# Composite Materials Questions and Answers – Fiber-Matrix Interactions in Unidirectional Lamina

This set of Composite Materials Multiple Choice Questions & Answers (MCQs) focuses on “Fiber-Matrix Interactions in Unidirectional Lamina”.

1. The mechanics of fiber-reinforced composites is very much complex compared to that of conventional materials.
a) True
b) False

Explanation: The fiber-reinforced composites are microscopically non-isotropic and in homogenous. The study on mechanics of such materials is not as easy as that of the materials with homogeneous and isotropic properties.

2. Which is the equation for longitudinal modulus for the composite?
a) EL=Em+vf(Em-Ef)
b) EL=Em+vf(Ef-Em)
c) EL=Ef+vm(Em-Ef)
d) EL=Ef+vm(Ef-Em)

Explanation: This equation is called the Rule of mixtures. The term Em represents the matrix modulus, Ef for fiber modulus and vf for fiber volume fraction. This equation conveys that for a unidirectional continuous fiber composite the longitudinal modulus is intermediate between the matrix modulus and fiber modulus and it raises linearly with an increase in the fiber volume fraction. So, the composite longitudinal modulus is more influenced by fiber modulus than the matrix modulus.

3. The fiber modulus is very much greater than the matrix modulus for polymer matrix composites.
a) True
b) False

Explanation: For the polymer matrix composite the fiber modulus is much higher than the matrix modulus such that in most cases, the Ef/Em ratio is greater than 10. Thus, even for a less value of fiber volume fraction, the modulus will be high and the fiber would carry the major composite load.

4. Longitudinal stress is the only stress acting on the composite fibers and matrix.
a) True
b) False

Explanation: There are many stresses acting on the composite fibers and matrix other than the longitudinal stress. Tangential stress, Radial stress are some other stresses which are generated due to the difference in the Poisson’s ratio between the matrix and fibers.

5. The difference in thermal contraction between fibers and matrix generates internal stresses.
a) True
b) False

Explanation: When the composite lamina cools down from a higher fabrication temperature to the room temperature, internal stresses are developed due to the difference in thermal contraction between the fibers and the matrix. Generally, the coefficient of thermal expansion is higher for matrix than the fibers. As a result, the matrix tends to contract more than the fibers and generates a squeezing effect on the fibers.

6. How does the tensile load applied to a discontinuous fiber lamina is transferred into the fibers?
a) By shearing mechanism
b) By thermal contraction
c) By fiber fracture
d) By fiber pull-out

Explanation: In a discontinuous fiber lamina, the tensile load applied is transferred to the fibers by a shearing mechanism between the matrix and fibers. The longitudinal strain in the matrix is greater than that in the fibers since the matrix phase has lower modulus. A shear stress distribution is developed in the fiber-matrix interface due to this difference in longitudinal strains.

7. Critical fiber length is essential for effective stiffening and strengthening of the composite material.
a) True
b) False

Explanation: The critical fiber length of a fiber reinforcement is the length needed to transfer a load equal to the fracture stress of the fiber. The effective stiffness and strength of the composites are influenced very much by the critical fiber length.

8. Which factor does not affect the critical fiber length?
a) Nature of fiber
b) Interfacial strength
c) Fiber diameter
d) Direction of fiber

Explanation: The critical fiber length depends upon the ultimate tensile strength of the fiber(σ), the shear strength of the fiber-matrix interface(τ) and the fiber diameter(df). The critical fiber length is expressed mathematically as, lc=σdf/2τ.

9. Which type of fiber would carry stress more efficiently?
a) Shorter and thicker fibers
b) Shorter and thinner fibers
c) Longer and thinner fibers
d) Longer and thicker fibers

Explanation: The shear stress at the interface transfers the tensile stress from the matrix to the fiber. For shorter fibers with near ends, the surface area to transfer the load will be small. While the longer fibers having larger surface area transfer load or stress efficiently.

10. The critical length can be controlled by altering interfacial shear strength.
a) True
b) False

Explanation: The critical length is inversely proportional to the interfacial shear strength. Using coupling agents that are compatible with the matrix, the shear strength can be increased and thereby the critical fiber length could be reduced. Effective reinforcements can be achieved by reducing the critical fiber length with respect to the reinforced fiber length.

11. What is determined by the single fiber fragmentation test?
a) Interfacial shear strength
b) Critical fiber length
c) Fiber diameter
d) Thermal expansion coefficient

Explanation: The fiber-matrix interfacial shear strength is obtained using the single fiber fragmentation test. In this test, an axial tension is applied to a single fiber which is embedded along the centerline of a matrix tensile specimen. The tensile stress is transferred from the matrix to fiber at the fiber-matrix interface. The fiber in the specimen will break when the tensile stress on the fiber reaches its tensile strength.

12. In polymer matrix composites the failure in longitudinal compression is initiated by localized buckling of fibers.
a) True
b) False

Explanation: The matrix modulus of the polymer matrix composites is relatively low compared to the fiber modulus. Two different localized buckling modes are observed in these composites depending on whether the matrix shows plastic deformation or behaves in elastic deformation. Fiber kinking and elastic micro-buckling are different buckling modes.

13. The fiber kinking is a failure mode in the longitudinal compressive loading.
a) True
b) False

Explanation: The fiber kinking occurs in highly localized areas where the fibers are slightly misaligned from the direction of the compressive loading. Fiber bundles in these areas form kink bands by tilting an additional angle from their initial configuration. As a result, the surrounding matrix experiences large shearing deformation.

14. Which factor on increasing will reduce the longitudinal compressive strength?
a) Fiber tensile modulus
b) Fiber misalignment
c) Fiber diameter
d) Fiber-matrix interfacial strength

Explanation: The Fiber misalignment or bowing tends to decrease the longitudinal compressive strength. Whereas, the increasing values of the fiber tensile modulus, fiber diameter, fiber-matrix interfacial strength, matrix shear modulus, matrix ultimate strain are the factors that improve longitudinal compressive strength.

15. Which of these diagrams represent shear mode of micro-buckling in a unidirectional continuous fiber composite?
a)
b)
c)
d)

Explanation: The shear mode of buckling in a unidirectional continuous fiber composite under longitudinal compressive is represented in this diagram. The shear mode of micro-buckling is found to be present at high fiber volume fractions. It also creates a shear strain in the matrix due to in-phase buckling of the fibers.

Sanfoundry Global Education & Learning Series – Composite Materials.

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