R. J. Clifton

Pressure-shear impact and the dynamic viscoplastic response of metals

Abstract Pressure-shear plate impact experiments are used to investigate the viscoplastic response of metals at shear strain rates ranging from 10 5 s −1 to 10 7 s −1 . Flat specimens with thicknesses between 300 μm and 3 μm are sandwiched between two hard, parallel plates that are inclined relative to their direction of approach. Nominal stresses and strains in the specimens are determined from elastic wave profiles monitored at the rear surface of one of the hard plates. Results are reviewed for two fcc metals: commercially pure aluminum and an aluminum alloy. New results are presented for bcc high purity iron, a high strength steel alloy and vapor deposited aluminum. For commercially pure aluminum the flow stress increases strongly with strain rate as strain rate increases from 10 4 s −1 to 10 5 s −1 . At strain rates above 10 5 s −1 the flow stress, based on results for thin vapor-deposited aluminum specimens, increases strongly, but less than linearly, with increasing strain rate until it saturates at strain rates between 10 6 s −1 and 10 7 s −1 . Preliminary results for high purity alpha-iron indicate that the flow stress increases smoothly over eleven decades of strain rate, and faster than logarithmically for strain rates from 10 2 s −1 to greater than 10 6 s −1 . In contrast, for a high strength steel alloy the flow stress depends only weakly on the strain rate, even at strain rates at high as 10 5 s −1 . Such contrasting behavior is attributed to differences in the relative importance of viscous glide and thermal activation as rate controlling mechanisms for dislocation motion in the various metals. Numerical studies indicate that experiments performed at the highest strain rates on the thinnest specimens are not adiabatic, thus requiring a full thermal-mechanical analysis in order to interpret the data.

Shear band formation in thermal viscoplastic materials

Abstract Shear strain localization at high strain rates is investigated through the analysis of a one-dimensional model for simple shearing deformation of thermal viscoplastic materials. Analytical investigations of shear band formation are reviewed. Understanding of the thermo-mechanical instability mechanism is developed through an exact solution for an idealized case, linear stability analysis, and numerical solutions of the fully nonlinear system of partial differential equations which govern the deformation. Several different material models are examined as well as several types of inhomogeneity. Parametric studies are presented to illustrate the effects of strain rate sensitivity, thermal softening, strain hardening, wave length of initial imperfections, inertia and surface texture on the onset of shear localization. From this investigation it is concluded that the vanishing of the slope of the adiabatic stress-strain curve, while a necessary condition for instability, does not adequately characterize the critical strain at which strong localization occurs in thermal viscoplastic materials. Inclusion of the effects of strain rate sensitivity and the strength of the initial nonuniformity are important for a satisfactory description of the onset of severe localization. For the class of high strain rate problems considered, which are representative of experiments on specimens with lengths of millimeters or more deformed at strain rates of 103 s–1 to 104 s–1, the effects of elasticity and heat conduction on the initiation of localization are shown to be negligible. Finally, a localization damage parameter is introduced and shown to be effective in characterizing the onset of severe localization.

A combined normal‐ and transverse‐displacement interferometer with an application to impact of y‐cut quartz

A new transverse‐displacement inteferometer (TDI) is described. This interferometer makes use of intensity variations of a beam obtained by superposition of two beams diffracted symmetrically from a diffraction grating copied onto a plane surface. The TDI is used to monitor the transverse motion of the rear surface of a y‐cut quartz target plate in a plate‐impact experiment. For this application, a 200‐line/mm grating is copied onto the rear surface of the target plate. The normal motion of the rear surface is monitored by means of a standard Michelson interferometer in which the zeroth‐order diffracted beam is used as the beam reflected from the moving mirror. The transverse motion is monitored simultaneously by means of a TDI employing the two fourth‐order diffracted beams, with a resulting sensitivity of 0.625 μm per fringe. The recorded motion confirms the predicted features of two coupled elastic waves, each involving both normal and transverse motion.

Finite element simulations of shear localization in plate impact

Abstract S hear band development in a tungsten heavy alloy (WHA) during pressure-shear plate impact is analysed numerically. The alloy has a microstructure of hard tungsten grains embedded in a soft alloy matrix. A two-dimensional, plane strain model of the alloy microstructure is used in the computations. For this model microstructure a fully coupled thermo-mechanical initial boundary value problem is formulated and solved, accounting for finite deformations, inertia, heat conduction, thermal softening, strain hardening and strain-rate hardening. Calculations are carried out for distributions of uniform grains and for micro-structures obtained from digitized micrographs of the actual alloy. The effects of variations in grain volume fraction and grain size are considered. Experiments and the numerical calculations show that the two phase alloy is more susceptible to shear banding than either of the constituent phases. While the onset of shear localization depends on the grain distribution and volume fraction, the shear band width is found to be set by heat conduction and is insensitive to the grain volume fraction and the grain morphology, The shear band width obtained from the calculations is in good agreement with what is observed in the experiments. Furthermore, the computed shapes of the deformed tungsten grains inside the band resemble closely the observed shapes of the deformed grains in the experiments.

