Norman Petch was trained in chemistry at Queen Mary College in London, in metallurgy at Sheffield, and in physics at the Cavendish Laboratory, University of Cambridge. The quantitative nature of his crystallographically-based earliest papers, dealing with the positions of iron and carbon atoms in steel, very probably contributed to the meticulous nature of his follow-on mechanical properties research, initially, into the influence of polycrystal grain size on the plastic yielding and fracturing behavior of iron and steel materials at low temperatures. This work, that was complementary to studies of the yield point behavior of steel by his Cambridge colleague, E.O. Hall, led to the well-established Hall-Petch equation for the stress dependence on reciprocal square root of average grain diameter; perhaps, the most widely quoted equation in materials science. Norman Petch's research, with students and colleagues, led on to predictive and/or interpretive Hall-Petch connected relations for the influence of carbon on the friction stress of steel, hydrogen embrittlement influences on the yield and fracture of steel, the ductile-brittle transition behavior of iron and steel and related materials, the plastic deformation properties of brass and aluminum materials, and the fracturing behavior of ceramic materials and laminated composites.

The explanation for the grain size dependence of the polycrystal yield stress or cleavage stress of steel, investigated in complementary studies by Hall and Petch, is rooted in dislocation pile-up theory first described by Eshelby, Frank and Nabarro just a step away from previous theoretical work on the stress concentrating properties of cracks. Beginning from Cottrelllocking of dislocations at grain boundaries by carbon that is responsible for the pronounced yield point behavior and the grain size dependence of the yield strength of steel, the same concepts have been shown to apply for the complete stress/strain behavior of steel and other materials. Other mechanical properties such as fatigue strength show a similar dependence on grain size. A notable application of such grain size based considerations has been to the ductile-brittle transition and fracture toughness properties of steel and related materials — because refinement of grain size both strengthens a material and improves its fracture toughness. Early results for the polycrystal hardness dependence on grain size gave evidence that the strength benefits of grain size refinement ought to extend to ultrafine grain sizes.

Impression creep tests on a Sn-Pb eutectic alloy showed a hyperbolic sine stress dependence of impressing velocity and an activation energy of 55 kJ/mole which is independent of the punching stress. A finite element simulation showed that this phenomena could be explained by a constitutive law in which the creep rate is also a hyperbolic sine function of stress. This simulation also gives an impressing velocity which is proportional to the punch size for the same punching stress. Then by using lubrication theory, it is possible to relate this constitutive law to an interphase shearing mechanism in which the rate of interphase shear is a hyperbolic sine function of the shear stress. This theory gives a creep rate which depends inversely on the third power of grain size at low stresses.

PC based computer programs have been developed to simulate twodimensional microstructural grain growth either by nucleation or transformation from an amorphous phase. By controlling the parameters of the rate of grain growth, nucleation rate, depletion zone size, and changes in these latter two variables most grain growth conditions can be achieved in practice. Several cases have been explored which include: constant nucleation rates, both increasing and decreasing rates, and the instantaneous saturation of nucleation sites. The evolution of domain sizes can be investigated which is dependent on the effective rate of nucleation during various stages of grain growth. Real time graphics displays are present the instantaneous growth parameters and their changes as well as information on fractional area growth.

The dislocation pile-up explanation for the Hall-Petch (H-P) relation is re-examined for ultrafine grain sizes when only a few dislocations are involved in the pile-up, formed necessarily at applied stress levels near to the theoretical limit. Each dislocation added to the pile-up produces a step reduction in the H-P stress. Consequently, differences in dislocation configurations and types of pile-ups are easily recognized in the limit of small dislocation numbers. A significant reduction occurs in the H-P slope value (i.e., microstructural stress intensity) for the extreme case of only one dislocation loop being expanded against the grain boundary obstacle stress.

