Estimating the fibre length distribution in fibre reinforced polymers

  • Fibre reinforced polymers(FRPs) are one the newest and modern materials. In FRPs a light polymer matrix holds but weak polymer matrix is strengthened by glass or carbon fibres. The result is a material that is light and compared to its weight, very strong.\par The stiffness of the resulting material is governed by the direction and the length of the fibres. To better understand the behaviour of FRPs we need to know the fibre length distribution in the resulting material. The classic method for this is ashing, where a sample of the material is burned and destroyed. We look at CT images of the material. In the first part we assumed that we have a full fibre segmentation, we can fit an a cylinder to each individual fibre. In this setting we identified two problems, sampling bias and censoring.\par Sampling bias occurs since a longer fibre has a higher probability to be visible in the observation window. To solve this problem we used a reweighed fibre length distribution. The weight depends on the used sampling rule.\par For the censoring we used an EM algorithm. The EM algorithm is used to get a Maximum Likelihood estimator in cases of missing or censored data.\par For this setting we deduced conditions such that the EM algorithm converges to at least a stationary point of the underlying likelihood function. We further found conditions such that if the EM converges to the correct ML estimator, the estimator is consistent and asymptotically normally distributed.\par Since obtaining a full fibre segmentation is hard we further looked in the fibre endpoint process. The fibre end point process can be modelled as a Neymann-Scott cluster process. Using this model we can find a formula for the reduced second moment measure for this process. We use this formula to get an estimator for the fibre length distribution.\par We investigated all estimators using simulation studies. We especially investigated their performance in the case of non overlapping fibres.

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Metadaten
Author:Jan Niedermeyer
URN:urn:nbn:de:hbz:386-kluedo-60654
Advisor:Claudia Redenbach
Document Type:Doctoral Thesis
Language of publication:English
Date of Publication (online):2020/08/30
Year of first Publication:2020
Publishing Institution:Technische Universität Kaiserslautern
Granting Institution:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2019/09/23
Date of the Publication (Server):2020/08/31
Page Number:128
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)