Question:
The slope of initial straight line portion of the stress - strain curve is known as
The slope of initial straight line portion of the stress - strain curve is known as
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Stress-Strain Slopes: Slope of initial linear stress-strain curve = Young's Modulus ($E$) $\equiv$ STIFFNESS (Resistance to elastic deformation).
Updated On: Sep 15, 2026
- Stiffness
- Relaxation
- Plasticity
- Creep
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Elastic constitutive slope: the slope of the initial linear elastic region of the tensile stress-strain curve ($\Delta \sigma / \Delta \epsilon$) represents the Modulus of Elasticity ($E$), which quantifies the fundamental material property of Stiffness.
Key Formula or Approach:
\[ \mathbf{Slope} = \frac{\Delta \text{Stress } (\sigma)}{\Delta \text{Strain } (\epsilon)} = \mathbf{Young's \text{ } Modulus \text{ } (E) \equiv Stiffness} \]
Step 2: Detailed Explanation:
In materials engineering and mechanical property characterization:
- On a standard tensile stress-strain curve:
1. Initial Straight Line Portion: Represents the linear elastic deformation zone where Hooke's law holds true.
2. Slope of this Line: Calculated as $\frac{\Delta \sigma}{\Delta \epsilon} = E$ (Young's Modulus of Elasticity).
3. Stiffness (A): The mechanical property of a material that enables it to resist elastic deformation or deflection when subjected to load, quantitatively measured by the Modulus of Elasticity (slope of the stress-strain curve).
4. (Plasticity = permanent deformation; Creep = time-dependent deformation under constant stress; Relaxation = time-dependent stress reduction under constant strain).
Step 3: Final Answer:
Hence, the slope of the initial straight line portion is known as Stiffness, matching option (A).
Elastic constitutive slope: the slope of the initial linear elastic region of the tensile stress-strain curve ($\Delta \sigma / \Delta \epsilon$) represents the Modulus of Elasticity ($E$), which quantifies the fundamental material property of Stiffness.
Key Formula or Approach:
\[ \mathbf{Slope} = \frac{\Delta \text{Stress } (\sigma)}{\Delta \text{Strain } (\epsilon)} = \mathbf{Young's \text{ } Modulus \text{ } (E) \equiv Stiffness} \]
Step 2: Detailed Explanation:
In materials engineering and mechanical property characterization:
- On a standard tensile stress-strain curve:
1. Initial Straight Line Portion: Represents the linear elastic deformation zone where Hooke's law holds true.
2. Slope of this Line: Calculated as $\frac{\Delta \sigma}{\Delta \epsilon} = E$ (Young's Modulus of Elasticity).
3. Stiffness (A): The mechanical property of a material that enables it to resist elastic deformation or deflection when subjected to load, quantitatively measured by the Modulus of Elasticity (slope of the stress-strain curve).
4. (Plasticity = permanent deformation; Creep = time-dependent deformation under constant stress; Relaxation = time-dependent stress reduction under constant strain).
Step 3: Final Answer:
Hence, the slope of the initial straight line portion is known as Stiffness, matching option (A).
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