Question

The resilience of steel can be found by integrating stress-strain curve up to the

Answer 1

In material science, resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading. Proof resilience is defined as the maximum energy that can be absorbed up to the elastic limit, without creating a permanent distortion. The modulus of resilience is defined as the maximum energy that can be absorbed per unit volume without 

creating a permanent distortion. It can be calculated by integrating the stress–strain curve from zero to the elastic limit. In uniaxial tension, under the assumptions of linear elasticity,

where Ur is the modulus of resilience, σy is the yield strength, εy is the yield strain, and E is the Young's modulus.[1] This analysis is not valid for non-linear elastic materials like rubber, for which the approach of area under the curve till elastic limit must be used.

Answer 2

The resilience of steel can be found by integrating the stress-strain curve up to the elastic limit.

Explanation:

• The energy stored in a body due to the deforming forces is called strain energy.
• When the strain energy is stored in a body due to the external forces, within the elastic limit, it is termed resilience.
• The maximum amount of energy that can be stored in a body up to the elastic limit is known as proof resilience.
• The proof resilience per unit volume is called the modulus of resilience.
• It is given by the area under the stress-strain curve up to the elastic limit.
• By integrating the stress-strain curve, the resilience of steel can be found.
• The stress-strain curve is given below in the figure.
• In the given graph, strain is represented by the x-axis and stress is represented by the y-axis.
• The point Y in the graph represents the elastic limit.

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