Topology optimization of bistable elastic structures — An application to logic gates
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42 ENGINEERING↗
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Linear Seismic Source Equivalents in 3D Nonlinear Models: Effects of Embedded Small-Scale, Near-Source Structures
Gaining a proper understanding of how Earth structure and other near-source properties affect estimates of explosion yield is important to the nonproliferation mission. The yields of explosion sources are often based on seismic moment or waveform amplitudes. Quantifying how the seismic waveforms or estimates of the source characteristics derived from those waveforms are influenced by natural or man-made structures within the near-source region, where the wavefield behaves nonlinearly, is required to understand the full range of uncertainty in those yield estimates. We simulate tamped chemical explosions using a nonlinear, shock physics code and couple the ground motions beyond the elastic radius to a linear elastic, full waveform seismic simulation algorithm through 3D media. In order to isolate the effects of simple small-scale 3D structures on the seismic wavefield and linear seismic source estimates, we embed spheres and cylinders close to the fully- tamped source location within an otherwise homogenous half-space. The 3 m diameters spheres, given their small size compared to the predominate wavelengths investigated, not surprisingly are virtually invisible with only negligible perturbations to the far-field waveforms and resultant seismic source time functions. Similarly, the 11 m diameter basalt sphere has a larger, but still relatively minor impact on the wavefield. However, the 11 m diameter air-filled sphere has the largest impact on both waveforms and the estimated seismic moment of any of the investigated cases with a reduction of ~25% compared to the tamped moment. This significant reduction is likely due in large part to the cavity collapsing from the shock instead of being solely due to diffraction effects . Although the cylinders have the same diameters as the 3 m spheres, their length of interaction with the wavefield produces noticeable changes to the seismic waveforms and estimated source terms with reductions in the peak seismic moment on the order of 10%. Both the cylinders and 11 m diameter spheres generate strong shear waves that appear to emanate from body force sources.
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
A hybrid calibration approach to Hertz-type contact parameters for discrete element models
This study aims at providing a hybrid calibration framework to estimate Hertz-type contact parameters (particle-scale shear modulus and Poisson ratio) for both two-dimensional and three-dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle-scale Hertz-type contact parameters for granular systems are derived under small-strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle-level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro-micro relationship in Hertz-based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. Here, the proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.
Constitutive law↗
Analytical integration of the tractions induced by non-singular dislocations on an arbitrary shaped triangular quadratic element
Here, an analytical model is proposed to evaluate the nodal force induced by a segment of dislocation upon an arbitrary shaped triangular element. This calculation is required in hybrid methods that associate dislocation dynamics to boundary or finite element to solve simultaneously the evolution of large ensembles of dislocations with complex boundary conditions. Nodal forces are defined as the triple integration of the unbalanced traction field induced by a straight dislocation upon the surface of the element. Following our previous approach (Queyreau et al 2014 Modelling Simul. Mater. Sci. Eng. 22 035004) on a simpler geometry and in the case of linear isotropic elasticity, triple integrals are solved by sequences of integration by parts that exhibit recurrence relations. The traction field is defined and finite everywhere even at the core of dislocations, thanks to the use of the non-singular stress expression formulated by Cai et al (2006 J. Mech. Phys. Solids 54 561–587). The nodal force expressions can be used when considering both a single convolution or double convolution of the Green's function with the core distribution. A solution is also proposed for the case of a semi-infinite segment through the study of the asymptotic behavior of the analytical expressions. The proposed approach is exact and very computationally efficient. The choice of an arbitrary shaped triangular element and quadratic shape functions allow the consideration of complex geometries and comply with automatic meshing procedures. These analytical expressions could also be employed to estimate dislocation interactions with interfaces.
