Dynamic Behavior of Materials, Volume 1

The split Hopkinson pressure bar (Kolsky bar) is an experimental tool that has been used to characterize materials at intermediate to high strain rates since 1949. Since the genesis of this method, several investigations into the validity of the data have led to general conclusions regarding the nuances of the method that affect the outcome of the data. The goal of this work is to review the sources of error for the Kolsky bar method and implement physically driven solutions that help to aid in the standardization of processing experimental Kolsky bar data. Correction methods for longitudinal wave dispersion in both tension and compression configurations are implemented using the analytical solutions by Pochhammer and Chree, the frequency domain method by Gorham and Follansbee and Frantz, and a special implementation of spectral analysis by James F. Doyle. Other corrections include a novel pulse detection method and strain correction due to elastic punching (compression).

Engineering materials are intrinsically heterogeneous owing to their processing history. For heat-treatable lightweight aluminum alloys, e.g., 7XXX alloys, the fracture behavior is governed by the size and distribution of second-phase particles. Modern empirical and micro-mechanically motivated computational failure models used for ductile fracture calculations do not include spatially heterogeneous microstructural information in any meaningful manner, despite recent significant advances in high-throughput, three-dimensional in-situ and ex-situ characterization techniques. Our hypothesis is that direct numerical simulations of particle-initiated failure, which will be informed by advanced testing and characterization, will provide the most realistic prediction of failure to date. This paper will focus on high-rate ductile fracture experiments using the mini-tension Kolsky bar with sample geometries that induce a wide range of stress triaxialities—from pure shear to plane strain tension. Samples are cut from near the surface and at the midplane of a thick plate because the size and distribution of the second-phase particles, and the texture of the matrix Al, are different at these locations. Deformation of the different geometries is recorded at 1 mfps, where the total loading time is approximately 100 μs. The experiments show there is a clear difference in the flow response between the two locations, but a clear strain to failure difference is not clear from these initial experiments.

This work describes the design, construction, and first experimental results of an innovative device of the Hopkinson bar type with a length of 90 m for performing high strain rate tests on metals in a combined tension-torsion state.

Analogously to the classic split Hopkinson bar technique, the system configuration consists of three bars: a pre-stressed bar, an input bar, and an output bar; the measurement is also based on the classical three-wave method, where the incident, transmitted, and reflected waves are measured. The length of the bars is designed so that the tensile wave reaches the sample from the output bar side at the same time as the torsion wave comes from the input bar. A successful test has been conducted on a hollow aluminum sample; it has been possible to measure the tension-torsion stress-strain curves; in addition, the dynamic equivalent stress-equivalent strain curves have been evaluated.

Penetration resistance of soils is described in a Poncelet framework in which it is due to the sum of an inertial drag term and a strength-related bearing stress. The problem addressed in this paper is how to determine the Poncelet bearing stress from a conventional cone-penetrometer test (CPT). For the case of a particular saturated sandy clay, it is shown that strength has an exponential dependence on strain rate, determined from unconfined compression experiments, which can be used to account for the difference in strength between a CPT carried out at 0.02 m/s and the strength resisting projectiles traveling impacting at 140–200 m/s. With that correction, the CPT tip resistance can be taken as the Poncelet strength.

Hydraulic fracturing is an important technique to produce oil and gas through the stimulation of unconventional hydrocarbon reservoirs, typically shale deposits. Quantifying elastic properties of bi-modulus shale under static and dynamic loading in different orientations is consequential. The in-situ bulk modulus of Wolfcamp shale is tested at two different loading rates. First, a universal testing machine was used for a quasi-static uniaxial compression test of a Brazilian disk, and then SHPB was utilized for a dynamic compressive load. Far-field loading data and local full-field deformation are used to calculate the physical properties through the linear elastic model. Static and dynamic mechanical properties of shales, such as elastic bulk modulus, compressive and tensile strength, were analyzed in two bedding orientations. The full experimental results are shown in detail, and in general, the elastic properties of shale under parallel and normal bedding conditions are different, as well as the static and dynamic in-situ elastic modulus are different.

