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Elasticity, Plasticity, and Yield Criteria(6)Dislocation Theory and Strengthening Mechanisms(9)Fracture, Fatigue, and High Temperature Deformation(18)

Elasticity, Plasticity, and Yield Criteria

6 Questions

GATE→2025→Mechanical Behaviour of Materials→Elasticity, Plasticity, and Yield Criteria

Q1

NAT[1 Mark]

The hydrostatic stress for the stress tensor provided below is _______ $\text{MPa}$ (in integer). $$\begin{bmatrix} 150 & 0 & 0 \\ 0 & -100 & 100 \\ 0 & 100 & 250 \end{bmatrix}\text{ MPa}$

Explanation

GATE→2025→Mechanical Behaviour of Materials→Elasticity, Plasticity, and Yield Criteria

Q2

NAT[2 Marks]

A cylindrical specimen is subjected to plastic deformation in tension up to a uniform elongation of $10\%$. The final cross-sectional area of the gage section is found to be $20\text{ mm}^2$. The initial cross-sectional area of the gage section is ___ $\text{mm}^2$ (rounded off to an integer).

Explanation

GATE→2024→Mechanical Behaviour of Materials→Elasticity, Plasticity, and Yield Criteria

Q3

MCQ[2 Marks]

An isotropic metallic cuboid block has coefficient of linear thermal expansion $\alpha$, Young's modulus $E$, and Poisson's ratio $\nu$. Dimensions are $a, b, c$ in $X, Y, Z$ directions. It is rigidly constrained against expansion in the $X$ direction, but free in $Y$ and $Z$. Heated by $\Delta T$. What would be the CHANGE in dimension in the $Y$ direction? (A) $b(1-\nu)\alpha \Delta T$ (B) $b(1+\nu)\alpha \Delta T$ (C) $b\alpha \Delta T$ (D) $b(1+\alpha)\Delta T$

(A)

b(1-\nu)\alpha\Delta T

(B)

b(1+\nu)\alpha\Delta T

(C)

ba\Delta T

(D)

b(1+\alpha)\Delta T

Explanation

GATE→2023→Mechanical Behaviour of Materials→Elasticity, Plasticity, and Yield Criteria

Q4

NAT[2 Marks]

A thin plate is loaded in plane stress condition with $\sigma_{xx} = 110\text{ MPa}$, $\sigma_{yy} = -50\text{ MPa}$, $\tau_{xy} = -70\text{ MPa}$\nThe maximum principal stress in MPa is ___ (round off to nearest integer).

Explanation

GATE→2022→Mechanical Behaviour of Materials→Elasticity, Plasticity, and Yield Criteria

Q5

MCQ[1 Mark]

For a material that undergoes strain hardening, necking instability occurs during tensile testing when\nGiven: $\sigma = \text{true stress}$ and $\epsilon = \text{true strain}$. (A) $\frac{d\sigma}{d\epsilon} = 0$ (B) $\frac{d\sigma}{d\epsilon} = \epsilon$ (C) $\frac{d\sigma}{d\epsilon} = \sigma$ (D) $\frac{d\sigma}{d\epsilon} = \infty$

(A)

\frac{d\sigma}{d\epsilon}=0

(B)

\frac{d\sigma}{d\epsilon}=\epsilon

(C)

\frac{d\sigma}{d\epsilon}=\sigma

(D)

\frac{d\sigma}{d\epsilon}=\infty

Explanation

GATE→2022→Mechanical Behaviour of Materials→Elasticity, Plasticity, and Yield Criteria

Q6

NAT[2 Marks]

Given the stress tensor $$\begin{bmatrix} 130 & 30 & 0 \\ 30 & 50 & 0 \\ 0 & 0 & 0 \end{bmatrix}\text{ MPa}$$\nthe maximum shear stress is ___ $\text{MPa}$ (round off to the nearest integer).

