Shock Compression of Cemented Tunsgten Carbides to 100 GPa: Structure of Shock Wave, Hugoniot relationships, evolution of elastic moduli and strength

Bingsen Wang

doi:10.7273/000007920

There has been a significant interest in the development of tungsten carbide (WC)–based cermets for applications related to extreme thermomechanical environments. For example, the Department of Defense is actively exploring the use of WC cermets for armor and anti-armor applications, while the civilian industry is pursuing their use as cutting tool materials, cold forging dies, and surface coatings, to name a few. Given the extreme dynamic environments in which cemented WCs are targeted to operate, a comprehensive understanding of their shock and impact behavior is of paramount importance. In this study, plate impact experiments are conducted on cemented tungsten carbides (WC) with cobalt binders of 3.7 and 6.0 wt. % to investigate their dynamic high pressure response to ∼ 100 GPa. The shock wave profiles measured by laser interferometry show propagation of steady structured waves. Standard impedance matching procedures are used to determine in-material shock quantities, including Hugoniot relations in the shock velocity versus particle velocity (Us − up) and longitudinal stress versus specific volume (P − V ) planes. The Hugoniot elastic limit of the samples is found to be controlled by the weight % of the cobalt binder and is determined to be 4.45 ± 0.29 GPa for the cemented WC with 3.7 wt.% cobalt and 3.72 ± 0.24 GPa for the 6.0 wt.% cobalt binder. Both grades show a non-linear Us − up relationship depending on whether the particle velocity is in the strength-dominated or hydrodynamic regime. In the strength dominated regime, a non-linear decrease in Us is observed as up increases from ambient to the material’s hydrodynamic limit. In the hydrodynamic regime, the Us − up Hugoniot is linear and is determined to be Us = 4.97(±0.006) + 1.446(±0.018)up km/s for WC with 3.7 wt.% Co and Us = 4.93(±0.006) + 1.463(±0.017)up km/s for 6 wt. % Co. Both WC grades indicate shear-stress hardening with mean stress immediately after yield, followed by pressure softening, and then a sharp drop in stress carrying capacity as the mean stress increases to ∼ 70 GPa (hydrodynamic limit) and beyond. This behavior is in contrast to pure WC ceramics, which show continued shear-stress hardening with mean stress to ∼ 80 GPa. In addition, the evolution of the elastic properties of cemented tungsten carbides up to 100 GPa is investigated to gain insight into the state of mechanical damage to shock-compressed samples. Eight plate impact experiments are conducted -- three front surface impact and five release wave overtake -- to make simultaneous measurements of Hugoniot states and longitudinal sound speeds in the shock-compressed WC samples with 3.7 wt.% cobalt binder. The sound speeds, together with estimates for the bulk sound speeds derived from the Birch-Murnaghan Equation of State (EoS), are examined to evaluate the elastic moduli -- longitudinal, bulk, and shear -- in relation to Hugoniot stress. In the studied Hugoniot states, the longitudinal and bulk sound velocities are observed to rise linearly with the longitudinal stress. This increase in sound speeds corresponds to an increase in both the longitudinal and the bulk moduli as a function of the Hugoniot stress. However, the increase in the longitudinal modulus is relatively small compared to predictions from theoretical models that consider the pressure and temperature dependency of elastic moduli without any damage. Meanwhile, the shear modulus remains nearly unchanged around 310 GPa in the explored Hugoniot states, which is significantly lower than the predictions of the Steinberg-Guinan model, assuming no damage. Initially, the Poisson ratio falls from its ambient value of 0.208 to ∼ 0.199 when the Hugoniot stress is around 10 GPa, suggesting microstructural consolidation in WC at low initial stress. However, as the Hugoniot stress increases to approximately 310 GPa, the Poisson ratio increases to 0.317, suggesting a reduction in shear moduli with increasing stress. After an initial increase, the product of density and Grüneisen parameter (ρΓ) remains fairly constant for volumetric strains around 0.07. The maximum estimated average temperature increase reaches about 286 ◦C at the highest Hugoniot stress level used in the study. Finally, a thermodynamically-consistent, finite-strain, rate- and pressure- dependent constitutive framework is implemented to analyze the shock-compression behavior of cemented tungsten carbides to 100 GPa. Central to this framework is the use of logarithmic strain with a set of invariant basis that allow the Cauchy stress tensor to be expressed as a sum of three response terms that are mutually orthogonal, thus permitting a complete separation of the deviatoric and volumetric (pressure) response. An overstress viscoplasticity model that includes strain and strain rate hardening along with thermal softening is used to represent the deviatoric response, while a complete Mie-Grüneisen equation of state (EoS) is used to obtain the pressure response. Using this formulation, the shock-induced compression behavior of cemented tungsten carbides with 3.7 wt. % of cobalt binder were analyzed to better understand the structure of the measured shock profiles and the associated in-material shock quantities to ∼100 GPa. Of particular interest was the evolution of material strength, material inelasticity, and sample temperatures in the shocked tungsten carbide samples. The simulations were reasonably successful in capturing the interfacial particle velocity profiles using a fixed set of model parameters, except for the rate sensitivity parameter, which was kept at 4.0 for pressures up to 40 GPa and then gradually reduced to 2.0, as Hugoniot pressures approach the hydro-dynamic limit of the material. This variation in the rate sensitivity parameter was found to be necessary to capture the high rate sensitivity of the WC just above its HEL and its reduced rate sensitivity at the higher pressures as the samples approach their hydrodynamic limit. The simulated and experimental profiles are observed to deviate considerably after the arrival of the release wave from the back of the flyer. These deviations become more prominent as the peak Hugoniot stresses are increased beyond the HEL of the WC samples, and are understood to be due to the change in deformation and failure physics/mechanics with increase in impact stress.

Shock Compression of Cemented Tunsgten Carbides to 100 GPa: Structure of Shock Wave, Hugoniot relationships, evolution of elastic moduli and strength

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