Predicting and controlling the failure of brittle materials against impacts have important applications in defense, mining, and medicine. To that end, the key is understanding at the mesoscale the events of crack initiation, propagation, branching, multiple crack interactions, and coalescence. Therefore, we developed an x-ray phase contrast imaging-based technique to directly visualize and quantify the cracking process. We chose to test our technique on single-crystal quartz because it has well-defined material and mechanical properties which computational models can use to accurately simulate the cracking process. Also, quartz serves as an ideal model material to developing experimental techniques/analysis and high-fidelity damage models for energetic materials and heterogenous geomaterials. To achieve the micron and nanosecond resolution required to resolve and track cracks in real-time, we use the high brilliance, spatially coherent synchrotron source at the Dynamic Compression Sector (Advanced Photon Source, Argonne National Laboratory) and the 8-frame LANL/DCS detector system coupled to a 150-μm thick single crystal LYSO scintillator. Quartz samples are uniaxially compressed at 10³–10⁴ s⁻¹ strain rates with a custom-built Kolsky bar and stress-strain histories are measured using PDV probes. To characterize the evolving crack morphology, a physics-based inverse model is developed that converts the phase contrast-enhanced image intensity of the cracks into crack volume orientation distributions inside the sample. Using this model, we study how sample surface finish affects the dynamic behavior of cracks.

The goal of this study was to demonstrate the role of nose shape on the embedment phase of long rod projectiles penetrating densely packed sand targets. Conical nose projectiles having various apex angles were launched into sand targets at an impact velocity of approximately 200 m/s. A vertical firing range was designed and calibrated for launching projectiles with a diameter of 14.3 mm. Aluminum rod projectiles with conical nose apex angles ranging from 30 to 180° were tested. Soil targets were prepared by means of dry pluviation. Velocity-time histories were resolved using a photon Doppler velocimeter (PDV). High-fidelity velocity-time histories were obtained through measurement of the frequency shift in the laser light wave reflecting from the back of the projectile. Highly reflective retroreflective tape was applied to the back of the projectiles to enhance the intensity of the reflected light. Optical probes were used to collect the reflected light. The results of the experiments revealed that both the magnitude of the peak deceleration and the depth corresponding to peak deceleration were a function of the nose shape. A decrease in the apex angle of a conical projectile led to a reduction in the peak deceleration, with the resulting peak stress occurring later in penetration for projectiles with smaller apex angles. Upon impact on the soil target surface, a near conical-shaped mass of compacted comminuted sand formed on the nose of the projectiles tested. These observations can be used to improve predictions of projectile depth of burial in phenomenological modeling of penetration and depth of burial.

A specimen geometry that has four flat dog bones circumferentially arranged around the axis of the sample is proposed for combined tensile-torsional loading experiments. Finite-element modelling was implemented to optimise the design and achieve appropriate deformation and failure in both tensile and torsional loading conditions. The capability of the proposed specimen configuration is demonstrated via an experimental campaign on commercially pure titanium at various strain rates. The quasi-static tests were conducted using a universal screw-driven testing machine, whereas the high-rate experiments were carried out on an in-house designed combined tension-torsion Hopkinson bar system. A wide range of stress states were obtained using the ligament specimen, covering uniaxial tension, shear, and different combinations of tension and shear. Three distinct failure modes of the ligament specimens subjected to monotonic tension, monotonic torsion, and combined tension-torsion loading at high strain rates are presented and discussed. The quasi-static and high-rate ultimate stress loci will be constructed using direct experimental measurements to assess the strain rate sensitivity of the material.

This work investigates the dynamic energy absorbed by a shale material, which is generally classified as transversely isotropic, as a function of bedding orientations using experimental and analytical analysis. Experimentally, circular disks or Brazilian specimens of shale are tested under a high-impact diametral compression load in the split Hopkinson pressure bar, SHPB. Analytically, fundamentals of uniaxial stress and elastic wave propagation theory are utilized to derive the dynamic energy absorbed by the material. Thus, the experimental output data is used as input to the analytical damage model. The model was applied to two different orientations of shale related to the bedding directions. The experimental setup and the analytical analysis are presented. In general, results display a significant difference in the total absorbed energy and peak values that are required for exciting and increasing the cumulative micro and macro cracks in shale. The average strain and local energy results are presented and discussed.

Weakened plane fracture has been an interesting topic for understanding unconventional oil extraction. Thus, the dynamic fracture characteristics of weakened planes are studied experimentally to investigate the failure mechanism when exposed to stress waves at varying angles. A split-Hopkinson pressure bar (SHPB) and digital image correlation (DIC) are used to test a range of cyanoacrylate-weakened plane specimens that are created between the two-polycarbonate sheet. The weakened plane specimens are made with different inclined angles. Theoretically, a crack surface displacement method using various angles, (β), and crack tip opening displacements are shown to identify the dynamic stress intensity factors of opening-mode KI(t), and in-plane shear mode KII(t). The SHPB is dynamically loaded to fracture the specimen while full-field strains are recorded using digital image correlation, and the data is imputed to the crack surface displacement formulas. A fracture envelope containing θ = 15°, 30°, 45°, and 60° angles is created, and the result of mode I, mode II, and mixed-mode (I/II) are discussed, and the major mode of each inclined angle is identified.