Explanation

Dislocation Theory and Strengthening Mechanisms

9 Questions

GATE→2026→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q7

MCQ[1 Mark]

Which one of the following dislocation dissociation reactions is feasible in face-centered cubic metals? (A) $\frac{a}{2}[0\bar{1}1] \rightarrow \frac{a}{6}[1\bar{2}1] + \frac{a}{6}[\bar{1}\bar{1}2]$ (B) $\frac{a}{2}[0\bar{1}1] \rightarrow \frac{a}{6}[1 1 2] + \frac{a}{6}[2 1 \bar{1}]$ (C) $\frac{a}{2}[0\bar{1}1] \rightarrow \frac{a}{6}[1\bar{1}2] + \frac{a}{6}[\bar{1}\bar{2}\bar{1}]$ (D) $\frac{a}{2}[0\bar{1}1] \rightarrow \frac{a}{6}[1\bar{2}1] + \frac{a}{6}[2\bar{1}\bar{1}]$

(A)

a/2[0\bar{1}1]\rightarrow a/6[1\bar{2}1]+a/6[\bar{1}\bar{1}2]

(B)

a/2[0\bar{1}1]\rightarrow a/6[1 1 2]+a/6[2 1 \bar{1}]

(C)

a/2[0\bar{1}1]\rightarrow a/6[1\bar{1}2]+a/6[\bar{1}\bar{2}\bar{1}]

(D)

a/2[0\bar{1}1]\rightarrow a/6[1\bar{2}1]+a/6[2\bar{1}\bar{1}]

Explanation

GATE→2026→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q8

NAT[2 Marks]

A cylindrical single crystal of copper having $10\text{ mm}$ diameter is deformed under uniaxial tensile load of $2200\text{ N}$. If $\alpha = \beta$, the critical resolved shear stress (CRSS) is ___ $\text{MPa}$.

Explanation

GATE→2025→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q9

MCQ[1 Mark]

Two randomly oriented polycrystalline copper samples with average grain sizes of $10\text{ }\mu\text{m}$ (Sample A) and $100\text{ }\mu\text{m}$ (Sample B) were tested at room temperature. Given: $E_A, E_B$ are Young's moduli and $YS_A, YS_B$ are yield strengths. Which one of the following statements is CORRECT? (A) $E_A > E_B$ and $YS_A > YS_B$ (B) $E_A = E_B$ and $YS_A < YS_B$ (C) $E_A > E_B$ and $YS_A = YS_B$ (D) $E_A = E_B$ and $YS_A > YS_B$

(A)

$E_{A}>E_{B}$ and $YS_{A}>YS_{B}$

(B)

$E_{A}=E_{B}$ and $YS_{A}<YS_{B}$

(C)

$E_{A}>E_{B}$ and $YS_{A}=YS_{B}$

(D)

$E_{A}=E_{B}$ and $YS_{A}>YS_{B}$

Explanation

GATE→2025→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q10

MSQ[1 Mark]

With reference to edge and screw dislocations, which of the following statements is/are CORRECT? (A) Both edge and screw dislocations can leave the slip plane by climb. (B) Burgers vector of a screw dislocation is parallel to its line vector. (C) Both edge and screw dislocations can leave the slip plane by cross-slip. (D) Strain energy per unit length of an edge dislocation is higher than that of a screw dislocation.

(A)

Both edge and screw dislocations can leave the slip plane by climb.

(B)

Burgers vector of a screw dislocation is parallel to its line vector.

(C)

Both edge and screw dislocations can leave the slip plane by cross-slip.

(D)

Strain energy per unit length of an edge dislocation is higher than that of a screw dislocation.

