Question

What property is measured by the slope of the initial, linear portion of a stress-strain diagram?

• A. Toughness
• B. Ductility
• C. Modulus of elasticity
• D. Malleability

Hint:

Think: Stiffness = slope of the elastic region. That slope is the modulus of elasticity (Young’s modulus).

Answer 1

The Correct Option is C

The stress-strain diagram is a graphical representation of how a material deforms under load. The initial straight-line portion of this graph corresponds to the elastic region — where the material will return to its original shape once the load is removed.
Modulus of Elasticity (Young’s Modulus):

• Defined as the ratio of stress to strain in the linear (elastic) region: \[ E = \frac{\text{Stress}}{\text{Strain}} \]
• It measures the stiffness of a material — i.e., how much it resists deformation when a force is applied.
• A steeper slope in this region means a stiffer material with a higher modulus.
• Typical values: Steel has a high modulus, while rubber has a low modulus.

Why the Other Options Are Incorrect:

• (A) Toughness: Represents the total area under the stress-strain curve — a measure of energy absorbed before fracture, not the slope.
• (B) Ductility: Indicates how much a material can stretch before breaking — measured by strain, not slope.
• (D) Malleability: Refers to the ability to deform under compressive stress — unrelated to the initial linear slope.

Thus, the slope of the initial linear portion of the stress-strain diagram gives the modulus of elasticity.