Fractal interpretation of failure of polyethylene under impact loading

Fractal analysis of macromolecules

“…3 Therefore, turbulent dissipative structures are described using `nonhomogeneous fractals,' the rules of formation of which are chosen at random at each step of scale hierarchy in accordance with some probability distribution. 120,121 In this case, the transfer of energy is described by virtue of random fragmentation model with the assumption that no correlations exist between stages of the process. Nevertheless, it is possible to calculate the fractal dimension of turbulent structures (D f ), which is defined by the relation…”

“…The limiting draw ratio l ? attained by stretching a polymer is determined, in terms of the rubbery high-elasticity theory, by the equality 121 l ? = n 1a2 st , (62) where n st is the number of statistical segments.…”

Structure and properties of polymers in terms of the fractal approach

“…90 The evolution of DS induced by various types of treatment of the polymer has been considered. 64,93,94 Figure 15 shows the dependence of the cluster functionality F on the curing agent : oligomer ratio (K st ) for epoxy polymers in deformed and nondeformed states. The most characteristic distinction between the plots being compared is the substantial increase in F after the yield point.…”

“…96,97 The opposite situation is observed during heat ageing, namely, the local order (V cl ) increases and the molecular mobility of chains is suppressed (D decreases). 94 Experimental evidence for the fractality of the cluster structure (or DS) has been obtained using wide-angle X-ray diffraction analysis. 98 ± 100 The integral intensity of the amorphous halo I cl can be regarded as a measure of distributed particles (clusters), while its half-width can be taken as a measure of their effective size; the relationship between these values is illustrated in Fig.…”

“…114 At relatively low temperatures (about room temperature), this process is fairly slow; it takes several years for substantial changes in the properties to occur. 94,148 Therefore, forecasting of these phenomena should be performed with allowance for both spatial and temporal disorder of systems. The spatial non-uniformity of the structure of amorphous vitreous polymers accounts for the rather broad range of the rates of relaxation processes.…”