Which of the following is a true statement about elastic modulus, E?

Question

BlackTom AI · Accepted Answer

First, let's restate the core idea being tested: the elastic modulus, E, is a property of a material that describes its stiffness.

The statement to evaluate is: 'It is the slope of the tensile stress-strain curve in the linearly elastic region.' In materials science, the stress-strain curve for many materials is linear at small strains, and the slope of that linear portion is defined as Young's modulus, E. This captures how much stress is required to produce a given amount of strain within the elastic limit, before plastic deformation occurs.

Why this statement is true: The linearly elastic region follows Hooke's law, where stress equals E times strain (σ = Eε). The ratio σ/ε is constant in that region, and that constant is precisely E. Therefore, describing E as the slope of the stress-strain curve in this region is accurate.

Why other hypothetical options (if any) might be incorrect: Common incorrect choices might define E as the yield strength, ultimate tensile strength, or as a property only related to plastic deformation. These would be mistaken because E specifically pertains to the elastic response, not to yielding or post-yield behavior. If an option claimed E reflects plastic flow or energy dissipation during failure, that would mischaracterize E, since those aspects relate to other material properties such as yield strength, ultimate tensile strength, or toughness.

In summary, the given statement correctly identifies elastic modulus as the slope of the tensile stress-strain curve within the linearly elastic region, reflecting Hooke's-law behavior and the fundamental definition of Young's modulus.

Which of the following is a true statement about elastic modulus, E?

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