Dynamic Behavior of Materials, Volume 1

The dynamic fracture of soda-lime glass (SLG) involves crack branching, underlying mechanics of which is not yet fully understood. Addressing this issue using full-field optical techniques is challenging due to severe spatio-temporal requirements as crack speeds in this material reach 1500 m/s or more and is accompanied by highly localized nanoscale deformations. Recent work by the authors have shown that transmission-mode Digital Gradient Sensing (DGS) method is capable of overcoming these challenges to visualize crack-tip fields over large regions of interest and quantify fracture parameters associated with each of the phases of crack growth event in SLG plates. In this work, time-resolved stress gradient measurements of two different SLG geometries subjected to dynamic wedge-loading are performed to quantitatively visualize single and cascading branch formations. The precursors of crack branching event are identified from the optical measurements leading up to the first and/or successive branch formations. These precursors are based on crack velocity, stress intensity factors, higher order coefficients of the asymptotic crack tip fields, and a non-dimensional parameter involving a combination of these measured quantities.

Hopkinson tubes can be used similarly to Hopkinson bars and undergo larger deformation than a solid Hopkinson bar of equal outer diameter. This is advantageous for loading that is small in magnitude, where the resulting strain in the bar may be too small to be measured with strain gages. The challenge with using Hopkinson tubes is that the force determined from the traveling stress wave in many cases does not match the contact force causing the deformation. This is due to the relatively complicated dynamics of the Hopkinson tube in comparison to the Hopkinson bar. In this work, simulations of the dynamics due to an impulse hammer striking a Hopkinson tube are used to investigate why the force measured from the impulse hammer does not match the force derived from measurements on the tube. Simulations are first validated with experimental data, and then used to demonstrate that the inertia of the end cap and tube length caused the significant force discrepancies in the experiment.

In this chapter, an effort has been made to investigate the constitutive behavior of aluminum alloy AA6063-T6 under different temperatures. Spectroscopy of the alloy is performed to get the chemical composition and weight percentage of elements in AA6063-T6. The quasi-static experiments under different strain rates at room (25 °C) and elevated temperatures (25 °C, 50 °C, 100 °C, 150 °C, and 200 °C) are performed. The tensile tests at high strain rates are performed using split Hopkinson tensile bar. It is observed that the flow stresses increase with an increase of strain rates, whereas flow stresses decrease at higher temperature experiment. Using these results, the constants of Johnson-Cook plasticity are evaluated by fitting the experimental data. These Johnson-Cook plasticity parameters are used as input parameters for finite element simulation.

In this study, the impact response and damage mechanisms of carbon fiber-reinforced polymer (CFRP) under equal impact energy but different mass-velocity combinations are investigated. CFRP samples are also subjected to impact at room temperature (23 °C) and low-temperature (−70 °C) conditions with the aim to understand composite behavior in cold Arctic environment. Furthermore, this study explores the effect of ice formed on substrate surface, so as to elucidate the influence of surface ice on impact damage. Results show longer test duration for large mass impactor case, whereas smaller impact mass causes shorter impact duration. Moreover, different damage modes are detected by X-ray micro-computed tomography for different mass-velocity configurations. Initial oscillations from force-time curves indicate that low-mass–high-velocity cases create substantial surface damage. Specimens at −70 °C show less damage than samples at 23 °C due to enhanced stiffness at lower temperature. This study reveals that the presence of surface ice has negligible effect due to the brittleness of ice and small fracture energy compared to the CFRP substrate. This research provides understanding on the dynamic behavior of CFRPs when deployed in low-temperature icy conditions.

Structural adhesives are cured thermoset polymers which are employed in a wide range of industrial, transportation, and consumer applications to provide structural joining. Structural adhesives are particularly valuable for joining dissimilar materials, bonding composite materials, and light-weighting structures in transportation in order to minimize energy consumption. These applications also require structural adhesive bonds to provide satisfactory toughness and bond integrity under high strain rate conditions, such as car crash. Direct tensile characterization of structural adhesives at relevant strain rates is therefore critical for engineering design. However, the Kolsky tension bar grip design has not been systematically evaluated to determine what effects gripping may have on results. Grips may alter the stress state near the clamping area and introduce spurious failure modes. Furthermore, gripping methods can influence specimen alignment and efficiency of loading specimens. In this study, the effects of different grip designs on measured stress–strain response and location of failure are evaluated. Three different wedge grip designs are employed along with shoulder grips and clevis grips. Recommendations for tensile grip design and selection are discussed.

