Dissemination of IT for the Promotion of Materials Science (DoITPoMS)


Interfacial debonding

Quick proof

Diagram for interfacial bonding

We need to start by considering short fibre composites as shown in the diagram above. The work done when a single fibre undergoes interfacial debonding is:

ΔW = 2 π r x0 Gic

Now we can sum this over all the fibres intersected by a unit area of the crack to find the work of debonding of the composite per unit crack area, Gcd. If there are N fibres per m2 where N is given by

\[N = \frac{f}{{\pi {r^2}_{^{}}}},\]

then there are ( N dx0 / L ) fibres per m2 with an embedded length between x0 and ( x0 + dx0 ).

\[{G_{cd}} = \int\limits_0^L {2\pi r{x_0}{G_{ic}}\frac{{Nd{x_0}}}{L}} \]

Integration gives: Gcd = f s Gic

This formula only applies to short fibre composites since fibre fracture does not occur if the fibre aspect ratio is less than the critical fibre aspect ratio, s* = σ f* / 2τ i*. (refer to TLP on short fibre composites, which does not exist yet). For long fibre composites there is a small probability that fibre fracture will occur away from the crack plane and debonding will not occur over the whole length of the fibre. In this case G>cd gives an idea of the magnitude of the energy absorbed.