Three elastic constants for a completely anisotropic elastic material which follows the Hooke's law are young's modulus, elastic limit stress and yield stress. Which of the following properties is most sensitive to increase in strain rate ?

From an alloy, two specimens are machined and tested separately under tension and compression. The engineering stress-strain curves as well as the true stress-true strain curves for tension and compression are plotted in the same diagram. Identify the correct statements:
P. The engineering stress-strain curves in tension and compression are identical.
Q. The true stress-true strain curve in compression is lower than the true stresstrue strain curve in tension due to Bauschinger effect.
R. The true stress-true strain curve in tension is above the corresponding engineering stress-strain, curve.
S. The true stress-true strain curve in tension and compression are identical.

A

P, Q

B

Q, R

C

Q, S

D

R, S

Elastic failure of a material occurs, when the tensile stress equals yield strength, yield point or the elastic limit. Also, the elastic failure occurs according to maximum strain theory, when the maximum tensile strain equals (where, $$\sigma $$ = yield strength and E = modulus of elasticity)

A

E

B

$$\sigma $$

C

$$\frac{\sigma }{{\text{E}}}$$

D

$$\frac{{\text{E}}}{\sigma }$$

Which of the following relationships is correct for relating the three elastic constants of an isotropic elastic material (where, E = Young's modulus, G = Modulus of rigidity or shear modulus v = Poisson's ratio)?

A

E = 2G (1 + v)

B

E = G (1 + v)

C

$${\text{E}} = \frac{{{\text{G}}\left( {1 + {\text{v}}} \right)}}{2}$$

D

E = 2G (1 + 2v)

E, G, K and μ elastic modulus, shear modulus, bulk modulus and Poisson’s ratio respectively. To express the stress strain relations completely for this material, at least __________

A

E, G and μmust be known

B

E, K and μmust be known

C

Any two of the four must be known

D

All the four must be known

What is the relationship between the linear elastic properties Youngs modulus, bulk modulus and rigidity modulus?

A

1/E = 9/k + 3/G

B

9/E = 3/K + 1/G

C

3/E = 9/K + 1/G

D

9/E = 1/K + 3/G

A steel has its yield strength of 200N/mm2 and modulus of elasticity of 1x105MPa. Assuming the material to obey hookes law up to yielding, what will be its proof resilience?

A

0.8 N/mm2

B

0.4 N/mm2

C

0.2 N/mm2

D

0.6 N/mm2

Identify the correct statements from the following:
P. 0.2% yield strength of a material implies 0.2% of the yield strength.
Q. Von-Misses yield criterion implies that yielding occurs when the distortion energy reaches a critical value.
R. Radius of the cylinderical Von-Misses yield surface increases as the grain, size of a single phase material decreases.
S. Tresca's yield criterion gives a circular cylinderical surface in the space of the three principal stresses.

A

P, Q

B

Q, R

C

P, R

D

Q, S

The true strain rate is given as ϒ, and conventional strain rate is given as ε. The engineering strain is equal to e. The relationship between conventional strain rate and true strain rate is _______

A

ϒ = ε

B

ϒ = ε/e

C

ϒ = ε/(1+e)

D

ϒ = ε*e

Determine the Poissons ratio and bulk modulus of a material, for which Youngs modulus is 1.2 and modulus of rigidity is 4.8.

A

7

B

8

C

9

D

10

If the specimen is deformed plastically beyond the yield stress in one direction, e.g., tension and then after unloading it is loaded in the opposite direction, e.g., compression, it is found that the yield stress is less than the original yield stress. This dependence of yield stress on direction loading is called ____________

A

bauschinger effect

B

strain hardening

C

residual stress

D

nabarro–herring effect