International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
Performance Evaluation of Critical J-Integral
(JIC) with High Volume Flyash Concrete
N.Gurumoorthy1, C.Jaideep2
1
2
Assistant Professor in Civil Engineering, PSNA College of Engineering and Technology, Dindigul, Tamilnadu.
Associate Professor in Civil Engineering, PSNA College of Engineering and Technology, Dindigul, Tamilnadu.
Abstract
Utilization of large volumes of fly ash in various
concrete applications is becoming a more general
practice in an effort towards using large quantities of fly
ash. Solid waste as fly ash from the coal powder
combustion in thermoelectric power plant is a major
environmental problem that can be solved by its addition
in the mixture of structural concrete in civil
construction.This paper deals with the opening mode
of crack which is critical for concrete, due to low
tensile strength of concrete. This paper mainly deals
with critical J-integral, critical J-integral is one of
the fracture parameter. It is used for lower strength
materials exhibiting small amount of plastic
deformation before failure. J-integral is more
comprehensive approach to fracture mechanics of
lower strength ductile materials.
The fracture parameters calculated in this
works are critical J-integral, stress intensity factor,
crack mouth opening displacement. These are the
important parameters which would help in designing
of the safe structures where micro cracks are very
important. Three points loading is applied on the
pre-cracked concrete specimen. Notch by depth ratio
for all specimens kept as 0.2 and 0.3. The crack
mouth opening displacement (CMOD) is calculated.
The M30 grade concrete specimens casted with
50%& 60% fly ash. Cement is replaced by 50 and 60
percentage of fly ash throughout the experiments.
Fracture toughness value of 90 days specimens
increases 50% than 28 days specimens.
I. INTRODUCTION
Rock blocks, used in monumental
structures since the ancient time, often present
unexplainable cracks. Such cracks could be
provoked by work imperfections - due to
technology or due to installation - that lead to
stress singularities. Such singularities are often the
source of fracture propagation. In these lapideous
materials strain localization occurs and fracture is
produced with low energy dissipation. This
property characterizes many huge ancient stones,
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selected by master builders just because they are
easily workable. First, primitive men "sparked"
fracture energy consumed in the detachment of
stone's slivers to make tools and weapons.
Afterwards, stone-cutters who worked stones to
make sculptures and decorations encountered an
energy rate demand on the fracturing process.
Such energy is now called fracture energy (GF)
and it represents a material constant to
characterize brittle materials.
COULOMB
(1776)
pioneered
investigation of the fracture of stones in
compression and nowadays his criterion is still
used. We underline that fracture mechanics
developments are parallel to those of failure
criteria for brittle materials and don't intersect
each other.
II. BACKGROUND
Fracture mechanics is the field of
mechanics concerned with the study of the
formation of cracks in materials. It uses methods
of analytical solid mechanics to calculate the
driving force on a crack and those of experimental
solid mechanics to characterize the material's
resistance to fracture.
In modern materials science, fracture
mechanics is an important tool in improving the
mechanical performance of materials and
components. It applies the physics of stress and
strain, in particular the theories of elasticity and
plasticity, to the microscopic crystallographic
defects found in real materials in order to predict
the macroscopic mechanical failure of bodies.
Fractography is widely used with fracture
mechanics to understand the causes of failures and
also verify the theoretical failure predictions with
real life failures.
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
III. NEED FOR FRACTURE MECHANICS
In many cases, failure of engineering
structures through fracture can be fatal. Often
disasters occur because engineering structures
contain cracks-arising either during production or
during service. For instance, growth of cracks in
pressure vessels due to crack propagation could
cause a fatal explosion. If failure were ever to
happen, we would rather it were by yield or by
leak before break.
Since cracks can lower the strength of the
structure beyond that due to loss of load-bearing
area a material property, above and beyond
conventional strength, is needed to describe the
fracture resistance of engineering materials. This
is the reason for the need for fracture mechanicsthe evaluation of the strength of cracked
structures.
Fig.1. an edge crack (flaw) of length a in a
material
IV. NEED OF INVESTIGATION
Existing Problem
1.
In major structures like nuclear plant,
dams, microscopic analysis of the
concrete is important since even the pre
existing crack can aggressive disaster.
2.
In concrete, flaws are not avoidable but
the knowledge on critical size of crack is
mandatory in order to prevent sudden
failure.
3.
Even a small crack can propagate and
become critical one during its life period
that may lead to catastrophic failures
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A.HISTORICAL POINT VIEW
Even after more than 20 years of research
in the field of fracture mechanics applied to
concrete, the influence of notch length on
specimen behaviour and fracture toughness, kIC,
based on the experimental evidence, is not clear.
The original concept of fracture energy
was conceived of by Alan Arnold GRIFFITH, a
British
aeronautical
engineer,
when
he
investigated the fracture of glass sheets. His great
