A shock compression investigation of failure waves and phase transition in soda-lime glass

These results and observations provide a possible explanation of the mechanism underlying the failure wave phenomenon. The tensile wave is expected to further aid in axial crack propagation. time charts and an X-plot. characteristic diagram for experiment #AJ-3.

LIST OF TABLES

INTRODUCTION

Motivation and Organization of Thesis

However, the same PRDs are also seen to undergo complete fragmentation when the internal traction zones are exposed by snapping off the tail end of the droplet. A more comprehensive background of the failure wave phenomenon together with the experiments and modeling undertaken as part of this work are discussed in Chapter 2.

Background Normal Shock relationsNormal Shock relations

The Lagrangian wave speeds (𝐶) are directly related to the slopes of the stress-strain curve as𝐶. The strength of the material can be deduced from the size of the quasi-elastic region.

Figure 1.1: Schematic of a 1-D shock. 𝑈 𝑆 denotes Lagrangian shock wave-speed and 𝑢 𝑆 denotes the same in Eulerian frame

PROBING THE PROPERTIES AND MECHANISMS OF FAILURE WAVES IN SODA-LIME GLASS

Introduction

Examples of non-local hypotheses for the failure wave phenomenon include Feng's [20] work and that of Kanel [1] and Espinosa et al. 12] and the nucleation of cracks seen behind the failure wave by Bourne et al.

Materials and methods

The values of the various constants used in the SLG simulation are shown in Table 2.2. The properties of the tungsten carbide (WC) impactor used in the experiments are summarized in Table 2.3.

Figure 2.1: Schematics of normal impact experiments on SLG and the velocity measurement using Photonic Doppler Velocimetry (PDV)

Results and discussion

2.6, has been used in the past by other authors to determine the speed of the failure wave from splash experiments [4, 33]. This may be due to the failure wave causing a partial reduction in transmittance of the SLG after 1550 nm laser light. However, unlike Dandekar and Beaulieu's work [13], no complete loss of light (opacity) was observed at the onset of the failure wave.

A recompression/retraction is expected at the trailing surface due to interaction of the tensile wave with the failure front. Therefore, it may instead be a previously unexplored feature of the failure wave phenomenon itself.

Figure 2.6: Free surface velocity vs. time alongside a schematic X-t characteristic diagram for experiment #AJ-1

Conclusions

Gupta, "Time-Dependent Inelastic Deformation of Soda-Lime Shocked Glass," Journal of Applied Physics 96, Publisher: American Institute of Physics. Field, "High-speed imaging of compressive failure waves in glasses," Journal of Applied Physics78, Publisher: American Institute of Physics. Feng, "Failure Formation and Propagation in Shocked Glasses", Journal of Applied Physics87, Publisher: American Institute of Physics.

Alexander, "Application of a computational glass model to the impact response of soda-lime glass," Journal of Dynamic Behavior of Materials. Chen, “Transformation of shock compression pulses in glass due to the fault wave phenomena,” Journal of Applied Physics.

Figure 2.14: Schematics of two possible mechanisms to explain the cause of the fail- fail-ure wave phenomenon

SHOCK COMPRESSION AND RELEASE STUDY TO PROBE PHASE TRANSITION IN SODA-LIME GLASS

Introduction

Studying the loading–unloading behavior of SLG subjected to shock compression to these stresses can provide significant insight into the existence and kinetics of a possible phase transition in the material at these aforementioned stresses. Previous impact compression and release experiments to study the loading–unloading behavior of SLG [16] observed a progressively stiffer release response with higher impact stresses. Therefore, a more careful analysis of the release behavior of SLG will be necessary to unequivocally establish the existence of a phase transition in SLG at relatively low shock stresses (4–7 GPa) under shock compression.

Permanent densification of SLG during shock compression may be indicative of its inelastic behavior or an irreversible phase transition or a combination of both. Thus, the present work presents shock compression and release experiments on SLG to construct the material's loading and complete unloading response.

