The Orientation of Strain-Induced Crystallites in Uniaxially-Strained, Thin and Wide Bands Made from Natural Rubber

Vulcanized natural rubber (unfilled and filled with 20 phr carbon black) is strained. We suppress the macroscopic formation of fiber symmetry by choosing strip-shaped samples ("pure-shear geometry") and investigate the orientation of the resulting crystallites by two-dimensional wide-angle X-ray diffraction (WAXD), additionally rotating the sample tape about the straining direction. Indications of a directed reinforcing effect of the strain-induced crystallization (SIC) in the thin strip are found. In the filled material fewer crystallites are oriented and the orientation distribution of the oriented crystallites is less perfect. The results confirm, that it is important for the evaluation of crystallinity under deformation to check, whether fiber symmetry can be assumed. This has consequences in particular on the quantitative interpretation of space-resolved scanning experiments in the vicinity of crack tips. Furthermore it raises the question, whether there is an asymmetric reinforcing effect of the SIC in the vicinity of crack tips inside natural rubber. © 2019 by the authors. Licensee MDPI, Basel, Switzerland

Indexing User Uploaded Videos For Late Arriving Reference Content

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On the asymptotic behaviour of cosmic density-fluctuation power spectra

We study the small-scale asymptotic behaviour of the cosmic density-fluctuation power spectrum in the Zel'dovich approximation. For doing so, we extend Laplace's method in arbitrary dimensions and use it to prove that this power spectrum necessarily develops an asymptotic tail proportional to $k^{-3}$ , irrespective of the cosmological model and the power spectrum of the initial matter distribution. The exponent $-3$ is set only by the number of spatial dimensions. We derive the complete asymptotic series of the power spectrum and compare the leading- and next-to-leading-order terms to derive characteristic scales for the onset of non-linear structure formation, independent of the cosmological model and the type of dark matter. Combined with earlier results on the mean-field approximation for including particle interactions, this asymptotic behaviour is likely to remain valid beyond the Zel'dovich approximation. Due to their insensitivity to cosmological assumptions, our results are generally applicable to particle distributions with positions and momenta drawn from a Gaussian random field. We discuss an analytically solvable toy model to further illustrate the formation of the $k^{-3}$ asymptotic tail.Comment: 22 pages, 4 figues, to be submitted to SciPost Physics Added arguments to section 1 and section 5, results unchange