Abstract
A closed form relation for the strain energy density in the vicinity of a macroscopic mode I crack in a random fiber network is derived using an implicit gradient nonlocal continuum field theory. An expression for the characteristic length, used in the nonlocal formulations, in terms of microstructural properties is derived and it is found that the characteristic length is proportional to the average fiber segment length to the power of two. It is illustrated that the crack-tip singularity vanishes for a characteristic length greater than zero. An open fiber structure exhibits a distributed strain energy field in the crack tip vicinity. As the network becomes relatively denser, the characteristic length decreases and the networks mechanical behavior approaches the behavior of a classic elastic continuum. Only for an infinitely dense network is the r−1-singularity in strain energy field achieved. The theory explains why open network structures have difficulties in localizing failure to macroscopic cracks. It is found that there is a one-to-one relation between characteristic length and size of the smallest crack that can initiate macroscopic failure.
Published Version
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