Materials and methods

The presence of the LiF[100] window ensures that the SLG material remains compressed while the PDV probe records the velocity of the SLG-LiF interface. The impact head cavity ensures that the stress on the rear surface of the impact head is reduced to zero. The only significant source of uncertainty in the calculated stress-strain profile is the shock slope/trigger time, which is shown in Fig.

It should be noted that when using impactors other than SLG (such as WC), one must account for the multiple reflections in the impactor plate.

Results and discussion Experiment #WSL-1Experiment #WSL-1

A plot of the observed and optically corrected interfacial velocity next to a material position-time diagram is shown in Figure. A plot of the observed and optically corrected SLG-LiF interfacial velocity next to a material position-time diagram is shown in Figure. A phase transition can be expected to change the pressure-volume response of the material and give rise to a hysteresis in the.

Thus, a change in loading and unloading paths in the EOS volume pressure of the material would indicate a phase transition. Thus, the slope of the pressure-strain curve after release will be identical to the slope of the Hugoniot stress at 𝜀𝑖𝑛𝑖𝑡.

Figure 3.2: Schematic of procedure to evaluate the wave speed in material frame, 𝐶 ℎ ( 𝑢 ).

Modeling

Interface velocity data for experiments AT-3 and AT-4 were taken from [16], corrected for SLG-LiF impedance mismatch, and then processed to obtain the stress-strain curve shown in the graph. Also, in the previously mentioned works on LiF [100], it can be observed that the relaxation wave velocities for plastic behavior (gradual reduction) were almost the same as the longitudinal compression wave velocities. Thus, for the highest pressure loads (𝜀𝑖𝑛𝑖𝑡), which are greater than the threshold for the occurrence of hysteresis (see Figure 3.8), the pressure release is prescribed by Figure 3.

The timing of the initial release and a two-wave structure on the first release is also captured. Although the initial release wave velocity is underestimated by the simulations, the timing and extent of release in the later part of the release fan is well captured.

Figure 3.10: Stress-strain response of SLG and other polymorphs of SiO 2 . (a) Stress-strain plots of symmetric shock-release experiments on SLG

Conclusion

Brar, "Effect of shear on failure waves in soda lime glass," AIP Conference Proceedings 429, Udgiver: American Institute of PhysicsAIP. Wackerle, "Shock-Wave Compression of Quartz", Journal of Applied Physics 33, Udgiver: American Institute of Physics. Dolan, "Nøjagtighedsgrænser og vindueskorrektioner for foton Doppler hastighed," Journal of Applied Physics 101, Udgiver: American Institute of Physics.

Davis, "Strength of lithium fluoride under shockless compression to 114 GPa," Journal of Applied Physics106, Publisher: American Institute of Physics. Gupta, "Effect of crystal orientation on dynamic strength of LiF," Journal of Applied Physics48, Publisher: American Institute of Physics.

PRESSURE-SHEAR PLATE IMPACT EXPERIMENTS ON SODA-LIME GLASS

Background

Symmetric PSPI experiments, in which the impactor and the target disc are made of the same material, are used to calibrate parameters for modeling anvil materials [6]. For experiments with normal impact stresses higher than the elastic limit of the anvils, these models are used to estimate the compressed material properties with forward simulations to reproduce the observed free surface transverse velocity profile.

Experiments to determine the shear-strength of SLG at various pressures

The sudden drop in free surface normal velocity after the first normal tension ring is emphasized. However, the simulations in [9] could not capture the sudden drop in free surface normal velocity observed in Expts. The cause underlying this drop in velocity was further investigated using the AJ-1909 and AJ-2007 normal impact experiments as described below.

4.5, the simulation can, as expected, reproduce a drop in normal speed that occurs between the first and second calls. This further supports the possibility that the velocity drop is a consequence of the material behavior of the glass.

