Mechanical Behaviour Questions and Answers – True Stress Strain Curve

This set of Tough Mechanical Behaviour Questions and Answers focuses on “True Stress Strain Curve”.

1. What is an expression of true stress?
a) Pu / Ai
b) Pu / A0
c) P / Ai
d) P / A0

Explanation: True stress is shown with symbol σT. It is given by expression σT = P / Ai here P is load and Ai is an instantaneous or true area of cross section.

2. True strain is ____ than the engineering strain corresponding to a given load.
a) Larger
b) Smaller
c) Equal
d) Either smaller or equal

Explanation: True strain is given by ƐT = ln (L/L0). It is smaller than the engineering strain. It can be illustrated by ƐT = ln (1 + Ɛ) expression.

3. What is a relation between true and engineering strain?
a) ƐT = ln (1 + Ɛ)
b) ƐT = ln (L/L0)
c) ƐT = ln (ΔL/L0)
d) ƐT = ΔL/L0

Explanation: ƐT = ln (1 + Ɛ). Here ƐT is a true strain and Ɛ is engineering strain. This expression can be calculated using ƐT = ln (L/L0) expression.

4. What is the relation between true and engineering stress?
a) σT = ln (L/L0)
b) σT = ln (1 + Ɛ)
c) σT = σ (1 + Ɛ)
d) σT = σ (1 – Ɛ)

Explanation: σT = σ (1 + Ɛ). Here σT is true stress, σ engineering stress and Ɛ is engineering strain. It is applicable before onset of necking.

5. What term defines plastic instability?
a) dP = constant
b) dP = 0
c) dP < 0
d) dP > 0

Explanation: Plastic instability is characteristic of ductile materials. It is expressed as dP = 0. Here dP is change in load due to strain hardening.

6. Plastic instability occurs when the slope of the true stress strain curve ____ the true stress at the point.
a) Exceeds
b) Equals
c) Is less
d) Is less or higher

Explanation: Plastic instability condition is given by dP = 0. It can be further simplified in dσT/dƐT = σT. Which means the slope of the true stress strain curve equals the true stress at the point.

7. True value of stress experience by material _____ than the conventional one for a given load.
a) Higher
b) Lower
c) Equal
d) Higher or lower

Explanation: The true area of cross section at any load in the plastic range is smaller. While it is larger for original value. So true value is always higher.

8. What is considered more in mechanical working processes?
a) Yield stress
b) Shear stress
c) True stress
d) Engineering stress

Explanation: metal forming processes are extrusion, drawing, rolling, etc. True stress is considered to be more important than engineering stress. To correlate the theory for different forms of loading, true values are preferred.

9. True stress strain curve _______
a) Continuously rises
b) After yield point comes down
c) After yield point remains constant
d) Uncertain after yield point

Explanation: Instantaneous area decreases continuously with strain in the plastic range. So true stress curve continuously rises. It rises till the breaking point.

10. The points on the true stress strain curve ______ the conventional stress strain curves up to the onset of necking.
a) Lie on the left of
b) Lie on the right of
c) Superimpose
d) May lie on left or right

Explanation: Points on the true stress strain curve lie on the left of the conventional stress strain curve. It is up to onset of necking. This can be obtained by superimposing both the curves.

11. Materials in general have higher elastic strain of 50% order.
a) True
b) False

Explanation: Materials generally have very low elastic strain. It may be approximately 0.1%. On strains above it, materials deform permanently.

12. True stress value is affected by strain hardening.
a) True
b) False

Explanation: True stress is affected by strain hardening. So it varies from material to material. It is because an instantaneous area is taken into account.

Sanfoundry Global Education & Learning Series – Mechanical Behaviour & Testing of Materials.

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