Elasticity and Stress-Strain Relations - Mechanical Behaviour of Materials - Metallurgical Engineering Previous Year Questions

1

2007 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2007

A cylindrical specimen of an isotropic metal (Young's modulus, \( E = 200 \) GPa) is elastically deformed in tension. Length of this cylinder before deformation is 100 mm and the diameter is 10 mm. After the deformation, they are 100.1 mm and 9.996 mm, respectively. The shear modulus, \( G \), of this metal is [Given: \( E = 2 G (1+\nu) \)]

A

71.43 GPa

B

76.92 GPa

C

83.33 GPa

D

100.00 GPa

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2

2007 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2007

A dislocation free single crystal of aluminium has a theoretical shear strength of about
[Given: Shear Modulus, \(G = 28\) GPa]

A

28.0 GPa

B

4.5 GPa

C

0.56 GPa

D

0.07 GPa

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3

2007 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2007

The mechanical response of an elastomer (such as rubber) is characterized by

A

an increase in elastic modulus with increasing temperature

B

large recoverable strains

C

a decrease in elastic modulus with increasing temperature

D

an adiabatic decrease in temperature on stretching

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4

2007 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2007

The composite exhibits a Young's modulus of 103 GPa in the longitudinal direction (parallel to the fibre orientation). The volume fraction of the fibre is

A

5%

B

10%

C

25%

D

40%

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5

2007 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2007

The specific Young's modulus of the same composite in the transverse direction (perpendicular to the fibre orientation) is

A

3 GPa

B

4 GPa

C

10 GPa

D

403 GPa

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6

2008 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2008

In a tensile test of a ductile material, necking starts at

A

lower yield stress

B

upper yield stress

C

ultimate tensile strength

D

just before fracture

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7

2008 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2008

The stress concentration factor \(K_t\) for a circular hole located at the center of a plate is

A

0

B

1

C

3

D

tends to \(\infty\)

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8

2008 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2008

A steel bar (elastic modulus = 200 GPa and yield strength = 400 MPa) is loaded to a tensile stress of 1 GPa and undergoes a plastic strain of 2%. The elastic strain in the bar in percent is

A

0

B

0.2

C

0.5

D

2.0

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9

2008 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2008

The structure-sensitive properties are (P) elastic modulus (Q) yield strength (R) melting point (S) fracture strength

A

P, S

B

Q, S

C

Q, R

D

P, R

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10

2008 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2008

The elastic modulus of the composite parallel to the fiber direction in GPa is

A

15.1

B

23.1

C

43.4

D

46.2

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11

2008 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2008

If a load of 100 kg is applied on the composite in the fiber direction, the load carried by the fibers in kg is

A

6

B

47

C

94

D

100

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12

2009 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2009

A property that CANNOT be obtained from a tensile test is

A

Young’s modulus

B

yield strength

C

ultimate tensile strength

D

endurance limit

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13

2009 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2009

During a sheet stamping operation, it is observed that sheet surface area triples. The true thickness strain is

A

-1.1

B

-0.333

C

+0.333

D

+1.1

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14

2009 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2009

The stress applied on a material is
\[\sigma_{ij} = \begin{bmatrix} 21 & 0 & 0 \\ 0 & 21 & 0 \\ 0 & 0 & 21 \end{bmatrix} \text{ MPa}.\]
The maximum shear stress experienced by it is

A

0 MPa

B

10.5 MPa

C

21 MPa

D

63 MPa

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15

2009 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2009

The rod is loaded to 1000 N, the magnitude of transverse strain is

A

0.025%

B

0.075%

C

0.15%

D

0.25%

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16

2009 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2009

The modulus of resilience of the material is

A

0.25 MJ/m³

B

0.50 MJ/m³

C

0.75 MJ/m³

D

1.25 MJ/m³

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17

2010 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2010

The engineering stress-strain curve for a ceramic material is

A

parabolic

B

exponential

C

logarithmic

D

linear

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18

2010 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2010

A square of 9 mm² area is subjected to simple shear displacement √3 mm along x-direction, as shown below

The shear strain imparted will be

A

1/3

B

1/√3

C

√3

D

3

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19

2010 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2010

The reduction in diameter on the application of tensile load is

A

0.011 mm

B

0.014 mm

C

0.018 mm

D

0.021 mm

Check answer

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20

2010 · Metallurgical Engineering · Mechanical Behaviour of Materials · Elasticity and Stress-Strain Relations

Metallurgical Engineering (MT) 2010

The elastic strain energy (in kJ m^-3) is approximately

A

200

B

240

C

280

D

320

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