A Methodology to Model the Statistical Fracture Behavior of Acrylic Glasses for Stochastic Simulation

verfasst von: Marcel Berlinger

Verlag: Springer Fachmedien Wiesbaden

Buchreihe : Mechanik, Werkstoffe und Konstruktion im Bauwesen

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

A statistical modelling method for simulating the fracture behaviour of acrylic glass is presented using the application case of an automotive rear side window. The collection of the necessary measurement data and their analysis is described. The aim is to give guidance to users of comparable materials. Finally, the model is integrated into the finite element simulation of a head impact test of the pane. Based on the resulting spread of the head injury criterion, the relevance of a statistical material characterisation for product safety is discussed.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

The weight of a vehicle is an essential factor for its fuel consumption, or rather energy demand when we think of electric cars. Reason are driving resistances like inertial or tractional forces the engine has to overcome. In the year 2008, the Massachusetts Institute of Technology (MIT) published a report [122] quantifying the potential for reducing fuel consumption by weight savings.

Marcel Berlinger

Chapter 2. Fundamentals

Abstract

Before the research topic is discussed, in this chapter the necessary groundwork is compiled. Conventions are established and definitions made, that are consistently used in further considerations. To begin with, the examined acrylic glasses are classified in a chemical context.

Marcel Berlinger

Chapter 3. Generalized Anderson-Darling Test

Abstract

The quality of a modeled distribution function for describing the distribution of a set of random variables is evaluated in statistical hypothesis testing. A null hypothesis H₀ is assumed, which claims the sample and the fitted probability distribution to have the same population [8]. Thereby, two errors can be made. A type I error, which is the rejection of a true null hypothesis, and a type II error, which is the non-rejection of a false null hypothesis.

Marcel Berlinger

Chapter 4. Experimental Investigations

Abstract

The data basis for stochastic analyses in this work is collected in ad-hoc performed laboratory testings. In this chapter, the individual test setups are introduced. Since primarily uniaxial tensile tests are considered, focus is placed on the three different types of applied testing machines.

Marcel Berlinger

Chapter 5. Sampling

Abstract

A statistical sample is a set of possible outcomes of a probabilistic experiment [66]. The phrase probabilistic experiment motivates the analyses of this chapter. To gain statistically valid samples, the bound conditions in the experimental research have to be consistent for every test of a kind.

Marcel Berlinger

Chapter 6. Statistical Modeling

Abstract

This chapter is the link between experimental measurements and stochastic simulation. A model is introduced that is able to be integrated directly into a conventional non-stochastic FE simulation. For that matter, certain requirements have to be fulfilled.

Marcel Berlinger

Chapter 7. Stochastic Simulation

Abstract

The introduced statistical model is now utilized in a practical application. In the studies of [113, 150] a head impact test on PMMA automotive rear side windows was chosen as validation test for the developed material models. As continuation of this work, the material models are extended by a stochastic failure criterion for FE simulation.

Marcel Berlinger

Chapter 8. Experimental Basis for Model Enhancements

Abstract

This final chapter is an extended outlook on the subject of the present work. As known from numerous studies, cf. Section 1.2, the material behavior of PMMA is besides strain rate likewise sensible to the applied temperature and stress state. Hitherto, all experiments are at room temperature.

Marcel Berlinger

Chapter 9. Summary

Abstract

With regard to two Plexiglas^® materials, one brittle and one impact resistant, the statistical fracture behavior is modeled for stochastic FE simulation. First of all, a common ground of necessary fundamentals is prepared for in the fields of chemistry, mechanics, and statistics. For the latter, an overview of existing probability estimators and relevant families of probability distribution functions is compiled.

Marcel Berlinger

Backmatter

Titel: A Methodology to Model the Statistical Fracture Behavior of Acrylic Glasses for Stochastic Simulation
verfasst von: Marcel Berlinger
Verlag: Springer Fachmedien Wiesbaden
Electronic ISBN: 978-3-658-34330-9
Print ISBN: 978-3-658-34329-3
DOI: https://doi.org/10.1007/978-3-658-34330-9