# Mechanical Behaviour Questions and Answers – Grain Boundary Strengthening

This set of Mechanical Behaviour Multiple Choice Questions & Answers (MCQs) focuses on “Grain Boundary Strengthening”.

1. Which factor doesn’t promote fine grain structure?
a) Fast cooling rates
b) Inoculating agents
c) Mechanical vibrations
d) Longer holding times at high temperature

Explanation: Fast cooling rates give high undercooling and promote nucleation. Inoculating agents and mechanical vibrations also favor nucleation while holding on high temperature favor growth of grains.

2. For ASTM grain size number 10, give the number of grains per square inch at a magnification of 100x.
a) 512
b) 1024
c) 2048
d) 200

Explanation: The number of grains per square inch is given by N * (M/100)2 = 2n-1
where n is ASTM grain size number
N is the number of grains in one square inch
M is the magnification
It gives 512 grains per square inch.

3. What is the ASTM grain size number for 1024 grains per square inch at 100x magnification?
a) 10
b) 11
c) 12
d) 13

Explanation: Number of grains per square inch are given by N = 2n-1. Where n is ASTM grain size number. It gives ASTM grain size number 11.

4. Hall-Petch equation gives the relation between grain size and ___
a) Toughness
b) Ductility
c) Yield strength
d) Tensile strength

Explanation: Yield strength can be related to grain size by Hall-Petch equation. On decreasing grain size, yield strength of material increases. This relation is taken care in grain boundary strengthening.

5. Which symbol represents frictional stress in the Hall-Petch equation?
a) σ0
b) σi
c) Ky
d) d

Explanation: σi represents frictional stress opposing motion of a dislocation. σ0 stands for yield strength. d is average grain diameter.
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6. What term is used for the temperature at which the strength of grain boundary and strength of grain is equal?
a) Equicohesive temperature
b) Curie temperature
c) Recrystallization temperature
d) Hardening temperature

Explanation: The temperature at which the strength of grain boundary and strength of grain is equal is known as equicohesive temperature. At a temperature lower than this, grain boundaries are stronger than grains.

7. Which property doesn’t improve on grain refinement?
a) Fatigue strength
b) Tensile strength
c) Hardness
d) Creep strength

Explanation: Tensile strength and hardness improve on increasing grain boundary area. It is shown by Hall-Petch relation. Creep strength on the other hand deteriorates on grain refinement.

8. A material shows maximum strength when it consists of ____ dislocations.
a) No
b) Large number of
c) Very less number of
d) Intermediate number of

Explanation: A material free from dislocations show maximum strength. Presence of dislocations make the slip and hence deformation easy. Thus, whiskers have very high strength.

9. The number of dislocations is directly proportional to ___ and inversely proportional to ___
a) Shear modulus, Burgers vector
b) Shear modulus, Stress
c) Stress, Shear modulus
d) Burgers vector, Stress

Explanation: N = π L τ k/G b
Here, the number of dislocations N which can be piled into a length L of a slip plane, b burgers vector and G is shear modulus. This relation was given by Eshelby.

10. Grain refinement decreases ductility of the material.
a) True
b) False

Explanation: On given boundary refinement 2 possibilities exist. It either slightly enhances ductility or doesn’t affect at all.

11. Grain size strengthening can be understood by __________
a) Orowan mechanism
b) Hall-Petch equation
c) Schmid’s law
d) Bragg’s law

Explanation: σ0 = σi + Ky d-1/2 Is Hall-Petch equation. Here, σ0 is yield strength, σi is frictional stress, Ky is constant and d is average grain diameter. This equation is a basis of grain boundary strengthening.

12. A coarse grained material shows better strength at higher temperatures.
a) True
b) False

Explanation: At temperatures higher than equicohesive temperature, grain boundaries are weaker than grains. It is due to the grain boundary slip. So coarse grained material is strong at higher temperatures.

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