. Figure shows the strain-stress curve for a givenmaterial. What are (i) Young's modulus and (ii)approximate yield strength for this material

1. Break Down the Problem

To determine Young's modulus and approximate yield strength from a stress-strain curve, we need to analyze specific regions of the curve:

1. Identify the slope of the initial linear region to find Young's modulus.
2. Identify the point at which the material begins to deform plastically to find the yield strength.

2. Relevant Concepts

1. Young's Modulus (E): This is defined as the ratio of stress (σ) to strain (ε) in the linear elastic region: $E = \frac{\sigma}{\epsilon}$ Here, σ is the stress, and ε is the strain.

2. Yield Strength (σ_y): The yield strength is the stress at which a material begins to deform plastically. This is typically indicated as the point where the curve deviates from the linear region.

3. Analysis and Detail

For a given stress-strain curve:

• Young's Modulus:

  • Identify two points in the linear region (Point A: σ₁, ε₁ and Point B: σ₂, ε₂).
  • Calculate the slope: $E = \frac{\Delta \sigma}{\Delta \epsilon} = \frac{\sigma_2 - \sigma_1}{\epsilon_2 - \epsilon_1}$

• Yield Strength:

  • Look for the point on the curve where the slope changes (this indicates plastic deformation begins).

4. Verify and Summarize

Using numerical values from the graph, substitute in the formulas to find Young's modulus and yield strength.

Final Answer

1. Young's Modulus (E) $\approx$ [calculated value in units of Pa].
2. Yield Strength (σ_y) $\approx$ [calculated yield point in units of Pa].

(Note: Actual numerical values would require specific points from the provided stress-strain curve).