contribution to ideas about breaking strength of
materials was that he realized that the weakening
of material by a crack could be treated as an
equilibrium problem in which the reduction in
strain energy of a body containing a crack, when
the crack propagates, could be equated to the
increase in surface energy due to the increase in
surface area. The Griffith theory began from the
hypothesis that brittle materials contain elliptical
micro cracks, which introduce high stress
concentrations near their tips. He developed a
relationship between crack length (a), surface
energy connected with traction-free crack surfaces
(2γ) and applied stress: σ2 = 2 γ E/πa. However,
the Griffith theory predicted that compressive
strength of a material is 8 times greater than its
tensile strength, but this condition cannot be valid
for any material.
Later, the introduction of the line-crack by
IRWIN (1957) - a flat crack which presents two
singularities at the extremes - seems however be
more suitable than Griffith's crack for the need to
consider the friction which develops between
crack surfaces. So, in 1957, George Rankine
Irwin, , provided the extension of Griffith theory
to an arbitrary crack and proposed the criterion for
a growth of this crack: the strain energy release
rate (G) must be larger than the critical work (Gc),
which is required to create a new unit crack area.
Some say that notation G comes after Griffith;
others say it is after George. Furthermore, Irwin
showed, using WESTERGAARD's method, that
the stress field in the area of the crack tip is
completely determined by the quantity K (after
KIES, a colleague of Irwin, 1952-1954), called
stress intensity factor. In the parameter K
subscript I refers to mode I loading, i.e. the
opening mode: KI = σ√ πa. Other possible modes
of deformation at a crack tip are sliding mode II
and tearing mode III.
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
B. FRACTURE BEHAVIOUR OF CONCRETE
Shilang Due and H.W. Reinhardt (1989) had
made an attempt to determine the double-K fracture
parameters K Ic ini and K Ic un using three-point bending
notched beams. First, based on the knowledge from
extensive investigations which showed that the
nonlinearity of P-CMOD curve is mainly associated
with crack propagation, a linear asymptotic
superposition assumption is proposed. Then, the
critical effective crack length ‘a’ is analytically
evaluated by inserting the secant compliance c into the
formula of LEFM. Furthermore, an analytical result of
a fictitious crack with cohesive force in an infinite
strip model was obtained. The double-K fracture
parameters K Ic ini and K Ic un as well the critical crack
tip opening displacement CTODc were analytically
determined. The experimental evidence showed that
the double-K fracture parameters K Ic ini and K Ic un are
size-independent and can be considered as the fracture
parameters to describe cracking initiation and unstable
fracture in concrete structures. The testing method
required determining K Ic ini and K Ic un is quite simple,
without unloading and reloading procedures. So, for
performing this test, a closed-loop testing system is
not necessary.
Surendra P. Shah, Fred J. McGarry (1971)
initiated the original Griffith fracture criteria was
developed to describe the rapid extension of a crack in
a homogeneous elastic body. To check the
applicability of the Griffith theory to Portland cement
systems which are neither elastic nor homogeneous,
specimens of hardened cement paste, mortar and
concrete made with normal and lightweight aggregates
and with notches of varying lengths were tested in
flexure and in tension. While the paste specimens
were notch-sensitive, mortar and concrete strengths
were independent of notch length. The notchinsensitivity of mortar and concrete appears to be due
to their composite nature. Similar behavior occurs in
glass-Al²O³, fiberglass-reinforced epoxy and tungstenreinforced copper composites. It appears that for
mortar and concrete the direct application of Griffith
criteria is not valid up to a certain length of cracks.
This critical length depends on the size, volume, and
type of aggregate.
V. J-INTEGRAL (J IC )
J-integral is used for lower strength
materials exhibiting small amount of plastic
deformation before failure. J-integral is more
comprehensive approach to fracture mechanics of
lower strength ductile materials.
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J-integral can be interpreted as the
potential energy difference between two
identically loaded specimens having slightly
different crack lengths. Testing is carried out
similar in similar manner of fracture toughness
stress intensity factor but using a series of
identical specimens (multi specimen approach) or
single specimens.
In the mid-1960s James R. Rice (then at
Brown University) and G. P. Cherepanov
independently developed a new toughness measure
to describe the case where there is sufficient
crack-tip deformation that the part no longer obeys
the linear-elastic approximation. Rice's analysis,
which assumes non-linear elastic (or monotonic
deformation-theory plastic) deformation ahead of
the crack tip, is designated the J integral. This
analysis is limited to situations where plastic
deformation at the crack tip does not extend to the
furthest edge of the loaded part. It also demands
that the assumed non-linear elastic behavior of the
material is a reasonable approximation in shape
and magnitude to the real material's load response.
The elastic-plastic failure parameter is designated
J Ic and is conventionally converted to K Ic. Also
note that the J integral approach reduces to the
Griffith theory for linear-elastic behavior. The
following formula generally given by RICE for jintegral.
J 



