A square of 9 mm2 area is subjected to simple shear displacement √3 mm along x-direction, as shown below: The strain imparted will be <img src="/images/question-image/metallurgical-engineering/miscellaneous-in-metallurgy/1684344946-M2-B-19-43.PNG" title="Miscellaneous in Metallurgy mcq question image" alt="Miscellaneous in Metallurgy mcq question image">

$$\frac{1}{3}$$

$$\frac{1}{{\surd 3}}$$

$${\surd 3}$$

Correct Answer: $$\frac{1}{{\surd 3}}$$

Engineering stress-strain curve for a metal under two conditions. A and B, are shown is the following figures. Identify the correct statement.

The resilience of the material is the same in conditions A and B

The resilience of the material is higher in condition B than in condition A

The toughness of the material is higher in condition A than in condition B

The toughness of the material is higher in condition B than in conditon A

Match the heat treatment for an eutectoid steel shown in the TTT diagram below (as P, Q, R and S) with the resulting microstructure listed below:
1. Fine pearlite
2. martensite
3. Bainite
4. Coarse pearlite

P-1, Q-2, R-4, S-3

P-4, Q-1, R-3, S-2

P-2, Q-1, R-3, S-4

P-1, Q-4, R-3. S-2

An elliptical dislocation loop is gliding on plane ABCD of a single crystal of BCC material as shown in the following figure. It is gliding along the burger vector 'b'. Identify the correct statement.

P. Plane ABCD belongs to the family of (110).
Q. Burger vector 'b' belong to direction.
R. Dislocation has the edge character at point x and the screw character at point z.
S. Dislocation has the screw character at point x

P, Q

Q, R

P, R

P, S

Thin layer of material B (of total amount m) is plated on the end faces of two long rods of material A. These are then joined together on the plated side (see the figure below) and heated to a high temperature. Assuming the diffusion coefficient of B in A is D, the composition profile CB along the rod axis x after a time t is described by

$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}\exp \left$$

$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}erf\left$$

$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}\left$$

$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}t$$

An alloy of overall composition, X_B = 0.7 was equilibrated at temperature T₁. Microstructural analysis showed two phases, (α and β, and that the phase fraction of β was 0.75. Given that the equilibrium composition of β at Ti is 0.9 as shown in the phase diagram below, the maximum solubility of B in α (in mole fraction) at this temperature is . . . . . . . .

0.05

0.10

0.50

0.85

The diffusion couple shown below is made from two A-B alloys. The initial compositions of the two alloys are indicated in the diagram. The centreline is at x = 0. The couple is held at an elevated temperature for 40 hours. Diffusivity; D = 3 × 10^-11 m^-2 s^-1. Assume the diffusion couple to be infinitely long.

Which of the parameters give the composition profile in the following form?
$$C\left( {x,t} \right) + {c_1} + {c_2}\,erf\left( {\frac{1}{{2\sqrt {Dt} }}} \right)$$

c1 = 0.45, c2 = 0.05

c1 = 0.5, c2 = 0.4

c1 = -0.05, c2 = 0.45

c1 = 0.1, c2 = 0.9

A furnace wall consists of four layers of different materials, M₁, M₂, M₃ and M₄. If the layers are of equal thickness and the steady state temperature profiles is as shown below, then the material with the lowest thermal conductivity is

M1

M2

M3

M4

A simplified energy band-diagram of an intrinsic semiconductor at thermal equilibrium (300 K) is shown. In the accompanying table, which one of the four cloumns correctly represents the listed parameters? Assume same effective mass for electrons and holes.

<table class="table-style-1"> <tr> <td rowspan="2">Parameter</td> <td colspan="4">Energy-difference</td> </tr> <tr> <td>Column 1</td> <td>Column 2</td> <td>Column 3</td> <td>Column 4</td> </tr> <tr> <td>Band-gap</td> <td>ΔE2</td> <td>ΔE1</td> <td>ΔE2</td> <td>ΔE1</td> </tr> <tr> <td>Electron affinity</td> <td>$$\frac{{\Delta {E_1}}}{2}$$</td> <td>ΔE2 - ΔE1</td> <td>$$\frac{{\Delta {E_2}}}{2}$$</td> <td>ΔE2 - $$\left( {\frac{{\Delta {E_1}}}{2}} \right)$$</td> </tr> <tr> <td>Work function</td> <td>ΔE1 + ΔE2</td> <td>ΔE2 - $$\left( {\frac{{\Delta {E_1}}}{2}} \right)$$</td> <td>ΔE1 - $$\frac{{\Delta {E_2}}}{2}$$</td> <td>ΔE2 + $$\left( {\frac{{\Delta {E_1}}}{2}} \right)$$</td> </tr></table> Column 1

Column 2

Column 3

Column 4

Which of the following cooling curves (shown in schematic) in an eutectoid steel will produce 50% bainitic structure?

From a 2 m × 1.2m sheet, squares are Cut out from each of the four comers as shown in the figure and then the sides are bent to form an open box. The maximum possible volume (in m³) of the box is

0.14

0.26

0.54

0.82