This set of Mechanical Metallurgy Multiple Choice Questions & Answers (MCQs) focuses on “Elastic Behaviour – Stress Concentration”.

1. A geometrical discontinuity in a body, such as a hole or a notch result in nonuniform distribution of stress at the vicinity of discontinuity. At the region near the discontinuity, the local stress will be higher than normal stress distribution.

a) True

b) False

View Answer

Explanation: The stress concentration occurs at discontinuity. The relative cross-sectional area of a specimen with a discontinuity is lower than the sample without discontinuity. But the value of total stress remains the same for both the specimen, so the extra stress per unit area will accumulate at a discontinuity in the form of stress concentration.

2. The stress concentration is generally expressed by a theoretical stress-concentration factor k_{t}. Generally, K_{t} is described as the ratio of _________________

a) σ_{max} / σ_{min}

b) σ_{min}/ σ_{max}

c) σ_{max}/σ_{nominal}

d) σ_{nominal}/σ_{max}

View Answer

Explanation: K

_{t}is described as the ratio of maximum stress to the nominal stress based on the net section. Higher the stress concentrations, more will the stress on discontinuity.

3. In addition to producing the stress concentration, a notch also creates a localized condition of the biaxial or triaxial stress.

a) True

b) False

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Explanation: A circular hole in a plate subjected to axial load creates the radial as well as longitudinal stress at the periphery of the hole. The leading cause of this state of stress is the geometry at the tip of the notch.

4. A rectangular plate has circular hole in center as shown in the figure. There are 4 points located in the plate, find out the point where localized stress will be maximum.

a) 1

b) 2

c) 3

d) 4

View Answer

Explanation: In addition to axial stress, the radial and longitudinal stresses will also be acting on the circular hole. The expression for longitudinal stresses given as:

\(\sigma\theta=\frac{\sigma}{2}(1+\frac{a^2}{r^2})-\frac{\sigma}{2}(1+3\frac{a^4}{r^4})cos2\theta\)

When ϴ=π/2 and r=a (the point 1); the value of the stress at σϴ=3σ.

5. The value of stress concentration for circular hole in a plate subjected to uniform stress of σ is equal to ________

a) 1

b) 4

c) 3

d) 10

View Answer

Explanation: Stress concentration is given as

=> σ

_{max}/σ

_{nominal}

For the circular hole σ

_{max}=3σ.

So, the stress concentration will 3σ/σ=3.

6. An elliptical hole in a plate as shown in the figure. The value σ_{max}= σϴ = __________

a) \(\sigma\theta=\frac{\sigma}{2}(1+\frac{a^2}{r^2})-\frac{\sigma}{2}(1+3\frac{a^4}{r^4})cos2\theta\)

b) \(\sigma\theta=\frac{\sigma}{2}(1+3\frac{a^4}{r^4})cos2\theta\)

c) \(\sigma\theta=\sigma(1+2\frac{a}{b})\)

d) \(\sigma\theta=\sigma(1+2\frac{a^2}{b^2})\)

View Answer

Explanation: The stress concentration for an elliptical hole is given as

\(\sigma\theta=\sigma(1+2\frac{a}{b})\)

If the values of a=b; then ellipse will become a circle: => σ

_{max}=3σ.

Therefore, a narrow hole will create more stress concentration than a wide hole.

7. The following diagram shows a rectangular plate with a circular hole at the ends. The dimension of the plate is shown in the figure. If the ratio of b/r increase, the stress concentration factor K_{t} will __________

a) increase

b) decrease

c) remain constant

d) cannot comment

View Answer

Explanation: As the ratio b/r increase, there are two possible cases:

(i) value of b is increasing –> depth of crack is expanding

(ii) value of r is decreasing –> crack is getting narrower

So, both the condition will increase the severity of the crack, and the stress concentration factor will increase.

8. The following diagram shows a rectangular plate with a circular hole at the ends. The dimension of the plate is shown in the figure. If the ratio of r/h increase, the stress concentration factor K_{t} will ______________

a) increase

b) decrease

c) remain constant

d) cannot comment

View Answer

Explanation: As the ratio r/h increase, there are two possible cases:

(i) value of r is increasing–> width of the crack is expanding.

(ii) value of h is decreasing –> area of the remaining specimen is decreasing

So, both the condition will decrease the severity of crack, and stress concentration factor will increase.

9. The effect of the stress riser is much more pronounced in a brittle material than a ductile material. Which of the following is not the correct explanation for this behavior?

a) Strain hardening occurs in ductile material, which increases the required stress for the flow of crack

b) Strain hardening does not occur in a brittle material, so it results in sudden propagation of the crack

c) Redistribution of stress does not occur in a brittle material

d) The toughness of brittle material is much more than ductile material

View Answer

Explanation: Strain hardening occurs in ductile material with an increase in strain. Brittle material does not show strain hardening because before reaching the level of hardening it fails. Redistribution of stress occurs by the propagation of dislocation in the material. Brittle material does not show such behavior, but ductile material does show. Finally, toughness is defined as the area under the stress-strain curve, which is more in ductile material not in a brittle material, so the toughness of ductile material is more than brittle material.

**Sanfoundry Global Education & Learning Series – Mechanical Metallurgy.**

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