On the estimation of parameters of a spheroid distribution from planar sections

Baaske, Markus; Ballani, Felix; Illgen, Alexandra

doi:10.1016/j.spasta.2018.07.003

Cited by 5 publications

(1 citation statement)

References 17 publications

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“…(1) using the simple rectangular quadrature rule applied to Eq. (2) by the quasilikelihood approach by Baaske et al (2018), which allows the use of a parametric models for the particle size distribution. Furthermore, the assumption of a modified non-Lambertian reflectance, e.g.…”

Section: Discussionmentioning

confidence: 99%

Estimation of filler macro‐dispersion in rubber matrix by radiometric stereo microscopy

Ohser¹,

Lacayo‐Pineda

Putman³

et al. 2019

Journal of Microscopy

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SummaryA new microscopic principle based on radiometric stereo microscopy is presented, which is designed for investigating macro‐dispersion of filler in rubber. The image acquisition is combined with a stereological method of estimating the volume‐weighted size distribution of the filler particles. Experimental results for carbon black filler in rubber obtained by radiometric stereo microscopy are compared with those from microtomography using synchrotron radiation, and, furthermore, a simulation study is used for evaluation. It turns out that using the new three‐dimensional microscopic method, the size distribution of the filler particles can be estimated from fresh cuts of rubber with high accuracy, and thus it is an interesting alternative to well‐established dark field microscopy.Lay DescriptionMacro‐dispersion of globular filler particles in a rubber matrix is an important quantity that depends on manufacturing parameters and influences various rubber properties. Therefore, it must be carefully adjusted during the incorporation process and investigated by industrial quality control (ASTM D7723‐18). Quality control is usually based on freshly made planar sections so‐called fresh cuts through rubber specimen. After stress retention of the rubber one obtains a rough cutting surface in which the filler particles appear as imprints or bumps, called nodges. These nodges can be made visible by classical light microscopy under dark field (DFM) illumination. The systems disperGRADER+ or the disperGRADER Alpha View were specifically designed for rubber inspection. However, it has proved to be very difficult estimating the size distribution of the filler particles from the observed white spots in the DFM image. In any case it is still necessary to compute the size distribution of the filler particles from an estimated size distribution of the section profiles. The latter is numerically unstable, i.e. small errors of the estimated size distribution of the section profiles lead to large errors of the computed filler size distribution.Applying DFM combined with filler dispersion estimation as described in ASTM D7723‐18 appears to be a fingerprint method only. For this reason, the new microscope nSPEC 3D was applied for rubber inspection. The principle used for surface imaging is based on radiometric stereo allowing for perfect three‐dimensional reconstruction of curved surfaces of fresh cuts. From this reconstruction it is possible to measure the height of particle nodges as well as their volumes. Furthermore, we present a new stereological method for estimating the filler size distribution from samples of the height and the volume of the nodges. Finally, microtomography with synchrotron radiation and computer simulation are applied to evaluate accuracy of the presented method.

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Section: Discussionmentioning

confidence: 99%