fluence of certain individual fibre parameters on the
position of these points and the contribution of tensile/
compressive interface stresses operating in addition to
the imposed shear stress have been made on the basis
of assumptions derived from the shape of the pull-out
curves.
The majority of the investigations into single fibre
pull-out in cementitious materials have been undertaken
with ordinary Portland cement based matrices. Al-
though it can be anticipated that many features of such
tests will be of general application, numerical values will
vary from matrix to matrix as may particular pheno-
mena. Magnesia phosphate cements and accelerated
calcium aluminate cements offer very rapid strength
development. For example compressive strengths of up
to 25 MPa can be obtained within 1 h of mixing, which
has advantages in rapid repair applications. The incor-
poration of fibres in such materials provides the same
range of benefits as with normal cements [11]. No data
has been reported in the literature of fibre pull-out
characteristics from such matrices.
A considerable variety of fibres is now available as
reinforcement. For instance, steel fibres have excellent
reinforcing features in terms of strength and stiffness. In
addition they are available in a wide range of geometric
shapes which provide different anchoring capability.
Although considerable amounts of data on pull-out
behaviour have been reported, a conceptual framework
relating transition points with fibre/matrix characteris-
tics, to the best knowledge of the authors, has not yet
been presented.
This paper reports the results of work directed at the
various issues referred to above and presents data on
the pull-out of two types of steel fibre. In particular, the
behaviour of fibres of similar length and cross-section
dimension but with significantly different geometry,
from two chemically different matrices is discussed. A
novel feature of one of the pull-out tests is the incor-
poration of a device to record the exact initiation of fibre
movement. The results are placed in the context of
transition points along the force/displacement curve and
fibre anchorage capability.
The main objectives of this study were:
•To identify the force at which the completion of ad-
hesional debonding and subsequent initiation of fric-
tional bonding occurred.
•To identify the force at which the initiation of fibre
movement occurred, that is the transition to dynamic
friction; this point is subsequently referred to as ‘‘the
onset of fibre pull-out’’.
•To compare the overall force/pull-out behaviour of
the four different systems.
2. Experimental procedure
2.1. Materials
One type of matrix was a magnesia phosphate based
cement [12], namely ASR-1 supplied by FEB Interna-
tional plc, Manchester, UK, whereas the other was an
accelerated calcium aluminate cement, namely Ultra-
crete RSC-1 supplied by Instarmac Repair Services,
West Midlands, UK. One type of fibre was a drawn low
carbon steel of regular section, smooth-surfaced round-
shaped, 25 mm long and diameter 0.5 mm, the other was
a melt overflow chromium stainless steel alloy fibre, of
irregular section, rough-surfaced kidney-shaped, 25 mm
long and variable maximum cross-section dimension
averaging around 0.4 mm. Both types were supplied by
Fibre Technology, Nottingham, UK. The data reported
are for fibre surfaces in the as-received condition.
2.2. Test specimens
Type 1: In this specimen type the fibre was embedded
into two matrix blocks prepared with a central region of
free fibre, Fig. 1(a).
Type 2: The matrix was cast into a mould with a lo-
cating hole and external jigs to ensure correct fibre
alignment, that was central and parallel to the block
faces. Additional locating holes enabled an embedded
insulated wire to be located making electrical contact
with the embedded end of the fibre. The wire had to be
insulated to eliminate short-circuit due to conductivity
of the matrix. Slight axial pressure was applied along the
Fig. 1. (a) Basic pull-out test specimen configuration, and (b) Modified
pull-out test specimen configuration with electrical instrumentation.
12 P. Frantzis, R. Baggott / Cement & Concrete Composites 25 (2003) 11–17
fibre to maintain fibre/sensor wire contact during cement
hardening. The resulting specimen was therefore an-
chored in a single block of matrix with a free fibre end
for subsequent gripping (Fig. 1(b)). Fibre embedment
length of up to 14 mm was used in both types of spec-
imen.
2.3. Pull-out tests
Type 1: Both matrix blocks were loaded via screw
tightened plate grips on that part of the matrix block
free from fibre.
