Effect of grain size on mechanical properties of nanocrystalline materials

The possibility of a dislocation mechanism in the deformation process of nanocrystalline materials is reviewed and analyzed. The present theoretical calculation, by taking the anisotropic characteristic of crystallographic symmetry and different choices of critical shear strength into account, results in a reasonable limit in grain size for applying dislocation pile-up theory to nanocrystalline materials. The deviation from the Hall—Petch relationship is rationalized in terms of a small number dislocation pile-up mechanism. A composite model is proposed to evaluate the strength of nanocrystalline materials. It is shown that this model can be used for interpreting the various cases observed in Hall—Petch studies. An analytical expression for assessing the creep rate of nanocrystalline materials by a diffusion mechanism, including triple line diffusion, is derived. It is predicted that the creep rate due to triple line diffusion will exhibit a stronger grain size dependence than that due to grain boundary diffusion.     

The effect of grain size and strain rate on the

The substructural developments taking place in nickel 200 with grain diameters of 47, 108, 141, and 274 μm have been studied at four different strain rates of 0.01, 0.25, 2.5, and 5/min during tensile testing at room temperature. The percent strain necessary to develop well-defined cell boundaries increases with an increase in grain size at a given strain rate. The cell size refinement takes place throughout the entire range of percent strains (up to 30 pct) in tension for the nickel samples with grain diameters of 47, 108, and 141 μm at all four strain rates used in this article. However, nickel, with the largest grain diameter of 274 μm, shows refinement and then sat- uration for tensile strains greater than 25 pct. The cell size strengthening described by the mod- ified Hall-Petch (MHP) equation at the selected four strain rates of this article indicates that the flow stress is higher for smaller grain size samples at a given cell size. The effect of strain rate on the slope from the MHP plots is such that even though it does not change with an increase in strain rate up to 0.25/min for the four grain sizes, the actual value of the slope decreases with an increase in grain size at a given strain rate. Beyond this strain rate, even though an increase in the slope value as a function of strain rate has been observed for all four grain diameter samples, the influence of grain size on the slope of the MHP plots is so small that it can be assumed that they may become grain size independent at extremely high strain rates. JYOTHI G. RAO, formerly Graduate Student, JYOTHI G. RAO, formerly Graduate Student, JYOTHI G. RAO, formerly Graduate Student,     

Thermal expansion behaviors in nanocrystalline materials with a wide grain size range

Thermal expansion behaviors of nanocrystalline (NC) Ni-P alloy samples with grain sizes ranging from a few to 127 nm were studied experimentally using thermal mechanical analysis. Porosity-free NC Ni-P samples with a wide grain size range were synthesized by completely crystallizing amorphous Ni-P alloy at different annealing temperatures. Measurements showed that the linear thermal expansion coefficient (α_L) increases markedly with a reduction of the average grain size in the as-crystallized NC Ni-P samples. The thermal expansion coefficient was also found to decrease during grain growth in the as-crystallized NC sample upon annealing. From the grain size dependence of α_L in these NC samples, we deduced that the difference in thermal expansion coefficients between the interfaces and the nm-sized crystallites diminishes when the grain size becomes smaller. This tendency agrees well with other experimental results on the structural characteristics of the interfaces and the nm-sized crystallites in NC materials.     

Effect of grain size on high strain rate deformation of copper

Experiments were performed to observe the deformation characteristics of oxygen-free high-conductivity (OFHC) copper at high strain rates (up to 40,000 s⁻¹) and to relate differenc in grain size with differences in deformation behavior. The rod impact and torsional Hopkinson bar test methods were used in these experiments. Results show that grain size reductions substantially reduce surface irregularities that develop during deformation. The effect of grain size on the yield stress and on the strain-hardening behavior of copper is small and is similar to the effect of grain size in copper at quasistatic strain rates. The observation that grain size has a substantial effect on surface irregularities may have important implications for applications in which stable deformation of thin sections is of concern.     

On the analysis of grain size in bulk nanocrystalline materials via x-ray diffraction

The Warren-Averbach (WA) analysis and other simplified methods that are commonly used to determine the grain size of nanocrystalline materials are discussed in terms of accuracy and applicabilities. The nanocrystalline materials used in the present study are prepared by cryomilling of A1 powders and subsequent consolidation (hot isostatic pressing and extrusion). Transmission electron microscopy observations of the as-extruded nanocrystalline A1 reveal a bimodal distribution of grain sizes centered around 50 to 100 nm and 250 to 300 nm. It is shown that the grain size determined by the WA analysis agrees with the lower bound grain size (e.g., 50 to 100 nm) observed experimentally. In the case of the integral method, it is useful to use a parabolic (Cauchy-Gaussian (CG)) relationship to approximate instrumental broadening and separate the intrinsic broadening. Compared to the Cauchy-Cauchy (CC) and Gaussian-Gaussian (GG) approximations, this is shown to give the best results. In addition, the reliability of the Scherrer equation is also discussed.     

