A Model for the Stochastic Fracture Behavior of Glass and Its Application to the Head Impact on Automotive Windscreens (Mechanik, Werkstoffe und Konstruktion im Bauwesen)

The book deals with the stochastic strength of glass and the application to the automotive windscreen. A finite element model is derived. This is then validated using known phenomena in connection with the fracture behaviour of glass. After the strength of a windscreen has been intensively investigated, experiments with wind windscreen, experiments with windscreens are simulated by means of the model. Finally, the probability of a pedestrian suffering a head injury on impact with a windscreen is predicted. of a pedestrian hitting a windscreen is predicted, taking into account the stochastic breakage behaviour of glass. Up to now, this has not been taken into account in EuroNCAP crash tests, for example. Abstract Zusammenfassung Contents Glossaries Abbreviations Sub- and Superscripts Symbols 1 Introduction 1.1 Motivation 1.2 State of the Art Strength of Glass Statistical Treatment Computational Models Head Injury Probability 1.3 Structure Journal Articles Book Contributions Conference Proceedings 2 Theoretical Background 2.1 Glass 2.1.1 Definition of Glass 2.1.2 Properties and Application 2.1.3 Production 2.2 Mechanical Behavior of a Crack 2.2.1 Stress Concentration 2.2.1.1 Stress at Circular Holes 2.2.1.2 Stress at Elliptic Holes 2.2.1.3 Energy-Based Fracture Criterion 2.2.1.4 Stress Field at the Crack Tip 2.2.2 Stress Intensity Factor 2.2.3 Geometry Factor 2.3 Statistical Treatment of Glass Strength 2.3.1 Probability Distribution Functions 2.3.1.1 Two-Parameter Weibull Distribution 2.3.1.2 Three-Parameter Weibull Distribution 2.3.1.3 Left-Truncated Weibull Distribution 2.3.2 Parameter Estimation Methods 2.3.2.1 Least-Square Method 2.3.2.2 Weibull Plot 2.3.2.3 Maximum Likelihood 2.3.2.4 Modified Maximum Likelihood 2.4 Acoustic Emission Localization 3 A Stochastic Fracture Model for Glass 3.1 Introduction 3.2 Subcritical Crack Propagation 3.3 Stochastic fracture Model 3.3.1 Initialization Procedure 3.3.1.1 Estimating Initial Flaw Sizes 3.3.1.2 Geometry Factor Shift 3.3.2 Fracture Calculation 3.3.3 Post-Fracture Behavior 3.4 Model Validation 3.4.1 Mesh Dependency 3.4.2 Surface Size 3.4.3 Stress Rate 4 Mechanical Parameter Quantification 4.1 Introduction 4.2 Fundamental Mechanical Parameters 4.2.1 Young’s modulus 4.2.2 Poisson’s Ratio 4.3 Subcritical Crack Growth Parameters 4.3.1 Experimental Part 4.3.1.1 Specimen Preparation 4.3.1.2 Dynamic Fatigue Experiments 4.3.2 Evaluation 4.3.2.1 Parameter Estimation 4.3.2.2 Evaluation of Environmental Influences 4.3.3 Discussion 4.4 Fracture Toughness 4.5 Stress Field Factor 4.6 Crack Growth Threshold 4.7 Geometry Factor 4.8 Summary 5 Stochastic Strength of an Automotive Windscreen 5.1 Introduction 5.2 Lower Bound for Glass Strength 5.3 Differentiation of Strength Populations 5.4 Experimental Part 5.4.1 Specimen Preparation 5.4.2 Surface Strength 5.4.3 Edge Strength 5.5 Residual Stress 5.6 Statistical Evaluation 5.7 Fractographic Verification 5.8 Summary 6 Displacement-Controlled Windscreen Tests 6.1 Introduction 6.2 Experimental Part 6.2.1 Experimental Setup 6.2.2 Experimental Results 6.3 Numerical Part 6.3.1 Finite Element Model 6.3.1.1 Head Impactor 6.3.1.2 Windscreen 6.3.1.3 Test Frame 6.3.2 Interlayer Stiffness Evaluation 6.4 Comparison of the Results 6.4.1 Impactor Displacement 6.4.2 Fracture Origin 6.5 Summary 7 Free-Flying Head Impact 7.1 Introduction 7.2 Head Injury Criterion 7.3 Head Impact Replacement Test 7.3.1 Experimental Part 7.3.2 Numerical Part 7.3.3 Comparison of Results 7.4 Head Injury Probability Distribution 7.4.1 Stochastic Head Impact Simulation 7.4.2 Head Injury Distribution 8 Summary and Future Research Topics 8.1 Summary 8.2 Future Research Topics References Appendix A Subcritical Crack Growth Parameters A.1 Experimentally Determined Parameters A.2 Literature Values Appendix B Windscreen Strength Test Results B.1 Coaxial Ring-on-Ring Tests B.2 Four-Point-Bending Tests Appendix C Geometric Correction Factor Shift Appendix D Newman and Raju Equation The book deals with the stochastic strength of glass and the application to the automotive windscreen in the case of a pedestrian head impact. A finite element model is derived. This model is then validated using known phenomena in connection with the fracture behaviour of glass and experimental values. After the strength of a windscreen has been intensively investigated, experiments with windscreens are simulated by means of the finite element model. Finally, the probability of a pedestrian suffering a head injury on impact with a windscreen is predicted, taking into account the stochastic fracture behaviour of glass. Up to now, this has not been taken into account in EuroNCAP crash tests, for example. Christopher Brokmann studied mechanical engineering at the University of Applied Sciences Mittelhessen from 2012 to 2017. He then completed his doctorate in the field of crash simulation at the Institute of Mechanics and Materials Research until 2021. In the research group of Prof. Dr. habil. Stefan Kolling, he worked on the stochastic fracture behavior of glass and its application in the field of crash simulation