## Study of Elastic behavior:

### Searle’s Experiment:

• Two identical wires A and B are suspended from a rigid support so that the points of suspension are very close to each other. Searle’s apparatus blocks are attached to the lower ends of the wires by means of chucks F1 and F2. Searle’s apparatus block consists of two metal frames P and Q. The two frames are loosely connected by cross strips in such a way that the frame Q can move relatively with respect to frame P. A spirit level S is hinged to the frame P and is rested on the tip of a micromeer screw M which can work in a nut fixed in the frame Q. At the lower end, each frame carries a hanger from which slotted weights can be suspended. Wire A is dummy wire from which a fixed load of about 1 kg (dead weight) is suspended.

#### Procedure:

• Initially, the length (L) of wire B is measured. Its mean radius (r) is found with the help of micrometer screw gauge. Micrometer screw is adjusted to bring the bubble in the spirit level at the centre and the reading is noted.
• The load suspended from wire B is then increased in equal steps of about 0.5 kg-wt. let ‘m’ be the mass in the hanger. Each time, after waiting for about two minutes, the bubble is brought to the centre by rotating the screw and micrometer reading is noted. This is extension or elongation (l1) in the wire. This way five to six readings are taken.
• After loading procedure is complete the wire is unloaded in the same steps of 0.5 kg-wt and the readings ( l2) are noted again for each step.

#### Calculations:

• The mean of the readings for loading ( l1) and unloading ( l2) is calculated and represented as (l) for each step. Then Young’s modulus of material is calculated in each step using formula,

• The average value of Young’s Modulus (Y) is calculated. A care should be taken to avoid possible errors.

#### Sources of Errors:

• Error due to kinks in the wire.
• Errors due to a backlash of the screw.
• Error due to bending (yielding) of the support.
• Error due to thermal expansion or contraction.
• Error due to the crossing of the elastic limit and/or slipping of the wire from the chucks.

#### Behaviour (Stress-Strain Curve) of Wire of Ductile Material Under Steadily Increasing Load:

• The behaviour of wire under increasing load can be studied using Searle’s apparatus. The wire whose behaviour is to be studied is used in the apparatus, at the free end, increasing loads are applied. For each load, stress and strain are calculated. Then the behaviour of wire is studied by plotting a graph, stress versus strain.

##### Important Points on the Stress-Strain Curve:
• Elastic limit: It is the maximum stress to which a body can be subjected without permanent deformation.
• Breaking Point: It is the point at which a body subjected to stress breaks (fails)
• Breaking Stress: The stress required to cause actual fracture of a material is called the breaking stress or the ultimate strength.
• Yield Point: It is the point at which the extension in a wire begins to increase even without any increase in load.
• Set: It is the permanent strain produced in a wire when it is stretched beyond the elastic limit.

#### Types of Material on Their Elastic Behaviour:

• Materials which have a great plastic range get stretched to long thin wires before they break, are called ductile materials. Hence thin wires can be formed using ductile materials. e.g. steel, aluminium, gold, copper, silver etc.
• Few materials break quite suddenly as soon as the stress-strain curve starts deviating from the straight line after the elastic limit. They are called brittle materials. Hence thin wires cannot be formed using brittle materials. e.g. glass, ceramics, cast iron etc.

### Applications of Study of Elastic behavior of Material:

• The concept of elasticity is useful in the design of bridges, construction of homes, designs of structures, machinery, industry etc.
• The concept of elasticity is used in the design of crane ropes. The diameter of the ropes and the material can be calculated using the concept of stress. When designing some margins using the concept of a factor of safety is kept to avoid accidents.