Gunes Lau Tuakta Ob CBM
Gunes Lau Tuakta Ob CBM
Gunes Lau Tuakta Ob CBM
h i g h l i g h t s
" Ductility plays an important role in earthquake resistant design of structures.
" Environmental factors may adversely affect the ductility due to premature failure.
" Characterization of ductility at different length scales is described.
" Discussion covers from the continuum regime to the atomistic level.
a r t i c l e
i n f o
Article history:
Available online 3 January 2013
Keywords:
Ductility
Concrete
FRP
Debonding
Fracture
Moisture
Temperature
Multi-scale
a b s t r a c t
Fiber reinforced polymer (FRP) materials have been increasingly used in the last two decades to improve
various structural characteristics of reinforced concrete (RC) bridges, buildings and other structures. Ductility of the resulting FRPconcrete system plays an important role in structural performance, especially
in certain applications such as earthquake resistant design of structures, where ductility and energy dissipation play a vital role. Wrapping RC columns with FRP has been shown to generally result in signicant
increase in ductility due to the connement of concrete by the FRP. Other applications such as exural
strengthening of beams involve tradeoffs between ductility and the desired load capacity. Furthermore,
environmental factors may adversely affect the FRPconcrete bond raising concerns about the ductility of
the system due to possible premature failure modes. Characterization of these effects requires the use of
more involved mechanics concepts other than the simple elastic or ultimate strength analyses. This paper
focuses on characterizing ductility of the FRPconcrete systems at different length scales using a combined experimental/computational mechanics approach. Effects of several parameters on ductility,
including constituent material properties and their interfaces, FRP reinforcement geometry at the
macro- and meso-level, and atomistic structure at the molecular level are discussed. Integration of this
knowledge will provide the basis for improved design strategies considering the ductility of FRPconcrete
systems from a global as well as local perspective including interface bond behavior under various
mechanical and environmental conditions.
2012 Elsevier Ltd. All rights reserved.
1. Introduction
Fiber reinforced polymer (FRP) composite materials have been
increasingly used to improve the load capacity and serviceability
of reinforced concrete (RC) members and structures in the last
two decades. Despite many favorable properties of FRP composites
that encourage their use in conjunction with RC structures, a key
concern is their typical brittle failure following a linearly elastic
stressstrain behavior [1]. The current transition in design codes
towards performance-based design and evaluation procedures
Corresponding author.
E-mail address: obuyuk@mit.edu (O. Bykztrk).
0950-0618/$ - see front matter 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.conbuildmat.2012.10.017
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(YPS) representation of the seismic demand which allows convenient graphical superposition of the ductility and drift limits as
shown in Fig. 1b [5,6]. Applicable to design and evaluation of
new and existing structures, respectively, this design approach calculates the base shear required to limit ductility and drift demands
based on an estimate of the yield displacement and uses a plastic
mechanism analysis to calculate the required member load capacities. The transition in the code design approaches is in parallel
with the developments in the performance-based evaluation and
design procedures that put greater emphasis on the inelastic deformation and ductility behavior of structures to characterize seismic
demand and performance.
Evaluation of an existing structure for seismic performance
assessment and possible retrotting is relatively less exible than
design of a new building since the structural system is xed and
typically the available information is limited. The evaluation procedure generally involves nonlinear static pushover analysis [7,8] of
the structure to obtain the capacity curve and estimation of the
corresponding seismic demand to determine the peak displacement response. Ductility of the system and its constituents at various scales play a vital role in the seismic performance level. Fig. 2
shows the ductility characteristics and measures at the scale of
structures, members, and constituent materials for an RC structure.
