Strength of fibers and films

The statistical description of the strength was introduced by Weibull. In his model the assumption is made that failure is due to sudden catastrophic growth of pre-existing defects corresponding to local failure stresses. Failure at the most serious defect, i.e. the defect with the lowest fracture stress, leads to immediate failure of the fiber. It is further assumed that the defects are uniformly distributed throughout the fiber. The cumulative failure probability function, P, which represents the fraction of fibers that fail at or below a stress cr is, according to Weibull, given by 

A theoretical study of the influence of the molecular weight and of the effect of the anisotropy between intrachain and interchain forces on the 

Apparently this model in its present form does not predict a fibrillated fracture morphology caused by shear failure, as has been clearly observed for the PpPTA, PBO and PBT fibers. KnofT noticed the similarity between the tensile failure morphology of PpPTA fibers and that of a uniaxially oriented fiber-reinforced composite. The latter fails in tension via matrix shear failure initiated at the fiber ends. This made him conclude that, if the shear forces at a discontinuity exceed the shear strength of the bond between the fibrils, the fiber tensile strength should be proportional to the fiber shear strength. 

An interesting and rather simple model for the fiber strength has been developed by Yoon. It uses the same principles that have been applied to estimate the strength of short-fiber-reinforced composites, i.e. an elastic load transfer with a debonding matrix which occurs through elastic deformation of the interface. In Yoon s model the fiber is not regarded as a continuum, but as a composite consisting of covalently bonded chains 

Film preparation by different techniques, such as extrusion, uniaxial draw-down and mandrel processing, has been explored by Aoki et and Bodaghi et alP The uniaxially oriented PpPTA films obtained by the drawing process exhibit highly anisotropic mechanical properties, whereas the mandrel-produced films show balanced properties. However, they found that the values for modulus and strength of these films are much lower than those obtained for fibers. 

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