42 ENGINEERING↗
High‐Pressure and High‐Temperature Single‐Crystal Elasticity of Cr‐Pyrope: Implications for the Density and Seismic Velocity of Subcontinental Lithospheric Mantle
Abstract Single‐crystal X‐ray diffraction and Brillouin spectroscopy experiments were performed on a natural Cr‐pyrope (Prp 71.0 Alm 12.6 Sps 0.7 Grs 3.5 Uvr 12.2 ) at high pressure and high temperature up to 11.0 GPa and 800 K. Fitting the collected data to the third‐order finite strain equation yields bulk modulus ( K S 0 ), shear modulus ( G 0 ), their pressure ((∂ K S /∂ P ) T and (∂ G /∂ P ) T ) and temperature (( ∂K S /∂T ) P and ( ∂G/∂T ) P ) derivatives, K S 0 = 167.7(8) GPa, G 0 = 91.5(5) GPa, (∂ K S /∂ P ) T = 4.3(1), (∂ G /∂ P ) T = 1.4(1), ( ∂K S /∂T ) P = − 0.0175(1) GPa/K and ( ∂G/∂T ) P = − 0.0073(1) GPa/K. Using the obtained results, we examined whether the elastic properties of the Cr‐pyrope can be accurately calculated from those of endmembers including pyrope, almandine, grossular, and uvarovite assuming a linear relationship between elastic properties and composition (end‐member model). The results indicate that the end‐member model provides a sufficient approximation for the elastic properties of Cr‐pyrope in calculating the density and velocity of the subcontinental lithospheric mantle (SCLM). We modeled the densities and velocities of three typical types of SCLM (Archon, Proton, and Tecton) in order to investigate how the variation of chemical composition influences the SCLM. We obtained that the compositional change from the Archon to the Tecton increases the density of the SCLM significantly, which can be an important prerequisite for SCLM delamination. However, the compositional variation only slightly changes the velocity of the SCLM and the change is within the uncertainty of the calculation. Moreover, in comparison to the velocity, ρ / V P and ρ / V S are much more sensitive to the compositional change of the SCLM.
Xu, Jingui↗
Polycrystal thermo-elasticity revisited: theory and applications
The self-consistent (SC) theory is the most commonly used mean-field homogenization method to estimate the mechanical response behavior of polycrystals based on the knowledge of the properties and orientation distribution of constituent single-crystal grains. The original elastic SC method can be extended to thermo-elasticity by adding a stress-free strain to an elastic constitutive relation that expresses stress as a linear function of strain. With the addition of this independent term, the problem remains linear. Although the thermo-elastic self-consistent (TESC) model has important theoretical implications for the development of self-consistent homogenization of non-linear polycrystals, in this paper, we focus on TESC applications to actual thermo-elastic problems involving non-cubic (i.e. thermally anisotropic) materials. To achieve this aim, here we provide a thorough description of the TESC theory, which is followed by illustrative examples involving cooling of polycrystalline non-cubic metals. The TESC model allows studying the effect of crystallographic texture and single-crystal elastic and thermal anisotropy on the effective thermo-elastic response of the aggregate and on the internal stresses that develop at the local level.
36 MATERIALS SCIENCE↗
The role of fast and slow dynamics in nonlinear resonant ultrasound spectroscopy of consolidated granular materials
Abstract Elastic nonlinearity observed in consolidated granular media can be attributed to the combination of slow and fast effects, which give rise to hysteresis and relaxation of both modulus and damping after the sample is perturbed. A consequence is a high level of complexity in the measurements of the sample linear and nonlinear elastic parameters. The results of experiments are dependent on the experimental protocol that is adopted to measure the relevant quantities and it is hard to quantify parameters with accuracy and repeatability. Here we focus on examining Nonlinear Resonant Ultrasound Spectroscopy, showing experimentally the role of slow dynamics in the process and quantifying/discussing its influence on the quantification of nonlinearity. We also propose a model to describe the process, which shows that different contributions to nonlinearity (e.g., classical and hysteretic) could be due to physical features (defects) relaxing with different relaxation times.
Science & Technology - Other Topics↗
Damage detection in a laboratory-scale wellbore applying Time Reversal and Nonlinear Elastic Wave Spectroscopy (TR NEWS)
We report Time Reversal and Nonlinear Elastic Wave Spectroscopy (TR-NEWS) has been used to focus acoustic energy, and make measurements correlated with damage in a variety of industrial materials. Most studies using TR-NEWS have focused on relatively small objects and may have multiple acoustic sources. In Earth, within energy extraction and carbon sequestration settings, the structure and scale of wellbores makes acoustic focusing challenging, as has been demonstrated through numerical simulations. This paper explores the feasibility of applying TR NEWS for damage detection in wellbores by constructing a laboratory-scale wellbore, and using TR to focus and make dynamic linear and nonlinear elastic measurements on it. During successive cycles of localized mechanical damage induced in the sample, the hysteretic nonlinear elastic parameter α increased with progressive mechanical damage. In addition to these strain-dependent changes in α, the width and peak amplitude of the time reversal focused energy changed near the damage site.
