Predicting the onset and characteristics of brittle fracture is important for a wide range of engineering and geological material applications. In this paper, we study important aspects of brittle fracture in a-quartz by phase-field modeling and experiments using a top-down approach. In the modeling framework, the work term in the Griffith energy balance is replaced with internal energy contributions that represent surface energy, thermal energy, and elastic strain energy stored in defects. This allows parametrization of individual energy contributions in terms of internal state variables and keeps track of energy partitioning after the onset of fracture. The path and history dependence of fracture is included in evolution laws for internal state variables, e.g., entropy evolution, while the energy remains a true potential. In the experimental part, dynamic compression experiments coupled with X-ray phase contrast imaging are performed on cube-like samples with a hole. In the top-down analysis, dynamic compression and three point bending experiments from the literature are simulated with the developed phase-field damage model. The fitted model highlights the strain rate, size, and stress state dependence of damage nucleation and evolution in single crystal a-quartz.

Determining the compression strength of advanced ceramics would appear to be a simple and straightforward process; however, it is not. During compression testing, tensile stresses typically develop at the specimen/load platen interface, leading to the formation of macrocracks at the specimen ends. These macrocracks then propagate through the specimen parallel to the loading direction. This type of failure is “end splitting,” which does not represent the true compressive failure process in ceramics and commonly results in misleading, low‐strength values with a significant scatter in the data. Cuboids and/or cylinders are the common specimen geometries used to determine compression strength, yet end splitting is the regularly observed fracture process with these specimens. A dumbbell‐shaped specimen has been shown to drastically reduce the likelihood of end splitting by promoting fracture in the reduced diameter section, leading to higher and more consistent strength values. This manuscript reviews the accepted compressive failure process in ceramics, examines issues related to the use of cuboids and cylinders as test specimens, the various standard test methods and specimens available, the development of a dumbbell‐shaped specimen, the applicability of the dumbbell geometry over a range of strain rates (0.0001/s to ∼300/s), previous studies comparing strength values, and the different failure process observed in ceramics when different specimen geometries are used. A summary and discussion of compressive strength data generated over different strain rates using a dumbbell specimen on a wide range of advanced ceramics is presented. Where available and appropriate, this new data is compared with previous values obtained using cuboids and cylinders. It is definitely shown that a dumbbell shape is the most appropriate and only specimen geometry that should be used to generate compression strength values for ceramics at strain rates between 10 −4 /s and 10 2 /s.

Rammed Earth (RE) is a low-cost alternative building material which can be used in construction. Like concrete, RE is composed of fine aggregate, coarse aggregate, cement, and water. RE and concrete differ in the type of aggregates used. In RE, the soil that is readily available is used as both the coarse and fine aggregate, mixed with cement and water, then compressed. The aim of this project was to research RE as a potential building material as a cheaper alternative to conventional concrete masonry units and concrete. While typical use case for structures typically involves low strain rate loading, the effectiveness of structures at high strain rate are of additional importance. To find low strain rate properties of RE, unconfined compression and Brazilian splitting tests were performed. Higher strain rate tests include Kolsky Bar tests and penetration tests with characterized spherical and dart penetrators. Compressive strengths of 18.06 +/- 5.90 MPa were roughly equivalent to traditional concrete masonry units and specimens were also shown to harden based on strain rate.

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.

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 catastrophic failure response of brittle solids is governed by the mechanics of crack nucleation and growth, which have been observed to be rate- and orientation-dependent. One property that is characteristic to this process is the failure strength. At low to intermediate strain rates, the failure strength has been observed to be nearly constant and equal to the strength observed under quasi-static conditions; however, at high-enough strain rates, the failure strength has been observed to become rate-dependent. The main objective of the present work is to interrogate the effects of loading rate and orientation on the failure strength of uniaxially compressed α-quartz at very high strain rates to ascertain the transition into rate sensitivity. For doing this, a miniature Kolsky bar is used to perform dynamic compression experiments on α-quartz at strain rates in the order of 103–104/s, and X-ray phase contrast imaging (XPCI) is used to directly visualize and quantify the cracking process. Experiments are carried out on nominally 1 mm and 2 mm rectangular α-quartz specimens compressed on the {-1,-1,2,0} and {-2,2,0,3} family of planes, resulting in strain rates of approximately 2000 - 5000/s to 20,000/s at the time of failure. The results show no appreciable orientation effects, suggesting that the loading configuration rather than the crystal orientation relative to the loading direction controls the orientation of crack propagation. However, the stress history and XPCI reveal that the failure strength is appreciably rate-sensitive within the present loading rate regimes. The stress history for both configurations exhibits an increasing average failure strength from around 2 GPa to 3 GPa as loading rates increase from 2000 - 5000/s to 20,000/s. The stress history and XPCI data are expected to provide crucial insight into the rate-dependence of the damage mechanisms occurring in this material.

