Gumbel-Exponentiated Weibull {Logistic} Lifetime Distribution and Its Applications

A new generalized exponentiated Weibull model called Gumbel-exponentiated Weibull {Logistic} distribution is introduced and studied. The new distribution extends the exponentiated Weibull distribution with additional parameters and bimodal densities. Some new and earlier distributions formed the sub-models of the proposed distribution. The mathematical properties of the new distribution including expressions for the hazard function, survival function, moments, order statistics, mean deviation and absolute mean deviation from the mean, and entropy were derived. Monte Carlo simulation study was carried out to assess the finite sample behavior of the parameter estimates by maximum likelihood estimation approach. The superiority of the new generalized exponentiated Weibull distribution over some competing distributions was proved empirically using the fitted results from three real life datasets.

Molecular Mobility in the Amorphous Phase Determines the Critical Strain of Fibrillation in the Tensile Stretching of Polyethylene

The microstructural development of bimodal high density polyethylene subjected to tensile deformation was investigated as a function of strain after annealing at different temperatures by means of a scanning synchrotron small angle X-ray scattering(SAXS)technique.Two different deformation mechanisms were activated in sequence upon tensile deformation:intralamellar slipping of crystalline blocks dominates the deformation behavior at small deformations whereas a stress-induced crystalline block fragmentation and recrystallization process occurs at a critical strain yielding new crystallites with the molecular chains preferentially oriented along the drawing direction.The critical strain associated with the lamellar-to-fibrillar transition was found to be ca.0.9 in bimodal sample,which is significantly larger than that observed for unimodal high-density polyethylene(0.4).This observation is primarily due to the fact that the bimodal sample possesses a greater mobility of the amorphous phase and thereby a reduced modulus of the entangled amorphous network.The conclusion of the mobility of the amorphous phase as a determining factor for the critical strain was further proven by the 1H-NMR T2 relaxation time.All these findings contribute to our understanding of the excellent slow crack growth resistance of bimodal polyethylene for pipe application.