The Hall-Petch relation σ = σo + kl−½, provides for the separate consideration of friction stress strengthening within the polycrystal grain volumes through σo and grain boundary strengthening through the product of the microstructural stress intensity k and the reciprocal square root of the grain diameter l Smaller grain diameters are normally obtained at higher alloy contents as illustrated for yield strength results reported for different face-centered-cubic Al-Mg alloys. Results on Al-Li alloy give an interesting example of substantial grain boundary strengthening that is associated with reduced ductility of the material. More complete results reported for the Cu-Al system, allow an evaluation of the strengthening component dependencies on alloy composition, in particular, connecting with a predicted square root of grain boundary obstacle stress in k. The much studied Cu-Zn alloys bring out subtle changes in σo and k

Crystallization in amorphous materials produces polycrystalline materials with fine grains which can be on the order of 1–2 microns, depending on the extent of annealing. Ductility in these materials with this range of grain sizes is generally low. This paper deals primarily with the lack of ductility in these classes of materials and will present a quasi-mathematical approach to this phenomenon. It will be shown that the influence of the plastic zone, the dislocation-free zone, and the grain size can be expressed by a unique formalism from which the propagation of cracks, and the lack of ductility, can be readily predicted. These deductions will become evident from the results of recent simulation experiments which will provide evidence to support the most essential elements of the approach presented in this paper.

Incursion of high density penetrators into ceramic armor is preceded by the formation of a finely comminuted rubble bed at the penetrator tip, the Mescall zone. The deformation and failure processes that result in the Mescall zone are critical to understanding penetration resistance and to modeling penetration behavior. Transmission electron microscopy (TEM) was used to examine shock loaded material in the vicinity of an explosive detonation in α-Al2O3 and to infer the phenomenology of plasticity and fracture occurring at the tip of an advancing penetrator in ceramic armor. Comminution proceeds by intergranular fracture until the fragment size approaches the grain size. Further fragmentation proceeds by transgranular cracks, which nucleate at preexisting microvoids and at intersections of basal twins and primary and secondary slip bands.

Experimental results show that a nanolayered composite structure made of two kinds of metals strengthens dramatically as the layer thickness is reduced. In epitaxial systems, this strengthening has been attributed classically, to the modulus and lattice parameter mismatches between adjacent layers. The modulus mismatch introduces a force between a dislocation and its image in the interface. The lattice parameter mismatch generates stresses and mismatch dislocations which interact with mobile dislocations. In addition to these two interactions, there is the difficulty of operating a Frank-Read source in any very thin layer. However, the calculations suffer from the drawback that elasticity theory is being used at such short range from the dislocations that it is not strictly valid. In this paper the issues in strengthening of multilayer systems are defined within a simple analytical model. Additionally, a parametric approach using the atomistic embedded atom method (EAM), is developed to study, dislocation-interface interactions in metallic multilayers. Preliminary results of the atomistic calculations verify that Koehler strengthening is significant especially when the lamellae are very thin. For thicker lamellae the lattice parameter mismatch effects, which have been modelled within continuum theory, contribute increasingly to the strength. In Cu-Ni, the peak in the yield stress occurs when single dislocations must overcome both barriers. The yield stress drops in thicker lamellae as pile ups of increasing length form in the lamellae, finally conforming to the Hall-Petch equation.

An attempt to employ the self-organization theory has been made in order to describe different types of dislocation patterning in fatigued metals. We demonstrate that the formation of certain patterns can be understood as a result of competition between the intrinsic length scales of the “reaction+diffusion” model, on the one hand, and grain size, L on the other hand. Our results indicate that a critical grain size, Lcr, exists such that below Lcr the formation of dislocation structures of any type in fatigued metals becomes impossible.

To study crack dynamics in sea ice fast measurements of ice electrical resistance and an electromagnetic emission (EME) from cracks were used. The sample dimensions ranged from 0.05 to 30 meters. In a laboratory grown fresh water ice crack velocities varied from a few hundreds to a thousand meters per second while in the natural sea ice crack velocity was very low, about 10 m/s. This remarkable difference in the crack velocities is likely due to the dynamic resistance of unfrozen water in brine pockets and channels and to the high ductility of sea ice. It was found that the cracks propagate in ice discontinuously owing to the strong interaction with such microstructural elements as liquid inclusions and grain boundaries. The high sensitivity of the method allowed to detect nucleation of very first microcracks.