At the scale of a structure (typically 1012 m), the total base shear
roof displacement/drift (VD) relation denes the capacity curve
for the structure which leads to its seismic performance. The measure of ductility at the structural scale is the ratio of the ultimate
drift (Du) and yield drift (Dy) identied on the bilinear approximation to the capacity curve in Fig. 2a. At the scale of members or
components (typically 1001 m) the forcedeformation relationship is generally expressed from a computational perspective
in terms of momentrotation (Mh) relation obtained from the
momentcurvature (Mu) relation using the estimated plastic
hinge length (Lp). Measures of ductility at the scale of members
and components include the ratio of ultimate curvature or rotation
(uu, hu) and yield curvature or rotation (uy, hy), respectively, as
shown in Fig. 2b. The load deformation behavior of members and
structures are determined by those of the constitutive materials
that make up the member section (typically 10(1)(0) m) at
macro-scale (typically 10(2)(1) m). The measure of ductility at
the scale of materials is the ratio of the ultimate strain (eu) and
the yield strain (ey) as shown in Fig. 2c for reinforcing steel and
concrete. While the ductility ratio (l) of reinforcing steel typically
exceeds 100, that of normal strength concrete (under compression)
is only about 2 using a bilinear approximation to the stressstrain
curve according to Eurocode 2 [9]. Composite use of these two
materials in a complementary fashion and proper design of the
members aim at producing a safe and economical structure with
Fig. 1. Signicance of inelastic deformation and ductility in structural design (adapted from [5]).
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Fig. 2. Ductility measures for (a) structures, (b) members and (c) constituent materials.
Fig. 3. Typical inuence of FRP retrotting on the load capacity and ductility behavior of beam and column elements. In the gure, la refers to after strengthening and lb to
before strengthening.
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Fig. 4. Failure behavior of GFRP wrapped concrete cylinders under axial compression.
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Fig. 5. Lateral load capacity and ductility behavior of an RC frame upon FRP retrotting.
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Fig. 7. (a) Idealization of loading state in FRP in the vicinity of a crack; (b) peel and shear fracture specimens for opening and shearing modes of loading.
Fig. 8. Typical loaddisplacement relationship of meso-scale peel and shear fracture specimens.
does not provide any insight into what is actually happening at the
vicinity of the interfacial crack. As a more fundamental approach at
the molecular level, molecular dynamics simulation has been
adopted for studying the interaction of materials at the interface.
In this section, we describe a new approach using the concept of free
energy for measuring the loaddisplacement response of the bonded
system at the nano-scale level, at which the uctuation of the response can be reduced. This approach is demonstrated using
epoxysilica bonded system as an example, in which the interface
is dominated by relatively weak van der Waals forces and Coulombic
interactions. Here, silica is chosen as a representative material for
concrete because it is a commonly found material in nature in the
form of sand or quartz and is the major constituent material in concrete (about 40% by mass). It is believed that the epoxysilica interface is representative of the FRPconcrete bonded system and the
investigation on the ductility of epoxysilica system can form the basis for future studies on ductility of FRPconcrete systems with the
consideration of the heterogeneous nature of concrete at nano-scale.
The rst step of this new approach is the reconstruction of the
free energy surface (FES) which describes the energy change in the
epoxysilica system from an attached stage to a detached stage.
Such reconstruction becomes feasible by using the metadynamics
approach [32,33] which is a powerful algorithm that can be used
for both reconstructing the free energy and for accelerating rare
events in the system. The principle of this algorithm can be qualitatively understood by lling the actual FES by a series of external
energy with a Gaussian distribution. By keeping track of the lled
Gaussians, the FES can be calculated. In other words, the debonding
process is initiated by an external energy source with a Gaussian
distribution of energy which is continuously added to the bonded
system and hence the entire process does not involve any direct
application of an external load to the system. It should be mentioned that the debonding mechanism of the bonded system captured from the FES is homogenous as shown in Fig. 9a and is not
likely to represent the detachment mechanism when a single
epoxy chain is separated from the silica surface by a mechanical
load acting at the far end of the epoxy chain. It is believed that
the nano-scale debonding mechanism can be regarded as homogeneous when such debonding is initiated at macro-scale structural
level.
After obtaining the FES between epoxy and silica from molecular
dynamics simulation as shown in Fig. 9b, the loaddisplacement
response as shown in Fig. 9c can be predicted by considering the
rst derivative of the FES. Fig. 8 summarizes the approach qualitatively. The reader is referred to [34,35] for more detailed information on his approach.
