Ronald W. Armstrong

Dislocation‐mechanics‐based constitutive relations for material dynamics calculations

An improved description of copper‐ and iron‐cylinder impact (Taylor) test results has been obtained through the use of dislocation‐mechanics‐based constitutive relations in the Lagrangian material dynamics computer program EPIC‐2. The effects of strain hardening, strain‐rate hardening, and thermal softening based on thermal activation analysis have been incorporated into a reasonably accurate constitutive relation for copper. The relation has a relatively simple expression and should be applicable to a wide range of fcc materials. The effect of grain size is included. A relation for iron is also presented. It also has a simple expression and is applicable to other bcc materials but is presently incomplete, since the important effect of deformation twinning in bcc materials is not included. A possible method of acounting for twinning is discussed and will be reported on more fully in future work. A main point made here is that each material structure type (fcc, bcc, hcp) will have its own constitutive beha...

Crystal size dependence for impact initiation of cyclotrimethylenetrinitramine explosive

The dislocation pile‐up avalanche model is used to explain the crystal size dependence for hot spot‐controlled initiation of chemical decomposition in cyclotrimethylenetrinitramine crystals subjected to drop‐weight impact testing. Deformation‐induced temperature rises, hot spot sizes, and lifetimes are related to previously reported values for direct thermal decomposition. A reasonable chemical reaction yield is estimated from available kinetic data.

High strain rate properties of metals and alloys

Abstract The high strain rate dependence of the flow stress of metals and alloys is described from a dislocation mechanics viewpoint over a range beginning from conventional tension/compression testing through split Hopkinson pressure bar (SHPB) measurements to Charpy pendulum and Taylor solid cylinder impact tests and shock loading or isentropic compression experiment (ICE) results. Single crystal and polycrystal measurements are referenced in relation to influences of the crystal lattice structures and nanopolycrystal material behaviours. For body centred cubic (bcc) metals, the strain rate sensitivity (SRS) is in the yield stress dependence as compared with the face centred cubic (fcc) case of being in the strain hardening property. An important consequence is that an opposite ductility influence occurs for the tensile maximum load point strain that decreases with strain rate for the bcc case and increases with strain rate for the fcc case. Different hexagonal close packed (hcp) metals are shown to follow either the bcc or fcc case. A higher SRS for certain fcc and hcp nanopolycrystals is explained by extrapolation from conventional grain sizes of an inverse square root of grain size dependence of the reciprocal activation volume determined on a thermal activation strain rate analysis (TASRA) basis. At the highest strain rates, additional deformation features enter, such as deformation twinning, adiabatic shear banding and very importantly, for shock induced plasticity, transition from plastic flow that is controlled by the mobility of the resident dislocation density to plasticity that is controlled by dislocation or twin generations at the shock front. The shock description is compared with the very different high rate shockless ICE type loading that occurs over nanoseconds and leads to higher compressive strength levels because of dislocation drag resistance coming into play for the originally resident mobile dislocation density. Among the high strain rate property, concerns are the evaluation of ductile to brittle transition behaviours for bcc and related metals and also, projectile/target performances in ballistic impact tests, including punching. Very complete metallographic and electron microscope observations have been reported in a number of the high rate deformation investigations.

On size effects in polycrystal plasticity

Abstract Two cumulative ‘size’ effects are responsible for the increased strength of a polycrystalline aggregate above the single crystal strength at low temperatures : a ‘specimen size’ effect and a ‘grain size’ effect. The ‘specimen size’ effect occurs when few grains are present in a specimen cross-section (say less than twenty), and this effect is due mainly to the orientation dependence of crystal plastic flow. The ‘grain size’ effect occurs when many grains are in a specimen cross-section (say more than twenty), and this effect results because, in addition to the orientation dependence of plastic flow within grains, internal concentrations of stress are necessary at grain boundaries to cause bulk yielding and subsequent plastic flow of the polycrystalline aggregate.

Pile-up based hall-petch relation for nanoscale materials

Abstract Recent success in fabricating nanocrystalline materials has raised again the question of the role that dislocation pile-ups play in determining the strength of the materials, vis-a-vis, the Hall-Petch effect. At the nanoscale some features of pile-up characteristics can have a significant effect. Aspects considered here include a small number of dislocations, a continuum versus discrete crystal dislocation description and the influence of elastic anisotropy.

