Abstract
The tensile behaviour of brittle materials can be
enhanced by fibres. The cracking stress may increase, but
the main influence is higher ductility after cracking. In
some cases the material may also exhibit multiple
cracking and tensile strain hardening behaviour
thereafter.
A computational tool for analysing structures made of
fibrereinforced brittle materials was developed,
starting from the micromechanical properties of fibres,
matrix, and interface. The constitutive model is fairly
general, including both single and multiple fracture, the
fracture mode being either fibre rupture or pullout.
The study is divided into three parts: First, the
mechanics of a single fibre is analysed. Second, the
statistical tensile behaviour is evaluated by taking all
fibre locations and orientations into account. Third, the
macromechanical constitutive relation is incorporated
into a finite element program for structural analysis.
The fundamental assumption in the single fibre analysis
is the existence of a symmetry fibre within the matrix
segment between cracks. This assumption enables the
pullout analysis of a short fibre bridging several
cracks. The strain energy of fibre and matrix, matrix
fracture energy, fibre debonding energy, and frictional
pullout energy are all included in the model. The
theoretical value of the bond modulus was studied by
means of the finite element method and dimensional
analysis. Its value was found to be several orders of
magnitude higher than the experimentally measured values
reported in the literature.
The macromechanical behaviour is derived from several
single fibre analyses by integrating over all possible
fibre locations and orientations. The fibre orientation
introduces additional phenomena: number of fibres
bridging the crack, snubbing effect at the fibre bending
point, and matrix spalling. The snubbing effect increases
the stress in the composite, while the other two have a
decreasing effect. Matrix spalling considerably increases
the crack width. The fundamental assumption is that the
fibres carry axial stresses only. The result is a
complete constitutive tensile relation of composite:
stressstrain or stresscrack width curve, as well as a
prediction of crack spacing. For the effects due to fibre
orientation, a systematic experimental procedure should
be developed.
The tensile model was extended into two and three
dimensions by using the finite element method with
smeared and discrete crack concepts and a multisurface
plasticity theory. The statistical tensile relation
represents the behaviour normal to the crack. Automatic
generation of interface elements on an existing geometry
was developed to facilitate the modelling of discrete
cracks after smeared crack analysis. The increase in the
peak load of flexural members due to fibres, as measured
in experimental tests, could be reproduced, which
supports the validity of the approach proposed in this
study.
Original language  English 

Qualification  Doctor Degree 
Awarding Institution 

Supervisors/Advisors 

Award date  4 Sep 1998 
Place of Publication  Espoo 
Publisher  
Print ISBNs  9513852520 
Electronic ISBNs  9513852539 
Publication status  Published  1998 
MoE publication type  G5 Doctoral dissertation (article) 
Keywords
 fibre reinforcement
 ductility
 multiple cracking
 micromechanics
 composite materials
 finite element analysis
 construction materials
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Kullaa, J. (1998). Constitutive modelling of fibrereinforced brittle materials: Dissertation. VTT Technical Research Centre of Finland. http://www.vtt.fi/inf/pdf/publications/1998/P358.pdf