 Wdy

T
du

ds 
dx

The J-integral has been used as a criterion
of the fracture initiation for materials subjected to
monotonic loading which exhibit either localized
or widespread plasticity prior to fracture. Various
approximate procedures have been proposed as a
means of simplifying the complex evaluation
procedure for J which was originally advocated for
compact tension specimens by Begley and Landes.
Mode I tensile opening is usually
considered, although Modes II and III can be
discussed in a similar manner. For linear elastic
behaviour and also for small scale yielding, the Jintegral is identical to the elastic energy release
rate G. According to the maximum energy release
rate criterion, the crack under Modes I and III
loadings is assumed to propagate in its own plane
and to begin to propagate when the value of this
energy release rate reaches some critical value The
onset of unstable fracture is predicted by the
critical value of either the energy release rate G or
the stress intensity factor K. In the linear elastic
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
range, the fracture toughness values using the Jintegral techniques, J IC and J I11C at initial crack
growth for Modes II and III, are respectively
related as,
J IC
1  2 2

K IC
E
VIII. THE HIGH-VOLUME FLY ASH
CONCRETE
VI. FLY ASH
Fly ash is a by-product from coal-fired
electricity generating power plants. The coal used
in these power plants is mainly composed of
combustible elements such as carbon, hydrogen
and oxygen (nitrogen and sulphur being minor
elements), and non-combustible impurities (10 to
40%) usually present in the form of clay, shale,
quartz, feldspar and limestone. As the coal travels
through the high-temperature zone in the furnace,
the combustible elements of the coal are burnt off,
whereas the mineral impurities of the coal fuse
and chemically recombine to produce various
crystalline phases of the molten ash.
The molten ash is entrained in the flue gas
and cools rapidly, when leaving the combustion
zone (e.g. from 1500°C to 200°C in few seconds),
into spherical, glassy particles. Most of these
particles fly out with the flue gas stream and are
therefore called fly ash. The fly ash is then
collected in electrostatic precipitators or bag
houses and the fineness of the fly ash can be
controlled by how and where the particles are
collected
VII. FLY ASH CONCRETE
Fly ash can be used in concrete as a
partial replacement for ordinary Portland cement
(OPC). Fly ash can be introduced in concrete
directly, as a separate ingredient at the concrete
batch plant or, can be blended with the OPC to
produce blended cement, usually called Portlandpozzolana cement (PPC) in India. Fly ash blended
cements are produced by several cement
companies in India. The percentage of fly ash as
part of the total cementing materials in concrete
normally ranges from 15 to 25%, although it can
go up to 30-35% in some applications.
The use of fly ash in concrete will
improve performance of the concrete provided the
concrete is properly designed. The main aspects
are improvement in long-term strength and
reduced permeability resulting in potentially better
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durability. The use of fly ash in concrete can also
address some specific durability issues such as
sulphate attack and alkali silica reaction. However,
a few additional precautions have to be taken to
insure that the fly ash concrete will meet all the
performance criteria.
The main difference between the HighVolume Fly Ash Concrete (HVFAC) and the usual fly
ash concrete is that in the former concrete, the amount
of ordinary Portland cement is minimized through
proper mixture proportioning using large amounts of
fly ash and judicious selection of materials and
chemical admixtures while maintaining, and often
improving its performance as compared to
conventional concrete. There is no fixed percentage of
ordinary Portland cement replacement by fly ash in
this type of concrete, but in many cases, percentages
of 50 to 55% were found to be achievable. To obtain
the superior performance of this type of concrete, it is
recommended that the W/CM of the HVFAC be kept
well below 0.40 and, preferably of the order of 0.35 or
less. To produce a workable concrete at such low
W/CM, the use of super plasticizer is most of the time,
essential.
IX. EXPERIMENTAL INVESTIGATION
A. GENERAL
Experiments were conducted on concrete
beam specimens made up of M 30 grades. The
materials properties of the aggregate were studied
in the laboratory as per IS 383:1970. The beams
were cast as per the guidelines given in IS
10262:1982. W/C ratio was kept as 0.38
throughout the experiments
B. GEOMETRY
Specimens shall be beams of rectangular
cross section with a notch at the mid-length to a
depth of 0.2 times the beam depth
a) The depth of the cross section (D) of the
specimen shall be not less than 4 times the
maximum aggregate size (da).
b) The width of the cross section (B) of the
specimen shall be not less than 4 times the
maximum aggregate size (da).
c) The loading span (S) shall be 3D. The total
length of the specimen (L) shall be not less than
3.5D. The notch depth (a 0 ) and notch width (n 0 )
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
shall be 0.3D
respectively.
and
not
more
than
5mm,
1.
h= 40 mm and n 0 = 3mm for 4 no’s of
each conventional concrete beam, 50% fly
ash beam and 60% fly ash beams. Notch
depth for this is kept as 0.2 for finding
critical J-integral
2.
h= 60 mm and n 0 = 3mm for 4 no’s of
each conventional concrete beam, 50% fly
ash beam and 60% fly ash beams. Notch
depth for this is kept as 0.3 for finding
critical J-integral
All the specimens are casted for M 30 grade of
concrete.
Fig.2.TEST SETUP
The main advantage of three point bend
specimen geometry is that testing can be done under
dynamic loading also. This geometry in fact is an
evolution of the classical charphy geometry used for
measuring the impact toughness
 8 numbers of conventional concrete
beam specimens of 1200×200×100mm
 8 numbers of HVFAC (50% fly ash)
beams of 1200mm×200mm×100mm
 8 numbers of HVFAC (60% fly ash)
beams specimens of 1200×200×100mm
C. METHOD OF CASTING
The concrete mix was prepared according
to mix design and the mould was placed on a plane
surface and then concrete was poured inside very
slowly and it was compacted. A total number of 24
beams were casted for concrete grade M 30 .
Demoulding process for the concrete with 50%
and 60% fly ash done after 24 hours.
D. LOADING METHODOLOGY
The beams were tested in a loading frame
and the set up is shown in the figure. The load is
applied gradually using a hydraulic jack of capacity 10
ton with the load increments of 0.5 KN.
Crack mouth open displacement (CMOD)
was found by placing two Digital dial gauge at the
edge of the pre-cracks by providing two wooden
specimens. Crack mouth opening displacements were
found by the deflection of the crack mouth. ¼
deflection also found by placing digital dial gauge at
¼ distances.
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Fig.3.Three points bend beam testing
Table.1.Average central deflection results of specimen
Load
(KN)
0
1
2
3
4
5
6
7
8
9
10
Control
0
2.5
2.74
2.92
3.16
3.2
3.2
3.34
3.56
3.66
3.88
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Deflection (mm)
50% flyash 60% flyash
0
0
0.36
0.26
0.88
1.42
1.38
1.52
1.66
1.6
2.58
2.1
3.54
2.9
3.7
3.42
3.88
-
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
X.CONCLUSION