Explanation

GATE→2024→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q11

MCQ[1 Mark]

The figure shows a dislocation loop, whose Burgers vector is $\mathbf{b}$ (horizontal arrow). Identify the nature of the dislocation segment at locations p, q, and r. (A) p: pure edge, q: mixed, r: pure screw (B) p: pure edge, q: pure screw, r: pure edge (C) p: pure screw, q: mixed, r: pure screw (D) p: pure screw, q: pure edge, r: pure screw

(A)

p: pure edge, q: mixed, r: pure screw

(B)

p: pure edge, q: pure screw, r: pure edge

(C)

p: pure screw, q: mixed, r: pure screw

(D)

p: pure screw, q: pure edge, r: pure screw

Explanation

GATE→2024→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q12

MCQ[1 Mark]

Match the concepts listed in Column I with the phenomena listed in Column II.\nColumn I:\nP. Peierls-Nabarro stress\nQ. Cottrell's atmosphere\nR. Paris law\nS. Considère's criterion\nColumn II: 1. Yield point phenomenon 2. Fatigue 3. Dislocation glide 4. Onset of necking (A) P-1, Q-2, R-3, S-4 (B) P-4, Q-1, R-2, S-3 (C) P-3, Q-1, R-2, S-4 (D) P-3, Q-4, R-2, S-1

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2024→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q13

NAT[1 Mark]

A single crystal is oriented such that the normal to the slip plane makes an angle of $60^\circ$ with the tensile axis. If the slip direction makes an angle of $45^\circ$ with respect to the tensile axis and the critical resolved shear stress for slip is $2\text{ MPa}$, then the tensile stress at which plastic deformation commences is ___ $\text{MPa}$ (Round off to one decimal place).

Explanation

GATE→2022→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q14

MSQ[1 Mark]

Given the strain rate ($\dot{\epsilon}$), dislocation density ($\rho$), dislocation velocity ($v$), which of the following relationship(s) is (are) correct? Assume that Orowan equation for plastic flow due to the dislocation movement is obeyed. (A) $\dot{\epsilon} \propto v^2$ (B) $\dot{\epsilon} \propto v$ (C) $\dot{\epsilon} \propto \rho^2$ (D) $\dot{\epsilon} \propto \rho$

(A)

\dot{\epsilon}\propto v^{2}

(B)

\dot{\epsilon}\propto v

(C)

\dot{\epsilon}\propto \rho^{2}

(D)

\dot{\epsilon}\propto \rho

Explanation

GATE→2022→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q15

MCQ[2 Marks]

Match the phenomena (Column I) with the descriptions (Column II)\nColumn I: (P) Cottrell atmosphere (Q) Suzuki interaction (R) Bauschinger effect (S) Nabarro-Herring creep\nColumn II: (1) Decrease in yield stress when loading direction is reversed (2) Stress assisted diffusion of vacancies resulting in plastic deformation in a polycrystalline material (3) Lüders bands (4) Segregation of solutes to the stacking fault (A) P-1, Q-2, R-3, S-4 (B) P-1, Q-2, R-4, S-3 (C) P-3, Q-4, R-1, S-2 (D) P-3, Q-1, R-4, S-2

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

Fracture, Fatigue, and High Temperature Deformation

18 Questions

GATE→2026→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q16

MCQ[1 Mark]

Deformation mechanism map of a given material is used for determining which one of the following properties? (A) Fatigue strength (B) Creep rate (C) Tensile strength (D) Impact toughness

(A)

Fatigue strength

(B)

Creep rate

(C)

Tensile strength

(D)

Impact toughness

Explanation

GATE→2026→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q17

MCQ[2 Marks]

Match the concepts listed in Column I with the associated terms listed in Column II:\nColumn I: (P) Paris Law (Q) Schmid Factor (R) Larson - Miller Parameter (S) Portevin - Le Chatelier Effect\nColumn II: (1) Creep (2) Fatigue (3) Dynamic Strain Aging (4) Critical Resolved Shear Stress (A) P-3, Q-1, R-2, S-4 (B) P-2, Q-4, R-1, S-3 (C) P-2, Q-4, R-3, S-1 (D) P-1, Q-3, R-2, S-4

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2026→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q18

NAT[2 Marks]

