Page 141 - Engineered Interfaces in Fiber Reinforced Composites

124 Engineered interfaces in fiber reinforced composites
involved in plastic yielding and the elasto-plastic stress-strain response of the matrix
material need to be established. The stress transfer phenomena affected by matrix
yielding has been analyzed recently, along with its effect on fiber fragment length
and effective fiber length (Kim, 1997).
There are other limitations of the model, besides the assumption of perfectly
elastic stress-strain behavior for both the fiber and matrix: neglect of the anisotropy
of fiber elastic properties (e.g. carbon and aramid fibers) and residual stresses in the
axial direction (in addition to those in the radial direction) generated from the
differential thermal contraction between fiber and matrix and a simplified fiber
fracture criterion. In particular, with regard to the fiber strength model, the fiber is
considered to have a strength varying only with its length, and thus it fractures
always in the center due to the axi-symmetric stress field. In other words, the mean
number of fiber segments always has to be a multiple of two independent of the
initial fiber length. In practice, however, the fiber can break at any weak spot when
the local stress exceeds the load-bearing capacity. The local stress is strongly
influenced by the spatial distribution of the flaws of random sizes inherent in the
brittle fiber surface, which cannot be adequately accounted for in the average tensile
strength model. Liu et a1.(1994a, b) have recently developed a fracture mechanics
based computer simulation model by including both the spatial and size distributions
of flaws along the fiber length to predict the evolution of the fiber fragmentation
process. There is good agreement between simulation and experiment.
Within the foregoing limitations of the micromechanics analysis, it is clearly
demonstrated for a carbon fiber<poxy matrix composite that one interface
condition cannot represent the interface debond/fiber fragmentation behavior
during the whole fiber fragmentation process. While the fully bonded interface
model can describe the early stage of the fiber fragmentation process (until the fiber
length reaches a characteristic value (2L), corresponding to initial debonding) at low
applied strains, the interface soon becomes partially debonded as the applied strain
increases. In the partially debonded interface model, the mean fiber fragment length
is the sum of the bonded and debonded lengths, the former diminishes while the
latter grows with the applied strain. Therefore, a non-zero critical value is always
reached for the mean fiber fragment length when the applied strain required for
further fiber fragmentation or interfacial debonding approaches infinity. In
experiment, the critical transfer length, (2L),, is defined as the mean fiber fragment
length determined after a further substantial increment in the applied strain leading
to no additional fiber fragmentation, which is exactly the same as what is predicted
in the analysis. It follows then that the critical transfer length can be considered as a
material constant for given properties of the composite constituents and the
interface. In view of the coexistence of bonded and debonded regions in the critical
transfer length, accurate measurements of their lengths in experiments are absolutely
necessary to properly characterize the relevant interfacial properties.
There is increasing evidence in recent years in the fragmentation test of some
brittle fiber-brittle matrix composites that a matrix crack is developed at the position
of the fiber break. The presence of the matrix crack and its physical size are shown
to alter the stress distributions at the fiber-matrix interface. As the applied strain