Tensile Behaviour of Continuous Fibre Reinforced Metal Matrix CompositesMetal matrix composites that are reinforced with continuous fibres present a special problem when trying to determine their tensile strength from a theoretical point of view. In general, the metal matrix will have a total elongation to failure well in excess of that of the stiff brittle ceramic fibres used to reinforce them. The metal matrix can also show extensive work hardening after the yield strength of the metal is exceeded. It is perhaps easiest to examine the effect of this particular type of matrix behaviour using a specific example so that a suitable theoretical approach to strength in the metal matrix, or similar composites can be derived.Consider the case of an aluminum alloy re-inforced with graphite fibres, the elastic strain to failure of the fibres is greater than the elastic strain to yield of the matrix but less than the plastic strain to failure of the aluminum alloy (see below)  The composite will behave exactly like other composites up to the point where the metal matrix reaches a strain equal to that of the yield point  and the yield strength of the composite will be If the composite is subjected to a further increase in load or deflection then the matrix will continue to deform, but plastically, while the embedded fibres continue to stretch elastically, the stress in the composite will continue to increase with increasing strain, but not in a linear fashion.  If the material is unloaded before the fibres break then both the matrix and fibres will unload elastically and therefore the composite will too. When the elastic strain in the matrix is fully relaxed (i.e. the stress in the matrix is reduced to zero) the fibre and composite will still be stretched by the amount of plastic strain imposed on the matrix and thus the fibres will still experience a residual tensile stress  as will the composite  . If the imposed stress is relaxed to zero then the matrix must be compressed elastically until the tensile force in the fibres is exactly balanced by the compressive force in the matrix.   If the material is reloaded then the total strain in the fibre cannot exceed the fibre failure strain.  If the stress train response of the metal matrix is represented by the usuall power law of work hardening then the stress in the composite at the point of fibre failure will be  where  and n are characteristic of the matrix material. Once the fibres have fractured all the load transfers to the matrix and if the resulting stress in the matrix jumps above the UTS of the matrix then the composite will fracture, if not the composite will continue to support the imposed loads until UTS is exceeded. The strength of the composite limited by matrix failure is, as before, and the ultimate tensile strength of the composite will depend on the volume fraction of fibres as shown below. 
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