The chart below allows exploration of components for composites with desired combinations of thermal conductivity and expansion, using light alloy or polymer matrices. Three possible matrices -aluminium, magnesium and titanium - are shown in red. The materials shown in green are available as fibres (f), whiskers (w) and particles (p). A construction like that of Fig. 12.14 allows the potential of any given matrix-reinforcement combination to be assessed. One criterion of excellence (the index for materials to minimize thermal distortion, \(\lambda / \alpha\) ) is shown; it increases in value towards the bottom right. Use the chart to compare the performance of a magnesium AZ63 alloy-matrix composite reinforced with

(a) alloy steel fibres,

(b) silicon carbide fibres, \(\mathrm{SiC}\)

(c) diamond-structured carbon particles. Keep it simple to calculate the upper and lower bounds for \(\alpha\) and \(\lambda\) at a volume fraction of \(f=0.5\) and plot these points. Then sketch curves linking matrix to reinforcement to pass through the outermost of the points. In making your judgement, assume that \(f=0.5\) is the maximum practical reinforcement level.

Data From Fig, 12.14

100 Composite design Conductivity/expansion 106 3x106 107 50 50 20 20 Linear expansion coefficient a (10-6/K) Criterion of excellence /, Bound 4:21 1000 series aluminium alloys Boron Bound 10 nitride Bound 3x107 Bound 108 Silicon carbide MFA 16 210 30 70 100 300 700 Thermal conductivity 1 (W/m.K)