For plane strain fracture toughness ($K_{Ic}$) testing of Maraging steel, minimum thickness to achieve valid $K_{Ic}$ is ___ (Given: $K_{Ic} = 90\text{ MPa}\sqrt{\text{m}}$, yield stress $= 900\text{ MPa}$)

Explanation

GATE→2025→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q19

MCQ[2 Marks]

Match the phenomena in Column I with the typical observations in Column II.\nColumn I:\nP. Dynamic strain aging\nQ. Recrystallization\nR. Bauschinger effect\nS. Superplasticity\nColumn II: 1. Grain boundary sliding 2. Decrease in yield stress with a reversal of loading direction 3. Decrease in dislocation density 4. Serrations in stress-strain curve (A) P-4, Q-1, R-2, S-3 (B) P-4, Q-3, R-2, S-1 (C) P-3, Q-4, R-2, S-1 (D) P-1, Q-4, R-2, S-3

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2025→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q20

NAT[2 Marks]

For a component fabricated from an alloy A with plane strain fracture toughness, $K_{IC} = 50\text{ MPa m}^{1/2}$, fracture was observed to take place at a crack length of $0.4\text{ mm}$ at a tensile service stress of $\sigma$. If the same component is instead fabricated from alloy B with $K_{IC} = 75\text{ MPa m}^{1/2}$, the crack length at which a similar crack geometry will result in fracture (under identical tensile service stress of $\sigma$) is ___ $\text{mm}$ (rounded off to one decimal place).

Explanation

GATE→2025→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q21

NAT[2 Marks]

In polycrystalline Ni, Nabarro-Herring diffusion creep was found to be the rate controlling creep mechanism at a certain temperature. At that temperature, if the steady state strain rate is $10^{-8}\text{ s}^{-1}$ at a stress of $10\text{ MPa}$, the steady state strain rate of $10^{-9}\text{ s}^{-1}$ will be obtained at a stress value of ___ $\text{MPa}$ (in integer).

Explanation

GATE→2024→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q22

MCQ[2 Marks]

Which one of the following graphs represents Griffith's criterion for the growth of a crack in a brittle isotropic infinitely large plate with a center crack? In the graph, $\Delta SE$ is the magnitude of total strain energy released (solid curve) and $\Gamma_s$ is total surface energy (dashed line), and $a_c$ is critical crack length (downward arrow).

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q23

MSQ[2 Marks]

A creep test of a pure polycrystalline metal is performed in tension and the creep strain rate is observed to decrease during the primary stage. The creep mechanism is later determined to be dislocation-climb-controlled. The observed decrease in creep strain rate is/are due to (A) an increase in dislocation density. (B) grain growth. (C) a decrease in the dislocation density. (D) an increase in the cross-sectional area of the sample.

(A)

an increase in dislocation density.

(B)

grain growth.

(C)

a decrease in the dislocation density.

(D)

an increase in the cross-sectional area of the sample.

Explanation

GATE→2024→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q24

NAT[2 Marks]

A steel bar is subjected to fatigue loading with a tensile mean stress. Given that the ultimate tensile strength is $1000\text{ MPa}$ and the fatigue limit under fully reversed loading is $250\text{ MPa}$, the fatigue limit for a mean stress of $100\text{ MPa}$, considering Goodman relationship is ___ $\text{MPa}$ (Round off to the nearest integer).

Explanation

GATE→2024→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q25

NAT[2 Marks]

A large rectangular component is undergoing fully-reversed cyclic loading, and the component is known to grow the dominant fatigue crack from the outer surface. If the stress amplitude ($\sigma_A$) is $100\text{ MPa}$ and the critical stress intensity factor $K_{IC}$ of the material is $50\text{ MPa m}^{1/2}$, then the crack length at which the component will fail catastrophically is ___ $\text{mm}$ (Round off to one decimal place).\nGiven: The geometric factor $Y$ (or $\alpha$) for this loading condition is $1.12$.

