Hall-Petch Type Research Articles

Microstructural Evaluation of Friction Stir Processed AZ31B-H24 Magnesium Alloy

The microstructural characteristics in an AZ31B-H24 magnesium alloy after friction stir processing (FSP) were examined. The effects of FSP parameters including forge force and traverse speed on the microstructure were evaluated. It was observed that the grain size increased from about 4 μm in the base metal to about 8 μm at the centre of the stir zone after FSP. The aspect ratio of the grains decreased towards the centre of the stir zone. The changes in the grain size and shape resulted in a drop in micro-indentation hardness from 75 HV in the base metal to about 55 HV at the centre of the stir zone. Increasing the forge force or decreasing the traverse speed increased the grain size due to a greater heat input. It was also observed that the annealing effects (recrystallization and subsequent softening) of FSP were less pronounced with increasing distance horizontally or vertically from the pin tool due to the presence of temperature gradient. Furthermore, the Hall-Petch type relationships between the microhardness and the grain size were found to be valid after FSP.

Microstructural Evaluation of Friction Stir Processed AZ31B-H24 Magnesium Alloy

The microstructural characteristics in an AZ31B-H24 magnesium alloy after friction stir processing (FSP) were examined. The effects of FSP parameters including forge force and traverse speed on the microstructure were evaluated. It was observed that the grain size increased from about 4 μm in the base metal to about 8 μm at the centre of the stir zone after FSP. The aspect ratio of the grains decreased towards the centre of the stir zone. The changes in the grain size and shape resulted in a drop in micro-indentation hardness from 75 HV in the base metal to about 55 HV at the centre of the stir zone. Increasing the forge force or decreasing the traverse speed increased the grain size due to a greater heat input. It was also observed that the annealing effects (recrystallization and subsequent softening) of FSP were less pronounced with increasing distance horizontally or vertically from the pin tool due to the presence of temperature gradient. Furthermore, the Hall-Petch type relationships between the microhardness and the grain size were found to be valid after FSP.

A multiscale approach to damage configurational forces

A two-scale homogenization method is used to construct a damage model in the framework of configurational mechanics. The upscaling procedure allows for the identification of damage configurational forces as the result of the microscopic fracture analysis. The obtained damage equation incorporates stiffness degradation, material softening, unilaterality, induced anisotropy. The balance of configurational forces naturally captures a microscopic length, leading to size effects in the overall damage response. The new approach is illustrated in the case of brittle damage, for a three point bending test. Extended finite elements are used for the numerical modeling of macro-crack initiation and growth. The influence of the microscopic size on the failure initiation stress is analyzed and it is shown that this dependence follows a Hall–Petch type rule.

Discrete dislocation plasticity analysis of the grain size dependence of the flow strength of polycrystals

The grain size dependence of the flow strength of polycrystals is analyzed using plane strain, discrete dislocation plasticity. Dislocations are modeled as line singularities in a linear elastic solid and plasticity occurs through the collective motion of large numbers of dislocations. Constitutive rules are used to model lattice resistance to dislocation motion, as well as dislocation nucleation, dislocation annihilation and the interaction with obstacles. The materials analyzed consist of micron scale grains having either one or three slip systems and two types of grain arrangements: either a checker-board pattern or randomly dispersed with a specified volume fraction. Calculations are carried out for materials with either a high density of dislocation sources or a low density of dislocation sources. In all cases, the grain boundaries are taken to be impenetrable to dislocations. A Hall–Petch type relation is predicted with Hall–Petch exponents ranging from ≈0.3 to ≈1.6 depending on the number of slip systems, the grain arrangement, the dislocation source density and the range of grain sizes to which a Hall–Petch expression is fit. The grain size dependence of the flow strength is obtained even when no slip incompatibility exists between grains suggesting that slip blocking/transmission governs the Hall–Petch effect in the simulations.

Sub-structure strengthening and work hardening of an ultra-fine grained aluminium–magnesium alloy

The mechanical properties of an Al–Mg1 alloy, processed to obtain grain sizes in the range from less than a micrometer to relatively coarse sizes, have been investigated by tensile and compression testing. A characteristic feature of the stress–strain curves of fine-grained Al–Mg-alloys is a sharp yield point followed by Lüders-band elongation. The flow stress at each given strain level followed a Hall–Petch type grain size dependence. However, the slope of the Hall–Petch curve is larger at the yield point than at strains beyond the yield-point elongation. The compression testing revealed a new phenomenon, namely that the range of stage-III deformation decreased with decreasing grain size, and disappeared completely for a grain size of about 0.5 μm.