Figure 4.2: Time-material position ( 𝑡 − 𝑋 ) schematic of a sandwiched PSPI experiment

Alumina AD995 as an anvil for PSPI experiments

Grunschel, "Pressure-sliding plate impact experiments on high-purity aluminum at temperatures approaching melting," Ph.D. Clifton, "Dynamic stress-strain curves at plastic shear strain rates of 105 s1", AIP Conference Proceedings78, Publisher: American Institute of Physics. Ravichandran, "Pressure-sliding plate impact experiments at very high pressure," AIP Conference Proceedings2272, Publisher: American Institute of Physics.

Clifton, "Flow behavior of soda-lime glass at high pressures and high shear rates", AIP Conference Proceedings 429, Publisher: American Institute of Physics. Dandekar, "On the Hugoniot Elastic Limit in Polycrystalline Alumina," Journal of Applied Physics 102, Publisher: American Institute of Physics.

Figure 4.6: Free surface velocities for symmetric PSPI of alumina AD 995 (Expt.

SUMMARY AND FUTURE WORK

Summary
Sandwiched PSPI experiments on SLG at 4-6 GPa normal stresses As discussed in Chapter 4, the sandwiched configuration PSPI technique offers aAs discussed in Chapter 4, the sandwiched configuration PSPI technique offers a
Normal plate impact experiments on SLG and other silica glasses
Imaging the SLG under impact at 3 GPa and 6 GPa
Determining shear modulus of SLG as a function of impact stress using oblique impact experimentsoblique impact experiments

Previous works [2] attempted to use PSPI experiments to capture the effect of failure waves on the strength of SLG. As discussed in Chapter 2, normal plate impact experiments to investigate the existence of failure waves in anomalous [3] glasses such as borosilicate and fused silica can provide insight into the role of network modifying ions in the failure wave phenomenon. The ability to accurately image the evolution of failure waves in SLG can be decisive in identifying mechanisms underlying the failure wave phenomenon.

As discussed in Chapter 2, previous works have attempted to image failure waves in SLGs using either band photography [4, 5] from a side view of the target or by imaging failure waves on the impact surface from the rear surface. the sample [5]. Photographing failure waves from the side of the SLG objective is hindered by "surface failure waves".

Figure 5.1: Schematic of a plate impact experiment involving imaging of failure waves in SLG.

EQUATION OF STATE FOR SODA-LIME GLASS

Therefore, point B corresponds to the in-material particle velocity and stress of the second wave/recompression bump. This stress wave is released at the free surface of the SLG at the velocity of the bump observed in experiment #AJ-1. The volume compaction due to the failure wave is evaluated by eq. A.6) The Grüneisen parameter (Γ0) is calculated from the shock-reshock data provided for SLG by Grady et al.

It was observed that the value of Γ0 did not significantly affect the outcome of the simulations. Templeton, "The Hugoniot elastic limit of soda-lime glass," AIP Conference Proceedings955, Publisher: American Institute of Physics.

Figure A.1: Lagrangian wave speed vs. particle velocity diagram for soda-lime glass (SLG)

WINDOW CORRECTIONS: OPTICAL AND IMPEDANCE MISMATCH

𝐶0in𝑆 are material parameters used to relate the shock wave velocity in the window to the particle velocity difference across the shock wave. The density and thus the refractive index of LiF changes continuously along the fan. Thus, the apparent particle velocity (𝑢𝑜 𝑏 𝑠) given in Eq. Further differentiating both sides by 𝑢𝑎 𝑐𝑡 𝑢 𝑎𝑙 and using Leibniz's rule for differentiating integrals we get:.

The optical corrections due to the shock wave and the release fan in the LiF[100] window are thus plotted in Figure B.6, the particle velocity observed at the SLG-LiF interface, after optical corrections (𝑢𝑖𝑛𝑡 𝑒𝑟 𝑓 𝑎 𝑐 𝑒) , is smaller than the particle velocity occurring in the SLG material (𝑢𝑖𝑛−𝑚 𝑎𝑡 𝑒𝑟 𝑖 𝑎𝑙) before the shock wave reaches the interface.