Type 2: The matrix block was loaded via screw
tightened plate grips acting on that part of the matrix
block sufficiently beyond the fibre to ensure freedom
from grip induced compressive forces along the fibre
length. The free end of the fibre was clamped (using non-
conducting pads between fibre and grip) as close as
possible to the matrix. At the beginning of the test the
circuit was completed via the exposed section of fibre
and its resistance continually monitored using a volt-
meter, V. The onset of fibre pull-out was identified by
the instantaneous increase in electrical resistance. Force
and displacements were measured by the test machine
load cell and cross-head movement transducer. The use
of the electrical device accounted for the high accuracy
of the method. Slip between grips and the matrix block
was eliminated with the set up used since the force that
would induce slippage was found to be much greater
than that at fibre onset.
Tests were undertaken 3 h after casting the matrix
using a computer-controlled Instron tensile-testing
machine. The cross-head movement was taken at a
constant rate of 0.5 mm/min recording force and dis-
placement continuously.
3. Results and discussion
3.1. Pull-out curves
Figs. 2 and 3 illustrate the shape of the typical pull-
out curves obtained for the four systems.
The four types of curves are quite distinct, the char-
acteristic differences being observed at all embedded
lengths. It can be seen in Fig. 2(a) that there are three
stages of deformation with the kidney section fibres
embedded in magnesia phosphate. A linear region, part
O–A, followed by a rising curve of decreasing gradient
up to the maximum force, part A–B, which in turn is
followed by a linearly decreasing force/displacement
region, part B–C. Points A, B and C are not determined,
merely they are reference points on the curves distin-
guishing a change in appearance. Part A–B shows a
gradually increasing stick-slip behaviour (repetitive fibre
obstruction followed by rapid movement) which devel-
ops into a regular, relatively large amplitude. Stick-slip
deformation in part B–C was an approximate linear
relationship between force and displacement. The onset
of pull-out, point L, occurs significantly before that of
maximum force in the early part of region A–B.
With round fibres in magnesia phosphate (Fig. 2(b))
the linear region O–A is followed by region A–C, initi-
ated after a rapid drop in force, region A–B, and pro-
ceeding with an increasing amplitude of stick-slip and
a non-linear force/displacement gradient, region B–C,
indicating an increase in localised resistance as pull-out
progressed. The onset of pull-out occurred at the maxi-
mum force, points A and L.
In the case of the calcium aluminate matrix, the
kidney section fibres were pulled out with a similar
overall curve shape to that of pull-out from magnesia
Fig. 2. Typical pull-out force/displacement curves with the magnesia phosphate matrix: (a) kidney fibre, and (b) round fibre.
P. Frantzis, R. Baggott / Cement & Concrete Composites 25 (2003) 11–17 13
phosphate (Fig. 3(a)). However, the onset of pull-out,
point L, occurred earlier within the non-linear region of
deformation, region A–B. Another difference was the
smoother nature of the curve during the linearly de-
creasing force/displacement region compared to the
pronounced stick-slip with the magnesia phosphate.
The round fibre started to pull out from the calcium
aluminate matrix well before the maximum force was
reached (Fig. 3(b)). Although there was a distinct tran-
sition at maximum force there was no catastrophic drop
in force before the normal frictional region which oc-
curred with larger stick-slip displacements than with
magnesia phosphate.
Finally, a substantially greater maximum pull-out
resistance was observed with the kidney shaped fibres
than with the round fibres and sufficient resistance to
pull-out could be developed to fracture fibres.
3.2. Semi-quantitative data
Tables 1 and 2 summarise the maximum pull-out
force and the nominal shear stress for different embed-
ded lengths of the various systems. Each data point is
the average of at least six tests. There was no significant
difference in the data produced by the two test methods
and the results are combined. The greater scatter (about
15%) in the data of the kidney sectioned fibres is due to
the irregularities of their cross-section. In order to make
comparisons maximum nominal shear stresses were
calculated from the maximum force, using a fibre pe-
rimeter equivalent to a circular cross-section of 0.4 mm
nominal diameter for the kidney section fibres. This is
equivalent to shear flow [4] as the irregularity of the
cross-section along the length of fibres and the influence
of surface roughness precluded accurate perimeter cal-
Fig. 3. Typical pull-out force/displacement curves with the calcium aluminate matrix: (a) kidney fibre, and (b) round fibre.
