Marc A. Meyers

Dynamic behavior of materials

Dynamic Deformation and Waves. Elastic Waves. Plastic Waves. Shock Waves. Shock Waves: Equations of State. Differential Form of Conservation Equations and Numerical Solutions to More Complex Problems. Shock Wave Attenuation, Interaction, and Reflection. Shock Wave-Induced Phase Transformations and Chemical Changes. Explosive-Material Interactions. Detonation. Experimental Techniques: Diagnostic Tools. Experimental Techniques: Methods to Produce Dynamic Deformation. Plastic Deformation at High Strain Rates. Plastic Deformation in Shock Waves. Shear Bands (Thermoplastic Shear Instabilities). Dynamic Fracture. Applications. Indexes.

THE ONSET OF TWINNING IN METALS: A CONSTITUTIVE DESCRIPTION

A constitutive approach is developed that predicts the critical stress for twinning as a function of external (temperature, strain rate) and internal (grain size, stacking-fault energy) parameters. Plastic defor- mation by slip and twinning are considered as competitive mechanisms. The twinning stress is equated to the slip stress based on the plastic flow by thermally assisted movement of dislocations over obstacles, which leads to successful prediction of the slip-twinning transition. The model is applied to body centered cubic, face centered cubic, and hexagonal metals and alloys: Fe, Cu, brasses, and Ti, respectively. A constitutive expression for the twinning stress in BCC metals is developed using dislocation emission from a source and the formation of pile-ups, as rate-controlling mechanism. Employing an Eshelby-type analysis, the critical size of twin nucleus and twinning stress are correlated to the twin-boundary energy, which is directly related to the stacking-fault energy (SFE) for FCC metals. The effects of grain size and SFE are examined and the results indicate that the grain-scale pile-ups are not the source of the stress concentrations giving rise to twinning in FCC metals. The constitutive description of the slip-twinning transition are incorporated into the Weertman-Ashby deformation mechanism maps, thereby enabling the introduction of a twinning domain. This is illustrated for titanium with a grain size of 100 µm.  2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Shock Waves and High-Strain-Rate Phenomena in Metals

These proceedings of EXPLOMET 90, the International Conference on the Materials Effects of Shock-Wave and High-Strain-Rate Phenomena, held August 1990, in La Jolla, California, represent a global and up-to-date appraisal of this field. Contributions (more than 100) deal with high-strain-rate deforma

Quasi-static and dynamic mechanical response of Haliotis Rufescens (Abalone) shells

Abstract Quasi-static and dynamic compression and three-point bending tests have been carried out on Haliotis rufescens (abalone) shells. The mechanical response of the abalone shell is correlated with its microstructure and damage mechanisms. The mechanical response is found to vary significantly from specimen to specimen and requires the application of Weibull statistics in order to be quantitatively evaluated. The abalone shell exhibited orientation dependence of strength, as well as significant strain-rate sensitivity; the failure strength at loading rates between 10×103 and 25×103 GPa/s was approx. 50% higher than the quasi-static strength. The compressive strength when loaded perpendicular to the shell surface was approx. 50% higher than parallel to the shell surface. The compressive strength of abalone is 1.5–3 times the tensile strength (as determined from flexural tests), in contrast with monolithic ceramics, for which the compressive strength is typically an order-of-magnitude greater than the tensile strength. Quasi-static compressive failure occurred gradually, in a mode sometimes described as “graceful failure”. The shear strength of the organic/ceramic interfaces was determined to be approx. 30 MPa by means of a shear test. Considerable inelastic deformation of the organic layers (up to a shear strain of 0.4) preceded failure. Crack deflection, delocalization of damage, plastic microbuckling (kinking), and viscoplastic deformation of the organic layers are the most important mechanisms contributing to the unique mechanical properties of this shell. The plastic microbuckling is analysed in terms of the equations proposed by Argon (Treatise of Materials Science and Technology. Academic Press, New York, 1972, p. 79) and Budiansky (Comput. Struct. 1983, 16, 3).

