Petch Relationship Research Articles

Maintain sort order of grain boundary to investigate the deformation mechanism of CoCuFeNiPd high–entropy alloys

Molecular dynamics simulations of tension tests on CoCuFeNiPd high–entropy alloys (HEAs) are performed to study the effects of grain sizes (d), temperatures, and strain rates on the mechanical properties. After a series of tension simulations with different grain sizes, the Hall – Petch (H–P) and inverse Hall – Petch relationships are discovered. Hall–Petch breakdown is observed at grain size (d) of 10 nm. In the inverse Hall – Petch region, the average flow stress (σ(ε)) decreases from 1.97 to 1.76 (GPa) when grain size is decreased from 10 nm to 4 nm. On the contrary, the average flow stress increased from 1.90 to 1.97 (GPa) as d reduced from 18 nm to 10 nm. The microstructural evolution of the CoCuFeNiPd HEAs model exhibits that the primary deformation process in the H–P relation (d > 10 nm) is dislocation slips. The grain boundaries (GB) prevent dislocation expansion in the H– P relation, causing mechanical strengthening. Meanwhile, the main deformation mechanisms for the inverse H–P (d < 10 nm) are grain rotation and GB migration, decreasing flow stress. In addition, Young's modulus of the HEAs model increases with grain size (d). The yield strength, flow stress, and Young's modulus of HEAs specimens tend to reduce at high temperatures. Additionally, the number dislocation length reduces at high temperatures due to the amorphization phenomenon. The results also showed that Young's modulus and yield strength increase when strain rates rise.

Effect of grain size and temperature on deformation mechanism of commercially pure titanium

To investigate the effects of grain size and processing temperature on the deformation behaviors of commercially pure titanium (CP-Ti), the tensile tests were conducted at room temperature (RT) and liquid nitrogen temperature (LNT) on the samples with the average grain size of 2, 9, 23, and 51 μm, respectively. The experimental results based on EBSD and TEM characterizations showed that dislocation slip was the main deformation mechanism at RT, while abundant deformation twins including {102} extension twins, {11} compression twins and some {11}−{102} secondary twins were observed under LNT condition. The transition of deformation modes from dislocation slip to dynamic twinning contributes to the outstanding mechanical properties of the samples with a larger grain size at LNT. Additionally, a modified Hall−Petch relationship was proposed to study the quantitative contribution of average grain size and deformation twins on yield stresses of CP-Ti under LNT condition.

Effects of structure and strain rate on deformation mechanism of twin lamellar Al0.3CoCrFeNi alloys

Lamellar twined materials display simultaneous ultrahigh strength and high ductility, which is attributed to the interaction between twin boundaries and dislocation. However, deformation at the atomic level is rarely seen in experiments. To study the deformation properties and mechanical behavior of the lamellar twined Al0.3CoCrFeNi high-entropy alloys (HEA) sample, we applied the uniaxial tension by employing molecular dynamics (MD) simulations. The impact of various twin inclination angles, twin boundary spacing (TBS), and strain rates are investigated. The mechanical softening as the increasing TBS from 4a to 12a was observed, which corresponds to Hall – Petch relationship. The yield strength of the medium inclination angle (450, 600) records the minimum value with all various TBS due to the elastic energy being easier released. The strain-hardening phenomenon appears at these angles. The sample with an inclination angle perpendicular to the tension loading axis (900) displays the highest stress value. The shrinking migration twin has been observed in 00, 150, and 300 twin inclination angles. The migration and disappearance of initial TBs lead to grains being reoriented into the same orientation at 450 and 600. With twin orientations of 750 and 900, the TB is no longer as crisp and straight as the initial TB under the tension process. An extensive dislocation process occurs at higher strain values, and their interaction with TB leads to establishing the shear band. After that, twin boundaries within the shear band are almost destroyed. Besides, the results also indicate that the flow stress, ultimate strength, and Young's modulus rise with the rising strain rate and decreasing temperature.

