furthermore, the modulus of elasticity of several ... modulus of elasticity, or young’s modulus...
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Asst. Lecturer Hasanein M Mahbuba 1
Tensile stressstrain curves for different materials. Shows in figure below
Furthermore, the modulus of elasticity of several materials effected by increasing temperature,
as is shown in Figure
Asst. Lecturer Hasanein M Mahbuba 2
Shear, or torsional stresses also evokes elastic behavior, Shear stress and strain are
proportional to each other through the expression
Where G is the shear modulus, shear strain. If the relationship between the applied shear
stress and shear strain rate -
is linear, we refer to that material as Newtonian. The slope of
the shear stress versus the steady-state shear strain rate curve is defined as the viscosity () of
the material. Water is an example of a Newtonian material. The following relationship defines
The modulus of elasticity, or Youngs modulus (E), is the slope of the stress-strain curve
in the elastic region. This relationship between stress and strain in the elastic region is known
as Hookes Law: E= /
Youngs modulus does depend on such factors as orientation of a single crystal material. For
ceramics, the Youngs modulus depends on the level of porosity. The Youngs modulus of a
composite depends upon the stiffness and
amounts of the individual components.
If a stress of 30,000 psi is applied to each material, the steel
deforms elastically 0.001.; at the same stress, aluminum deforms
0.003 in./in. The elastic modulus of steel is about three times
higher than that of aluminum.
Asst. Lecturer Hasanein M Mahbuba 3
Tensile strength (TS)
It is the ability of a material to withstand tensile (stretching) loads without breaking.
Relates the longitudinal elastic deformation produced by a simple tensile or compressive
stress to the lateral deformation that occurs at same time:
= - lateral/ longitudinal
When a tensile stress is imposed on a metal specimen, an elastic elongation and accompanying
strain z result in the direction of the applied stress as shown in figure
As a result of this elongation, there will be constrictions in the lateral (x and y), If the
applied stress is uniaxial (only in the z direction), and the material is isotropic, then x = y.
Asst. Lecturer Hasanein M Mahbuba 4
For many metals and other alloys, values of Poissons ratio range between 0.25 and 0.35.
Also the maximum value for is 0.50.
For isotropic materials, shear and elastic moduli are related to each other and to
Poissons ratio according to
In most metals G is about 0.4E; thus, if the value of one modulus is known, the other
may be approximated.
A tensile stress is to be applied along the long axis of a cylindrical brass rod that has a diameter
of 10 mm. Determine the magnitude of the load required to produce a 2.5 * 10-3 mm change in
diameter if the deformation is entirely elastic. (Poissons ratio for brass is 0.34, modulus of elasticity
is 97 GPA). Ans 5600 N
-Resilience (modulus of resilience)
The area contained under the elastic portion of a stress-strain curve, is the elastic energy
that a material absorbs during loading and subsequently releases when the load is removed. For
linear elastic behavior:
It is the ability of a material to deform under load and return to its original size and shape
when the load is removed.
Asst. Lecturer Hasanein M Mahbuba 5
It is the measure of a material's ability not to deflect under an applied load. Stiffness
of a component is proportional to its Youngs modulus. A component with a high
modulus of elasticity will show much smaller changes in dimensions
So cast iron more rigid than steel,
This property is the exact opposite to elasticity, it is the state of a material which has
been loaded beyond its elastic limit so as to cause the material to deform permanently. Under
such conditions the material will not return to its original shape.
Asst. Lecturer Hasanein M Mahbuba 6
The energy absorbed by a material prior to fracture is known as tensile toughness, it is
the ability of the materials to withstand bending or it is the application of shear stresses without
fracture, so the rubbers and most plastic materials do not shatter, therefore they are tough.
Is the ability of a material to be permanently deformed without breaking when a force is
A metal that experiences very little or no plastic deformation upon fracture is termed brittle.
Figure shows comparison of
stress-strain of brittle and ductile
The percent elongation %EL is the percentage of plastic strain is:
Asst. Lecturer Hasanein M Mahbuba 7
It is the property of a material that shows little or no plastic deformation before fracture when
a force is applied. Also it is opposite of ductility.
It is the ability of material to withstand deformation under compression without rupture or
the ability of material allows a useful amount of plastic deformation to occur under compressive
loading before fracture occurs. Such a material is required for manipulation by such processes
as forging, rolling and rivet heading.