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Unit 14: Structural Mechanics in Construction and Civil Engineering
Material Properties
4.1
Concept of Brittle and Ductile Materials
Definitions:
Brittle – a property applicable to a material if fracture occurs soon after
the elastic limit is passed.
Ductile – a property applicable to a material if a large amount of plastic
deformation takes place between the elastic limit and the fracture point.
Ductility – the ability of a material to be permanently deformed without
breaking when the applied load is removed.
The stress-strain diagrams of various materials vary widely, and different
tensile tests conducted on the same material may produce different results,
depending upon the temperature of the specimen and the speed of loading.
It is possible, however, to distinguish some common characteristics among
the stress-strain diagrams of various groups of materials and to divide
materials into two broad categories on the basis of these characteristics,
namely, brittle materials and ductile materials. Typically brittle materials
have a fracture strain less than 0.05 (∊f < 0.05) and ductile materials have
a fracture strain greater than or equal to 0.05 (∊f ≥ 0.05).
test
specimen
brittle
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ductile
Ductile
materials
deform
much
more
than
brittle
materials.
Brittle materials fail suddenly, usually with no prior indication that collapse
is imminent. On the other hand, ductile materials, such as structural steel,
normally undergo a substantial deformation called yielding before failing,
thus providing a warning that overloading exists.
Brittle Materials
Brittle materials, which comprise cast iron, glass, and stone, are
characterized by the fact that rupture occurs without any noticeable prior
change in the rate of elongation. Thus, for brittle materials, there is no
difference between the ultimate strength and the breaking strength. Also,
the strain at the time of rupture is much smaller for brittle than for ductile
materials. From the figure, note the absence of any necking of the specimen
in the case of a brittle material, and observe that rupture occurs along a
surface perpendicular to the load. It is concluded from this observation
that normal stresses are primarily responsible for the failure of brittle
materials.
Ductile Materials
Ductile materials, which comprise structural steel, as well as may alloys of
other metals, are characterized by their ability to yield at
normal temperatures. As the specimen is subjected to an increasing load,
its length first increases linearly with the load and at a very slow rate. Thus,
the initial portion of the stress-strain diagram is a straight line with a steep
slope. However, after a critical value σy of the stress has been reached, the
specimen undergoes a large deformation with a relatively small increase in
the applied load. This deformation is caused by slippage of the material
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along oblique surfaces and is due, therefore, primarily to shearing stresses.
The elongation of the specimen after it has started to yield can be 200 times
as large as its deformation before yield. After a certain maximum value of
the load has been reached, the diameter portion of the specimen begins to
decrease, because of local instability. This phenomenon is known
as necking. After necking has begun, somewhat lower loads are sufficient
to keep the specimen elongating further, until it finally ruptures. Rupture
occurs along a cone-shaped surface which forms an angle of approximately
45° with the original surface of the specimen. This indicates that shear is
primarily responsible for the failure of ductile materials, and confirms the
fact that, under an axial load, shearing stresses are largest on surfaces
forming an angle of 45° with the load.
Ductility is important to both designers and manufacturers. The designer of
a component prefers a material that displays at least some ductility, so
that, if the applied stress is too high, the component deforms before it
breaks. Fabricators want a ductile material in order to form complicated
shapes without breaking the material in the process.
Ductility is a valuable property of many metals, including aluminum, gold,
iron, nickel, and silver. These metals can be drawn into wire, hammered
into various shapes, or rolled into sheets. The term malleability is often
used in place of ductility to describe the property of metals that allows them
to be hammered into thin sheets. Metals are not the only ductile substances
and not all metals are ductile. For example, modeling clay is a ductile
nonmetallic substance and impure tungsten is a nonductile metal.
These
notes
were
taken
http://www.engineeringarchives.com/les_mom_brittleductile.html
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4.2
Stress strain graphs for brittle and ductile materials
Typical stress: strain graphs. Source http://www.cyberphysics.co.uk/graphics/graphs/stress_strain.gif
The graph above depicts the stress: strain behaviour of the main types of
materials. Mild steel can be considered to be a ductile material and in such
a material up to a certain stress level (which is referred to as the yield)
stress, the relationship between stress and strain is linear. Once the
material is unloaded the object will return to its original shape or length. If
an attempt is made to increase the stress above the yield stresses. After
that, the object enters the plastic phase in which there is an increase in
stress due to an increase in strain. Once the material reaches its maximum
stress, it will snap and fail. Necking also occurs after the elastic region in
which there is a disproportionate increase in strain localize in small region
of the material.