The molecular dynamics simulation results show a softening
behavior in the loaddisplacement response once the peak stress
is reached (Fig. 9c). It is mainly because the interactions between
epoxy and silica at nano-scale are governed by the weak van der
Waals and Coulombic forces which do not allow any plastic shear
deformation to occur in the post-peak regime of the loaddisplacement curve. The ductility ratio (l) in the nano-scale epoxysilica
bonded system can be dened as the ratio between the total area
under the loaddisplacement curve (energy per unit area =
569 nJ/mm2) and the elastic energy per unit area (60.5 nJ/mm2)
which is calculated as l = 9.4. Such a high ductility ratio cannot
be observed at macro-scale structural level in general since the
weak van der Waals and Coulombic forces become extremely
insignicant when the separation is more than few nanometers.
Hence, the ductility will generally decrease from nano-scale to
macro-scale if the bonded systems lack meso-scale material features (e.g. surface roughness leading to mechanical interlock, connement effect) which can lead to signicant energy dissipation to
occur at the interface.
3.4. Ductility insights from various length scale viewpoint
For an FRP-bonded concrete system, multi-scale investigations
indicate that the ductility generally displays a decreasing trend
from nano-scale to macro-scale level. At nano-scale, the van der
Waals forces and Coulombic interactions are still signicant in
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which certain portion of energy can be dissipated during the debonding process (e.g. sliding of epoxy chain on the concrete substrate). However, at the sub-micro-scale level, such interaction
becomes insignicant and the bonded system can be very brittle
if there is no other means to dissipate energy during debonding.
It is the reason why little ductility can be observed at the mesoscale with ductility values calculated in the range of 23 from
the tests. At the structural scale, the failure is not solely governed
by the interfaces of the FRP-bonded system. Various deformation
mechanisms can be involved at this scale, which lead to signicant
energy dissipation during the deformation process, such as the
connement effect in the column and the mechanical interlock between concrete and epoxy in the FRP retrotted RC beam. Therefore, even though FRP itself does not possess any ductility, the
ductility of the entire bonded system can still be within an acceptable level by introducing appropriate energy dissipation mechanisms when the system is beyond its elastic limit. This requires
implication of efcient design strategies at the structural level.
It should be mentioned that the above discussion is founded on
the basis that the system failure is initiated by the local debonding
at the interface between the adhesive and the concrete substrate.
Such an interface becomes the most critical region when the
FRP-bonded concrete system is subjected to prolonged moisture
and elevated temperature as reported in various research studies
[31,36,37]. Recently, the use of a higher elongation ductile resin
system as adhesive has been proposed for the ductility improvement of the FRP-bonded concrete systems [38,39]. However, the
long term performance of a ductile adhesive material in FRPbonded concrete systems still remains unanswered. Further investigation is required to understand how the ductility changes across
different length scales using ductile adhesive materials.
4. Factors affecting ductility of FRPconcrete systems
The discussions in the preceding sections illustrate the ever
increasing importance of ductility in structural evaluation and design of FRPconcrete systems through investigations at different
length scales. Implicit in these discussions, however, are a number
of assumptions that idealize or disregard the potential inuence of
various factors that may affect the ductility behavior of FRPconcrete systems at all length scales. Some of these factors are related
to the design issues. For instance, the FRP strengthened member
behaviors conceptually illustrated in Fig. 3 cannot be migrated to
the structural scale evaluations shown in Fig. 5 without considering and ensuring satisfactory performance of beam-column joints
[4042]. Other factors are related to the performance of materials
and their interfaces under mechanical effects, such as premature
debonding failures that may signicantly reduce structural
ductility and performance unless adequate bond or mechanical
Fig. 9. Illustration of the process of using molecular dynamics simulation (a) to determine the free energy surface (b) using advanced molecular dynamics methods such as
Parrinellos metadynamics (to sample for rare events while reconstructing the FES), to identify (c) the loaddisplacement response of the bonded system.
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Fig. 10. Effect of moisture on bond strength of shear (a) and peel (b) specimens.
Fig. 11. Effect of Mode I interface properties on debonding behavior of FRP-plated RC beam.
steel reinforcement,
(Fig. 12).
