Materials for engineering, 3rd Edition - (Malestrom)

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Materials for engineering
carbide (Young’s modulus 703.4 GPa) in a matrix of cobalt (Young’s
modulus 206.9 GPa), if 60 volume % of the particles are present.
[Answers: see Fig. 6.6].
2. A model fibre–composite system is prepared consisting of a uniform
array of continuous tungsten wires in a copper matrix. If the wires
occupy 50% of the cross-section, what will be the value of Young’s
modulus for the composite specimen? (The data required are in Appendix
III).
[Answer: 270.4 GPa]
3. A directionally solidified eutectic alloy has a microstructure consisting
of alternate continuous lamellae of phase α (of Young’s modulus
70 GPa) and phase β (of Young’s modulus 150 GPa) – the volume
fraction of β-phase being 0.4.
The value of Young’s modulus of the alloy is measured with the
tensile axis being first parallel to the lamellae and then with the tensile
axis perpendicular to the lamellae. Calculate the degree of elastic
anisotropy of the material.
[Answer: 0.146]
4. A unidirectional fibre composite consists of a volume fraction of 0.6 of
continuous carbon fibres in a matrix of epoxy. Find the maximum tensile
strength of the composite if the matrix yields in tension at a stress of
40 MPa and the fracture strength of the fibres is 2700 MPa.
[Answer: 1636 MPa]
5. A composite material consists of a mixture of short glass fibres (fracture
strength 2000 MPa) of diameter 15 µm, in a polyester matrix the shear
strength of which is 30 MPa. What is the critical fibre length (l c ) for this
system? Estimate the maximum work of fracture of the composite. How
would you expect the work of fracture to change if the fibres were
substantially longer than l c ?
[Answer: 0.5 mm; 25 kJ m –2 ]
6. Calculate the value of Young’s modulus (a) parallel to the grain, and (b)
perpendicular to the grain for a softwood of density 550 kg m –3 . The
value of Young’s modulus of cellulose is 40 GPa, and its bulk density
can be taken as 1500 kg m –3 .
[Answers: (a) 14.6 GPa; (b) 5.4 GPa]
7. Explain why the interfacial shear stress is important in controlling the
fracture behaviour of fibre-reinforced composites.