58 GEOSCIENCES↗
Gamma Decay of the 154 Sm Isovector Giant Dipole Resonance: Smekal-Raman Scattering as a Novel Probe of Nuclear Ground-State Deformation
𝛾 decays of the isovector giant dipole resonance (IVGDR) of the deformed nucleus 154 Sm were measured using 2$^{+}_{1}$-Smekal-Raman and elastic scattering of linearly polarized, quasimonochromatic photon beams. The two scattering processes were disentangled through their distinct angular distributions. Their branching ratio and cross sections were determined at six excitation energies covering the 154 Sm IVGDR. Both agree with the predictions of the geometrical model for the IVGDR and confirm 𝛾 decay as an observable sensitive to the structure of the resonance. Consequently, the data place strong constraints on the nuclear shape, including the degree of triaxiality. The derived 154 Sm shape parameters 𝛽 = 0.2925(25) and 𝛾 = 5.0(15)° agree well with other measurements and recent Monte Carlo shell-model calculations.
150 ≤ A ≤ 189↗
Investigating genomic prediction strategies for grain carotenoid traits in a tropical/subtropical maize panel
Abstract Vitamin A deficiency remains prevalent on a global scale, including in regions where maize constitutes a high percentage of human diets. One solution for alleviating this deficiency has been to increase grain concentrations of provitamin A carotenoids in maize (Zea mays ssp. mays L.)—an example of biofortification. The International Maize and Wheat Improvement Center (CIMMYT) developed a Carotenoid Association Mapping panel of 380 inbred lines adapted to tropical and subtropical environments that have varying grain concentrations of provitamin A and other health-beneficial carotenoids. Several major genes have been identified for these traits, 2 of which have particularly been leveraged in marker-assisted selection. This project assesses the predictive ability of several genomic prediction strategies for maize grain carotenoid traits within and between 4 environments in Mexico. Ridge Regression-Best Linear Unbiased Prediction, Elastic Net, and Reproducing Kernel Hilbert Spaces had high predictive abilities for all tested traits (β-carotene, β-cryptoxanthin, provitamin A, lutein, and zeaxanthin) and outperformed Least Absolute Shrinkage and Selection Operator. Furthermore, predictive abilities were higher when using genome-wide markers rather than only the markers proximal to 2 or 13 genes. These findings suggest that genomic prediction models using genome-wide markers (and assuming equal variance of marker effects) are worthwhile for these traits even though key genes have already been identified, especially if breeding for additional grain carotenoid traits alongside β-carotene. Predictive ability was maintained for all traits except lutein in between-environment prediction. The TASSEL (Trait Analysis by aSSociation, Evolution, and Linkage) Genomic Selection plugin performed as well as other more computationally intensive methods for within-environment prediction. The findings observed herein indicate the utility of genomic prediction methods for these traits and could inform their resource-efficient implementation in biofortification breeding programs.
59 BASIC BIOLOGICAL SCIENCES↗
Soliton Generation in Negative Thermal Expansion Materials
Strain solitons have been observed statically in several 2D materials and dynamically in substrate materials using ultrafast laser pulses. The latter case relies on lattice relaxation in response to ultrafast heating in a light-absorbing transducer material, a process which is sensitive to the thermal expansion coefficient. Here we consider an unusual case where the sign of the thermal expansion coefficient is negative, a scenario which is experimentally feasible in light of rapid and recent advances in the discovery of negative thermal expansion materials. We present numerical solutions to a nonlinear differential equation which has been repeatedly demonstrated to quantitatively model experimental data and discuss the salient results using realistic parameters for material linear and nonlinear elasticity. The solitons that emerge from the initial value problem with negative and positive thermal expansion are qualitatively different in several ways. The new case of negative thermal expansion gives rise to a nearly-periodic soliton train with chirped profile and free of an isolated shock front. We suggest this unanticipated result may be realized experimentally and assess the potential for certain applications of this generic effect.