The topic of this article is to investigate mechanical behaviors and dynamic characteristics under working conditions. The verification of finite element model (FEM) performed by experimental modal analysis (EMA) is discussed. The finite volume model (FVM) is established to analyze the aerodynamic and thermal effects under working conditions by computational fluid dynamics (CFD). With the consideration of loading conditions coupled with the results of CFD, the deformation, stress distribution, and modal parameters of the impellers are estimated by finite element analysis (FEA). To verify the reliability of FEM of the fluid-thermal-structure coupled analysis, modal verification is employed to ensure the consistency between the FEM and the actual structure. The modal assurance criterion (MAC) is applied as an indicator to quantify the consistency of mode shapes. In coupled stress analysis. The results show that the centrifugal load is the main factor of stress concentration, and the corresponding location of maximum stress is on the center of the impeller. In coupled modal analysis, the centrifugal force is also sensitive to the change of dynamic characteristics, however, only obviously influences the natural frequency of structures.

The mechanical response of a polyamide syntactic foam under combined tension-torsion loading is measured experimentally at quasi-static (10⁻³ s⁻¹) and high rates of strain (10³ s⁻¹). The dynamic experiments were conducted on a newly developed tension-torsion Hopkinson bar (TTHB) equipped with high-speed photography equipment. Quasi-static experiments were carried out using a universal screw-driven machine. The multiaxial high-rate experiments demonstrate the ability to achieve synchronization of longitudinal and shear stress waves upon loading of the specimen. The capacity to achieve force and torque equilibrium under combined loading on materials characterized by relatively low-stress wave propagation velocities is also demonstrated. Approximately constant strain rate conditions were attained. The failure envelope of the polyamide foam studied was analyzed over a wide range of stress states including pure torsion, shear-dominated combined tension-shear, tension-dominated combined tension-shear, and plain tension.

Additional low rate and dynamic experiments in tension, compression, and torsion were conducted at higher than ambient and sub-ambient temperature conditions using bespoke temperature conditioning equipment, to assess the temperature dependence of the material.

The multiaxial failure stress locus was constructed in the normal versus shear stress space as well as in the principal stress space from experiments conducted at low and high rates of strain. The failure stress locus of a polymer syntactic foam and its rate and temperature dependence are presented for the first time. The newly developed TTHB apparatus allows for the direct measurement of the failure stress locus of lightweight materials and therefore for the evaluation of existing failure criteria.

Digital image correlation (DIC) is an imaging technique that enables full-field measurements of a material motion and deformation (displacement, velocity, strain, and strain rate). Advances in high-speed (HS) and ultra-high-speed (UHS) camera technology have driven widespread adoption of HS and UHS DIC especially when sampling rates in the kHz to MHz are required. A common challenge in the application of DIC to high-rate material loading are issues with the applied speckle pattern failing during high-rate loading. A primary requirement of DIC is that the applied speckle pattern follows the underlying surface. When materials of interest are subjected to high-velocity impact, the applied pattern can debond or otherwise fail to follow the motion and deformation of the material surface. This work will evaluate common speckle pattern preparations for both distributed loading and localized deformation. The study will outline unique challenges associated with characterization high-rate material testing and describe a laser-based methodology for probing time-resolved pattern integrity. Photonic Doppler velocimetry will be used to study the effectiveness of the various patterns in tracking the surface deformation including woven composite panels and thin metal plates. The technique offers a simple, objective means of quantifying pattern integrity at selected measurement points and directly comparing different pattern techniques.

An experimental investigation was performed on an artificial human lung to evaluate its response and behavior after being subjected to an underwater explosive blast. The experiments were performed using a 63 mg TNT equivalent explosive charge placed 0.5 m from the front of the lung. The specimen used was a to-scale lung model representative of a 50th-percentile male. The experiments were performed on an 8200 l water tank. The artificial lung was instrumented with internal pressure sensors to record changes in the cavity pressure. Additionally, the underwater tank was instrumented with underwater blast transducers to measure the pressure from the explosive charge. Results show a significantly delayed response to the underwater blast due to the lung’s inertia. The lung initially contracts after the underwater shock, followed by an expansion showing a 50% change in relative volume within 7 ms. Results and observations qualitatively relate to the types of injuries observed during preexisting case studies.