Concrete is the most widely used building material in the world by volume and has historically be an integral component of the construction of US military assets. These assets have the requirement to protect against extreme events such as blast and penetration. Conventional ordnance impacts involving concrete materials at velocities on the order of 500 to 1300 m/s has been studied for many decades. One area that has received little study is in the area of ultraordnance impacts on concrete in which impact velocities exceed 1300 m/s. In this velocity range, material strength becomes less of a factor in the overall impact and penetration process. Due to the lack of relevant experimental data, a newly acquired two-stage light gas gun will be used in this study to perform ultraordnance impact experiments against concrete. Specifically, spherical projectiles will be fired against concrete targets at velocities ranging between 1 km/s and 7 km/s. The experimental data will help identify trends in this velocity range where little data exist in the literature for concrete. The experiments will also provide excellent validation data for computational methods that will model this type of extreme loading condition.

Shales are the primary resource to produce unconventional oil and gas using hydraulic fracturing. Thus, understanding and evaluating the evolution of damage in shale materials under dynamic loading conditions will support the development and improve current extraction techniques. An experimental–analytical approach was developed in this work to observe microcrack growth under dynamic stress loading conditions. The developed method was used to measure the local damage across the in-plane of a circular disk (Brazilian disk) subjected to a compressive stress waves. Experimentally, circular disk specimens are prepared from Anadarko basin, Oklahoma, USA and tested with different bedding stacking orientations. The Split Hopkinson pressure bar (SHPB) was used to generate a compressive stress wave. The localized strain and damage initiation as a function of time are monitored using digital image correlation. The experimental data was used as input to the macro-damage (time-depend macro-damage) model. The experimental setup, specimen preparation was presented, as well as a critical local damage-initiation related to the orientation of the layers and cracking density were discussed.

Inertial cavitation is a common phenomenon in nature, which is also similarly present in many engineering and medical applications including laser eye surgery and lithotripsy procedures. In a recent study, we showed experimentally that violently collapsing bubbles, i.e., material Mach numbers that exceed a critical value of 0.1 with respect to the longitudinal material wave speed, can significantly damage the surrounding hydrogel material. Here, we quantitatively characterize the change in mechanical properties of the surrounding material following a violent bubble collapse. To accomplish this, we introduce a second bubble in the vicinity of the violently collapsed bubble to re-initiate its growth and cavitation cycle through propagating pressure fields. By studying the secondary Bjerknes interaction force between these two bubbles, we find that the viscosity of the damaged material is reduced to the viscosity of the solvent (water) whose value is one order smaller than the undamaged polyacrylamide hydrogel, with the pre-determined bulk shear modulus of the initial bubble being essentially unaltered. In addition, we also estimate the magnitude of the re-initiating pressure wave that drives the regrowth of the first bubble. We anticipate that this work also paves the way for a fundamental understanding of bubble pair and bubble cloud interactions in compliant hydrogels and soft polymers.

This work focuses on the development of a new simple IBII test configuration that is designed to maximize identifiability of all four orthotropic stiffness components for bone and glass fiber-reinforced polymer (GFRP) composites. A limitation of current ultra-high speed camera technology is the spatial resolution so it is desirable to explore test configurations that do not require the use of geometrical stress concentrators. Here, the heterogeneity of the kinematics is increased using three parameters: (1) impacting over a percentage of the sample’s height, (2) changing the angle of the input loading pulse, and (3) changing the material orthotropy angle relative to the specimen edges. Two identification strategies based on the virtual fields method are explored including the generalized stress–strain curves and the special optimized virtual fields. This chapter focuses on the presentation of the image deformation simulations used to find optimal test configurations.

The high strain rate material behaviour of armour ceramics is important for the design of armour systems. The current standard test technique for obtaining high strain rate material properties is the split Hopkinson pressure bar (SHPB). This technique relies on several assumptions including that the sample must be in a state of quasi-static equilibrium and that the sample undergoes uniform 1D deformation. These assumptions limit the ability of the SHPB technique to accurately identify the high strain rate response of ceramics because they fail at extremely low strains, especially when under tensile loading.

