Questions: Stress-Strain Behavior and Elastic Properties

Question 1

A steel bar is pulled in a tensile test beyond its yield point and into the necking region. What happens to engineering stress and true stress during necking?

• A. Both engineering stress and true stress decrease
• B. Both engineering stress and true stress continue to increase
• C. Engineering stress decreases while true stress continues to increase
• D. Engineering stress increases while true stress decreases

Answer: (C)

Engineering stress is force divided by the original cross-sectional area, which stays fixed. During necking, the actual load decreases (less force needed as the bar thins dramatically), so engineering stress drops. True stress, however, is force divided by the actual (current) cross-sectional area — and because the area shrinks faster than the load drops, true stress continues to rise until fracture. This divergence is why engineering and true stress-strain curves look very different beyond the ultimate tensile strength.

Question 2

Heat treatment and cold working significantly change a metal's Young's modulus (elastic modulus).

• T. True
• F. False

Answer: False

Young's modulus reflects the stiffness of interatomic bonds — how strongly neighboring atoms resist being pulled apart. This is a fundamental property of the atomic species and crystal structure, not of microstructure or processing history. Heat treatment and cold working alter yield strength and ductility by changing dislocation density, grain size, and precipitate distribution, but they leave the elastic modulus essentially unchanged. This is why you can stiffen a spring by cold-drawing the wire (raising yield strength) without changing how stiff it feels per unit strain.

Question 3

What physical quantity does the area under the stress-strain curve represent, and why is it important for material selection?

Model answer: The area under the stress-strain curve represents toughness — the energy per unit volume that a material can absorb before fracture. It is important because applications requiring resistance to impact or sudden loading (car bumpers, pressure vessels, crash structures) need materials that can absorb energy without breaking, not just materials that are strong or stiff.

Strength (yield or ultimate) tells you how hard it is to deform a material; stiffness (modulus) tells you how much it deforms under load. Neither alone captures whether a material survives an impact. Toughness combines both — a tough material must be both strong and ductile. Comparing curves: a brittle ceramic may have high strength but low toughness (small area) because it fractures before significant plastic deformation; a soft rubber has high ductility but low strength; a structural steel combines reasonable strength with significant ductility for high toughness.