Adiabatic heating at a dislocation pile-up avalanche

Abstract Most model calculations of the adiabatic heating which can be produced by plastic deformation give only small increases in the bulk temperature of a material. This occurs because a very significant averaging and presumed continuity of the plastic flow processes are built into the description of what otherwise is undoubtedly an extremely localized and sudden action of energy conversion on the microstructural scale. For the opposite case description, an appreciable localized heating is estimated to occur within a material if a dislocation pile-up is catastrophically released in an avalanche configuration from a collapsed obstacle. The estimated temperature rise at such a hot spot is found at the limiting dislocation velocity to be directly proportional to the Hall-Petch stress intensity factor for the strength of the internal obstacle originally impeding the growth of a slip band (or twin or crack). Thus, this description of adiabatic heating has been shown to be a particularly important effect for materials which exhibit sudden load drops in their deformation responses and for materials which are susceptible to the onset of brittle fracturing. Although this work gives emphasis to metallic materials, the same considerations are relevant for other types of crystalline solids as well, such as explosive molecular crystals and inorganic crystalline oxidizer ingredients incorporated in propellant formulations.

The limiting grain size dependence of the strength of a polycrystalline aggregate

Abstract Recent experiments on high strength steel having a very fine microstructure have been interpreted in terms of the Petch relationship with the apparent dislocation pile-up lengths as small as 85 A. For this reason, the behaviour of such small dislocation pile-ups has been examined theoretically. The results indicate that the Petch relation can be extended in a modified way to these extremely small grain sizes, e.g. < 50 A. The main point is that for a small number of straight dislocations, the discontinuous nature of the Petch relation is important because each dislocation has a significant influence upon the stress concentrating character of the pile-up.

Influences of strain rate and grain size on yield and serrated flow in commercial Al-Mg alloy 5086

Much attention has been paid to the rather special stress-strain characteristics of Al-Mg alloys. Beginning with the pioneering work of Portevin and LeChatelier in 1923, the focus has been on the appearance of tensile band-type deformation markings that are observed coincident with the appearance of serrated flow in stress-strain curves. The serrations are the result of dynamic strain aging (DSA). A major influence of the DSA phenomenon is to produce both a higher flow stress and, very importantly, greater strain hardening at lower strain rates than for higher ones at which serrations do not appear. Physically-based constitutive equations, for example, of Zerilli-Armstrong type, that are derived for thermally-activated dislocation-lattice or dislocation-dislocation interactions, are susceptible to interference from DSA. For this reason, clarification of the importance of strain aging in accounting for laboratory tests of the stress-strain behavior of the alloy has been investigated. Of special interest was the solute influence on the combined yield and strain hardening behavior.

Ductile fracture toughness of polycrystalline armco iron of varying grain size

Abstract The influence of polycrystalline grain size on the ductile fracture toughness (Jic) of Armco iron has been studied over the grain size range of 38–1050 μm. Experimental evidence for the various stages of ductile fracture during fracture toughness testing was obtained through scanning electron metallography. Jic decreases with coarsening of grain size and follows a parabolic relation with d−1/2. The critical stretch zone width in fracture mechanics specimens decreases with increasing grain size; at 1050 μm grain size, the stretch zone is not detectable and the material fails by cleavage fracture. The cleavage fracture behaviour at room temperature has been explained in terms of a stress concentration ahead of the crack tip that reaches the level of the cleavage fracture stress. The variation of fracture toughness Jic with grain size was studied in terms of the plastic zone size. Indirect methods based on Kjc and Pj fail to estimate the plastic zone size correctly. Microhardness measurements were found to be quite suitable for estimation of the plastic zone size. At finer grain sizes, the plastic zone size encompasses a substantial number of grains while at the coarsest grain size (1050 μm it is confined to a single grain, a feature that corresponds with the occurrence of cleavage fracture. The present measurements on Armco iron are shown to be consistent with the Jic data of Klasen et al. [Mater. Sci. Engng80, 25 (1986)] on microalloyed steels once one has accounted for inclusions and the higher carbon content.

Thermally-activated glide in magnesium crystals from 4·2° to 420°k

Abstract The effect of changes in strain rate ad temperature on the flow stress of Mg single crystals VIM determined m the range of 4·2° to 420°k. The present data, along with those obtained previously, indicate that the intersection of dislocations is the controlling mechanism. Cottrells original model must, however, be modified to include an effect of stress on the activation volume. This effect appears to be due primarily to the fact that the force between two intersecting dislocations varies with their distance of separation rather than a change in the effective forest spacing.