Explanation

GATE→2023→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q26

MCQ[1 Mark]

The mechanism of creep for a single crystal as depicted in the schematic is... (A) Nabarro-Herring creep (B) Grain boundary sliding (C) Dislocation creep (D) Coble creep

(A)

Nabarro-Herring creep

(B)

Grain boundary sliding

(C)

Dislocation creep

(D)

Coble creep

Explanation

GATE→2023→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q27

MSQ[1 Mark]

When cracks propagate in a brittle material, the following option(s) is/are correct (A) elastic strain energy decreases (B) surface energy increases (C) surface energy decreases (D) elastic strain energy increases

(A)

elastic strain energy decreases

(B)

surface energy increases

(C)

surface energy decreases

(D)

elastic strain energy increases

Explanation

GATE→2023→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q28

MSQ[1 Mark]

Which of the following is/are responsible for reducing the high cycle fatigue life of a component? (A) increasing the mean stress at constant amplitude (B) increasing the surface roughness (C) employing shot peening (D) absence of sharp corners in the component

(A)

increasing the mean stress at constant amplitude

(B)

increasing the surface roughness

(C)

employing shot peening

(D)

absence of sharp corners in the component

Explanation

GATE→2023→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q29

NAT[2 Marks]

A specimen containing maximum initial surface crack of size $1.5\text{ mm}$ is subjected to cyclic loading with $\sigma_{max} = 300\text{ MPa}$ and $\sigma_{min} = 0\text{ MPa}$. Assuming specimen geometric factor of $1$, and referring to the given figure, the crack growth rate in $\mu\text{m cycle}^{-1}$ is ___ (round off to nearest integer).

Explanation

GATE→2022→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q30

MCQ[1 Mark]

With reference to the stress intensity factor, find the correct match of nomenclature (Column A) with the mode of deformation applied to the crack (Column B).\nColumn A: (P) Mode I (Q) Mode II (R) Mode III\nColumn B: (X) Forward shear mode (Y) Parallel shear mode (Z) Crack opening mode (A) P-Z, Q-Y, R-X (B) P-Z, Q-X, R-Y (C) P-Y, Q-X, R-Z (D) P-Y, Q-Z, R-X

(A)

P-Z, Q-Y, R-X

(B)

P-Z, Q-X, R-Y

(C)

P-Y, Q-X, R-Z

(D)

P-Y, Q-Z, R-X

Explanation

GATE→2022→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q31

MSQ[1 Mark]

While designing a material for high temperature application, which of the following characteristic(s)/attribute(s) is (are) desirable for achieving better creep resistance? (A) Fine grain size (B) FCC crystal structure (C) High melting point (D) Cold worked microstructure

(A)

Fine grain size

(B)

FCC crystal structure

(C)

High melting point

(D)

Cold worked microstructure

Explanation

GATE→2022→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q32

NAT[2 Marks]

From high temperature tensile testing, the flow stress (measured at the same value of strain) of an alloy was found to be $50\text{ MPa}$ at a strain rate of $0.1\text{ s}^{-1}$ and $70\text{ MPa}$ at a strain rate of $10\text{ s}^{-1}$. The strain rate sensitivity parameter is ___ (round off to 3 decimal places).

Explanation

GATE→2022→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q33

NAT[2 Marks]

High cycle fatigue data for an alloy at various alternating stresses, $\sigma_a$, is given below: $500\text{ MPa} \rightarrow 1000\text{ cycles}$ $400\text{ MPa} \rightarrow 10000\text{ cycles}$ $300\text{ MPa} \rightarrow 100000\text{ cycles}$ $200\text{ MPa} \rightarrow 1000000\text{ cycles}$\nA specimen is subjected to: (i) $5000\text{ cycles}$ at $400\text{ MPa}$, (ii) $25000\text{ cycles}$ at $300\text{ MPa}$, and finally (iii) at $500\text{ MPa}$. Assuming Miner's law is obeyed, the number of cycles to failure at $500\text{ MPa}$ is ___.

Explanation