- Steel exhibits ductile behavior by allowing large strains before rupturing or failing. It can stretch substantially under tension. - Concrete and cast iron exhibit brittle behavior, failing abruptly with little warning once their strength limits are exceeded. Their stress-strain curves are steep with little plastic deformation. - Reinforced concrete can show ductile behavior if designed properly with sufficient confinement and ductile reinforcement to allow inelastic deformations without collapse.

1. GAZIANTEP UNIVERSITY
GRADUATE SCHOOL NATURAL AND APPLIED SCEINCE
DEPARTMENT OF CIVIL ENGINEERING
M.SC IN CONSTRUCTION ENGINEERING
COURSE CODE: CE545
DEFORMATION AND FRACTURE THEORIES
STUDY No: 3
Brittle Ductile Behaviour For ( STEEL - RIENFORCED CONCRETE - CONCRETE )
Submitted by
AHMED ASSIM ABDULLAH
STD No: 201444960

2. Brittle: The ability of a material to show little or no yielding before
failure.
Ductile: The ability of a material to be subjected to large strains before it
ruptures or fails.
Concrete: The ability of a material to show little or no yielding before
failure.
Reinforced concrete: A concrete member with steel embedded inside it
to resist tensile forces.
Steel: Refined iron that contains virtually no impurities.
Typical Material Properties and Engineering Terms
Structural engineers use material properties when designing
members. Stress (σ) is the applied load divided by the material area
it is acting on (typically the cross-sectional area of the member).
Strain (ε) is the elongation or contraction of a material per unit
length of the material. According to Hooke's Law (σ = Eε) stress is
dependent on strain in the material. The modulus of elasticity (E) or
Young's modulus of a material is a constant associated with Hooke's
Law. The modulus of elasticity indicates the stiffness of a material.
Tensile strength is the amount of tensile stress that a material can
resist before failing. Compressive strength is the amount of
compressive stress that a material can resist before failing. A
material that exhibits ductile properties can be subjected
to large strains before it ruptures or fails. A material that exhibits
brittle properties shows little or no yielding before failure.

3. 1. Failure of Concrete
It has been proposed elsewhere that a realistic lower bound for the
above peak level appears to be the level at which the volume of a
specimen attains a minimum value. This minimum volume level has
been found to lie very close to the maximum stress level that can be
sustained by a concrete specimen and considered to provide a failure
criterion suitable for practical structural analysis Although for a given
concrete the variation of the above level in stress space has been
found to be slightly stress path dependent the unsystematic
variability of the results obtained from the tests on various concretes
is such that it renders the above dependency insignificant for any
pratical purpose (figure 1).
Fig 1 : A, Unsystematic variability of "failure" data obtained from
tests using stress path 1 for concretes with f~(N/mm 2) varying
between approximately 15 and 65. B, Stress path effect on "failure"
data for a typical concrete (f~= 31.7 N/mm2).

4.  Deformational behaviour during loading
he trends of behaviour exhibited by concrete under stress increasing
to failure have been established in previous investigations by
analysing experimental data on the multiaxial behaviour of a wide
range of concretes likely to be used in practice with uniaxial cylinder
compressive strength (fc) varying between approximately 15 N/mm z
and 65 N/mm 2 . The most realistic representation of these
experimental data is achieved by decomposing each state of stress
and strain into hydrostatic and deviatoric components in the form of
normal and shear octahedral stresses and strains, respectively. In this
form of representation, the deformational behaviour of concrete
under increasing stress (behaviour under decreasing stress is
discussed later) can be completely described by the relationships
between (a) hydrostatic stress, Co, and volumetric strain, %h, (b)
deviatoric stress, Xo, and deviatoric strain, %, and (c) deviatoric
stress. Typical relationships are shown in figures 2 and 3 for a
cc.~crete with 20 mm maximum size of gravel aggregate and f~= 31.7
N/ram 2.
Fig 3 : Hydrostatic component of deformationai
response of typical concrete under deviatoric stress.
Fig2 : Deformational response of a typical concrete under (a)
hydrostatic and (b) deviatoric stress

5. The CrO-eo~relationship defines completely the deformational
response of concrete under increasing hydrostatic stress, since the
measured deviatoric strain under such a state of stress has been
found to be negligible Furthermore, it has been found that
specimens subjected to various levels of uniaxial compression below
the failure level, when unloaded and then reloaded hydrostatically,
exhibit a stress-strain relationship essentially the same as that
exhibited under increasing hydrostatic stress by specimens without
any previous loading history In view of this experimental evidence, it
appears realistic to consider that the volumetric strain (%h) of
concrete due to the hydrostatic component (Co) of the applied state
of stress is independent of the deviatoric component (Xo), and thus
%h may be expressed irr terms of r o only. The deformational
response of concrete under increasing deviatoric stress (%) is defined
by both Xo- Yo and % - %d relationships which have been found to be
essentially independent of the direction of zo on deviatoric planes,
i.e. planes orthogonal to the stress space diagonal at given levels of
cro As for ero--%h relationship, the To - % relationship has been
found to be essentially unique, i. e. for a given concrete, 70 is
dependent on % only On the other hand, the zo-%d relationship is
dependent on (ro and appears to represent the only form of
interaction (coupling) between the hydrostatic and deviatoric
components of the stress and strain states .
 Defornmtional behaviour during unloading
An indication of the stress-strain behaviour of concrete during
unloading may be given by uniaxial and triaxial experimental data
obtained from cyclic tests. The hysteresis loop exhibited by such data
during the first cycle is so small that the same linear stress-strain
relationship may realistically describe concrete behaviour during
both unloading and subsequent reloading up to the maximum stress

6. level previously experienced by the material Figure 4 indicates that
this linear relationship has an essentially constant inclination and its
distance from the origin of the monotonically increasing stress-strain
curve increases with the maximum stress level of the cyclic load. For
stress levels beyond this maximum stress, concrete response is
described by the monotonically increasing stress-strain relationships
discussed in the preceding section.
Fig 4 : Measured and predicted stress-strain behaviour during
loading and unloading/reloading for a typical concrete under ( a )
uniaxiai and (b) t r i a x i a l compression.