DYNAMIC RECRYSTALLIZATION IN HIGH-STRAIN, HIGH-STRAIN-RATE PLASTIC DEFORMATION OF COPPER

When copper is deformed to high plastic strain (y ~ 34) at high strain rates (~ ~ I04 s -1) a microstructure with grain sizes of ~0.1 am can be produced. It is proposed that this microstructure develops by dynamic recrystallization, which is enabled by the adiabatic temperature rise. By shock-load- ing the material, and thereby increasing its flow stress, the propensity for dynamic recrystallization can be enhanced. The grain size-flow stress relationship observed after cessation of plastic deformation is consistent with the general formulation proposed by Derby (Acta metall, mater. 39, 955 (1991)). The temperatures reached by the specimens during dynamic deformation are calculated from a constitutive equation and are found to be, for the shock-loaded material, in the 500-800 K range; these temperatures are consistent with static annealing experiments on shock-loaded specimens, that show the onset of static recrystallization at 523 K. A possible recrystallization mechanism is described and its effect on the mechanical response of copper is discussed.

Dynamic fracture (spalling) of metals

Abstract The fundamental mechanical aspects of dynamic fracture in metals are presented, with emphasis on spalling produced by the interactions of shock and reflected tensile waves. The major research efforts conducted in this area are reviewed; the process has been successfully described as a sequence of nucleation—growth—coalescence of voids or cracks. Quantitative models predicting the extent of damage have been successfully compared with experimental observations, by incorporating them into computer codes. A number of metallurgical aspects of importance are discussed: failure initiation sites, crack propagation paths, strain-rate-dependent ductile to brittle transition, grain size effect, intergranular versus transgranular spalling. Of particular importance in iron and steels is the change in spall morphology when the 13 GPa stress is exceeded. This change is documented and interpreted in terms of the α(BCC)→ϵ(HCP) phase transformation undergone at that pressure. Micromechanical models describing the growth of voids in terms of dislocation motion are discussed. Areas requiring additional research effort are identified.

ANALYTICAL AND COMPUTATIONAL DESCRIPTION OF EFFECT OF GRAIN SIZE ON YIELD STRESS OF METALS

Four principal factors contribute to grain-boundary strengthening: (a) the grain boundaries act as barriers to plastic flow; (b) the grain boundaries act as dislocation sources; (c) elastic anisotropy causes additional stresses in grain-boundary surroundings; (d) multislip is activated in the grain-boundary regions, whereas grain interiors are initially dominated by single slip, if properly oriented. As a result, the regions adjoining grain boundaries harden at a rate much higher than grain interiors. A phenomenological constitutive equation predicting the effect of grain size on the yield stress of metals is discussed and extended to the nanocrystalline regime. At large grain sizes, it has the Hall-Petch form, and in the nanocrystalline domain the slope gradually decreases until it asymptotically approaches the flow stress of the grain boundaries. The material is envisaged as a composite, comprised of the grain interior, with flow stress sfG, and grain boundary work-hardened layer, with flow stress sfGB. The predictions of this model are compared with experimental measurements over the mono, micro, and nanocrystalline domains. Computational predictions are made of plastic flow as a function of grain size incorporating differences of dislocation accumulation rate in grain- boundary regions and grain interiors. The material is modeled as a monocrystalline core surrounded by a mantle (grain-boundary region) with a high work hardening rate response. This is the first computational plasticity calculation that accounts for grain size effects in a physically-based manner. A discussion of statisti- cally stored and geometrically necessary dislocations in the framework of strain-gradient plasticity is intro- duced to describe these effects. Grain-boundary sliding in the nanocrystalline regime is predicted from calcu- lations using the Raj-Ashby model and incorporated into the computations; it is shown to predispose the material to shear localization.  2001 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.

