Relative Displacements and Degradation Function

Degradation of frictional resistance at the debonded interface will cause the relative axial displacement between fiber and matrix to increase gradually. There are 

from the general relations between strains and stresses given by Eqs. (4.8) and (4.9), and the additional radial stress 9i(u,z) of Eq. (4.18), the strains in the fiber and matrix at the interface for fiber pull-out are obtained as  

for the fiber pull-out, the residual strains after complete unloading when the external stress is zero now become  

Consequently, the residual relative displacement in fiber pull-out is obtained by combining Eqs. (4.141), (4.148) and (4,149)  

140) and (4.150)-(4.152) are used to evaluate the response of the model composites in cyclic loading and the displacements 6 and 8, can be expressed as a function of the alternating stress, Aff, and the number of cycles, N. In experiments, degradation of the interface properties, e.g., the coefficient of friction, p or A(= 2pjfc/a), can also be expressed in terms of the cyclic loading parameters, A r and N. In practice 8 and 8, can be measured using optical methods (with a microscope) or by means of more complicated instruments (see for example Naaman et al. (1992)) in fiber pull-out. Alternatively, they can be directly determined from the load and load-point displacement records in the case of fiber push-out. 

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