This set of Composite Materials Multiple Choice Questions & Answers (MCQs) focuses on “Stress-Strain Relations for a Anisotropic Materials – String – Set 2”.

1. What does the terms S_{11}, S_{22} and S_{33} in the compliance matrix represent?

a) Extensional bending to an individual applied stress

b) Extensional stiffness to an individual applied stress

c) Normal stresses to an individual applied stress

d) Normal strains to an individual applied stress

View Answer

Explanation: All the terms in the compliance matrix represents the couplings for an arbitrarily stressed body. Out of which, S

_{11}, S

_{22}and S

_{33}represents the extensional response to an individual applied stresses σ

_{1}, σ

_{2}and σ

_{3}respectively.

2. The terms representing the coupling between the dissimilar normal stresses and normal strains are __________

a) s_{11}, s_{22} and s_{33}

b) s_{12}, s_{22} and s_{33}

c) s_{12}, s_{13} and s_{23}

d) s_{11}, s_{23} and s_{33}

View Answer

Explanation: The extension–extension coupling is more commonly known as the Poisson’s effect that relates the normal shear stress to the normal shear strain as a relation of Τ

_{xy}and γ

_{12}. They are linked in the compliance matrix as the co-efficient S

_{12}, S

_{13}and S

_{23}.

3. The terms s_{44}, s_{55} and s_{66} in the compliance matrix represents __________

a) shear modulus

b) extension modulus

c) coupling

d) bending stiffness

View Answer

Explanation: The terms s

_{44}, s

_{55}and s

_{66}in the compliance matrix represents the shear and they will be related to the shear moduli in the 2-3,3-1 and 1-2 planes respectively.

4. The elasticity tensor C_{mnrs} in the transformed system is given as __________ (where T = Transformation matrix)

a) C_{mnrs} = T_{i} T_{k} T_{i} T_{l} C_{ijkl}

b) C_{mnrs} = T_{i} T_{j} T_{k} T_{l} C_{ijkl}

c) C_{mnrs} = T_{j} T_{i} T_{l} T_{k} C_{ijkl}

d) C_{mnrs} = T_{j} T_{i} T_{k} T_{l} C_{ijkl}

View Answer

Explanation: While transforming from the original coordinate system to any other transformed coordinate system, the sequence of the transformation has to be followed in order to have the same representation in the transformed system. That transformation is given by the transformation matrix (T) i.e., C

_{mnrs}= T

_{i}T

_{j}T

_{k}T

_{l}C

_{ijkl}.

5. Which of the following is not an anisotropic material?

a) Diamond

b) Composite material

c) Bone

d) Glass

View Answer

Explanation: Anisotropic material properties are different in different directions. Common anisotropic materials include wood, because its properties are different in parallel and perpendicular to the grain, and layered rocks such as slate. Similar explanation can be given to diamond and composite materials including bone as well when it comes to anisotropic properties. Glass is an isotropic material.

6. What is the S11 term of the compliance matrix of a glass/epoxy lamina whose material property E_{1}= 181GPa?

a) 9.709 * 10^{-9} Pa^{-1}

b) 5.525* 10^{-9} Pa^{-1}

c) 5.525* 10^{-12} Pa^{-1}

d) 9* 10^{-9} Pa^{-1}

View Answer

Explanation: Given E

_{1}= 181GPa

We know that,

S

_{11}= 1/ E

_{1}

= 1/ (181 * 109)

= 5.525* 10

^{-12}Pa

^{-1}.

7. What is the value of S_{44} in the compliance matrix of a glass/epoxy lamina whose G_{23} = 3GPa?

a) 3.33* 10^{-9} Pa^{-1}

b) 3.33* 10^{-10} Pa^{-1}

c) 3.33* 10^{-12} Pa^{-1}

d) 3.33* 10^{-15} Pa^{-1}

View Answer

Explanation: Given G

_{23}= 3GPa

We know that,

S

_{44}= 1/ G23

= 1/ (3 * 109)

= 3.33* 10

^{-10}Pa

^{-1}.

8. Which of the following coupling term is not linked in the compliance matrix?

a) Extension – extension coupling

b) Shear – extension coupling

c) Shear – shear coupling

d) Bending coupling

View Answer

Explanation: The terms S

_{11}, S

_{22}, S

_{33}represents extension in the same direction. S

_{12}, S

_{13}, S

_{23}represents extension – extension coupling and the terms S

_{14}, S

_{15}, S

_{16}, S

_{24}, S

_{25}, S

_{26}, S

_{34}, S

_{35}, S

_{36}represents the shear – extension coupling while the terms S

_{44}, S

_{55}, S

_{66}signifies shear and S

_{45}, S

_{46}, S

_{56}represents the shear – shear coupling.

9. The relationship between the terms C_{1212}, C_{1111} and C_{1122} is given by ___________

a) C_{1212} = C_{1111} + C_{1122}

b) C_{1212} = C_{1111} – C_{1122}

c) C_{1212} = ½ (C_{1111} + C_{1122})

d) C_{1212} = ½ (C_{1111} – C_{1122})

View Answer

Explanation: The isotropy of a material results in the following additional relationship among the materials. C

_{1212}= ½ (C

_{1111}– C

_{1122}).

**Sanfoundry Global Education & Learning Series – Composite Materials**.

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