BEFIB2012 – Fibre reinforced concrete
Joaquim Barros et al. (Eds)
© UM, Guimarães, 2012
NUMERICAL SIMULATION OF THREE-POINT BENDING TESTS:
TWO DISTINCT APPROACHES
Vitor M.C.F. Cunha
*
, Joaquim A.O. Barros
†,1
and José M. Sena-Cruz
†,2
*
ISISE, Dep. Eng., School Science and Tech., University of Trás-os-Montes e Alto Douro
Quinta de Prado 5001-801 Vila Real, Portugal
e-mail: vcunha@utad.pt , vcunha@civil.uminho.pt web page: www.isise.net
†
ISISE, Dep. Civil Eng., School Eng., University of Minho
Campus de Azurém 4800-058 Guimarães, Portugal
e-mail:
1
barros@civil.uminho.pt ,
2
jsena@civil.uminho.pt , web page: www.isise.net
Keywords: FEM, numerical modelling, indirect tensile tests, fibre reinforced composites.
Summary: In this work are presented and discussed the numerical simulations carried out for indirect
tensile tests of steel fibre reinforced self-compacting concrete specimens. The post-cracking behaviour
was modelled with two distinct approaches. Within the scope of the first one, the -w relationships
were obtained by an inverse analysis procedure up to distinct ultimate crack widths. The other
approach consisted on modelling the behaviour of the composite based upon the micro-mechanical
behaviour of the fibres. For this purpose the composite was modelled as two-phase material under the
FEM basis, with an unreinforced concrete matrix phase (paste + aggregates) and a fibre phase. The
fibre phase comprises information about fibre density and orientation depending on where and how
the material is applied.
1 INTRODUCTION
The post-cracking behaviour of a cement based material (either plain or fibre reinforced) can be
predicted by the use of a stress-crack opening displacement relationship, -w. Regarding plain
concrete, the post-cracking behaviour can be characterised by its tensile strength and fracture energy,
since the -w shape is not too dependent of the concrete strength class, e.g. [1-3]. Furthermore, in
general, a bilinear -w relationship renders a good estimation of the plain concrete's post-cracking
behaviour. On the other hand, for fibre reinforced composites, FRC, the shape of -w curves differs
considerably depending on the fibre type, content and quality of the concrete matrix. Therefore, for
each specific FRC composition it is necessary to determine the -w law that best characterizes the
mechanical behaviour of the composite in tension. Usually, “indirect” tensile tests are carried out and
an inverse analysis procedure is used to determine the best fit parameters of the -w curve throughout
an optimization procedure [4]. For FRC, and in comparison with plain concrete, it is more suitable to
model the post-cracking behaviour with a tri-linear diagram, as used by several researchers, e.g. [5-8],
although good results have been achieved with a bilinear diagram [9,10]. The use of poly-linear
functions (more than three branches) is another approach for representing the -w relationships
[11,12], the use of these laws will lead to an increase of the fitting quality. However, some researchers
state that this approach will render inconsistent results on the estimation of the first part of the -w
curve and, particularly, the tensile strength [13,14].
The -w relationship may be determined either directly, in a uniaxial tension test (UTT), or indirectly
by performing an inverse analysis with test results of three point bending tests (3PBT), split cylinder
tests (SCT) or wedge splitting tests (WST). Nevertheless, “indirect” tests methods for determining -w