7.  Causes Of Observed Behaviour
It is generally accepted that the short-term nonlinear behaviour of
concrete under increasing stress is dictated by internal processes
which take the form of extension and propagation of cracks, some of
which exist within the material even before the application of load
Crack extension and propagation occurs in localised regions in order
to relieve high tensile stress concentrations which develop near the
crack tips .This process results in formation of voids which
tend to increase the volume of concrete. However, the reduction of
high tensile stress concentrations may be considered equivalent to
the application of an internal compressive state of stress which tends
to decrease the volume of the material . The effect of void formation
on deformation, although detectable is small and may be ignored .As
a result, the internal compressive state of stress is considered to be
the predominant cause of the observed nonlinear response of
concrete under increasing stress. During unloading, the fracture
processes cease and, as discussed in the preceding section, concrete
behaviour is essentially linear. Fracture resumes when the maximum
stress level previously experienced by the material is exceeded.
 Failure criterion
Unsystematic variability of "maximum stress" level
exhi'bited by concretes with f~ (N/ram 2)
varying between approximan of fadure" revel trom max
tely 15 and 65. B, Deviatio stress"
level for a typical concrete (f~=47 N/ram2).

8. 2. Ductility and fracture of Reinforced Concrete Structural
The basic reason most buildings do not collapse under seismic action
is a material property called ductility. It is the property of a material
to deform permanently without loosing its strength, i.e. without
decreasing its ability to resist during deformation. A piece of wire,
e.g. an office clip bends but not brake. Due to ductility a system
“resists” mobilizing all its reserves (Fig. 2.1).
Figure 2.1 Ductility of a steel beam under bending
Ductility of metals occurs due to the relocation of zones of molecules
while they are still bonded with tensile forces. This behaviour occurs
under tensile and compressive stress. Concrete exhibits satisfactory
ductility in compression caused only by the slide mechanism (friction)
when it is simultaneously laterally under compression. When concrete is
not laterally compressed it exhibits reduced ductility since the
fracture mechanism is functioning that quickly exhausts the limits of its
further deformation (Fig. 2.2). The behaviour of concrete in tension and
in shear is not ductile but brittle.
Figure 2.2 Conventional concrete under compression without (1) or with confinement (2)

9.  Reinforced concrete exhibits ductile behaviour when:
- its longitudinal reinforcement is low (under-reinforced).
- it is over-reinforced transversely (stirrups).
- it sustains limited compressive stress.
- it contains everywhere the minimum constructional reinforcement
to be protected against tensile / shear brittle failure.
- it is confined and has compressive reinforcement in highly
compressed zones and in plastic hinges regions.
- it is appropriately designed as a system, i.e. does not receive major
concentrated deformations in particular positions (ground floor
pilotis, short columns).
- reinforcements are sufficiently anchored to prevent loss of
concrete cover or spalling at these positions. Finally it should be
emphasized that current understanding of earthquake resistant
design of structures is the assurance of the ductile behaviour of the
system through the definition of appropriate positions where
inelastic deformations will occur. This method is called capacity
design and comprises the basis of many modern earthquake
resistant design Codes (e.g. EC 8, EAK 2003).
 Notes about ductility and fracture of reinforced concrete
Other materials e.g. fiber-reinforced mortars, high-strength concretes exhibit
ductility under compression and under tension due to the slip (friction) of
fibers within the mortar’s matrix.

10. 3. Ductile , Brittle Behavior in Steel
Before fracture mechanics - impact testing was used to measure
impact behaviour and likelihood of brittle fracture. Developed in
response to onset of brittle failure in ductile materials e.g. steel
ships, bridges etc.
- Still used in quality control and Standards (ship plate etc).
 Primary function of Charpy test
 at high temperature, CVN for steel is relatively high but drops
with decrease in temperature.
 at low temperature steel can be brittle.
 the sudden drop in impact energy is the ductile-to-brittle
transition (DBT).
 steels should always be used above their DBT .
 ceramics and polymers also experience DBT .
The stress-strain curve for different material is different. The figure
below shows the comparison of the curves for mild steel, cast iron
and concrete. It can be seen that the concrete curve is almost a
straight line. There is an abrupt end to the curve. This, and the fact
that it is a very steep line, indicate that it is a brittle material. The

11. curve for cast iron has a slight curve to it. It is also a brittle material.
Both of these materials will fail with little warning once their limits
are surpassed. Notice that the curve for mild steel seems to have a
long gently curving "tail". This indicates a behavior that is distinctly
different than either concrete or cast iron. The graph shows that
after a certain point mild steel will continue to strain (in the case of
tension, to stretch) as the stress (the loading) remains more or less
constant. The steel will actually stretch like taffy. This is a material
property which indicates a high ductility.
If the original cross-sectional area is used to calculate the stress for
every value of applied force, then the resulting diagram is known as
the Engineering Stress-Strain Diagram. However, if the applied force
is divided by the actual value of the cross-sectional area, then the
resulting diagram is known as the True Stress-Strain Diagram.
Therefore, in engineering stress-strain diagram the ultimate and
failure strength points do not coincide whereas in the true diagram
they do. The difference in the two diagrams becomes apparent in the
inelastic region of the curve where the change in the cross-sectional
area of the specimen becomes very significant.