Question

During material testing, stress is applied from time \(t_i\) to \(t_f\) as shown below: 

Choose the option(s) where the strain response is correctly mapped to its material class.

• A. P- purely elastic; Q- purely viscous; R- viscoelastic
• B. P- purely elastic; Q- viscoelastic; R- purely viscous
• C. P- purely viscous; Q- purely elastic; R- viscoelastic
• D. P- purely viscous; Q- viscoelastic; R- purely elastic

Hint:

In material testing, {purely viscous} materials deform continuously under stress and do not recover, {purely elastic} materials recover fully once stress is removed, and {viscoelastic} materials show a combination of both behaviors.

Answer 1

The Correct Option is D

In this question, we are analyzing the stress and strain response of three different materials under stress applied from \( t_i \) to \( t_f \). The plots provided (P, Q, and R) show the strain responses for each material. Let’s break down each material’s behavior based on the strain response.
- Plot P: In this plot, we see that the strain increases linearly as the stress is applied and then remains constant after the stress is removed. This behavior is characteristic of a purely viscous material. Viscous materials are time-dependent and exhibit a continuous deformation under stress without recovering once the stress is removed. Hence, Plot P corresponds to a purely viscous material.
- Plot Q: The strain increases initially with the application of stress and reaches a maximum, followed by a gradual decrease. This behavior suggests a material that exhibits both elastic and viscous characteristics, which is typical of a viscoelastic material. In viscoelastic materials, stress results in both immediate deformation (elastic) and time-dependent deformation (viscous). Hence, Plot Q corresponds to a viscoelastic material.
- Plot R: The strain increases as the stress is applied but returns to zero immediately after the stress is removed, indicating full recovery. This is typical of a purely elastic material. Elastic materials deform under stress but fully recover once the stress is removed, which is represented by Plot R.
Therefore, based on the analysis of the plots, the correct answer is (D) P- purely viscous; Q- viscoelastic; R- purely elastic.