Table 1
Summary of pull-out test results from the magnesia phosphate cement matrix
Kidney fibres
Embedded length (mm) 2.5 3 6 6.5 9 10 12 14a
Ultimate force (N) 38 40 90 110 137 156 149 164
Shear stress (MPa) 12.1 10.6 11.9 13.5 12.1 12.4 9.9 9.3
Force at end of debonding (N) 0.63 0.75 1.5 1.6 2.3 2.5 3 3.5
Round fibres
Embedded length (mm) 8.5 9 9.5 10.5
Ultimate force (N) 57 72 77 87
Shear stress (MPa) 4.3 5.1 5.2 5.3
Force at end of debonding (N) 2.6 2.8 3 3.3
a
Fibre fracture.
14 P. Frantzis, R. Baggott / Cement & Concrete Composites 25 (2003) 11–17
culations. Since displacements were determined from
cross-head movement they include displacements in
addition to actual specimen extensions. These are sig-
nificant primarily in the linear regions of the curves.
3.3. Transition points
All pull-out tests have three fundamental transition
points [3,5], that is to say: (i) the initiation of fibre/
matrix adhesional debonding, (T1), (ii) the completion
of adhesional debonding and subsequent initiation of
frictional bonding, (T2), and (iii) the onset of fibre pull-
out, (T3).
Until recently it was generally assumed that all three
points were more or less coincidental in the case of
straight fibres and that they occurred at the maximum
force or at the force at which there was a gross change in
gradient to a much flatter slope. This was justified on the
grounds that the force/displacement curve was usually
linear to maximum force. The transition points can be
related to the force/displacement curves by direct ob-
servation in the case of transparent matrices. Con-
versely, with opaque matrices they can be related either
by inference, for example from the shape of the curves
[6,10], from acoustic emission and in situ video imaging
[13], or by exposing part of the fibre at the surface and
using optical microscopy and scanning electron mi-
croscopy [8,14]. When using the latter approach it has
been shown that T1 and T2 occurred in the linear region
well before the maximum load was reached [14]. It has
also been identified in the same tests, where steel melt
extracted smooth surfaced fibres were used, that initia-
tion of fibre movement, T3, occurred before the maxi-
mum load.
On the other hand, other investigations indicated T2
(full fibre debonding) occurring beyond the maximum
force [15], where the modelling of pull-out behaviour of
aligned, straight, smooth, round steel fibres from an
ordinary cement matrix containing a polymer (airvol-
203) as an additive, was based on analysis of the pull-out
curves. It was then concluded that, the addition of the
polymer improved frictional resistance to pull-out in this
type of fibres and thus catastrophic debonding was
avoided.
The present data indicates that the position of maxi-
mum force identifies in effect a fourth transition point
corresponding to a change of micromechanical pull-out
from interactive locking to conventional frictional pull-
out, which is discussed below.
The form of the curve for round fibres pulling out of
magnesia phosphate can be considered as representative
of one end of the spectrum observed in practise. That is
a linear region to maximum force followed by a drop in
force and a curve of decreasing force approximately
linearly related to pull-out. The conductivity monitor
indicated that the onset of pull-out, T3, occurred at
maximum force thereby confirming the usual theoreti-
cal assumption although not supporting other obser-
vations [14]. This confirms the interpretations made in
the literature for similar systems where catastrophic
debonding occurs at maximum force [10]. No knowl-
edge could be gained from the literature regarding T1
and T2 because of the linear nature of the force/dis-
placement relationship. In other words, there are no
features corresponding to a change in mechanism of
force transfer from fibre to matrix. It cannot be as-
sumed that all three transition points occur almost si-
multaneously because of the linearity, unless the fibre
displacement profile is mapped in detail along its length
as undertaken by some investigators [14]. The expla-
nation for the linear relationships frequently observed
is the insensitivity resulting from measuring gross dis-
placement from a point on the fibre well outside the
embedded region. It should be noted that A, B and C
are distinguishing points on the curves whereas, T1, T2
and T3 are transition points which may or may not
coincide with A, B and C.