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 mu s. 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 paper describes the novel “fracture” gun recently built at the US Army Research Laboratory (ARL) to study dynamic deformation and fracture mechanisms under impact loading using high-speed cameras with DIC. This gun combines the precise projectile/target alignment capabilities typical of a plate impact experiment with the ability to observe phenomena over wide spatial and temporal scales. The velocity capabilities and the target tank will be outlined. The target tank is small with large windows, so that cameras can be placed very close to the impact location which allows for small fields of view that are not typically achievable in these experiments. Velocity measurement, triggering, and lighting solutions will be presented. Of special concern are the DIC errors that develop when imaging through a window that distorts due to a vacuum being pulled in the target chamber; these errors have been quantified. There are very few experimental methods to probe fundamental deformation and fracture mechanisms within the ballistic regime, but this gun and the associated instrumentation are a big step toward better understanding these mechanisms.

Split-Hopkinson Pressure Bars (SHPB) or “Kolsky” bars are often employed for determining the high-rate compressive failure strength of high-strength brittle materials. However, experiments generating very high strain-ratesHigh strain-rate demand miniaturization of the setup for appropriately measuring decreasingly short loading events. Miniature aluminum and steel bars are often sufficient for this. However, for high enough strain-rates, miniaturization of these bars may require prohibitively small test specimens that can be inappropriate for inferring representative properties of materials with large grain size relative to the specimen size. The low Poisson’s ratio of beryllium relative to aluminum and steel is expected to minimize the effect of elastic wave dispersionDispersion on the measurable strain-rates in Kolsky barKolsky Bar experiments. For these reasons, we have developed a Be Kolsky barKolsky Bar apparatus, and, in this paper, we experimentally determine the dispersionDispersion characteristics of these bars and compare the results with those of similarly size setups made from aluminum and steel. The results show no appreciable dispersionDispersion in the data from the beryllium Kolsky barKolsky Bar setup, demonstrating its advantage over aluminum and steel.

It is well documented that the hot-pressing procedures used for many strategic ceramics may introduce microstructural texturing that can lead to anisotropic mechanical properties. Therefore, knowing the existence and extent of anisotropy and any potential impact on properties is important to proper application of these ceramics. Many hot-pressed ceramics are produced as plates that are relatively thin (around 25 mm or less). This makes it challenging to identify anisotropy in commonly measured properties such as flexure strength and fracture toughness since the standard beam specimens used to determine these properties are typically more than 25 mm in length. However, the use of a small dumbbell-shaped specimen has been successfully useful to determine the compression strength of several advanced ceramics. In this study, small dumbbell specimens were machined from a hot-pressed boron carbide and three hot-pressed silicon carbides. The major axis of the specimen was aligned at 0° (vertical), 45°, or 90° (horizontal) to the hot-pressing direction to determine any potential intrinsic anisotropy in the compression strength. Specimens were tested across a range of strain rates to discern the presence of rate effects on the compressive strength and fracture behavior of these strategic materials.

A miniature tensile Kolsky bar has been developed. The bars are steel and 1.6 mm in diameter. Because of the small size, each bar is instrumented with a normal displacement interferometer instead of strain gages. The projectile is accelerated with a spring to avoid the complexities of building a gas gun on this small scale. The bar is used to test pure aluminum samples with gage lengths of 1.0 mm and rectangular cross sections of 90 μm by 200 μm. A simple gripping design is used where the dog-bone-shaped sample is placed into recesses that are machined into the ends of the bars; the sample is then secured in place with glue. A high-speed camera is used to observe the sample deformation and failure.