Two aspects of fast cracks are considered: 1. the terminal velocity, and corresponding relative kinetic energy; 2. the grain size dependence of the fracture. It is argued that this is determined by the kinetic energies of cracks when they have expanded enough to reach the boundaries of the grains in which they lie. This is more consistent with the observed facts than the more usual quasi-static models.

By considering the limiting conditions at the very tip of a moving crack, many complications are avoided in calculating the terminal velocity. The maximum transverse acceleration of material is limited by the maximum stress (cohesive) that can be applied. The resulting terminal velocity is: 0.4 vs, where vs is the longitudinal sound speed; compared with measured values which average about: 0.31 vs.

In polycrystals, microcracks are found when the applied stress exceeds the yield stress. However, the microcracks do not propagate in fine-grained specimens because they do not have enough kinetic energy to cross a typical grain boundary. This leads to the observed dependence of the fracture stress on the grain size.

Atomic transport properties in rapidly solidified glassy alloys are not fully understood in spite of much experimental data on the subject. Nevertheless, a thorough understanding of these properties is of fundamental importance when studying the practical limits of the application of rapidly solidified glassy alloys.

Several attempts are made in this paper to explain our experimental results on the mechanical flow properties near the transition temperature, Tr. These results are interpreted in the context of possible operating mechanisms such as diffusion and/or relaxation processes. Some inferences have been made on the nature of viscosity and its fluctuation near the transition temperature. The linear temperature dependence of the viscosity near the transition temperature is explained by invoking the free-volume concept for the viscosity of the glassy alloys.

These results are used to provide appropriate data for the selection of feasible processing paths which will produce alloys with advanced thermomechanical properties.

The present investigation explores the use of nitride precipitates for grain-size stabilization in a 18Cr-2ONi austenitic stainless steel for high temperature applications in oxidizing atmospheres. The potential for reductions in alloying contents of such steels has become a focus of research out of concern for the conservation of strategic alloying elements such as Cr. In order for the alloy to maintain superior oxidation resistance, it must sustain a fine grain size by virtue of effective grain boundary pinning by stable precipitates.

Al and Ti microalloyed 18Cr-20Ni steels have been nitrided using rapid solidification processing (spray forming) and subjected to thermomechanical treatments to precipitate nitrides from the supersaturated solid solutions. The spray formed deposits were cold rolled to increase the density of dislocations, which act as sites for nucleation of nitride precipitates. The alloys were then annealed to nucleate and grow the precipitates, followed by cold rolling and recrystallization to generate a stable, fine grained microstructure. The Ti-microalloyed steel demonstrated high-temperature grain size stability by maintaining a grain size of≈7μm after 600h at 1000°C.

The Ti-microalloyed steel has been subjected to isothermal oxidation in air at 900°C. The results of preliminary oxidation experiments are reported. The spray deposited and thermomechanically processed alloy demonstrated high-temperature oxidation behavior superior to conventionally processed (hot rolled and annealed) alloys.

Effects of antiphase domain (APD) size and inter-twin spacing on the hardness of CuAu I-phase in the overaging stage were investigated by hardness testing, transmission electron microscopy, and X-ray powder diffraction. Overaging in CuAu I-phase upon progressive ordering at 300°C was found to proceed through three stages: stages I through III. In the stage I, twinning actively occurred, and most of the coherency strains were removed. Average inter-twin spacing slightly increased. These microstructural evolutions slightly decreased the hardness of the alloy. In the stage II, both APD size and average inter-twin spacing grew larger with time, leading to a continuous decrease in hardness. In the stage III, the APD size markedly grew larger, while the growth rate of average inter-twin spacing markedly slowed down. The continuous growth of APD size apparently contributed to the further decrease in hardness. Although the crystal structure changes during the CuAu I ordering, a perfectly ordered alloy with no planar defects was suggested to be not so strong as the corresponding disordered alloy.