36 MATERIALS SCIENCE↗
Hyperelastic nature of the Hoek–Brown criterion
In this article, we propose a nonlinear elasto-plastic model, for which a specific class of hyperbolic elasticity arises as a straight consequence of the yield criterion invariance on the plasticity level. We superimpose this nonlinear elastic (or hyperelastic) behavior with plasticity obeying the associated flow rule. Interestingly, we find that a linear yield criterion on the thermodynamical force associated with plasticity results in a quadratic yield criterion in the stress space. This suggests a specific hyperelastic connection between Mohr–Coulomb and Hoek–Brown (or alternatively between Drucker–Prager and Pan–Hudson) yield criteria. We compare the elasto-plastic responses of standard tests for the Drucker–Prager yield criterion using either linear or the suggested hyperbolic elasticity. Notably, the nonlinear case stands out due to dilatancy saturation observed during cyclic loading in the triaxial compression test. We conclude this study with structural finite element simulations that clearly demonstrate the numerical applicability of the proposed model.
97 MATHEMATICS AND COMPUTING↗
Experimental investigation on the effects of fabric architectures on mechanical and damage behaviors of carbon/epoxy woven composites
The mechanical behaviors and damage evolutions of carbon/epoxy woven fabric composites with three different geometries, i.e., one plain weave and two twill weave patterns with different areal densities, are studied under tensile loading. The effects of weave patterns on mechanical properties are investigated by monotonic and cyclic tension tests. Remarkable variations in stress–strain curve, Poisson’s ratio, residual strain and strain map exist in the three composites. Crimp ratio is found to be a critical factor to govern the mechanical properties. With smaller crimp ratio, a quasi-linear stress–strain curve with higher elastic modulus and strength is observed. The stress–strain curves of composites with higher crimp ratio contain transition stages with significant tangent modulus degradation. Elastic modulus, strength and damage initiation are all correlated with the crimp ratio linearly regardless of the fabric pattern. Dramatic nonlinear evolution in Poisson’s ratio occurs in the composite with higher crimp ratio. Cyclic tension results indicate that the residual strain is a more appropriate damage indicator than the unloading elastic modulus. Microstructure examination shows that damage developments are essentially related to the fabric geometry, and result in various mechanical behaviors. This work provides important insights into the geometry-deformation mechanism-mechanical property relationship of the woven composites.
36 MATERIALS SCIENCE↗
Near-field terahertz nonlinear optics with blue light
Abstract The coupling of terahertz optical techniques to scattering-type scanning near-field microscopy (s-SNOM) has recently emerged as a valuable new paradigm for probing the properties of semiconductors and other materials on the nanoscale. Researchers have demonstrated a family of related techniques, including terahertz nanoscopy (elastic scattering, based on linear optics), time-resolved methods, and nanoscale terahertz emission spectroscopy. However, as with nearly all examples of s-SNOM since the technique’s inception in the mid-1990s, the wavelength of the optical source coupled to the near-field tip is long, usually at energies of 2.5 eV or less. Challenges in coupling of shorter wavelengths (i.e., blue light) to the nanotip has greatly inhibited the study of nanoscale phenomena in wide bandgap materials such as Si and GaN. Here, we describe the first experimental demonstration of s-SNOM using blue light. With femtosecond pulses at 410 nm, we generate terahertz pulses directly from bulk silicon, spatially resolved with nanoscale resolution, and show that these signals provide spectroscopic information that cannot be obtained using near-infrared excitation. We develop a new theoretical framework to account for this nonlinear interaction, which enables accurate extraction of material parameters. This work establishes a new realm of possibilities for the study of technologically relevant wide-bandgap materials using s-SNOM methods.
47 OTHER INSTRUMENTATION↗
Consistent linearization of micromorphic continuum theories
We outline the procedure of consistent linearization and apply it to the micromorphic, microstretch, and micropolar theories of continua. This yields tractable linear theories for nonlinearly elastic microstructured materials undergoing finite deformations. The results may be readily utilized in computational mechanics, stability and bifurcation analyses, and small-deformation problems in the context of these types of continua. Our results generalize those existing in current literature and facilitate their recovery upon incorporating appropriate kinematic and constitutive assumptions.
