Load transfer between matrix and fibre

It was already stated that the considerations of the previous section were simplified. In particular, the assumption of continuous fibres extending throughout the component and loaded directly by the external load is almost never valid. If the fibres are completely embedded within the matrix, the load transfer between matrix and fibre is crucial in determining the strengthening effect. For this reason, we will now discuss this load transfer. 

The load transfer between fibre and matrix is mainly due to friction caused by interface roughness or to adhesion between fibre and matrix on the lateral surface of the fibre. Although the strains at the front and back side of the fibre can be large, only small loads are transferred there because these sides are much smaller. Crucial in determining the properties of the composite is the maximum interfacial shear stress t.  

To estimate the stress (7f within the fibre, we consider an infinitesimal fibre segment with a constant interfacial shear stress —t acting on its surface (figure 9.5). The forces within the fibre are —erf 7rd /4 at position x and 

The stress changes linearly with position if Ti is constant.  

The maximum stress within the fibre is limited by the strain in the fibre (index f ) which can never exceed the matrix (index m ) strain. The maximum possible fibre stress is thus 

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