Recently, the Image-Based Inertial Impact (IBII) test has emerged as an alternative technique that does not rely on the assumption of quasi-static equilibrium and is specifically designed to obtain the high strain rate tensile strength of brittle materials. Therefore, this work focuses on the application of the IBII test to obtain the high strain rate properties of several armour materials including: boron carbide, silicon carbide and the recently developed MAX phase ceramics. Results for the boron and silicon carbide show that there is no rate sensitivity on the identified elastic properties (modulus and Poisson’s ratio) at strain rates on the order of 1000/s. Additionally, results for the tensile strength of boron and silicon carbide compare well with quasi-static values despite exhibiting high scatter. The MAX phase ceramics will be tested in the future and the results will be presented at the conference.

A Kolsky Bar method for high-rate indentation is being developed. Samples are adhered to the end of the input bar and the indenter is mounted directly on the end of the output bar. When the input pulse reaches the sample, the sample is driven into the output bar and loaded. By carefully choosing the lengths and impedances of the bars and striker, the maximum load and loading duration can be reliably controlled. It can furthermore be ensured that the sample is only subjected to a single loading, i.e., the sample is not reloaded due to later stress-wave reverberations in the bars even though a momentum trap is not used. Depending on the sample and desired indentation load, very small output bars may be needed. For this reason, the output bar is instrumented with a normal displacement interferometer on the free-end. This choice of instrumentation is highly sensitive and also can be used to verify that the sample only experiences a single loading cycle. The current study is preliminary and focuses on Vickers indentation of OFHC Cu. However, the method is applicable to a wide range of materials and has the potential for loading times less than 5 μs, about a factor of 20 shorter than the current state of the art.

Nondestructive structural interrogation using guided waves for damage detection is an established engineering assessment technique. In this research, a novel composite mini impactor tool is presented as an excitation source for the use in the evaluation of composite structures. Nondestructive evaluation (NDE) of aerospace composite structures is critical since non-visible internal damage, such as barely visible impact damage (BVID), can affect the safety of the structure. Traditional impact hammers have been used in NDE of composite structures, but the excitation frequency range produced is limited (less than 40 kHz). A unidirectional carbon/epoxy mini impactor device was designed to excite a frequency range between 40 and 500 kHz. Parameterization of the device was performed to define its operational domain and underlying physics. The effect of varying the mini impactor stiffness and total impactor mass, which includes an aluminum tip (i.e., tip + beam), was evaluated for time-domain features, frequency content, and amplitude ranges. During the parameterization, different waveguide materials (flat plates) were explored, which included both isotropic and anisotropic materials, thereby allowing for a mapping of structural response to the waveguide’s density, stiffness properties, and thickness. The parametrized mini impactor data were captured using piezoelectric acoustic contact sensors for structural response to the mini impactor. High-speed imagery was used to directly observe the physical motion of the mini impactor.

The deformation characteristics of polymeric foams, when subjected to high-speed impacts are highly dependent on the impact velocity. At low impact velocities, the deformation is homogeneous. In contrast, at high impact velocities, the deformation is highly localized with the occurrence of progressive cell crushing initiated from the impact end. This leads to a “shock wave” like propagation of the deformation. In this study, the dynamic deformation behavior of a low-density rigid polyurethane foam material is investigated through high-speed impact experiments. Cylindrical polycarbonate projectiles are fired on the foam specimens at velocities ranging from 40 m/s to 120 m/s using a gas gun setup. The images of the deforming specimen are captured with a high-speed camera and processed using digital image correlation to obtain full-field deformation. It is shown through experiments that the deformation behavior at high impact velocities is significantly different from the response at low impact velocities. It is found that the strain behind the shock front significantly increases with the impact velocity.

With a wide variety of applications, fiber-reinforced plastic composite materials experience a wide range of loading conditions which span the entire spectrum of strain rates. Patch repairs on roadways and bridges experience long-term fatigue and environmental loading. Such repair jobs can experience pure compressive or tensile stresses, while others experience large shear and bending stresses. The same is true for composite armors, which can experience high-velocity piercing impact events or large-scale blast pressures. With such a variety of conditions, experimental methods must have the capability to replicate these conditions. The three-point bending test is one of the standard methods for evaluating the flexural performance of a material or structure at quasi-static loading rates. The adaptation of this standard method to high loading rates requires a careful balance of replicating standard geometries and simplifying the data reduction process. The current study employs a custom shaped loading bar attached to the end of the incident bar in a conventional Kolsky bar apparatus. This loading bar transitions the incident bar geometry from a circular cross-section to that of a superellipse. This end shape evenly distributes the applied load across the width of the beam sample, while minimizing the reflections of the incident wave prior to contact with the bar-sample interface. To evaluate this geometry, beam samples were cast using Pro-Set INF114 epoxy resin. This method was evaluated with a bar-end velocity of 4 m/s, and a comparison was made between the superellipse shape and an unchanged bar geometry. For each case, the strain signals, local damage, and global failure modes were compared.

