@phdthesis{,
    author = {Bauer, Steffen},
    title = {Novel Experimental and Analytical Concepts for the Characterization and Modeling of Soda-Lime Glass under Impact Conditions},
    editor = {},
    booktitle = {},
    series = {},
    journal = {},
    address = {},
    publisher = {},
    edition = {},
    year = {2021},
    isbn = {},
    volume = {},
    number =  {},
    pages = {},
    url = {},
    doi = {},
    keywords = {soda-lime glass; ballistic impact; constitutive modeling; equation of state; damage; strength degradation},
    abstract = {The objective of this thesis is to improve the predictive power of existing numerical simulation models of soda-lime glass (SLG), with the focus on highly dynamic impact scenarios. To achieve this goal, new characterization and analysis methods are developed. Furthermore, the new results are used to modify and improve an existing literature model. 
Altough the first academic works on the ballistic properties of glass date back over 90 years, certain issues are still unclear that are crucial to the material behavior of SLG in ballistic impact scenarios. One of the most important issues is the lack of experimental data characterizing the residual strength as a function of the degree of damage. Another important aspect is the determination of the equation of state (EOS) and the Hugoniot Elastic Limit (HEL). Both issues are addressed in this thesis by new experimental and evaluation methodologies. Within the framework of this work, several novel methodologies for the characterization and modeling of SLG are developed and applied. Several experimental test series are designed and carried out covering quasi-static as well as highly dynamic loading rates. In addition, advanced analysis concepts are developed, which are supported by numerical simulations. The first part of this work is focused on the characterization of the material properties under shock loading. An extensive planar plate impact (PPI) test series is carried out to determine the Shock Hugoniot, the HEL and the EOS of SLG. In addition, new insights into the failure front phenomena are obtained by means of a novel high-speed video observation setup. Several results of this test series have been pre-published by the author in [A1]. An incremental analysis concept is developed and applied to evaluate the PPI data. The validity of the concept is investigated by a simulation study. Furthermore, a novel error analysis approach is carried out for the determination of the Shock Hugoniot and the HEL. As a result, the Shock Hugoniot is determined for longitudinal compressive stresses of up to 20.8 GPa. Especially noteworthy are the derived Shock Hugoniot and the EOS, which clearly differ from reported literature data. In order to investigate the discrepancies, a selection of reported velocity profiles is digitized and analyzed using the derived analysis concept. For the detailed investigation of the failure fronts, a novel methodology is developed, which includes a “streak analysis” of the high-speed videos. These results are combined with the laser interferometry results in a new way. Lagrange diagrams are created that allow for an in-depth investigation of the failure front properties. The second part of this work is focused on the characterization of the shear strength of SLG. This includes both the strength of intact material at high pressures and the residual strength of pre-damaged SLG. A novel test methodology is developed to dynamically generate different degrees of pre-damage in small SLG cylinders. For this purpose, the cylinders are loaded by a plane stress wave, initiated by the impact of an aluminum plate at a defined velocity. This is done in a new way: the SLG is damaged dynamically by a shock wave while being completely confined by a demountable aluminum confinement. The confinement holds the SLG fragments in place, which are generated during the pre-damaging. This is essential, since the residual strength of the specimen strongly depends on the friction between the fragments. The residual strength is considerably higher if all fragments are kept in place and are “interlocking”, in contrast to a loose accumulation of fragments similar to e.g. rough gravel. In order to ensure that the fragments are kept in place in the subsequent characterization tests, a thin aluminum sleeve is retained around the SLG cylinder even after removing the demountable confinement. This concept turns out to be a significant improvement in comparison to the characterization tests of previous studies, which used loosely poured glass quartz powder or granular silica sand. A further significant improvement compared to previous studies is the contact-free investigation of the pre-damage prior to the measurement of the residual strength. An extensive CT test series is carried out in order to analyze and quantify the crack volume in the pre-damaged SLG cylinders. X-ray CT scans are conducted at two different facilities, at a micro-CT device of the Ernst-Mach-Institut and at the synchrotron of the Paul Scherrer Institut. For the identification of the crack volume, a software tool developed by the Australian National University is used. Utilizing the advanced 3D image processing and segmentation techniques of the software, an analysis method for the SLG specimens is developed. As a result, the pre-damage of selected specimens is quantified and parameterized. The residual strength of pre-damaged and categorized specimens is subsequently characterized in confined triaxial compression tests. These tests are an enhancement of experimental techniques reported in previous studies. One new aspect is that the steel confinement is replaced in most tests by a tungsten carbide confinement. This has the advantage that the occurring radial deformation of the SLG specimens is more limited. In addition, the loading of the tungsten carbide confinement can be regarded to be elastic since exceeding its elastic limit would result in brittle fracture. A second new aspect is that the experiments were supported by an elaborated simulation study. The results of the simulations allow accounting for the influence of friction and the effects of the detailed test setup. Additional tests on low-strength polyurethane specimens are conducted to verify the analysis methods. As a result, new yield curves of SLG are obtained, which are functions of the hydrostatic pressure and the degree of initial pre-damage. The determined model parameters are especially suited for the simulation of ballistic impact scenarios, since the characterized pre-damaged SLG is representative for the damaged transparent armor in front of a bullet during impact. In summary, the novel methodology developed within the second part of this work allows determining several yield curves that are dependent on the degree of initial damage. The results extend the available literature data in four ways. First, the pre-damage is created dynamically by means of defined PPI tests instead of a thermal shock. This allows a drastic increase of the degree of pre-damage, which represents the damage in front of a ballistic projectile more closely. Second, for the first time, the degree of pre-damage is directly measured and quantified using a novel X-ray CT analysis. Third, different yield curves for different degrees of pre-damage are determined. Finally, the resulting yield curve for entirely failed SLG is significantly different from curves that are used by other authors in constitutive models. In the final part of this work, a new simulation concept is developed, which is based on the implementation of the novel results into a constitutive material model. A two-dimensional, axisymmetric model approach based on the Johnson-Holmquist-2 (JH2) model is chosen for this purpose. However, it is important to note that the concept is generally neither restricted to the JH2 model nor to the two-dimensional approach. The new concept includes the implementation of the EOS found in the present work as well as the development of a improved strength model based on the new yield curves. In addition, a novel approach is developed that enables a coupling of the damage model to the experimental observed damage. For this purpose, the improved model is utilized to reproduce the pre-damaging PPI tests. This direct calibration of the damage model is a significant improvement, since in previous studies, these parameters had to be deduced simultaneously with several other parameters by matching the depth of penetration of experiments with long rods penetrating SLG laminates. The performance of the improved SLG model is investigated in a representative ballistic impact scenario. It is demonstrated that the model represents an improvement for the investigated ballistic scenario. 
Finally, it is noteworthy that the novel test and analysis methods are not restricted to the characterization of SLG only. In principle, most new concepts are suited to be applied to other materials, like ceramics, rocks or even high-strength steels. Especially for materials that do not exhibit a shock response with a clear two-wave structure, the incremental analysis represents an improvement to common analysis methods. Furthermore, the methodology of characterizing the residual strength of quantitatively pre-damaged specimens is also expected to be generally applicable to other brittle materials.},
    note = {},
    
    school = {Universität der Bundeswehr München},
    
}