# Mechanical Metallurgy Questions and Answers – Hot Torsion Test

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This set of Mechanical Metallurgy Multiple Choice Questions & Answers (MCQs) focuses on “Hot Torsion Test”.

1. The fracture stress according to Orowan’s theory of brittle fracture is __________ (where E is Yong’s modulus, ϒp is the plastic work required to extend the crack wall of the length 2a).
a) (Eϒp/a)1/2
b) (Eϒp/a)
c) (Eϒp/2a)1/2
d) (Eϒp/2a)

Explanation: The first theory for brittle fracture was given by Griffith. But this was later modified by Orowan’s which uses the term of plastic work required to extend a crack, and this quantity is easy to measure experimentally.
-> (Eϒp/a)1/2.

2. The young’s modulus of the steel is 600 MPa, and the plastic stress required to extend the crack is 50*10-9, and the initial crack length is 2 microns. Find the fracture stress required to crack the material?
a) 15 MPa
b) 50 MPa
c) 15 GPa
d) 10 MPa

Explanation: The fracture stress according to Orowan’s theory of brittle fracture is (Eϒp/a)1/2
So; (600*106 * 50*10-9)/2*10-6
-> 15*106
-> 15 MPa.

3. The fracture stress according to Irwin’s modification is given as ________
a) (Eδc/πa)1/2
b) (Eδc/πa)
c) (Eδc/2πa)1/2
d) (Eδc/2πa)

Explanation: Irwin modified the hard to find plastic work term with the crack extension force δc.
So the term becomes (Eδc/πa)1/2

4. The unit of crack extension force δc is ____________
a) N m
b) N m-1
c) N m2
d) N m-2

Explanation: The crack extension force is defined as the:
-> σf=(Eδc/πa)1/2
δc=(σf*π*a/E)2
So the unit will be N m-1.

5. According to the fracture theory of the material, the critical value of the crack extension force, which makes the crack propagate to the fracture is called the fracture toughness of the material.
a) True
b) False

Explanation: The crack extension force can be assumed equivalent to the strain energy release rate, Or the rate of transfer of energy from the elastic strain field of the cracked structure to the inelastic process of the crack extension.

6. As the crack length increases, the required load value to extend the crack ______
a) remains constant
b) increases
c) decreases
d) cannot be determined

Explanation: As the crack length increases, the required stress values for the crack extension will eventually reduce. 7. The stress intensity factor at local crack tip is proportional to __________
a) length of crack
b) half-length of crack
c) square of half-length of the crack
d) square root of half-length of the crack

Explanation: The stress intensity factor is directly proportional to the square root of the half-length of the crack. Mathematically it is expressed as K.
-> K=σ√(a/2r)
Where σ is the nominal stress, and 2a is total crack length.

8. The stress intensity factor for a Sharpe elastic crack in the infinity wide plate is equal to ________
a) K=σ√(πa)
b) K=σ(πa)
c) K=σ(πa)2
d) K=σ√(π/a)

Explanation: In general, the stress intensity factor is given as the:
-> K=σ√(a/2r)
So in case of infinity wide plate with sharpest possible crack, K=σ√(πa).

9. The Dimension of the stress intensity factor K is __________
a) MPa m-1/2
b) MPa m1/2
c) MPa m
d) MPa m-1

Explanation: The Stress intensity factor K is defined as the K=σ√(πa).
The unit of σ is MPa and length has unit m, and the square root is equal to m-1/2
So the final unit will be MPa m-1/2

10. If the two flows of different geometry have the same value of K, then the stress field around each of the flow will be identical.
a) True
b) False 