McAvoy, Ryan C.↗
Sub-pilot-scale Production of High-Value Products from U.S. Coals
Investigators from the University of Utah, University of Wyoming and Marshall University pursued a program to study the conversion of raw coal to high-value products of carbon fiber and silicon carbide. Team members also developed an initial framework for a data portal that can incorporate laboratory data on coal processing and product quality, and also work with tools for machine learning for data analysis, data visualization and economic assessment. Experimental R&D efforts focused on the conversion of raw coal to coal tar and other byproducts, and the resulting tar intermediates were upgraded to form anisotropic and isotropic pitch materials. These pitch materials were produced from coal using both thermal (pyrolysis) and chemical (mild solvolysis liquefaction) decomposition of raw coal. Four different coals were studied: Utah bituminous coal (Sufco), Wyoming PRB coal (Black Thunder), Illinois bituminous coal (Illinois #6), and West Virginia bituminous coal (Flying Eagle). Both metallurgical-grade coking coals and lower-grade steam coals were investigated, and controlled secondary gas-phase reactions were used during a two-stage pyrolysis process to induce cracking and condensation reactions among the pyrolytic tar species. This approach successfully improved the performance of the lower grade coals for yielding pitch materials, with properties more consistent with a commercial-grade pitch that had previously demonstrated success for quality carbon fiber production. The use of waste plastic materials was also studied, to help improve physical and chemical characteristics of the intermediate tars and final pitch product; in particular, for lowering the pitch softening point to an acceptable level for melt spinning carbon fiber. Mild solvolysis liquefaction was also used as a method for producing pitch for carbon fiber production. As expected, significantly higher pitch yields were obtained using this approach, and waste plastic materials were also successfully used to reduce pitch softening point to an acceptable level. The plastic materials were also utilized to create a solvent for the mild solvolysis process, and this plastic-derived solvent was shown to provide results consistent with more expensive commercial chemical solvents, and could thus avoid the need for costly recovery and recycle of a liquefaction solvent. Additional experimental R&D focused on the production of silicon carbide (β-SiC) from the residual char byproduct from pitch production, and also on the production of carbon fiber from the anisotropic pitch. SiC was successfully synthesized using a mixture of residual char and sandstone at a ratio of 1:1. Reaction temperature and residence time were optimized and yielded a product purity of 81%. For carbon fiber production, the most successful pitch samples were obtained from the mild solvolysis liquefaction approach, combined with the use of a plastic (HDPE)-derived solvent. Fiber properties improved over time as laboratory fiber production methodologies improved, and final yields of carbon fiber were obtained with a diameter of 12.14 ± 1.10 um, Modulus of 173.73 ± 15.25 GPa, and Tensile Strength of 1.04 ± 0.10 GPa. A proof-of-concept Modern Community Research Data Portal (MCRDP) was developed and deployed for coal and coal-derived pitch characterization, with the full support of (i) remote web-based access, (ii) distributed analysis, (iii) interactive visualization and exploration, (iv) shared and long-term data access, (v) advanced query capabilities and (vi) real-time collaboration. The Coal to Products Data Portal “coaltoproducts.org” provides researchers with space to store and share data within a project, tools for analyzing and understanding data for scientific investigation, and the ability to publish data to the broader community for reproducibility. The portal leverages the Material Commons 2.0 (MC) platform developed by the Center for PRedictive Integrated Structural Materials Science (PRISMS) of the University of Michigan, to achieve long-term longevity of data collections and, more importantly, collaborative science. A number of data visualization tools were also assessed and implemented for interrogating the experimental and modeling data. The machine learning portion of this project analyzed datasets from two different coal conversion processes performed on a diverse set of coal samples from both the coal pyrolysis experiments and the solvent liquefaction experiments. The work was initiated by exploring standard regression models on the pyrolysis data, aiming to understand the impact of sample characteristics and processing conditions on key product metrics. Over the course of the project, the focus expanded to include a variety of machine learning tools, delving into both supervised and unsupervised learning methods. Models tested on the pyrolysis data included linear, ridge, lasso, elastic-net, Gaussian process, random forest regression, and AutoSklearn, and the approach was continually refined to enhance predictive accuracy and model interpretability. Similar techniques were applied to the liquefaction data with an additional focus on feature engineering. Along with mesophase content, additional outputs of interest were the pitch yield, softening