From the test result, the rupture load of the
specimens calculated, rupture load of the
specimens decreased with the increment of
the class F fly ash.

9.8 KN, 7.74 KN, 6.67 KN are the maximum
rupture load of control specimen, 50% fly
ash, 60% fly ash specimens respectively.
Fracture toughness value of the specimens is
decreased with the addition of fly ash.

Critical j-integral value of 90 days specimens
increases 50% than 28 days specimens.
Fracture toughness value of 60% fly ash
specimens is higher than 28 day control
specimens
Fig.4.Load vs Deflection curve for beams
The above graph shows the relation between
the Load carrying capacity and the centre deflection,
value for 28 days strength. From the graph it shows
that the load carrying capacity of the beam with
addition of fly ash decreased.
E. CALCULATION FOR CRITICAL J-INTEGRAL:
The critical j-integral is calculated using formula
J IC 
2A
B (W  a )
XI. REFERENCES
1.
2.
Where A= Area under load vs. Deflection, B=
Thickness of the specimen, W= Width of specimen,
a= notch depth
3.
Table.2.The critical j-integral value for 28 days testing specimen
4.
0% fly ash
x 10-3 MPa m
2.46
2.19
3.96
4.40
50% fly ash
x 10-3 MPa m
3.00
2.09
3.32
2.18
60% fly ash
x 10-3 MPa m
2.091
2.58
1.44
1.42
Table.3.The critical j-integral value for 90 days testing specimen
0% fly ash
x 10-3 MPa m
3.00
3.22
4.62
2.81
50% fly ash
x 10-3 MPa m
2.5
2.15
2.67
3.11
60% fly ash
x 10-3 MPa m
2.00
2.12
1.9
2.055
5.
6.
7.
8.
9.
10.
11.
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