Stochastic Approach to Rupture Probability of Short Glass Fiber Reinforced Polypropylene Based on Three-Point-Bending Tests PDF by Nikolai Sygusch

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Stochastic Approach to Rupture Probability of Short Glass Fiber Reinforced Polypropylene Based on Three-Point-Bending Tests
by Nikolai Sygusch
Stochastic Approach to Rupture Probability of Short Glass Fiber Reinforced Polypropylene


Contents

1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objective and Structure of the present Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 State of the Art 5
2.1 Experimental Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Numerical Investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Statistical Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Mechanical Testing 15
3.1 Studies on the Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.1 Characterization of the glass fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.2 μCT scans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Macroscopic Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.1 Specimen preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.2 Tensile tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.3 Three point bending tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4 Statistical Analysis 41
4.1 Mathematical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.1 General definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.2 Distribution functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.3 Goodness of fit tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 Statistical Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.1 Quasistatic three point bending tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.2 Dynamic three point bending tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5 Material Modeling 59
5.1 Explicit Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 Constitutive Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.1 Material theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.2 Orthotropic modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2.3 Rupture condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3 Contact Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6 Numerical Results 73
6.1 Deterministic Three Point Bending Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.2 Stochastic Three Point Bending Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.2.1 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.2.2 Evaluation and validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2.3 Influence of the explicit time integration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7 Summary and Outlook 93
Bibliography 97
List of symbols 105
A Appendix 111
A.1 Technical data sheet Hostacom G3 R05 105555 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
A.2 Fiber length analysis . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . 114
A.3 μCT scans . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . 116
A.4 Surface roughness measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
A.5 Three point bending test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
A.6 Results Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
A.6.1 Histograms of all design variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
A.6.2 Scatter plots of all design variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139


Abstract
Increasing regulatory standards in the vehicle development create the demand for new computer aided engineering methods that improve the predictability of the simulations. A method for incorporating and comparing stochastic scatter of macroscopic parameters in crash simulations is developed in the present work and applied on a 30 wt.% short glass fiber reinforced polypropylene.

The application of fiber reinforced polymers is of great interest for different crash worthiness and pedestrian protection load cases. However, the orientation and strain rate dependent material behavior has to be considered and the brittle rupture behavior has to be taken into account as well.

A statistical testing plan on the basis of three point bending tests with 30 samples for each configuration is carried out in this work. The tests are conducted at 0◦, 30◦, 45◦ and 90◦ orientation angles and at strain rates of 0.021 s−1 and 85 s−1. The obtained results are evaluated statistically by means of probability distribution functions. The normal and lognormal distributions are able to model most of the data accurately, however, the Weibull distribution provides better results for some of the configurations. An orthotropic elastic plastic material model is utilized for the numerical investigations. Monte Carlo Simulations with variations in macroscopic parameters are run to emulate the stochastic rupture behavior of the experiments. The stochastic rupture behavior in terms of the probability density functions can be recreated very well for the 0◦ orientation. Data analysis of the stochastic simulations shows that only two of the initial seven parameters can be identified as main influential parameters. These are the maximum principal strain at rupture and the specimen width. This finding is verified in a validation study that proves the validity of the introduced method.

Introduction
Today the vehicle development in the automotive industry is mostly driven by computer aided engineering practices. Currently, the application of advanced material models and comprehensive optimization and robustness studies are two of the challenges in the crash simulation environment in the vehicle development process [24]. New material models are developed that e.g. emulate the material behavior of polymers more physically than commonly used material models. Furthermore, the improvement of methods for rupture modeling plays an important role as well. One main focus is to model the stress state and load path dependent rupture behavior accurately [19], whereas another main focus is the use of capabilities of today’s increasing CPU power in order to run stochastic simulations for advancements in the field of non deterministic rupture modeling [67].

The present work is contributing to the field of CAE vehicle development because a new approach to stochastic rupture modeling for fiber reinforced polymers is introduced. The stochastic simulations are complemented by a large number of experiments that consolidate the conclusiveness of this work.

 

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