This paper presents a comprehensive experimental study of the evolution of Poisson's ratio and tangent modulus of polymeric foams during rate dependant uniaxial compression. In this study, polyurethane foams with densities of 195 kg/m(3), 244 kg/m(3), and 405 kg/m(3) obtained from PORON (XRD series) were examined under uniaxial compression loading at strain rates ranging from 0.001 s(-1) to 5000 s(-1). All compression experiments were coupled with a high-speed camera to enable Digital Image Correlation to measure and visualize deformation strains. These measurements enable us to study mechanical property evolution during compression and provide qualitative description of damage and failure in these materials. A non-linear evolution of Poisson's ratio is observed in-situ in these materials. The compressive stress-strain response is predicted through least square fitting using the Avalle model [1], and model coefficients are found to follow a power-law to scale across strain rates. The stress-strain curves, mechanical property evolution, and scaling coefficients are compared with microstructural parameters of interest such as pore size and wall thickness to inform on damage accumulation mechanisms in the material.

Conventional Split Hopkinson Pressure Bars (SHPB) or "Kolsky" bars are often used for determining the high-rate compressive yield and failure strength of materials. However, for experiments generating very high strain-rates (>10(3)/s) miniaturization of the setup is often required for minimizing the effects of elastic wave dispersion in order to enable the inference of decreasingly short loading events from the data. Miniature aluminum and steel bars are often sufficient for meeting these requirements. However, for high enough strain-rates, miniaturization of steel or aluminum Kolsky bars may require prohibitively small diameter bars and test specimens that could become inappropriate for inferring representative properties of materials with large grain size relative to the test specimen size. The use of a beryllium Kolsky bar setup is expected to enable high rates to be accessible with larger diameter bars/specimen combinations due to the inherent physical properties of beryllium, which are expected to minimize the effects of elastic wave dispersion. For this reason, a series of beryllium Kolsky bars have been developed, and, in this paper, the dispersion characteristics of these bars are measured and compare the data with those of similarly sized 7075-T6 aluminum and C350 maraging steel. The results, which agree well with the theory, show no appreciable frequency dependence of the elastic wavespeed in the data from the beryllium bars, demonstrating its advantage over aluminum and steel in application to Kolsky bars.

In this study in situ neutron diffraction investigations of a fully austenitic medium-Mn steel enabled key insights into the temperature dependence of the deformation response with a focus on twinning. In situ tensile loading at multiple temperatures enabled the calculation of the temperature and strain dependence of the effective stacking fault energy (SFE), which was compared with theoretical SFE calculations and ex situ tensile tests. These comparisons revealed that the γ-austenite/ϵ-martensite interfacial energy plays a critical role in determining the boundary between twinning and transformation induced plasticity. The interfacial energy, which also exhibits temperature dependence, was found to be lower than the conventionally accepted range for medium-Mn steels deforming via twinning. Dynamic strain aging (DSA) was also found to impact the deformation response. DSA contributes to increasing the separation of partial dislocations, which in turn lowers the effective SFE and was observed as fluctuations in the measured SFE when DSA was active. The additional extrinsic contributions to the SFE from DSA, which operates over a limited range of temperatures and strain rates, has not previously been accounted for.

The goal of this paper is to probe the effect of strain gage instrumentation bandwidth (BW) on the measured and calculated mechanical response of a brittle material under dynamic loading using a mini-Kolsky bar. If the BW on the strain gage instrumentation is too low, relative to the loading time, there will be a filtering effect whereby the “true” signals are not measured. As researchers miniaturize the Kolsky bar to increase the strain rate, anomalous data may be recorded, especially when testing brittle materials. The filtering effect was systematically studied by compressing a representative brittle material with progressively shorter loading times, while simultaneously recording the strain gage signals at two different bandwidths, 500/800 kHz (no filtering) and 100 kHz (possible filtering), to determine when deviations occur. The results show that there is only a small filtering effect but that it occurs at rise times that are greater than what would be expected based on the typically used BW-rise time relationship or from the frequency components of the measured waves. Concerningly, there is no obvious way to know if the signals are being inadvertently filtered, and the calculated stress–strain curves are only slightly affected. The filtering effect is discussed further in relation to Kolsky bar testing in general.