Brittle materials such as glass and stone do not show any plastic plateau
and the linear portion continues right up to the ultimate stress.
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
Generally engineers avoid subjecting materials to stresses which
might result in a brittle failure as there will be no warning signs or an
impending failure.
Plastic objects exhibit a very small elastic region and a very long plastic
plateau in which there are large increases in strain for a very small increase
in stress.
Another graph which can be use to explain the concept to students is:
Typical stress: strain graphs. Source
http://www.teachengineering.org/collection/cub_/lessons/cub_images/cub_brid_lesson04_image6.jpg
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•
4.3
Note how concrete has a very small plastic plateau and is almost
simply elastic. Obviously due to steel its properties are altered.
Students should be encouraged to observe these details as it will help
in future units.
The various points along a Stress strain graph
Stress-Strain curve of a medium carbon structural steel
Elastic Limit
The elastic limit is the limit beyond which the material will no longer go
back to its original shape when the load is removed, or it is the maximum
stress that may be developed such that there is no permanent or residual
deformation when the load is entirely removed.
Elastic and Plastic Ranges
The region in stress-strain diagram from O to P is called the elastic range.
The region from P to R is called the plastic range.
Yield Point
Yield point is the point at which the material will have an appreciable
elongation or yielding without any increase in load.
Ultimate Strength
The maximum ordinate in the stress-strain diagram is the ultimate strength
or tensile strength.
Rapture Strength
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Rapture strength is the strength of the material at rupture. This is also
known as the breaking strength.
Modulus of Resilience
Modulus of resilience is the work done on a unit volume of material as the
force is gradually increased from O to P, in N·m/m3. This may be calculated
as the area under the stress-strain curve from the origin O to up to the
elastic limit E (the shaded area in the figure). The resilience of the material
is its ability to absorb energy without creating a permanent distortion.
Modulus of Toughness
Modulus of toughness is the work done on a unit volume of material as the
force is gradually increased from O to R, in N·m/m3. This may be calculated
as the area under the entire stress-strain curve (from O to R). The
toughness of a material is its ability to absorb energy without causing it to
break.
Working Stress, Allowable Stress, and Factor of Safety
Working stress is defined as the actual stress of a material under a given
loading. The maximum safe stress that a material can carry is termed as
the allowable stress. The allowable stress should be limited to values not
exceeding the proportional limit. However, since proportional limit is
difficult to determine accurately, the allowable stress is taken as either the
yield point or ultimate strength divided by a factor of safety. The ratio of
this strength (ultimate or yield strength) to allowable strength is called the
factor of safety.
4.4
Properties of Hardened Concrete
In the context of mix design the most important properties of concrete are
strength and durability.
Compressive Strength
This is normally considered to be the most important property in relation
to mature concrete. In the UK, ‘strength’ most commonly means
compressive strength as measured by cubes manufactured, cured and
tested according to BS 1881
(Note that the European Standard (BS EN 206) will refer to cylinders also,
which in general give lower strength results for a given concrete mix than
cube test results. When specifying strength it is therefore important that
the type of test required is included in the description. All references made
to strength below will be to compressive cube strength.) The compressive
strength is the most important property of concrete. The characteristic
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strength is measured by the concrete grade which in turn is measured by
the 28 day cube strength. Standard cubes are 150 mm or 100mm.
The strength of concrete is affected by the following aspects of mix
materials and proportions:
Tensile Strength
The tensile strength of concrete is about a tenth of the compressive
strength. The tension capacity is very poor and hence must be reinforced.
Modulus of elasticity
This is a typical stress-strain graph of concrete.
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Stress: strain graph for concrete. Source _ http://article.sapub.org/image/10.5923.j.jce.20110101.02_002.gif
Reinforcing steel
The reinforcing steel placed in concrete consists of a steel bar or wire mesh
used to make up for the poor tension capacities in concrete. The surface of
the steel bar is usually patterned to form a better bond with the concrete.
Steel is used due to the fact that it has a similar coefficient of thermal
expansion to that in concrete.
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Typical steel rebar. Source _ http://image.made-in-china.com/2f0j00gCvTjMyKLsur/Wire-Rod-and-Steel-Rebar.jpg
Typical steel mesh Source http://www.bestwiremesh.com/image/p-reinforced-steel-mesh-0-d.gif
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Stress strain graphs for rebar
This is a typical stress-strain graph of steel bars. Note that steel is much
more ductile than concrete which is brittle. At failure steel yields whilst
concrete crushes or cracks.
Typical stress: strain graph for steel. Source: http://images.tutorvista.com/content/solids-and-fluids/stress-straincurve.gif
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