A size-dependent crystal plasticity finite-element model for creep and load shedding in polycrystalline titanium alloys

A rate-dependent anisotropic elastic-crystal plasticity based finite-element (FE) model with size-dependent yield strength is developed for polycrystalline Ti-6242. The initial slip system deformation resistances in the crystal plasticity relations are expressed as Hall–Petch type relations, where the grain size, lath size and colony size are chosen as characteristic lengths depending on the nature of slip. The FE model incorporates accurate phase volume fractions and orientation distributions that are statistically equivalent to those observed in orientation imaging microscopy (OIM) maps of the microstructure. The model is validated with experimental results on constant strain rate and creep tests. A relationship between the macroscopic flow stress and grain size and lath size for two-phase Ti-6242 is proposed. The effect of grain morphology on creep-induced load shedding and localization is discussed.

Microstructure and tensile properties of friction stir welded AZ31B magnesium alloy

The microstructural change in AZ31B-H24 magnesium (Mg) alloy after friction stir welding (FSW) was examined. The effects of tool rotational speed and welding speed on the microstructure and tensile properties were evaluated. The grain size was observed to increase after FSW, resulting in a drop of microhardness across the welded region from about 70 HV in the base metal to about 50 HV at the center of the stir zone. The obtained Hall–Petch type relationship showed a strong grain size dependence of the hardness. The aspect ratio and fractal dimension of the grains decreased towards the center of the stir zone. The welding speed had a significant effect on the microstructure, with larger grains at a lower welding speed. The yield strength and ultimate tensile strength increased with increasing welding speed due to a lower heat input. A lower rotational speed of 500 rpm led to higher yield strength than a higher rotational speed of 1000 rpm. The friction stir welded joints were observed to fail mostly at the boundary between the weld nugget and thermomechanically affected zone at the advancing side. Fracture surfaces showed a mixture of cleavage-like and dimple-like characteristics.

Discrete dislocation simulation of nanoindentation: Indentation size effect and the influence of slip band orientation

Nanoindentation is modelled on the computer by means of a simple two-dimensional discrete dislocation model in order to study the influence of the orientation of predefined slip bands on certain phenomena, which often occur during real indentation experiments, systematically. By assuming single slip, different simulations were performed, which show that the increase of the hardness with decreasing indentation depth, known as the indentation size effect, is significantly influenced by the slip band orientation in such a model. Compared to a case where the slip bands are oriented parallel to the surface, a less pronounced decrease of the hardness with increasing indentation depth is observed for the non-parallel slip band orientation. The value at which the hardness remains constant independent of the indentation depth is also significantly affected by these assumptions. Possible reasons for the origin of the different effects, which can partly be attributed to the discrete nature of plasticity, apparent in the nanometer regime, and Hall–Petch type mechanism, will be discussed.

Interfaces within strain gradient plasticity: Theory and experiments

In this paper, it is shown that the occurrence of dislocation pileups across grain boundaries, as well as subsequent emission to the adjacent grains, is captured theoretically by gradient plasticity and confirmed experimentally by nanoindentation. From a theoretical point of view, this is accomplished (within a deformation theory framework applicable to continued loading) by accounting for a specific interfacial term in the overall potential of the material, in terms of which its response, taken to conform to strain gradient plasticity, is defined. The main features that result from the addition of this interfacial term are (i) significant size effects of Hall–Petch type in the overall stress–strain response of polycrystals and (ii) the determination of an analytical expression for the stress corresponding to the onset of dislocation transfer across interfaces. From an experimental point of view, the effective stress at which dislocation transfer takes place across an interface can be obtained from nanoindentations performed in close proximity to an Fe–2.2 wt.% Si grain boundary, since they exhibit a distinct strain burst that is related to the presence of the boundary. It is possible, therefore, to fit the theoretically determined analytical expression for the interfacial yield stress to the experimental data. From this fit, first estimates are obtained for key material parameters, namely the interfacial term and the internal length, that are required for the theoretical formulation. Dislocation mechanics are employed to provide physical insight of these parameters.

An experimental assessment of grain size effects in the uniaxial straining of thin Al sheet with a few grains across the thickness

The mechanical behaviour under uniaxial tension of polycrystalline 99.999 at.% Al sheet with a thickness of a single or a few crystallites is investigated experimentally. The specimens are cold rolled to a thickness ( t) of 100 up to 340 μm and the grain size ( d) is varied by recrystallisation between 75 and 480 μm. All specimens have a similar texture and a regular grain structure. For t/ d < 1 the flow stress varies only slightly with t/ d, independently of t or d itself. For 1 < t/ d < 3, a strong increase in the flow stress is observed. The main explanation for this different behaviour in tension, stems from the grain boundaries parallel to the specimen surface, impacting the deformation and rotation of the grains. Furthermore, it is shown that a single Hall–Petch type relation does not apply to these kinds of specimen. Extrapolations towards specimens with columnar grains are made through the analysis.