The role of grain size and strain in work hardening and texture development

Polycrystalline copper (99.999 pct) having four different grain sizes (from 4 to 220 μm) was strained in tension at room temperature to true plastic strains of 0.05, 0.10, 0.20, and 0.30. The initial texture of the materials was determined by neutron diffraction, as were the deformation textures. Both inverse pole figures and calculated TaylorM factors were then derived from the data. In general, it was observed that the texture strengthens at increasing strain and that the effect of grain size on this development is not very pronounced. The measured change in the volume concentration of the (111) texture component was compared to that obtained from a model simulation, and in general, the experiments and the simulations agreed well. The effect on the flow stress of the initial texture, and on the texture which develops during straining, could be accounted for on the basis of TaylorM factors calculated from the experimental results, and it was found that there is an effect of texture on the flow stress. The flow stress at strains above yield, expressed as a modified Hall-Petch relationship, was not greatly affected by corrections toM induced by strain and grain size.     

Mechanical properties, ductility, and grain size of nanocrystalline iron produced by mechanical attrition

The main goal of this investigation is to determine the influence of grain size on the mechanical properties and, specifically, the intrinsic ductility of nanocrystalline (nc) Fe. Ball-milled nc Fe was consolidated into compacts of near theoretical density by uniaxial warm pressing. Compaction parameters and annealing treatments resulted in a range of grain sizes for subsequent mechanical testing. The miniaturized disk bend test, hardness, and the automated ball indentation (ABI) method were used to test nanocrystal (nc) iron in compression and tension. The deformation and fracture morphologies of the tested samples were characterized by light and scanning electron microscopy. The hardness, as a function of the grain size, was described with a Hall-Petch slope, which was smaller than that in coarse-grained Fe. In tension, the material failed in a macroscopically brittle manner, while local ductility in very concentrated shear bands was observed. The compressive characteristics of the nc Fe were similar to those of a perfectly plastic material. The results are discussed in the context of the mechanical behavior of coarse-grained polycrystalline metals and alloys. This article is based on a presentation made in the symposium “Mechanical Behavior of Bulk Nanocrystalline Solids,” presented at the 1997 Fall TMS Meeting and Materials Week, September 14–18, 1997, in Indianapolis, Indiana, under the auspices of the Mechanical Metallurgy (SMD), Powder Materials (MDMD), and Chemistry and Physics of Materials (EMPMD/SMD) Committees.     

The effect of grain size and plastic strain on slip length in 70-30 brass

Polycrystalline 70−30 brass of varying grain size has been studied. Measurements were made of slip line lengths on the polished surface of specimens which had undergone different plastic strains. A relation between the slip line length and the grain size and plastic strain was found based on experimental data using a multiple regression technique. Qualitative agreement was found between the observed slip lengths and slip lengths calculated from a published work-hardening model. The effect of the boundary on slip behavior was observed, and both passive and active types of obstruction to slip by boundaries are suggested. H. DONG, formerly with Carnegie-Mellon University, is now with Jilin Institute of Engineering, Changchun, China. A. W. THOMPSON     

Bulk strain and grain strain in axisymmetric deformation

Bulk strain, defined in terms of original and final dimensions of a specimen, correlates well with the logarithm of the average number of intercepts per unit length on test lines parallel to axes of symmetry after uniaxial deformation of an axisymmetric specimen. This suggests a definition of principal grain strain based on the mean linear intercepts before and after deformation, measured along principal directions. Results of type 304 stainless steel strained to varying amounts between necking and fracture support the hypothesis that the axial gradient of the total grain boundary area projected onto any cylindrical surface coaxial with the axis of deformation remains unchanged as deformation progresses. Although the behavior of the grain boundary network leads to simple correspondences between grain and bulk strains, they are not numerically equal for this type of deformation.     

The combined effect of grain size and strain rate on the dislocation substructures and mechanical properties in pure aluminum

The effect of grain size on the development of dislocation substructures has been studied as a function of strain rate. Pure aluminum rods with grain diameters of 70, 278, and 400 μm were deformed in tension at room temperature to various percent strains at strain rates of 0.01, 0.25, 2.5, and 5/min. It has been confirmed that the smaller grain size results in higher flow stress in this strain-rate range. The cell size strengthening described by the modified Hall-Petch (MHP) equation is applicable to samples with 70 and 278 μm grain sizes at all four strain rates used in this study, while 400 μm grain sizes show deviation from this because of inhomogeneities developed in the microstructure. The influence of strain rate on the slope of the MHP plots, for a grain size of 70 μm, is such that at lower strain rates, the slope does not change much, but at higher strain rates, there is an increase in the slope value. At all strain rates, the values of slopes from the MHP plots of the smaller grains are higher than for the larger grains.