Uniaxial compression of single crystal and polycrystalline tantalum

A series of compression experiments characterising the elastic-plastic response of single crystal and polycrystalline tantalum from quasi-static to intermediate strain-rates (10^−3 – 10^3 s−1) over a range of temperatures (233–438 K) are reported in this paper. The single crystal experiments show significant differences in the response of the three principle crystal orientations of tantalum in terms of yield, work hardening and ultimate deformed shapes. Modelling is undertaken using a dislocation mechanics based crystal plasticity finite element model giving insight into the underlying microscopic processes that govern the macroscopic response. The simulations show the importance of the dislocation mobility relations and laws governing the evolution of the mobile dislocation density for capturing the correct behaviours. The inclusion of the twinning/anti-twinning asymmetry is found to influence [100] orientation most strongly, and is shown to be critical for matching the relative yield strengths. In general the simulations are able to adequately match experimental trends although some specific details such as exact strain hardening evolution are not reproduced suggesting a more complex hardening model is required. 3D finite element simulations approximating the tests are also undertaken and are able to predict the final deformed sample shapes well once the twinning/anti-twinning asymmetry is included (particularly for the [100] orientation). The polycrystalline data in both as-received and cold rolled conditions shows the initial yield strength is highest and work hardening rate is lowest for the cold-rolled material due to the increase in mobile dislocation density caused by the prior work. The general behavioural trends with temperature and strain-rate of the polycrystalline materials are reproduced in the single crystal data however the specific form of stress versus strain curves are significantly different. This is discussed in terms of the similar active slip systems in polycrystalline material to high symmetry single crystals but with the significant added effect of grain boundary interactions

An Equation of State of a Carbon-Fibre Epoxy Composite under Shock Loading

An anisotropic equation of state (EOS) is proposed for the accurate extrapolation of high-pressure shock Hugoniot (anisotropic and isotropic) states to other thermodynamic (anisotropic and isotropic) states for a shocked carbon-fibre epoxy composite (CFC) of any symmetry. The proposed EOS, using a generalised decomposition of a stress tensor [Int. J. Plasticity \textbf{24}, 140 (2008)], represents a mathematical and physical generalisation of the Mie-Gr\"{u}neisen EOS for isotropic material and reduces to this equation in the limit of isotropy. Although a linear relation between the generalised anisotropic bulk shock velocity $U^{A}_{s}$ and particle velocity $u_{p}$ was adequate in the through-thickness orientation, damage softening process produces discontinuities both in value and slope in the $U^{A}_{s}$-$u_{p}$ relation. Therefore, the two-wave structure (non-linear anisotropic and isotropic elastic waves) that accompanies damage softening process was proposed for describing CFC behaviour under shock loading. The linear relationship $U^{A}_{s}$-$u_{p}$ over the range of measurements corresponding to non-linear anisotropic elastic wave shows a value of $c^{A}_{0}$ (the intercept of the $U^{A}_{s}$-$u_{p}$ curve) that is in the range between first and second generalised anisotropic bulk speed of sound [Eur. Phys. J. B \textbf{64}, 159 (2008)]. An analytical calculation showed that Hugoniot Stress Levels (HELs) in different directions for a CFC composite subject to the two-wave structure (non-linear anisotropic elastic and isotropic elastic waves) agree with experimental measurements at low and at high shock intensities. The results are presented, discussed and future studies are outlined.Comment: 12 pages, 9 figure

The shock induced equation of state and shear strength of polyvinylidene difluoride

Polyvinylidene difluoride (PVDF) has found application as a piezoelectric stress gauge for the measurement of the shock response of materials. Therefore, it is perhaps surprising that little data concerning its bulk response to shock loading has reached the open literature. In this paper, we examine the behaviour of this polymer, both hydrostatically (equation of state; shock stress, shock velocity and particle velocity), and its deviatoric response (shear strength behind the shock front). Equation-of-state measurements show close agreement with existing data, but also a strong non-linearity in shock velocity at low particle velocities. The calculated hydrodynamic response also agrees well with existing pressure measurements, but is significantly lower than the measured shock stresses, suggesting that the shear strength of this material has a strong positive dependence on the applied shock pressure. Subsequent measurements of the lateral component of stress, which in combination with the known longitudinal stress has been used to calculate the shear strength, has confirmed this

On impact upon brittle solids

The response of brittle materials to uniaxial compressive shock-loading has been the subject of much recent discussion. The physical interpretation of the yield point of brittle materials, the Hugoniot elastic limit (HEL), the rate-dependence of this threshold, and the effect of polycrystalline microstructure still remain to be comprehensively explained. Evidence of failure occurring in glasses behind a travelling boundary that follows a shock front has been accumulated and verified in several laboratories. Such a boundary has been called a failure wave. The variations in properties across this front include complete loss of tensile strength, partial loss of shear strength, reduction in acoustic impedance, lowered sound speed and opacity to light. Recently we have reported a similar behaviour in gabbro and the polycrystalline ceramics SiC, alumina and titanium diboride. It is the object of this work to present further observations of these phenomena and their relation to ballistic performance

On the dynamic response of four polymers

Il is a pressing objective to understand the mechanical behaviour of polymeric materiais at high strain rate for a range of industrial and defence applications. Some are used as the binder phase in plastic bonded explosives (PBXs) and propellants. Others are used either as components for structures or as the binder phase in various composite Systems. Such materials need to be understood so that their response may be understood and constitutive descriptions constructed. This work presents experimental data focused at the evaluation of the equation-of-statc (EOS) and strength behaviour of four selected polymers. The equation of state and the shear strength of each polymer were measured as a function of impact stress and this gives insight into the role of the microstructure and its relation to response

Impact and Penetration of a Borosilicate Glass

The impact and penetration of brittle solids has been the subject of study for many years. Recently, the development of gauge techniques to measure the deviatoric response of various materials has highlighted the role of the shear strength in determining the ballistic performance. Recent experiments on various glasses using plate impact and ballistic geometries have characterised materials and provided a detailed analysis of penetration behaviour using simultaneous X-ray, high-speed photography and gauges. We present a study of impact on a borosilicate glass using a combination of these techniques.La pénétration des solides fragiles fait l'objet de nombreuses études depuis plusieurs années. Récemment, l'utilisation de jauges de contrainte pour mesurer la réponse déviatoire des matériaux a mis la lumière sur le rôle de la résistance au cisaillement pour interpréter les performances balistiques. De récentes expériences sur divers verres ont été conduites tant en impact de plaque qu'en impact balistique. L'utilisation simultanée de la radiographie, de la cinématographie rapide et des jauges a permis d'apporter des éléments sur le comportement durant la pénétration. Nous présentons une étude sur l'impact d'un verre borosilicate utilisant cette approche

Lateral stress measurements and shear strength in a shock-loaded γ- TiAl alloy

Manganin stress gauges have been placed in samples of a γ-titanium aluminide alloy in such orientation that renders them sensitive to the lateral component of stress during one-dimensional shock loading. The impact stresses were in the range 1.8 to 6 GPa. The resultant stress histories show clear evidence of a transition from elastic to plastic behaviour, which, through the elastic relations correlates with the Hugoniot Elastic Limit of this material. In combination with the longitudinal stress data, it has been possible to use the lateral stresses from this series of experiments to calculate the shear strength during shock loading. The Hugoniot of the γ-titanium aluminide studied is seen to be significantly different than a standard α-β Ti-alloy such as Ti-6Al-4V. The results show this titanium aluminide alloy displays a significant degree of hardening with increasing shock stress