point, and QI content. Insights derived from these analyses are crucial in determining the factors influencing the quality and yield of coal-derived products. As the work progressed, the research evolved from foundational model comparisons to analyses of random forests, decision paths, and feature importance scores. A thorough market analysis was performed to examine the prospects of coal-based carbon fibers. The best opportunities for coal come from its lower and more stable price relative to petroleum, particularly for subbituminous coals, which is the primary advantage that a coal refinery may have over a petroleum refinery. Before a commercial CTP production facility can be modeled, however, several things need to be understood regarding the nature of the would-be coal refinery. These include the technology to be deployed, the size of facility, the volume(s) of co-product(s), and the waste and emissions profile of the plant. The volume of co-products and waste may be substantial and will require separate market analysis to ensure viability. In the near-term, the importance of coal tar pitch, in the form of carbon pitch, to the aluminum and steel industries is likely to overshadow the alternative use of this material as an input for carbon fiber. The importance of steel and aluminum in building materials, and the need for carbon materials in their manufacturing, will ensure that demand for these products remains for the long run. In addition, carbon fiber may also be the best substitute for steel and aluminum well into the future. While society will eventually be able to shift production of much of its electricity needs to renewables, it will not be able to shift away from fossil fuels for production of high-strength construction and vehicular materials. Demand for carbon fiber is expected to increase quickly, but the volume of carbon fiber and the amount of coal that would be needed to produce even a sizeable share of this market may still be relatively small compared to current coal production. Thus, other coal-based products like graphene, graphite, carbon foams, resins, and carbon-based building products will play important roles in sustaining coal production as coal-fired power generation continues to decline.
01 COAL, LIGNITE, AND PEAT↗
Shear reflectivity compensation in full-waveform inversion using least-squares reverse-time migration
SUMMARY The computational cost of elastic-waveform inversion is too high for inverting PP reflections, while using acoustic full-waveform inversion (FWI) is inaccurate because it does not depend on the shear modulus/velocity/impedance that affects elastic PP wavefield amplitudes. To solve this problem, we develop a waveform inversion method that uses acoustic least-squares reverse-time migration (LSRTM) to compensate the shear reflectivity for acoustic FWI. Our method is based on the quasi-elastic-wave equation developed by Chapman et al. (2014). The quasi-elastic-wave equation uses a linearized acoustic-wave equation with shear modulus μ as a virtual source to correct the acoustic PP wavefield amplitudes toward elastic ones. Our waveform inversion method inverts for elastic parameters by minimizing the L2 norm of the difference between recorded and predicted PP reflections modelled using the quasi-elastic-wave equation. Numerical tests on synthetic and field data show that our method can properly handle the amplitudes of elastic PP reflections and provides an accurate estimate of the P- and S-wave velocities/impedances and, in some cases, the density. The method does not need the computationally expensive numerical solution to the elastic-wave equation. It also gives a better estimate of elastic parameters than a pure LSRTM method for elastic PP reflections.
Feng, Zongcai↗
Sound speed measurements in shock-compressed cemented Tungsten carbides at pressures up to 100 GPa
To gain insights into thermodynamic states attained during shock compression of cemented tungsten carbide with 3.7 wt.% cobalt binder, we present results of longitudinal sound (release wave) speed measurements and their analysis at peak stresses up to 100 GPa (volumetric compression ratio ~ 15%). The sound speeds are determined using front-surface impact and release-wave overtake plate impact experimental configurations using laser interferometry. The measured sound speed data along with estimates for bulk sound speeds obtained using the fourth-order Birch-Murnaghan EoS and thermodynamics are used to determine the longitudinal moduli and shear moduli of shocked tungsten carbide at the various peak compression states attained in the experiments. Here, the longitudinal sound speeds were found to increase linearly with volume compression ratio from 6.97 ± 0.010 km/s at ambient conditions to 8.26 ± 0.156 km/s at a volume compression ratio of ~ 15%. The corresponding longitudinal elastic moduli also increase nearly linearly with the volume compression ratio but remain consistently lower than their theoretical predictions based on continuum models with no damage. Also, the sensitivity of shear moduli to pressure, as predicted by the Steinberg-Guinan model, is reduced substantially and the shear moduli of cemented WC with 3.7 wt.% Co remains nearly constant at ~ 310 GPa at the various peak compression stress states investigated in the present study.
36 MATERIALS SCIENCE↗