Lecture 4

Asst. Lecturer Hasanein M Mahbuba 1

Tensile stress–strain 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

Lecture 4

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, ϒ shear strain. If the relationship between the applied shear

stress and shear strain rate ϒ -

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 (ɳ) of

the material. Water is an example of a Newtonian material. The following relationship defines

viscosity:

Elastic Properties

The modulus of elasticity, or Young’s 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 Hooke’s Law: E= σ/ϵ

Young’s modulus does depend on such factors as orientation of a single crystal material. For

ceramics, the Young’s modulus depends on the level of porosity. The Young’s 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.

Lecture 4

Asst. Lecturer Hasanein M Mahbuba 3

Tensile strength (TS)

It is the ability of a material to withstand tensile (stretching) loads without breaking.

Poisson’s ratio

Relates the longitudinal elastic deformation produced by a simple tensile or compressive

stress to the lateral deformation that occurs at same time:

υ = -ℰ lateral/ ℰ longitudinal

When a tensile stress is imposed on a metal specimen, an elastic elongation and accompanying

strain ϵz 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 ϵx = ϵy.

Lecture 4

Asst. Lecturer Hasanein M Mahbuba 4

For many metals and other alloys, values of Poisson’s ratio range between 0.25 and 0.35.

Also the maximum value for υ is 0.50.

For isotropic materials, shear and elastic moduli are related to each other and to

Poisson’s 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.

Example

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. (Poisson’s 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:

- Elasticity

It is the ability of a material to deform under load and return to its original size and shape

when the load is removed.

Lecture 4

Asst. Lecturer Hasanein M Mahbuba 5

-Stiffness (rigidity)

It is the measure of a material's ability not to deflect under an applied load. Stiffness

of a component is proportional to its Young’s modulus. A component with a high

modulus of elasticity will show much smaller changes in dimensions

So cast iron more rigid than steel,

- Plasticity

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.

Lecture 4

Asst. Lecturer Hasanein M Mahbuba 6

-Toughness

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.

-Ductility

Is the ability of a material to be permanently deformed without breaking when a force is

applied.

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

materials

The percent elongation %EL is the percentage of plastic strain is:

Lecture 4

Asst. Lecturer Hasanein M Mahbuba 7

-Brittleness

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.

- Malleability

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.