Scale effects induced by strain-gradient plasticity and interfacial resistance in periodic and randomly heterogeneous media

A recently introduced variational formulation for strain-gradient plasticity with an additional potential that penalises the build-up of plastic strain at interfaces is summarised and applied to some one-dimensional examples. Novel features include a new strict upper bound for the effective potential of a single nonlinear medium containing interfaces distributed according to a Poisson process and approximate mean stress versus mean plastic strain curves for media with two power-law nonlinear phases separated by interfaces with their own nonlinear potential. Two-phase media with periodic and random microstructure are considered. In the case of random media, the results depend on the statistics of points, taken two at a time, in the combinations medium–medium, medium–interface, and interface–interface. In every case, the effective relation displays a Hall–Petch type of effect, the effective response becoming stiffer as the scale of the microstructure is refined. The admission of the interfacial potential removes a limitation of earlier work, that the response could not exceed the “Voigt” or “Taylor” bound of the corresponding classical material.

Dislocation pile-ups: From {1 1 0} cracking in MgO to model strength evaluations

The researches of Professor J.C.M. Li and his colleagues and students have been involved with dislocation pile-up descriptions in a number of ways: beginning from the interpretation of microindentation experiments on MgO single crystals, then carrying over to tabulation of various pile-up characteristics including those for dislocation loops expanding against the grain boundary resistance, and, lastly, interpreting grain size dependent material strength properties. The pioneering work is related here to accumulated pile-up results and Hall–Petch type interpretations also extending downwards in scale to nanocrystalline grain size materials.

Nanocrystalline aluminum and iron: Mechanical behavior at quasi-static and high strain rates, and constitutive modeling

The responses of nanocrystalline aluminum powder of different grain sizes, prepared by ball milling and consolidated into bulk specimens by hot pressing, were determined under quasi-static and dynamic compression. The experiments demonstrated that the reduction in grain size resulted in several-fold increase in hardness and strength; the responses of nanocrystalline aluminum was found to be strain-rate-dependent. Using these measurements, Khan, Huang and Liang (KHL) viscoplastic model was modified by including a bi-linear Hall–Petch type relation to correlate with the response of nanocrystalline aluminum, including the variation of work hardening with grain size. The modified constitutive equation gives results very close to the experimental observations on nanocrystalline aluminum. In addition, the response of nanocrystalline iron, previously published, was also correlated with proposed model. Both correlations of strain-rate-dependent responses for different grain sizes were in good agreement with the experimental results over a wide range of grain sizes (micrometer to nanometer) and strain rates.

Nanocrystalline growth and grain-size effects in Au–Cu electrodeposits

The processing–structure–property relationship is investigated for electrodeposited foils of the gold–copper alloy system. A model is presented that relates the deposition process parameters to the nanocrystalline grain size. An activation energy of 1.52 eV atom − 1 for growth is determined for a long-pulse (> 10 msec) mode, and is 0.16 eV atom − 1 for short pulses (< 5 msec). The effect of nanocrystalline grain size on the mechanical properties is assessed using indentation measurements. A Hall–Petch type variation of the Vickers microhardness with nanocrystalline grain size (> 6 nm) is observed for Au–Cu samples with 1–12 wt.% Cu as tested in cross-section. The hardness increases three-fold from a rule-of-mixtures value < 1 GPa to a maximum of 2.9 GPa.

The effect of microstructural characteristics of pearlite on the mechanical properties of hypereutectoid steel

The relationship between mechanical properties and microstructural characteristics of pearlite was investigated using various heat treatments on a hypereutectoid steel. The materials were reheated between 900 and 1200 °C and these microstructures were then subjected to isothermal transformation at temperatures of 550, 580 and 620 °C. For the hypereutectoid steel, the mean value of the interlamellar spacing was observed to increase with increasing reheat and transformation temperatures. Examination of the mechanical properties of the resulting pearlitic microstructures indicated that the strength was related primarily to the interlamellar spacing by a Hall–Petch type relationship, while the ductility was dependent also on the prior-austenite grain size and pearlite colony size.

