In a continuous fibre composite it is unlikely that all the fibres will have to be pulled out from the matrix since the fibres often fracture. Due to the statistical nature of the defect distribution in the surface of the fibres, not all fibres will wish to break in the plane of the crack. If the bonding between the fibre and matrix is weak then since the fibres are carrying the bulk of the stress at the crack tip, there will be a greater poisson's contraction in the fibre than in the matrix and as such a tensile stress will develop perpendicular to the interface between the fibre, which is contracting and the matrix which is not. This stress can fracture the weak fibre matrix interface and the crack is forced to run up, down and around the fibres. In order for the crack to proceed past the fibre, the fibre must break. This only occurs when the stress in the debonded fibre is raised to the fracture strength of that fibre - recall the statistical distribution of fibre strengths so this stress may be less the maximum value of sf. This requires an additional amount of elastic strain energy to be input into the debonded region of the fibre at the crack tip - energy which is released as heat and noise as the fibre fractures. Since the fibres are linearly elastic, the elastic strain energy per-unit volume of fibre is
where sf is the fracture strength of the fibre and Ef, the elastic modulus of the fibre. The total additional energy required is the product of the number of fibres per unit area, the additional strain energy per unit volume of fibre and the volume of debonded fibre, ie.
If we further assume that the crack running along the interface is
limited to a length no shorter than the critical fibre length ie. 
then
to which we must add the additional surface area of the fibre-matrix debond mutliplied by the surface energy (x2 for the two new surfaces created).
Example Problem
Estimate the contribution to toughening of interfacial fracture relative to fibre pullout in the carbon fibre epoxy composite studied in the previous example.
G = 0.6/2 x 8x10-6 x (1800x106)3 /(2 x 290x109 x 85x106) + (8 x (0.6/2) x1800x106 / 85x106) = 335 Jm-2.