Pressure-shear impact investigation of strain rate history effects in oxygen-free high-conductivity copper

A combined experimental and computational investigation of the behavior of oxygen-free high-conductivity copper under very high shear rates is presented. Pressure-shear plate impact is used for conducting constant strain rate tests and strain rate change texts in which the specimen is strained at shear rates up to 106s−1 for 1μs and then strained at substatially lower shear rates for another microsecond. The specimen is sandwiched between two hard elastic plates to impose conditions of simple shear at very high strain rates and constant hydrostatic pressure. Marked increases in flow stresses are observed at strain rates of 105s−1 and higher. Flow stresses decrease gradually after a sharp drop in strain rate in all strain rate change tests. Homogeneous equiaxed dislocation cells are found as the predominant substructure in the deformed specimens. Theoretical analyses of the nonlinear wave propagation within the specimen are carried out using a general internal variable formulation in which the hardening rate depends on the rate of deformation. The governing system of hyperbolic partial differential equations is solved using a finite-difference scheme; computational results are compared with the experimental results. Both small- and finite-deformation formulations are considered. Only the internal variable model which incorporates a strong rate sensitivity of strain hardening is successful in describing the observed response to the change in strain rate. The enhanced rate sensitivity at high strain rates is concluded to be related primarily to the rate sensitivity of strain hardening, not the rate sensitivity of the flow stress at constant dislocation structure. The generation and evolution of dislocation cells appears to be the dominant micromechanical process during the high- rate deformation of pure metals.

Plate impact response of ceramics and glasses

Soft‐recovery plate impact experiments have been conducted to study the evolution of damage in polycrystalline Al2O3 samples. Examination of the recovered samples by means of scanning electron microscopy and transmission electron microscopy has revealed that microcracking occurs along grain boundaries; the cracks appear to emanate from grain‐boundary triple points. Velocity‐time profiles measured at the rear surface of the momentum trap indicate that the compressive pulse is not fully elastic even when the maximum amplitude of the pulse is significantly less than the Hugoniot elastic limit. Attempts to explain this seemingly anomalous behavior are summarized. Primary attention is given to the role of the intergranular glassy phase which arises from sintering aids and which is ultimately forced into the interfaces and voids between the ceramic grains. Experiments are reported on the effects of grain size and glass content on the resistance of the sample to damage during the initial compressive pulse. To fu...

Determination of the critical-stress-intensity factor KIc from internally pressurized thick-walled vessels

Stable crack growth is obtained by subjecting prenotched thick-walled cylinders to internal pressure, with the bore jacketed to keep the crack faces traction free. The critical-stress-intensity factor KIc is determined from the pressure at failure. Results are presented for PMMA and a variety of rocks.

The oblique-plate impact experiment

An experimental method is presented for the study of one-dimensional plane waves corresponding to combined pressure and shear. The experiment involves the impact of two skewed flat plates. A projectile plate is accelerated using a gas gun and made to impact a target plate in a vacuum chamber. The projectile and target plates are parallel, but inclined relative to the axis of the gun so that the particle velocity in the target has components both normal and parallel to the plane of impact.The particle velocity at the target rear (free) surface is recorded as a function of time. The normal velocity component is monitored using a laser velocity interferometer; the transverse motion is monitored using a shadow technique.The measured wave profiles can be compared to theoretical predictions based on one-dimensional-wave theory.

Analysis of Failure Waves in Glasses

Recent plate impact experiments have been interpreted as indicating the existence of {open_quotes}failure waves{close_quotes} during the compression of glass by impact at sufficiently high velocities. In experiments on soda-lime glass, Brar et al. reported the propagation of a wave across which the shearing strength dropped sharply from 2 GPa to 1 GPa, and the spall strength dropped from 3 GPa to zero. Such a drop in spall strength has also been reported by Raiser et al. in an aluminosilicate glass. Kanel et al. interpreted a small jump in the rear surface particle velocity in experiments on K19 glass as the reflection of a recompression wave from a wavefront propagating at approximately the speed reported for {open_quotes}failure waves{close_quotes}. In this paper, such {open_quotes}failure waves{close_quotes} are interpreted within the context of nonlinear wave theory. In this theory the {open_quotes}failure wave{close_quotes} corresponds to a propagating phase boundary-called a transformation shock. The theory is analogous to the theory of liquifaction shocks in fluids. 18 refs., 5 figs.

Response of materials under dynamic loading

The dynamic response of materials is important to the performance and failure resistance of many engineered systems. Experimental methods are now available to measure this response over a wide range of strain rates and temperatures. Application of these methods to the investigation of the dynamic response of metals, glasses and ceramics has led to important advances in understanding, while bringing into focus important issues that remain to be resolved. In this paper, a number of these issues are discussed and potentially fruitful research directions are suggested.