Yunyi Zou, Ph.D., P.E.1; and Arthur Huckelbridge, P.E.2
Experimental results show that the crack growth of fiber-reinforced polymer (FRP) reinforced concrete
experience a crack development stage followed by crack stabilization. The crack length and elastic crack mouth
(CMOD) increase during the crack development stage until reaching the crack stabilization stage. A finite-element
proposed to predict the initial CMOD. A debonded length was specified to account for the bond-slip between FRP
bar and concrete. It was
assumed that there was no tangential displacement between the reinforcement and concrete outside of the
debonded length. A fatigue
model was created using the Paris equation to simulate the growth of elastic CMOD. The model displayed good
agreement with the test
results. A size effect was also observed for the exponential parameter in the Paris equation.
CE Database subject headings:
Fiber reinforced polymers; Cracking; Fatigue; Concrete, reinforced.
Fiber-reinforced polymer (FRP) reinforcement has been known for its high ratio of strength to mass, excellent
fatigue characteristics, excellent corrosion resistance, electromagnetic neutrality,
and low axial coefficient of thermal expansion. There is significant potential for applying FRP RC in bridge
engineering for structural elements in corrosive environments with low ductility demand. Due to the high strength
of FRP, serviceability becomes a critical issue. The main serviceability requirements are maximum deflection and
crack width control. For quasi-brittle materials such as concrete, there exists an inelastic zone at the tip of a crack,
which is called the fracture process zone. Shah (1995) summarized the interaction within the fracture process zone
as microcracking, crack deflection, aggregate bridging, crack face friction, crack tip blunting by voids, crack
Gergely and Lutz (1968) analyzed test results from various investigators on crack width, using multiple
regression analysis. A regression equation was proposed to predict crack width. In ACI 440 (2001), the
Gergely-Lutz equation has been adapted to estimate the crack width of FRP RC members.
In the early 1960s, Paris (1963) applied fracture mechanics to fatigue problems.
( 1 )
is the crack length;
is the number of cycles;
is the stress intensity factor range at maximum and
are material parameters that also depend upon load frequency, environment, and mean
load. Although the Paris equation was developed for steel, researchers have tried to verify if it was also valid for
concrete. Perdikaris et al. (1987) found that the
Paris equation resulted in significant errors when applied to concrete. Baluch et al.(1987) concluded that
independent of mean stress. Bazant et al. (1991) combined the Paris law with a size effect law for fracture under
Efforts have been made to predict the growth of cracks due to fatigue loading. Balaguru and Shah (1982)
proposed a model to simulate the increase of deflection and crack width for steel RC at large rebar stress ranges.
The general trend of the model was that crack width always increased with the number of cycles applied.
Carpinteri et al.(1993) used linear elastic fracture mechanics (LEFM) to model a simply supported steel RC beam.
The total stress intensity factor was represented as the superposition of
due to bending moment and rebar force.
It was assumed that cracks would propagate if the peak moment exceeded the fracture moment. Apparently, these
models were designed for the case of low cycle fatigue.
The finite-element method has been widely used in reinforced concrete analysis. There are two major
approaches in crack modeling in finite-element analysis. One approach is smeared crack modeling, which is
advantageous when overall load/deflection is concerned. The other method is discrete cracking modeling, which is
advantageous when detailed local behavior is investigated.
So far, crack growth in FRP reinforced concrete is not yet fully understood. Investigation of FRP RC fatigue
performance is crucial in applications such as bridge deck slabs. First, a summary of experimental results on
fatigue testing of FRP RC will be presented. Subsequently, a finite-element model will be developed to simulate
the evolution of crack opening observed in test specimens. An empirical estimation for final crack width will be
proposed. Sensitivity analysis on the crack growth model will also be presented to evaluate the effects of
uncertainty and randomness for different parameters. Finally, the finite-element model developed will be utilized
to simulate the set of test specimens.