Effect of WC/TiC grain size ratio on microstructure and mechanical properties of WC–TiC–Co cemented carbides

Microstructure and mechanical properties of WC–TiC–10 wt%Co cemented carbides fabricated by sintering with hot isostatic pressing (Sinter-HIP) process were investigated. The WC/TiC grain size ratio of WC–TiC–10 wt%Co cemented carbides was controlled by changing the average size of WC powders ranged from 0.5 to 4 μm, with keeping the average size of TiC powder as 1 μm. The microstructures of sintered WC–TiC–10 wt%Co cemented carbides were sensitively dependent on the WC/TiC grain size ratio. In WC–TiC–10 wt%Co cemented carbides with WC/TiC grain size ratio of 0.5, the TiC/(Ti, W)C core-rim phases were distributed in WC/Co matrix. While, in WC–TiC–10 wt%Co cemented carbides with WC/TiC grain size ratio above 0.8, the WC and TiC/(Ti, W)C core-rim phases were surrounded by Co binder phase. Hardness of WC–TiC–10 wt%Co cemented carbide increased with decreasing the WC/TiC grain size ratio from 4 to 0.8 following the modified Hall–Petch type equation. However, the hardness of WC–TiC–10 wt%Co cemented carbides with WC/TiC grain size ratio of 0.5 shows much higher values than that expected by modified Hall–Petch type equation. Transverse rupture strength of WC–20TiC–10 wt%Co cemented carbides increases with decreasing the WC/TiC grain size ratio.

Two hardening mechanisms in single crystal thin films studied by discrete dislocation plasticity

Two-dimensional discrete dislocation plasticity simulations of the evolution of thermal stress in single crystal thin films on a rigid substrate are used to study size effects. The relation between the residual stress and the dislocation structure in the films after cooling is analyzed using dislocation dynamics. A boundary layer characterized by a high stress gradient and a high dislocation density is found close to the impenetrable film-substrate interface. There is a material-dependent threshold film thickness above which the dislocation density together with the boundary layer thickness and stress state are independent of film thickness. In such films the stress outside the boundary layer is on average very low, so that the film-thickness-independent boundary layer is responsible for the size effect. A larger size effect is found for films thinner than the threshold thickness. The origin of this size effect stems from nucleation activity being hindered by the geometrical constraint of the small film thickness, so that by decreasing film thickness, the dislocation density decreases while the stress in the film increases. The size dependence is only described by a Hall–Petch type relation for films thicker than the threshold value.

Hardness and fracture toughness of ultra-fine WC-10Co-X cemented carbides prepared from nanocrystalline powders

Abstract Microstructure and mechanical properties of ultra-fine WC-10Co-X cemented carbides were investigated. Nanocrystalline WC-10Co-X powders with an average WC size of 100 nm were prepared by spray drying of solution containing ammonium metatungstate and cobalt nitrate. Varying amounts of TaC, Cr3C2 and VC were added into ultra-fine WC-10Co cemented carbides as grain growth inhibitors. The hardness of WC-10Co cemented carbides increased with decreasing WC grain size following the Hall–Petch-type relationship. The fracture toughness of ultra-fine WC-10Co fabricated by the spray conversion process was lower than that of conventional WC-10Co. These differences in fracture toughness arose from solute content in the Co binder phase. The fracture toughness of WC-10Co-X cemented carbides with the same solute content in the Co binder phase varied with WC grain size and Co mean free path.

A study of microstructural length scale effects on the behaviour of FCC polycrystals using strain gradient concepts

Grain size is a critically important aspect of polycrystalline materials and experimental observations on Cu and Al polycrystals have shown that a Hall–Petch-type phenomenon does exist at the onset of plastic deformation. In this work, a parametric study is conducted to investigate the effect of microstructural and deformation-related length scales on the behaviour of such FCC polycrystals. It relies on a recently proposed non-local dislocation-mechanics based crystallographic theory to describe the evolution of dislocation mean spacings within each grain, and on finite element techniques to incorporate explicitly grain interaction effects. Polycrystals are modeled as representative volume elements (RVEs) containing up to 64 randomly oriented grains. Predictions obtained from RVEs of Cu polycrystals with different grain sizes are shown to be consistent with experimental data. Furthermore, mesh sensitivity studies revealed that, when there is a predominance of geometrically necessary dislocations relative to statistically stored dislocations, the polycrystal response becomes increasingly mesh sensitive. This was found to occur especially during the early stages of deformation in polycrystals with small grains.

Effect of growth rate and lamellar spacing on microhardness in the directionally solidified Pb-Cd, Sn-Zn and Bi-Cd eutectic alloys

Lead-cadmium, Zinc-tin and Bismuth-cadmium of (99.99%) high purity eutectic alloys were melted in a graphite crucible under vacuum atmosphere. These eutectic alloys were directionally solidified upward with a constant temperature gradient G and different growth rates V in the Bridgman type directional solidification furnace. The lamellar spacings λ and microhardness H V were measured from both transverse section and longitudinal section of the specimen. The variations of H V with respect to V and λ have been determined by using the linear regression analysis method. H V values increase with the increasing values of V and decrease with the increasing λ values. The Hall-petch type relationships obtained in this work have been compared with the previous works.