GATE MT branch:mt PYQs & Answers — Page 39 — Exam Papers

Questions 381–390 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 39 of 65

Two dislocation lines parallel to z-axis lying in the x-z plane are shown in the figure. The glide force (in Newton) exerted by the edge dislocation on the screw dislocation is: __________ (round off to nearest integer).

Diagram for Metallurgical Engineering question 46

For the edge, the shear stress component is given by:

Given: Shear modulus, G = 28 GPa Poisson’s ratio, ν = 0.3 Burgers vector, b = 0.29 nm Distance between the two dislocations = 0.5 nm

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In a material, a shear stress of 100 MPa is required to bow a dislocation line between precipitates with a spacing of 0.2 μm. If the spacing between the precipitates is increased to 0.5 μm, the shear stress (in MPa) to bow the dislocation would be: __________ (round off to nearest integer).

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A metal plate is in a state of plane strain (

) with

and

. If the Poisson’s ratio is 0.3, the ratio,

is __________ (round off to 1 decimal place).

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An infinite metal plate has a central through-thickness crack of length

mm. The maximum applied stress (in MPa) that the plate can sustain in mode I is: __________ (round off to nearest integer). Assume: Linear elastic fracture mechanics is valid Given: Fracture toughness,

MPa m

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A hypothetical binary eutectic phase diagram of A – B is shown below. An alloy with 5 wt.% B solidifies with no convection. Assuming steady state, the critical temperature gradient (in K mm⁻¹) required to maintain planar solidification front is: __________ (round off to nearest integer). Given: Diffusivity of B in liquid =

m² s⁻¹ Velocity of solidification front = 4 μm s⁻¹

Diagram for Metallurgical Engineering question 50

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A thick steel plate containing 0.1 wt.% C is carburized at 950 °C. The plate’s surface carbon concentration is maintained at 1.1 wt.% C. After 9 hours, the depth (in mm) below the surface at which the carbon concentration is 0.6 wt.% C will be: __________ (round off to 2 decimal places). Given: Diffusivity of carbon in γ-Fe at 950 °C =

m² s⁻¹ Error function table:

z	0.35	0.40	0.45	0.50	0.55	0.60
erf(z)	0.3794	0.4284	0.4755	0.5205	0.5633	0.6039

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At 25 °C, iron corrodes in a deaerated acid of pH 3 with a corrosion current density of 4 μA cm⁻². The corrosion potential (V) is: ________ (round off to 2 decimal places).

Given: βc = 0.1 V per decade of current density Exchange current density of hydrogen on iron surface = 10⁻⁹ A cm⁻² R = 8.314 J mol⁻¹ K⁻¹, F = 9600 C mol⁻¹ All potentials are with reference to standard hydrogen electrode.

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The radius of an interstitial atom which just fits (without distorting the structure) inside an octahedral void of a bcc-iron crystal (in nm) is: ________ (round off to 3 decimal places).

Assume the radius of Fe atom to be 0.124 nm.

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Nickel undergoes isothermal oxidation at 800 K for a duration of 400 s resulting in a weight gain of 2 mg cm⁻². The weight gain (mg cm⁻²) after a duration of 1600 s is: ________ (round off to nearest integer).

Assume: Weight gain is proportional to square root of time.

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A solid sphere (0.5 m radius) is enclosed within a larger hollow sphere (1 m radius), as shown in figure. The radiation exchange takes place between the outer surface (surface 1) of the small sphere and the inner surface (surface 2) of the bigger sphere. The value of the view factor, F₂₂ is: ________ (round off to 2 decimal places).

Given: View factor (Fᵢⱼ) is the fraction of the radiation leaving surface i that is intercepted by surface j.

Diagram for Metallurgical Engineering question 55

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