Stress-Strain Curve - UNSOLVED PRACTICE SET

Q7. Draw a labelled stress-strain curve for a ductile metal and identify the following points: proportional limit, elastic limit, yield point, ultimate strength, and fracture point.

Q8. What is the difference between the proportional limit and the elastic limit? Can a material have different values for these two limits?

Q9. Explain what happens in the region between the yield point and the breaking point on a stress-strain curve.

Q10. In your school, a student stretches two wires — one of steel and one of copper — and plots their stress-strain curves. The steel curve is steeper but breaks at a lower strain than copper. What does this tell you about the two materials?

Q11. Why does the stress-strain curve for rubber look very different from that of a metal? Sketch and compare.

Q12. What is "permanent set" in a material? How is it related to plastic deformation?

Q13. Describe the stress-strain curve for a ductile material (like mild steel) in detail. Explain each region:

(i) Proportional limit (OA)

(ii) Elastic limit

(iii) Yield point and yield strength

(iv) Strain hardening region

(v) Ultimate tensile strength

(vi) Necking and fracture

Draw a neat diagram and explain the significance of each point for engineering design.

Q14. The stress-strain curve for a material is shown (describe verbally): From O to A, linear with slope 2 × 10¹¹ Pa. Point A at strain 0.001. From A to B, curve rises to stress 3 × 10⁸ Pa at strain 0.002. From B to C, stress remains nearly constant while strain increases to 0.02. From C to D, stress rises to 5 × 10⁸ Pa at strain 0.15. From D to E, stress falls to 4 × 10⁸ Pa at strain 0.2 where fracture occurs.

(a) Calculate Young's modulus.

(b) Identify the elastic limit and yield point.

(c) Calculate the yield strength.

(d) Identify the ultimate tensile strength.

(e) Calculate the toughness (approximate area under the curve).

(f) Classify this material as ductile or brittle.

Q15. Compare and contrast the stress-strain curves for:

(a) A ductile metal (like mild steel)

(b) A brittle material (like glass)

(c) An elastomer (like rubber)

(d) A composite material (like bone)

For each, discuss:

(i) The shape of the curve

(ii) The presence or absence of a plastic region

(iii) The energy absorption capacity

(iv) A practical application based on these properties

Q16. The following data was obtained in a school experiment where a steel wire was stretched:

Table

Load (N) 0 10 20 30 40 50 60 70 80

Extension (mm) 0 0.5 1.0 1.5 2.0 2.5 3.5 5.0 7.0

(a) Plot a graph of stress vs strain (wire: L = 2 m, A = 0.5 mm²).

(b) Identify the proportional limit from your graph.

(c) Calculate Young's modulus from the linear portion.

(d) Identify where the elastic limit might be.

(e) Estimate the yield strength and discuss any uncertainties.

Q17. Two materials A and B have the following stress-strain characteristics:

Material A: Breaks at strain 0.005 with stress 4 × 10⁸ Pa; shows no plastic deformation

Material B: Yield point at strain 0.002 (stress 2.5 × 10⁸ Pa); ultimate strength 5 × 10⁸ Pa at strain 0.2; breaks at strain 0.25

(a) Calculate Young's modulus for both materials (assume linear up to yield/proportional limit).

(b) Which material is stronger? Which is tougher?

(c) Which would you choose for making a spring? Why?

(d) Which would you choose for making safety glass? Why?

(e) Sketch both curves on the same axes.

Q18. In a school project, students are asked to analyse the stress-strain behaviour of different materials used in construction:

(a) Why are stress-strain curves important for civil engineers when designing buildings?

(b) What properties would you look for in materials used for earthquake-resistant buildings?

(c) Why is concrete often reinforced with steel?

(d) Discuss why the stress-strain curve of bone is different from that of steel and what advantage this provides.

(e) Design an experiment to obtain the stress-strain curve for a rubber band and compare it with a metal wire.