Materials can have distributions of grain sizes. These distributions can have effects on the material's mechanical properties that are more complicated than an average grain-size dependence. The omission of distribution effects on properties is understandable in view of the great amount of labor required in the experimental measurement of grain volume distribution, together with the predominantly two-dimensional nature of micrography-based grain-size estimation. Ultrasonic techniques have been used to nondestructively measure the grain size of materials on a scale of microns. We suggest using ultrasonic attenuation as an alternative to micrography for three reasons. One advantage is that the ultrasonic dependence on size is a true, three-dimensional dependence. Secondly, through careful selection of wavelength, various grain-size distribution parameters can be extracted. The third justification is that ultrasonic techniques are quick and nondestructive. Previous theoretical development will be reviewed, and the experimental verification will be presented. Through numerical modeling we show the advantages of using ultrasonic techniques that are sensitive to grain-size distribution parameters. We demonstrate that samples with equal average grain size but different grain-size distributions have significantly different attenuation wavelength dependencies.

The mechanical behavior of explosives subjected to high acceleration (high g) has been studied in an ultracentrifuge. The experiments reported here reveal new information on the mechanical behavior of such materials and the influence of grain size on the fracture process. Through measurement and analysis of fracture surfaces, we have found that predominately intergranular failure occurs when the shear or tensile strength of the explosive is exceeded. We have found that the mechanical strength of melt-cast polycrystalline TNT varies inversely with crystal size. That is, if the sample consists of large, homogeneous crystals, these are found to separate from the sample at lower g-levels due to the larger mass-to-binding surface area ratio of the crystals. Conversely, smaller original crystallites are found to separate at higher g-levets due to the smaller mass-to-binding surface area ratio. Our results show that single crystals of TNT fracture under a higher g-level at crystal defects. We have also found that the fracture acceleration of Octol decreases with increasing percent TNT and decreasing percent HMX. Hexanitrostilbene (HNS) has been shown by other investigators to be an effective additive to prevent growth of large TNT grains. We have found that the fracture acceleration increases when HNS is added to Octol.

Dispersion strengthening of the most wear-resistant soft magnetic alloy Sendust (Fe-9.5 wt.%Si -5.5 wt.% Al, HV=5000 MPa) by carbide and boride phases allowed to increase its wear-resistance by a factor of 2 to 3. Hardness of the dispersion strengthened alloys is HV=5500–6250 MPa. The changes in grain size, ordering and hardness of the Sendust and two dispersion strengthened alloys have been studied after spinning and various regimes of laser melting. Both types of rapid solidification caused a significant decrease of both the solid solution grain size and the size of carbide and boride phases. While spinning only significantly decreased the amount of ordered Fe3(Si,Al) phase in all the alloys, laser melting completely suppressed the ordering. The hardness of the boride strengthened alloy increased up to 7550 MPa after laser melting.

Nickel and iron ultraflne powders have been produced by the method of hydrogen reduction of the low-water hydroxides obtained by geterogeneous interaction between solid salt and alkaline solution. Suggested method allows to obtain ultrafine powders with narrow particle size distribution and low impurity contents. Bulk samples based on nickel and iron ultrafine powders were produced by hot Isostatic pressing and high-temperature gas extrusion methods.

The dependence of the twinning stress on grain size is similar to the dependence of the athermal part of the flow stress on grain size. Previous numerical simulations included a twinning effect based upon the premise that twinning refines the grain size and gives additional Hall-Petch strengthening. If a grain reaches the stress level given by σT = σT0+ kT ∓-1/2, it is considered twinned and a constant increment is added to the flow stress. Once twinned, the new twinning threshold stress is much higher than the original and so further twinning is unlikely to occur. The twinning model used in this work is based on the idea that enough twinning will occur in a grain to accommodate the excess by which the Von Mises equivalent stress exceeds the twinning threshold stress. The previous twinning model required knowledge of the number of twins per grain produced. With this model, the parameters for iron are known a priori (σT0 = 330 MPa and kT = 2.8 MPa m1/2) and numerical simulations of Taylor cylinder impacts produced good agreement with experimental results. For titanium and zirconium, σT0 and kT were determined by matching the computed and experimental shapes. The results here indicate that twinning hardens these metals by effectively changing the material grain size and the microstructure within the grains.