Shear localization in dynamic deformation of materials: microstructural evolution and self-organization

The plastic deformation of crystalline and non-crystalline solids incorporates microscopically localized deformation modes that can be precursors to shear localization. Shear localization has been found to be an important and sometimes dominant deformation and fracture mode in metals, fractured and granular ceramics, polymers, and metallic glasses at high strains and strain rates. Experiments involving the collapse of a thick walled cylinder enable controlled and reproducible application of plastic deformation at very high strain rates to specimens. These experiments were supplemented by hat-shaped specimens tested in a compression Hopkinson bar. The initiation and propagation of shear bands has been studied in metals (Ti, Ta, Ti–6Al–4V, and stainless steel), granular and prefractured ceramics (Al2O3 and SiC), a polymer (teflon) and a metallic glass (Co58Ni10Fe5Si11B16). The first aspect that was investigated is the microstructural evolution inside the shear bands. A fine recrystallized structure is observed in Ti, Cu, Al–Li, and Ta, and it is becoming clear that a recrystallization mechanism is operating. The fast deformation and short cooling times inhibit grain-boundary migration; it is shown, for the first time, that a rotational mechanism, presented in terms of dislocation energetics and grain-boundary reorientation, can operate within the time of the deformation process. In pre-fractured and granular ceramics, a process of comminution takes place when the particles are greater than a critical size ac. When they are smaller than ac, particle deformation takes place. For the granular SiC, a novel mechanism of shear-induced bonding was experimentally identified inside the shear bands. For all materials, shear bands exhibit a clear self-organization, with a characteristic spacing that is a function of a number of parameters. This self-organization is analyzed in terms of fundamental material parameters in the frame of Grady–Kipp (momentum diffusion), Wright–Ockendon, and Molinari (perturbation) models.

Structure and mechanical properties of crab exoskeletons

The structure and mechanical properties of the exoskeleton (cuticle) of the sheep crab (Loxorhynchus grandis) were investigated. The crab exoskeleton is a natural composite consisting of highly mineralized chitin-protein fibers arranged in a twisted plywood or Bouligand pattern. There is a high density of pore canal tubules in the direction normal to the surface. These tubules have a dual function: to transport ions and nutrition and to stitch the structure together. Tensile tests in the longitudinal and normal to the surface directions were carried out on wet and dry specimens. Samples tested in the longitudinal direction showed a convex shape and no evidence of permanent deformation prior to failure, whereas samples tested in the normal orientation exhibited a concave shape. The results show that the composite is anisotropic in mechanical properties. Microindentation was performed to measure the hardness through the thickness. It was found that the exocuticle (outer layer) is two times harder than the endocuticle (inner layer). Fracture surfaces after testing were observed using scanning electron microscopy; the fracture mechanism is discussed.

Evolution of microstructure and shear-band formation in α-hcp titanium

The evolution of the microstructure generated by high strain-rate plastic deformation of titanium was investigated. A testing geometry generating controlled and prescribed plastic strains under an imposed stress state close to simple shear was used; this testing procedure used hat-shaped specimens in a compression Kolsky bar which constrains the plastic deformation to a narrow region with approximately 200 Ixm width. Within this band, localization sets in, initiated at geometrical stress concentration sites, at a shear strain of approximately 1.4. The shear-band widths vary from 3 to 20 Ixm and increase with plastic strain. High strain-rate deformation induces, at lower plastic strains (7 < 1.4), planar dislocation arrays and profuse twinning in titanium. In the vicinity of the shear band, elongated cells are formed, which gradually transform into sub-grains. The break-up of these sub-grains inside the band leads to a microstructure composed of small grains ( ~ 0.2 txm) with a relatively low dislocation density. The combined effects of plastic strain and temperature on the microstructural recovery processes (dynamic recovery and recrystallization) are discussed. The experimental results are compared with predictions using a phenomenological constitutive equation and parameters obtained from compression experiments conducted over a wide range of strain rates. The experimental results indicate that the formation of shear bands occurs in two stages: (a) instability, produced by thermal softening and the enhancement of the thermal assistance in the motion of dislocations; (b) localization, which requires softening due to major microstructural changes (recovery and recrystallization) in the material. The calculated temperature rises required for instability and localization are 350 K and 776 K, respectively. Whereas instability may occur homogeneously throughout the entire specimen, localization is an initiation and propagation phenomenon, starting at geometrical (stress concentration sites) or microstructural inhomogeneities and propagating as a thin (3-20 ixm) band.