The form of the curves obtained in all other cases in
the present work can be considered as transitional to-
wards that of the other extreme, a fibre mechanically
locked at the embedded end for example that of a
hooked ended fibre. The conductivity monitor identified
T3 as occurring at point L on a typical curve which was
Table 2
Summary of pull-out test results from the accelerated calcium aluminate cement matrix
Kidney fibres
Embedded length (mm) 6a91011
a12
Ultimate force (N) 64 97 155 175 143
Shear stress (MPa) 8.5 8.6 12.3 12.7 9.5
Round fibres
Embedded length (mm) <10 10 13 14
Ultimate force (N) – 21 32 36
Shear stress (MPa) – 5.1 5.2 5.3
a
Fibre fracture.
P. Frantzis, R. Baggott / Cement & Concrete Composites 25 (2003) 11–17 15
located significantly before the maximum force. In this
case the observations made in the literature were con-
firmed [14]. It is not possible to establish unambiguously
from the force/displacement curves where T1 is occur-
ring, but T2 can be located from previous work [16],
where a novel tensile test method was developed. This
allowed direct measurements to be made of the average
force, to separate a fibre from a matrix, and thus to
evaluate the average fibre/matrix interfacial chemical
bond strength magnitude. The nature of the bonding
between the fibre and the matrix in that test was purely
adhesional and the interfacial chemical tensile bond
strength was calculated as the nominal perpendicular
stress on the curved surface of the fibre. This has been
quantified by considering the average force to separate
a fibre from the matrix and including both the tensile
component and the shear component created at the in-
terface by restrained shrinkage of the matrix. It was
found that a maximum interfacial bond stress of 0.2
MPa could be measured for the magnesia phosphate
matrix [16]. In the case of the calcium aluminate mate-
rial, the chemical bond tests revealed the very poor
bonding of this matrix and no value of the interfacial
bond stress could be measured [16]. Turning to the pull-
out tests, then at the end of the debonding process the
tensile component may be considered to be zero in
magnitude and that the shear component will approxi-
mately be equal to the maximum interfacial bond stress,
that is a value of 0.2 MPa. Thus, the forces at which
adhesional bonding resistance was entirely replaced by
frictional resistance during the pull-out process could be
estimated and are given in Table 1. These forces, which
fell in the linear regions thus confirming observations
made in the literature [14], define the end of the adhe-
sional debonding process and the subsequent beginning
of purely frictional resistance to pull-out, that is T2. Since
the forces resisting pull-out continue to increase for sig-
nificant displacements it is clear that there are additional
micromechanical processes occurring than conventional
frictional resistance since once pull-out initiates embed-
ment length must be decreasing. Collectively, these
processes can be termed ‘‘interactive locking’’.
In the case of the fibres pulling out of the calcium
aluminate matrix, the onset of pull-out before maximum
force with the round fibres and the mixture of pull-out/
fracture with the kidney fibres, are indicative of yet
further mechanisms of interactive locking. That is more
matrix (calcium aluminate matrix is by nature a more
brittle material than magnesia matrix) or interface fric-
tional bond dependent than due to fibre shape.
It follows that once the first transition point is
reached, T1, the subsequent shape of the force/dis-
placement curve is fortuitous resulting from the com-
bination of three separate unrelated force/displacement
relationships: one for elastic shear resistance across the
unbonded interface until T2, one for frictional resistance
as pointed out in the literature throughout the subse-
quent deformation [15], and more importantly one for
interactive locking.
The implications of this for modelling lie in the need
to identify mechanisms for interactive locking in addi-
tion to dynamic frictional resistance in order to develop
constitutive relationships.