This research arises from the concern of damage to submersible marine structures such as underwater vehicles and pipelines and the need to understand dynamic failure. This work focuses on analyzing the dynamic bubble-to-structure interaction of curved metallic plates subjected to air-backed underwater explosive loading. This work aims to expand the current understanding of gas bubble formations during nearfield underwater explosion events with experimental analysis. The experiments were performed in an underwater explosive facility using high-speed cameras to measure full-field displacement and velocities during deformation through a digital image correlation technique. In addition, during the experiments, pressure transducers were used to record the pressure pulses emanated from the explosive charge. Experiments were performed for two plate curvatures (112 and 305 mm) and three standoff distances from the plate’s surfaces (55, 73, and 110 mm) for each curvature. The experiments show that deformations are higher if the explosive standoff is smaller or the structural radius of curvature is higher. In addition, the increase in structural deformation also leads to distorted bubble shapes that increase their repulsion from the structural specimen and decrease the bubble collapse period. Nearfield bubble dynamics are highly sensitive to the proximity of nearby structures and the compliance of such structures. Though they have higher deformations in general, complicated structures may be able to mitigate bubble attachment or jetting for specific explosive charges

The performance of density-graded elastomeric foams has been a cynosure of the pursuit of superior impact mitigation materials and structures. Elastomeric foams exhibit a remarkable mechanical response, including resilience, toughness, and recoverability. However, recent research has only focused on the performance of uniform-density foam paddings in response to various strain rates. Concurrently, the body of research on the potential of density gradation has been burgeoning, suggesting an untapped potential to achieve higher levels of protection than those offered by their ungraded counterpart. This research aims to elucidate the layering interfaces effect on the performance of density-graded elastomeric foams in response to quasi-static and impact loading. The approach is to manufacture foam laminates consisting of bi- or tri-layered polyurea elastomeric foams using two different layering techniques. In one set of samples, the foam was natively adhered by casting subsequent layers with different densities by adjusting the mixing and pouring ratios. In the second set of samples, separately cast polyurea sheets were adhered using ultrathin polyurea adhesive to mimic the configuration of the first set. All foam samples were submitted to quasi-static loading up to densification and impact loading at 7 J. The static and dynamic stress-strain curves were accompanied by full-field digital image correlation analysis, revealing the contributions of the density gradation and layering interfaces to the overall deformation. While the primary outcomes include insights into the mechanistic processes responsible for the mechanical behavior, the natively bonded density-graded polyurea foams provide an exciting platform to explore additional mechanics of elastomeric foams.

The suitability of cellular solids for a specific energy absorption application, whether packaging or sports gear padding, depends on their dynamic mechanical behaviors under impact loadings. The latter is imperative not only to simulate real-life loading conditions but also to interrogate the realistic response of the material, contributions of the geometry, and determination of prominent deformation mechanisms. This research aims to extend the application domain of polyurea elastomeric foams through a mechanistic understanding of their response to loading scenarios at moderate impact velocities. Recent research focused on either leveraging quasi-static stress-strain response to forecast the impact efficacy of these foams or submitting the foam pads to low-velocity impacts. Hence, the approach here is to develop a small-scale shock tube to release a projectile into polyurea foam plugs ~31 cm apart. The shock tube was mounted vertically to (1) reduce the logistical impact of the setup and (2) leverage gravity-assisted increase in impact velocity. The impact velocity was controlled by adjusting the pressure in the driver (high pressure) section of the tube. The impact-induced deformation was captured using a high-speed camera. The velocity-time profiles were used to calculate the stress, while the high-speed images were analyzed using digital image correlation (DIC) to report the evolution of strains and inertia stresses. Samples were also examined post-deformation using optical microscopy to assess the induced structural damage. The outcomes of this research extend the property map of polyurea elastomeric foams, gearing them closer to transition into realistic sports protective gear applications.

This study described the creation of a physical human thorax surrogate dedicated to blunt ballistic impacts called SurHUByx. The geometry of this new surrogate is based on an existing numerical model, named HUByx, which consists of a biofidelic 50th percentile human torso finite element model. In order to build the physical dummy, and to choose appropriate materials for anatomical structures, able to reproduce correctly the human behavior, a reverse engineering procedure was applied. Material properties of the numerical model (especially the bone structures, as well as internal organs) were simplified in order to match properties of manufacturable materials: Trabecular and cortical bones, as well as costal cartilage were merged, and then modeled with a homogeneous material, whereas internal organs were made of synthetic gel, which has already proven its biofidelity. These simplifications lead to the creation of a new numerical “simplified” biomechanical model (named SurHUByx FEM). It was then used to replicate experimental reference cases conducted on Post Mortem Human Subjects. Results were consistent with the experimental biomechanical corridors. The model being validated, the construction of the physical dummy began: Internal organs (heart, lungs, liver, and spleen) were molded in 3D printed molds with SEBS gel. Muscle and Mediastinum were molded with 3D printed molds using various concentrations of SEBS gel. Skin was made with the vinyl skin of the Hybrid III dummy. In the same way as for the numerical validation, the new physical dummy was submitted to the same impact cases. The whole procedure allowed creating a biofidelic dummy with manufacturable materials, which can be used for ballistic accident reconstruction, as it was already performed in the literature in the crashworthiness framework.