Jeremy Millett

On the shock induced failure of 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 dependence of this threshold on propagation distance and the effect of polycrystalline microstructure 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 of 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 the polycrystalline ceramics silicon carbide and alumina. It is the object of this work to present our observations of these phenomena and their relation to failure and the HEL in brittle materials.

On the analysis of transverse stress gauge data from shock loading experiments

The importance of understanding the variation of shear strength with pressure in the formulation of constitutive models has long been recognized. Previously, this had been deduced by measurements of the offset of the Hugoniot curve for a material from the calculated hydrostat. In recent papers, a direct measurement technique has been suggested in which both principal components of stress are measured using piezoresistive gauges. The reduction of the data collected from transverse stress gauges has attracted some debate and is reviewed here. In particular, the stress and strain states experienced by the gauge must be considered. The hardening of the gauge with longitudinal stress or pressure was investigated. Examples from experiments in metals and ceramics are given. The effect of gauge geometry was assessed and results show that the measured stresses from either gauge were within 0.5% of each other when subjected to identical impact conditions. An investigation was also performed on the effect of insulation thickness around the gauge and again no effect on the measured stress was found.

Delayed failure in shocked silicon carbide

Plate impact and split Hopkinson pressure bar (SHPB) experiments have been conducted on three grades of silicon carbide produced by different routes. Data are presented which indicate that the failure of the materials was delayed for some time after the maximum stress had been achieved. In particular, the measured lateral component of the stress in plate impact was found to increase across a front which traveled behind the shock. This phenomenon is akin to the failure wave which has been observed to occur in glasses but has not previously been reported in polycrystalline materials. Hopkinson bar experiments have revealed significant differences in the behaviors between the three materials. These may be related to the effects observed in the plate impact experiments. These results explain the anomalous ballistic phenomena that have been reported for the penetration behavior of SiC. Additionally the Hugoniot elastic limit (HEL) and shear strength were found to vary with the production route used.

Shear strength measurements in a tungsten alloy during shock loading

Lateral stress measurements in a tungsten alloy, in combination with known Hugoniot data, have been used to find the shear strength of this material, and its variation with longitudinal shock stress, up to 14 GPa. Results show that the shear strength increases significantly with increasing stress. Prior to this work, there has been disagreement in the literature on the effect of shock stress on the shear strength of tungsten and its alloys. The present work agrees with the data obtained by Zhou and Clifton [J. Appl. Mech. 64, 487 (1997)] who used pressure shear. However, the range of stresses studied has been greatly extended.

Shear stress measurements in copper, iron, and mild steel under shock loading conditions

A series of experiments have been conducted on metals subjected to planar impact loading in which a biaxial stress state and a uniaxial strain state is induced. Longitudinal and transverse stresses have been measured in copper, iron, and mild steel, using manganin stress gauges. The results have been used to calculate shear stress from the difference between the stress components. Results indicate that copper displays an increase in shear stress with pressure, showing similar trends to other work. An increase in dislocation density has been suggested as a possible mechanism. Iron shows a constant shear stress with increasing pressure, again in accordance with other workers. Finally, mild steel has been observed to have a significant increase in shear stress with increasing pressure. The inclusion of a hard second phase in the microstructure is thought to produce a large amount of dislocation debris, again explaining the observed hardening.

Failure in a shocked high‐density glass

One of the outstanding questions concerning the compressive behavior of brittle materials concerns the failure wave observed in glasses. While much work has centered around relatively open structure, low density glasses such as borosilicate (pyrex) and soda‐lime (float, which is partially filled), none has addressed the response of highly filled lead glasses. This work presents the results of a series of plate impact experiments carried out on the lead glass DEDF.TM This material was shocked in uniaxial strain and the longitudinal and lateral components of stress and strain were measured. The failure wave, observed in lower density glasses, was observed in this material but its velocity reached that of the shock at less than twice the Hugoniot elastic limit (HEL).

Measurement of the shear strength of pure tungsten during one-dimensional shock loading

The behavior of a pure tungsten under conditions of one-dimensional shock loading has been monitored using Manganin stress gauges, in longitudinal and lateral orientations. The shock induced equation of state, in terms of stress and particle velocity (from the longitudinal gauges), shows that the Hugoniot of this pure material agrees with the results of previous workers, both in pure tungsten and tungsten alloys. Lateral stress traces show an increase in stress (and hence decrease in shear strength) behind the shock front, in a manner similar to that observed in a tungsten heavy alloy and pure tantalum. It has been proposed that this is due to the high Peierl’s stress initially restricting dislocation generation, followed by a later increased in dislocation density. However, the brittle manner in which tungsten fails under shock loading indicates that other mechanisms are in operation. It has been suggested that the shock front nucleates cracking, which progressively grows behind it, which in combination ...

Direct measurements of strain in shock‐loaded glass specimens

Direct measurements of the uniaxial strain behind wave fronts in shock‐loaded glass specimens reveal several new aspects of their dynamic response. The measurements have been achieved by embedding longitudinal strain gauges in the shocked specimen in such a way that gauge length is along the shock propagation direction. Following the resistance changes of the gauges, we were able to find differences in the loading characteristics below and above the Hugoniot elastic limit of the glass, measure residual strains when shocked above this limit, and find interesting aspects of the strain histories behind the failure wave fronts.

The role of cold work on the shock response of tantalum

The effect of prior cold work on the shock response of tantalum has been investigated via plate impact. As-received and 50% cold-rolled material has been studied to determine the Hugoniot Elastic Limit (HEL), shear strength evolution behind the shock front, and spall strength. Results show that there is a significant drop in both HEL and shear strength due to cold-rolling, but as the thickness of the target (or time) increases, results converge between the two states. Results suggest that this is due to the cold-rolling process moving dislocations away from the surrounding interstitial solute atoms that collect there, thus reducing the initial stress to initiate yield. In other words, the main contribution of cold-rolling is to increase the population of mobile dislocations within the microstructure rather that just increase the dislocation density as a whole. In contrast, the spall strength in both states appears almost identical. It is suggested that the high Peierls stress prevents a large increase in dislocation density during rolling and hence reduces any post rolling strengthening that might be observed in the spallation response. Finally, we observe a significant change in spall response below a pulse width of 150 ns. We believe that this represents a change from a nucleation and growth of ductile voids type mechanism to one based on ductile fracture of atomic planes. The fact that at these low pulse durations, results appear to trend towards the theoretical strength of tantalum would lend support to this hypothesis.

Shock, release and Taylor impact of the semicrystalline thermoplastic polytetrafluoroethylene

The high strain-rate response of polymers is a subject that has gathered interest over recent years due to their increasing engineering importance, particularly in load bearing applications subject to extremes of pressure and strain rate. The current work presents two specific sets of experiments interrogating the effect of dynamic, high-pressure loading in the regime of the phase II to phase III pressure-induced crystalline phase transition in polytetrafluoroethylene (PTFE). These are gas-gun driven plate- and Taylor impact. Together these experiments highlight several effects associated with the dynamic, pressure-induced phase transitions in PTFE. An elevated release wave speed shows evidence of a pressure-induced phase change at a stress commensurate with that observed statically. It is shown that convergence between analytic derivations of release wave speed and the data requires the phase II to III transition to occur. Taylor impact is an integrated test that highlights continuum behavior that has origin in mesoscale response. There is a rapid transition from ductile to brittle behavior observed that occurs at a pressure consistent with this phase transition.