The explosively driven expanding ring tension test is a method for loading a sample ring of material in dynamic tension that avoids some issues associated with other dynamic tension methods. In this work, we build on previously reported work and our own modeling and simulation efforts to improve the geometry and material selection for the driver and the explosive. We modeled two of the many geometric variables in the explosively driven expanding ring test: charge size and buffer ring geometry. We tested two different explosives and several different heat treatments. Through our modeling efforts, we found larger buffer rings increased sample ring velocity. Testing revealed that the maraging 350 steel drivers required careful heat treatment or driver failure during the test would result. Some additional candidate driver materials, 300M and HY 100, are examined and appear to be reasonable alternatives.

Owing to their exceptional thermal and mechanical properties, materials such as Carbon Graphite Foam (CGF) and silica Nanoparticle-Treated Kevlar (SNK) are of interest in many multifunctional applications. It is therefore desirable to evaluate their ballistic performance in comparison to baseline foams or untreated Kevlar, for instance. In this study, we evaluate CGF and SNK composite samples using compressed-air guns (CAG). Two CAGs are used in this study, a large-bore (2.5″) and a small-bore (0.357″) CAG. Firstly, an improved analytical model was developed to predict the projectile’s velocities for the CAGs. This Loss-Compensated Model (LCM) builds upon existing analytical models such as the Adiabatic, Lagrange, and the Pidduck and Kent models by incorporating clearance leakage, improved surface friction, and air drag effects. The CAGs were calibrated using projectiles of multiple weights in order to establish the cylinder pressure versus projectile velocity characteristics. Velocity measurement was accomplished using a high-speed camera. Correlation with predictions from analytical models demonstrates that the LCM gives excellent agreement with the high-speed camera (HSC) measurements in comparison to the other models. For CAGs with a higher degree of losses due to projectile or barrel imperfections, the LCM provides a significant improvement in projectile velocity prediction. After achieving confidence on velocity measurement by HSC via LCM model, ballistic tests are performed on CGF and SNK. CGF composite samples were constructed from modular foam blocks with aluminum face sheets bonded together using an epoxy adhesive. Baseline aluminum foam composite samples were also constructed using the same procedure. For the SNK samples, a multistep treatment process was established that allows for a more uniform distribution of the nanoparticle in the fabric. Neat Kevlar K745 fabric was considered as the baseline. 10%, 30%, and 40% by weight of silica nanoparticle addition using an 80–100 nm particle size, water-based colloidal solution were considered for the SNK samples. Multiple samples were made and tested for the same test case. Both non-penetrative and penetrative test cases were considered. For the CGF, the depth of backing signature measurement as per NIJ Standard 0101.06 is considered as the performance parameter. A plasticine clay witness block was used as the backing material. For the SNK testing, the projectile’s kinetic energy reduction is used as the performance metric as per NIJ Standard 0108.01. Custom boundary fixtures were constructed, and consistent sample holding procedures were implemented to minimize any influence of boundary imperfections. The test and baseline samples were evaluated under the same conditions for all cases. The results show that the CGF composite absorbs nearly double the amount of energy as the baseline aluminum foam composite. The failure mode and mechanisms were identified and contrasted using high-speed camera footage. For the SNK cases, it was seen that the addition of nanoparticles improved the fabric’s ballistic performance by providing a 20% mass advantage (due to three less layers) for the 40 wt.% SNK vis-à-vis neat Kevlar for the non-penetrative case. This improvement in specific ballistic performance is attributable to the enhanced frictional mechanisms and shear rigidity for SNK fabric. In conjunction with current additive and hybrid fabrication processes, materials such as CGF and SNK present strong potential to enable multifunctional structural solutions for emerging engineering challenges.

Testing polymer matrix composites in shear at high strain rates is a difficult task using standard test methods like the Kolsky bar because of the low wave speed and low strain to failure. Moreover, it is well known that such composites exhibit a non- linear response in shear generally attributed to a combination of damage and matrix plasticity. In quasi-static conditions, such models are generally identified by performing cycles of loading and unloading to discriminate damage from plasticity.

However, current high strain rate test methods are unable to do this. The present paper details how the new Image-Based Inertial Impact (IBII) test naturally provides loading/unloading and how a damage model can be identified using the Virtual Fields Method from full-field strain and acceleration maps.