Mechanical Properties of Materials - 1 - GATE ME Strength Free MCQ Test

The strain is defined as the ratio of change in dimension to the original dimension.

If ‘δl’ changes in the length and ‘l’ is the original length, strain = δl/l

Important Terms:

• The ratio of change in length to the original length is called the longitudinal strain.
• The ratio of change in diameter/breadth to original diameter/breadth is called the lateral strain.
• The volumetric strain of a deformed body is defined as the ratio of the change in volume of the body to the deformation to its original volume.
• Shear strain is defined as the strain accompanying a shearing action. It is the angle in radian measure through which the body gets distorted when subjected to external shearing action.

The stress-strain diagram for steel is a graphical representation of the relationship between stress and strain during the deformation of steel. The diagram typically shows stress on the y-axis and strain on the x-axis.

Statement 1 is correct because, for small values of strain, the relationship between stress and strain is linear, and stress is proportional to strain. This behavior is known as Hooke’s Law, and it is valid until the stress reaches the proportional limit. The proportional limit is the point beyond which the relationship between stress and strain is no longer linear.

Statement 2 is also correct because, if the stress exceeds the proportional limit, the strain begins to increase more rapidly, and the slope of the curve decreases. This behavior is due to the onset of plastic deformation, which causes the steel to permanently deform even after the stress is removed. The stress at which plastic deformation begins is known as the yield strength, and it is typically higher than the proportional limit.

Therefore, both statements 1 and 2 are correct.

The linear relationship between stress and strain for a bar in simple tension or compression can be expressed by the equation

in which Eis a constant of proportionality known as modulus of elasticity for the material. The modulus of elasticity is the slope of the stress- strain diagram in the linearly elastic region and its value depends upon the particular material being used.

Plasticity is defined as the property of a material due to which it is permanently deformed due to loading. Elasticity is the temporary form of deformation. Twinning and Slip are mechanisms of Plastic deformation.

At first, the strain is proportional to strain or elongation is proportional to the load giving a straight-line relationship.

A further increase in the load after yield load will cause marked deformation in the whole volume of the metal. The maximum load which the specimen can withstand without failure is called the load at the ultimate strength.

To match List-I (Materials) with List-II (Poisson's Ratio), it's essential to know typical values for each material:

• Rubber: Poisson's ratio is typically around 0.5.
• Brass: Ranges from 0.34 to 0.36.
• Grey cast iron: Around 0.25 - 0.30.
• Steel: Approximately 0.27 - 0.30.

This corresponds to the code (a) 2 4 1 3

Thus option A is correct.

Ultimate tensile strength is corresponding to the maximum load and cross-sectional area of the specimen at the start of the test.

Ultimate tensile strength = 

Area = 1 cm² and maximum load = 5 tonnes
So ultimate tensile strength = 5 tonnes/1 cm² = 5 tonnes/cm²

The point of stretching where it increases suddenly is known as yield strength, i.e. the region where the stretch is elastic. Tensile strength is the force needed to fracture the material. Impact strength is the capacity of a material to resist shock energy before a fracture.
 

It is the property of materials to absorb energy and to resist shock and impact loads. It is measured by the amount of energy absorbed per unit volume within elastic limit this property is essential for spring materials. The resilience of material should be considered when it is subjected to shock loading.