Dependence of the hardness of WC - Co alloys on the character of the distribution of WC grains in size

The paper presents the results of studying the dependence of the hardness of WC - Co alloy with a Co content of 10 wt.% on the character of the size distribution of WC grains. An equivalent diameter of the circle with an area matching the cross-section area of the grain was chosen as a grain size of the carbide phase. The WC grain sizes were averaged over their number, area and volume. It is shown that for the alloys with a narrow WC grain size distribution the hardness of the alloys as function of the average grain size follows the Hall - Petch relation. As for a wide distribution, a deviation from this function is observed. It is shown that the use of the area-averaged WC grain size enables description of the hardness as a function of the grain size via a unified Hall - Petch equation, regardless of the nature of the grain size distribution. In this case, the average scatter of hardness values around the trend line does not exceed 12 HV. The use of the volume-averaged grain size in description of the hardness dependence results in practice in a large scatter from the regression line, which is attributed to the error in determination of the content of coarse and very coarse grains, when one needs to measure significantly larger number of grains, as compared to averaging over the area. The results obtained may be used in analysis of single-phase and two-phase materials with grain size distributions with a varying width.

Surface hardness of pristine and laser-treated zinc as a function of indentation load and its correlation with crystallite size valued by Williamson-Hall analysis, size-strain plot, Halder-Wagner and Wagner-Aqua models

To get a range of crystallite size, 5 N pure polycrystalline zinc specimens were shined with 50–100 Nd:YAG laser shots. Williamson-Hall, Size-Strain Plot, Halder-Wagner, and Wagner-Aqua models were employed to evaluate the crystallite size and lattice strain of pristine and laser-treated specimens. Surface hardness of the specimens were measured under 0.2 and 0.3 kgf indentation loads for 10 s. In each case, the surface hardness followed inverse Hall – Petch Relation. For a fixed number of laser shots, the surface hardness was greater for 0.2 kgf indentation load than that for 0.3 kgf. The surface hardness of pristine zinc specimen increased on treatment with 50 laser shots. With further rise in laser shots up to 80, the surface hardness progressively decreased close to that of pristine specimen. Later, it again increased for 90 laser shots and then slightly decreased for 100 laser shots.

Influences of grain size, temperature, and strain rate on mechanical properties of Al0.3CoCrFeNi high–entropy alloys

This study investigates the mechanical properties and deformation behaviours of Al0.3CoCrFeNi high-entropy alloys (HEA) under tension tests by using molecular dynamics (MD) simulations. The effect of different grain sizes (d), temperatures, and strain rates are examined. By varying the grain size from 4.0 nm to 20.0 nm, the shift from mechanical softening to strengthening was observed for the simulated samples. The result shows that the critical grain size of the inverse Hall – Petch and Hall – Petch regime is 12.0 nm. The average flow stress varies slightly increases from 3.02 to 3.19 GPa (5.3%) with the decrease of grain size from 20.0 to 12.0 nm in the Hall – Petch relation. While in the inverse Hall – Petch regime, the average flow stress significantly reduces from 3.19 to 2.7 GPa (15.3%) with grain size reducing from 12.0 to 4.0 nm. The migration of grain boundary (GB), and the rotation of grains are the dominant deformation mechanism in the inverse Hall – Petch regime. Meanwhile, in the Hall-Petch region, the dislocation activities are the main contribution to the deformation mechanism of polycrystalline. The GB plays as a barrier to hinder the dislocation propagation. Therefore, in the Hall - Petch regime, the fraction of GB increases as the grain size decreases, resulting in higher barrier densities for samples with small grain sizes and thereby causing the flow stress to increase. The result points out that Young's modulus of the HEA specimen increased with an increase of the average d. In addition, the result also shows that the ultimate stress, flow stress, and Young's modulus increase with rising the strain rate or decreasing the temperature.

Effect of extrusion ratios on hardness, microstructure, and crystal texture anisotropy in pure niobium tubes subjected to hydrostatic extrusion

Nb tubes were fabricated through hydrostatic extrusion at extrusion ratios of 3.1 and 6.1 at ambient temperature, and then their microstructure, texture, and Vickers hardness were investigated based on electron back-scattered diffraction (EBSD) data. The fraction of low-angle boundaries (LABs) largely decreased with a sharp decrease in mean grain sizes after hydrostatic extrusion and was not proportional to extrusion ratios, assuming that mixed-asymmetrical junctions forming LABs dissociate at high extrusion ratios from the external stress (>981 MPa) with thermal activation by the generated heat. The correlation between grain size and Vickers hardness followed the Hall−Petch relationship despite the texture gradient of the 〈111〉 cyclic fiber textural microstructure at low extrusion ratios and the 〈100〉 true fiber textural microstructure at high extrusion ratios. The increase in hydrostatic pressure on the Nb tubes contributed to texture evolution in terms of extrusion ratios due to the difference between {110}〈111〉 and {112}〈111〉 components based on EBSD data.

