# Mechanical Metallurgy Questions and Answers – Griffith Theory of Brittle Fracture – 2

This set of Mechanical Metallurgy MCQs focuses on “Griffith Theory of Brittle Fracture – 2”.

1. The form of microcrack nucleation equation is_________
a) (τsi)nb = 2ϒs
b) (τsi)nb = 3ϒs
c) (τsi)nb = 4ϒs
d) (τsi)nb = 8ϒs

Explanation: Cottrell gave the equation for microcrack nucleation. Its physical significance is that a crack will form when the work done by the applied shear stress in producing the displacement nb is equal to work done in moving the dislocation against the friction stress and additionally the work in producing the new fracture surface.

2. Which of the following force is responsible for forcing dislocation together during cracking?
a) Tensile force
b) Shear force
c) Bending force
d) Torsional force

Explanation: The shear force is responsible for piling the dislocation together in micro-cracking, but the tensile strength is required to make crack propagation.

3. The grain size has an effect on the ductile or brittle failure of material.
a) True
b) False

Explanation: The micro-cracks propagation in any material is strongly influenced by the barrier such as grain boundary. So, the smaller the grain size, higher will be the fracture strength.

4. Which of the following equation depicts the Cottrell formulation of ductile to brittle transition?
a) (τiD1/2+k’)k’ = Gϒsβ
b) (τiD1/2+k’)k’ > Gϒsβ
c) (τiD1/2+k’)k’ < Gϒsβ
d) (τiD1/2+k’) = Gϒsβ

Explanation: When the left side of the equation is greater than the right side of the equation, the shear stress is equal to yield stress. Thus, equation describes the ductile to brittle transition.

5. The ductile to brittle transition does not depend on the metallurgical feature. It is material-specific property.
a) True
b) False

Explanation: The limiting equation for transformation suggested by Cottrell is (τiD1/2+k’)k’ > Gϒsβ;
Here the factor k’ is dependent on both the material and metallurgical properties.

6. As the grain size decreases, the ductile to brittle transition temperature _________
a) increases
b) decreases
c) remains the same
d) no defined relationship between them

Explanation: As the temperature decreases, the lattice friction for dislocation movement increases which causes a brittle fracture in the material. If the grain size is smaller, it can withstand the lattice friction at temperature. Also, it will resist the brittle fracture.

7. If the surface energy is high then _____________ is not likely to happen.
a) brittle fracture
b) ductile fracture
c) fatigue fracture
d) pure shear fracture

Explanation: The brittle fracture leaves fresh surface on cracking. If the surface energy is high, it requires more energy for the brittle fracture to propagate, so it is unlikely for the brittle fracture to occur.

8. The necking is phenomena observed in ___________
a) ductile fracture
b) brittle fracture
c) fatigue fracture
d) creep fracture

Explanation: Ductile fracture occurs by gross plastic deformation before fracturing. So the cross-section area is reduced by the process of necking which eventually leads to fracture of the material.

9. Rupture is a type of _________
a) ductile fracture
b) brittle fracture
c) fatigue fracture
d) creep fracture

10. In the ductile material the necking begins, at the point where ________________
a) increased strain hardening cross the yield point
b) increased strain hardening fails to compensate for the decrease in the cross-section area
c) the decrease cross-sectional area reaches half the initial cross-sectional area
d) the decrease cross-sectional area reaches one-fourth of the initial cross-sectional area

Explanation: The ductile failure necking starts at ultimate tensile strength point in the engineering stress-strain curve. This is the point where the increased strain hardening fails to compensate for the decrease in cross-sectional area, so the curve shifts downwards. Sanfoundry Global Education & Learning Series – Mechanical Metallurgy.

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