The mechanical properties of transformation-induced plasticity (TRIP) steels are attractive in many applications that benefit from high work hardening and high total elongation. Under dynamic loading rates (ε˙>103s−1) TRIP steels lose these beneficial properties and are one of the few known materials whose dynamic response is softer than the quasi-static response (ε˙≈10−3s−1). Here we show that after quasi-static pre-straining a TRIP steel to 10%, the dynamic strength increases three-fold from approximately 500 MPa to 1500 MPa while retaining the high work hardening response. The mechanical response during strain-rate history tests indicates that the yield strength is nearly insensitive to strain rate while strain hardening is extremely sensitive to temperature rise. Micrographs of the microstructural evolution taken from interrupted tests indicate that phase transformation is delayed at dynamic rates and ceases after an adiabatic temperature rise of 100−140∘C, which is consistent with existing thermodynamic theory.

The interconnected phenomena of dynamic recrystallization (DRX) and adiabatic shear bands (ASBs) are critical features of dynamic deformation and fracture in metals. Despite their importance, observations of these phenomena have largely been restricted to post-mortem analyses. Here we report on the first in situ X-ray diffraction (XRD) observations of DRX. By combining high strain rate loading via Kolsky bar with high speed X-ray diffraction, time resolved observations of microstructural evolution in Ti–7Al are made. XRD measurements are coupled with explicit finite element simulations to assess the stress, strain, and temperature dependence of the microstructural evolution. These observations reveal a continuous evolution of the microstructure with increasing plastic strain up to a maximum stress. At the maximum stress, the structure ceases evolving and the subsequent softening suggests the onset of shear banding. As a whole, these unique experiments definitively reveal the onset of DRX to be driven by accumulation of plastic strain and not the temperature rise associated with plastic deformation. The observed sequence of events further suggests DRX results in microstructural softening and precedes ASB formation.

Background A better understanding of the effect of density, microstructure, and strain rate on the mechanical response of polymeric foam materials is needed to improve their performance. Objective The objective of this paper is to study the combined influence of density, microstructure, and strain-rate on the compressive stress-strain response of polymeric foams. Methods Microstructural morphological parameters (e.g., pores sizes and wall thicknesses) have been quantified using Micro X-ray tomography and MATLAB-based techniques. Polymeric foam samples were examined under uniaxial compression loading at quasistatic (0.001 to 0.1s(-1)), intermediate (1 to 250s(-1)), and dynamic strain rates (3200 to 5700s(-1)). All experiments were coupled with high speed cameras to measure strain using 2D digital image correlation, and to visualize deformation. Results The variation of the mechanical properties across alldensities (e.g., elastic modulus and collapse stress) are found to behave in a powerlawfashion with respect to strain rate. A comprehensive data set across a varied rangeof densities and strain rates, especially intermediate strain rates, is lacking in previous research, and generalized phenomenological relationships developed in this paper topredict combined influences of density, microstructure, and strain-rate over variedrange of materials are important contributions of this work. Conclusions The results showed that the power-law relationships act as a good predictor for the prediction of mechanical properties and elastic response, and as an indicator for damage mechanisms in these polymeric foams.

A low density, high strength medium-Mn steel was processed to produce a bimodal duplex microstructure consisting of coarse grained gamma-austenite with fine 6-ferrite grains decorating the gamma-austenite boundaries. Using combination of ex situ analysis and in situ neutron diffraction, the deformation mechanisms and lattice strains within each phase were identified for specimens undergoing uniaxial tension during room and elevated temperature loading up to 473 K. The coarse-grained high stacking fault energy gamma-austenite deformed by dislocation glide, providing work hardening and ductility. Simultaneously, the fine grained 6-ferrite produced an elevated yield strength by strengthening the steel via a composite reinforcing mechanism. Neutron diffraction reveals that the yield strength reduction at elevated temperatures is due to a reduction in the 6-ferrite strength. The resulting combination 1200 MPa ultimate strength and 0.3 ductility achieved in this microstructurally engineered bimodal duplex steel exceeds that of typical hot worked medium-Mn steels.