3.4. Numerical values
A comparison of the nominal maximum shear stresses
of the two fibre types indicates a doubling of resistance
to pull-out of the irregular sectioned, rough surfaced
kidney section fibre compared to that of the regular
smooth circular sectioned fibre with both the magnesia
phosphate and calcium aluminate matrices.
The kidney fibres fractured at a 14 mm embedment
length with the magnesia phosphate matrix whereas a
mixture of pull-out/fracture was observed with the cal-
cium aluminate matrix at almost all embedment lengths.
Fibre fracture could not be induced with the round
fibres with the maximum possible embedment length of
14 mm. The values of maximum nominal shear stress
were up to twice those of initiation of fibre movement,
the latter not shown in Tables 1 and 2. The maximum
values shear stresses compare to data reported in the
literature for ordinary Portland cement based systems
[5,10,14,15].
3.5. Mechanisms of pull-out failure
The region of increasing force to produce pull-out
indicates the substantial forces that can be imposed on
the fibres by the locally fractured matrix. It is envis-
aged that crushing damage with extensive and con-
tinuing matrix cracking enables wedging/plug forces to
develop between the uncracked matrix and the sliding
fibre [8].
The eventual increase of pull-out shear stress ob-
tained in most cases, is in contrast to the constant post
maximum pull-out shear stress. An explanation for this
could be the eventual enhancing of matrix cracking and
accompanying build-up of debris after significant sliding
had occurred.
3.6. Limitation of test procedure
While similar testing arrangements reported in the
literature are two-dimensional in nature and therefore
differ from the actual situation in the composite [8,14],
the testing arrangement used in this study is three-
dimensional in nature since the fibre is surrounded on
all sides by the cement matrix. However, a limitation of
16 P. Frantzis, R. Baggott / Cement & Concrete Composites 25 (2003) 11–17
the present test method is the conductive nature of
the fibre.
4. Conclusions
1. The force at which adhesional bonding resistance was
entirely replaced by frictional resistance during the
early stages of the pull-out process laid in the linear
regions of the force/displacement curves. It defined
the end of the adhesional debonding process and
the subsequent beginning of purely frictional resis-
tance to pull-out, that is T2.
2. The forces resisting pull-out continued to increase for
significant displacements after T2 had been reached.
It is concluded that there were additional microme-
chanical processes occurring than conventional fric-
tional resistance. Collectively these processes can be
termed interactive locking.
3. The initiation of pull-out, that is T3, occurred in most
cases before the maximum force was reached and
identified unambiguously the start of sliding pull-
out, one of the key parameters necessary for
pull-out modelling. The region of increasing force
to produce sliding pull-out indicates the substantial
forces that can be imposed on the fibres by the locally
fractured matrix.
4. The eventual increase of pull-out resistance with most
fibres and matrices after T3 was reached, was in con-
trast to the constant post maximum pull-out shear
stress. An explanation for this could be the eventual
enhancing of matrix cracking and accompanying
build-up of debris around the maximum force.
5. The position of maximum force identified in effect a
fourth transition point corresponding to a change
of micromechanical pull-out from interactive locking
and conventional frictional pull-out.
6. A comparison between the two types of fibres used,
indicated a doubling of resistance to pull-out of the
irregular sectioned, rough surface kidney fibre com-
pared to that of the regular sectioned, smooth circu-
lar fibre.
7. The shapes of the curves highlighted the effect of in-
creasing mechanical interlocking on pull-out charac-
teristics. The circular sectioned, smooth straight
fibres embedded in the magnesia phosphate matrix
showed the typical behaviour reported in the litera-
ture. However, an increased amount of stick slip
was observed. In all other cases, a more complicated
behaviour transitional along the route to that of a
fully mechanically anchored fibre was observed.
Acknowledgements
The authors gratefully acknowledge the financial
support of the Science Research Council. We also like
to thank Mr. P.B. Unsworth, Senior Technician, and
Mr. I. Hambridge, Technician, at Salford University.
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