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Fig. 12. Effect of mode II interface properties on debonding behavior of FRP-plated RC beam.
Fig. 13. Inuence of debonding failures on the ductility of FRP strengthened beams.
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Fig. 14. Damage evolution and debonding propagation at the epoxyconcrete interface.
ment ratio, the ductility ratios of the beams vary between 1 and 2.7
depending on the beam shear capacity and the anchorage conditions, the latter of which cannot be designed using the conventional ultimate strength design approaches.
Different debonding failure modes and associated ductility levels are also shown in Fig. 13 which illustrates the essential design
issues in FRP strengthening of exural members. Cover debonding
was the most brittle failure mode which took place at the steel
reinforcement level and resulted in a ductility ratio of l = 11.2.
Absence of anchorage and insufcient shear capacity were responsible for this brittle failure mode. When adequate shear capacity
was provided through additional internal transverse steel reinforcement, the ductility ratio rose to l = 1.61.9 without any bond
anchorage. In this case, the failure was at the epoxyconcrete
interface, within the concrete substrate. Fig. 14 shows the evolution of debonding damage and propagation at the epoxyconcrete
interface [45,46]. Addition of transverse FRP reinforcement for
bond anchorage along half and full length of the shear span resulted in ductility ratios of l = 2.2 and l = 2.7, respectively. This
wide range of ductility behavior may have signicant impact on
the behavior at the structural scale and requires advanced mechanics tools for modeling and design. A fracture energy based design
approach was proposed for bond anchorage design for exural
FRP reinforcement to ensure ductile failure behavior of FRPstrengthened exural members [43].
6. Knowledge gaps and further research needs
Throughout the paper, discussions on ductility of FRPconcrete
systems at different scales were performed with the help of ductility ratios as a quantitative measure of the systems ability to undergo inelastic deformation before failure. Some important
observations can be distilled from these discussions that provide
guidance for identication of knowledge gaps and further research
needs:
FRP composite materials, due to their favorable mechanical and
durability characteristics have secured a permanent and growing share in the construction market with current emphasis on
strengthening of RC members. Diverse applications of FRP composites on RC structures enjoy various degrees of success inuenced by various material and strengthening parameters.
From ductility perspective, FRP and concrete materials with
ductility ratios approximately l 1 and l 2, respectively,
do not form an ideal couple considering that higher ductility
ratios are required at the structural level for satisfactory structural performance. However, in reinforced concrete applications, existence of reinforcing steel with superior ductility
characteristics may result in high system ductility ratio of the
FRPconcrete structures. In that respect, more research is
needed for better understanding of the interactive system
behavior under various mechanical and environmental effects.
Multi-scale investigations on the ductility of FRPconcrete systems indicate a reduction in ductility at larger scales. This
important observation emphasizes the need for more fundamental research at smaller scales to better understand the ductility characteristics of FRPconcrete systems and to optimize
material parameters at smaller scales to minimize the reduction
in ductility at larger scales.
Understanding and modeling the inuence of moisture, temperature and other environmental exposure conditions on the
integrity and ductility of FRPconcrete systems is a priority
research area that also concerns the performance and safety
of existing FRPconcrete systems. More fundamental research
at smaller scales is necessary to properly characterize the coupled chemo-thermo-mechanical processes associated with
environmental exposure conditions that adversely affect the
integrity, load and failure behavior as well as ductility of FRP
concrete systems in an effort to improve their overall
performance.
7. Conclusions
Multi-scale investigations on ductility characteristics of FRP
concrete systems are presented and discussed in this paper sharing
the insights gained into mechanics and durability of FRP concrete
systems with emphasis on failure behavior and ductility. Knowledge gaps and further research needs are highlighted with emphasis on the need for more fundamental research at smaller scales for
better understanding and modeling of coupled mechanisms and
processes as a basis for improved design strategies for better performance and ductility.
Acknowledgement
This research was supported by the National Science Foundation (NSF) through the grants CMS Grant Nos. 0010126, 0510797
and 0856325 to Massachusetts Institute of Technology.
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