Size effects and magnetoelastic couplings: a link between Hall–Petch behaviour and coercive field in soft ferromagnetic metals

ABSTRACTSize effects regarding Hall–Petch (HP) relation are studied in this work for cobalt, nickel and Fe–3wt.%Si (FeSi), from polycrystalline to multicrystalline states. The materials show a breakdown in HP plot for thickness (t) to grain size (d) ratio less than a critical value. This appears in the beginning of plasticity for cobalt and FeSi whereas a plastic strain threshold must be overcome for nickel. Measurements of the coercive field on strained samples are able to depict such modification for low t/d ratio. Values of the coercive field in the polycrystalline domain allow an estimation of the magnetocrystalline anisotropy energy, related to the grain volume fraction concerned by reversal mechanisms for magnetic domains. Multicrystalline samples of cobalt and FeSi becomes magnetically softer at the yield stress. This is linked to a delay of the maximum intergranular stress towards higher strains for FeSi. For cobalt, non-linear elasticity and strong basal texture modify the magnetoelastic effects in coarse grain samples. For nickel, size effect on the coercive field appears after a few per cent of plastic strain as for HP relationship. A mean internal stress can be captured by magnetic measurements on polycrystals, related to the intragranular part of the kinematic stress. The softening of the magnetic properties for strained nickel multicrystals is due to a competition between the apparition of dislocation cells, which increases the coercive field by mechanisms of magnetic domain wall pinning, and surface softening of multicrystals, which tends to decrease the value of Hc.

Establishing the microstructure-strengthening correlation in severely deformed surface of titanium

ABSTRACTSurface nanostructuring of engineering materials can be utilised to enhance materials performance for various applications. The aim of this work was to investigate the evolution of microstructure and its correlation with strengthening mechanisms in nanocrystalline commercially pure titanium (cp-Ti) produced by surface mechanical attrition treatment (SMAT). The individual contributions of dislocation slip and twining as the deformation mechanisms during SMAT have been quantified using X-ray line profile analysis and corroborated with transmission electron microscopy and electron backscattered diffraction techniques. It is found that twining is operative only in the early stages of deformation. The absence of twin–twin intersections suggests that twining is not directly responsible for the initial refinement of grain size. Dislocation slip is the major deformation mode, which leads to the refinement of the microstructure by forming low-angle lamellar boundaries. Continuous dynamic recrystallisation is demonstrated to be the mechanism of nanocrystallisation in cp-Ti using detailed microscopic analysis. In contrast to previous studies, which have neglected the contribution of Taylor strengthening, it is observed that a combination of Hall–Petch and Taylor relationships can explain the strength only if separate set of parameters K (Hall–Petch constant) and α (geometrical factor in Taylor relationship) are used for the nanocrystalline surface and severely deformed sub-surface of cp-Ti. Taken together, this work provides new insights into the underlying mechanisms for engineering nanocrystalline materials.

Microstructure and texture of zinc deformed by extrusion with forward-backward rotating die (KoBo)

The KoBo device is a press with a cyclically rotating die enabling extrusion of ingots with the permanent destabilization of their substructure. The method involves a cyclic change of deformation path that increases the plasticity of the material and inhibits formation and propagation of cracks. The possibility of using KoBo for obtaining zinc wires with high mechanical properties was explored. A polycrystalline zinc ingot of purity of 99.995% was subjected to extrusion at room temperature. The microstructure of the material was investigated primarily via high-resolution electron backscatter diffraction using a scanning electron microscope. The microstructure is heterogeneous and consists of grains elongated slightly in the extrusion direction (ED). The material has a relatively sharp nearly axial texture with the ED scattered between the <1 0 -1 0> and <2 -1 -1 0> directions. More than 95% of high-angle grain boundaries do not correspond to any twin or low Σ CSL boundaries. The dimensions of the grains range from 10 - 20 micrometers down to the sub-micron scale. Despite the relatively large grains, the final product exhibits very good mechanical properties, which could not be explained by the Hall - Petch relation. It was found that besides grain refinement two other effects could affect the material mechanical properties. These effects are formation of nanograins inside the large, micrometer-sized grains and formation of broad areas of high-density crystal lattice defects extended along the HAGBs.

On the Roles of Grain Size Dispersion and Microscale Hall&amp;ndash;Petch Relation on the Plastic Behavior of Polycrystalline Metals

Micro-macro scale transition theories were essentially developed to model the inelastic behavior of polycrystals starting from the local behavior of the grains. The anisotropy of the plastic behavior of polycrystalline metals was mainly explained by taking into account the crystallographic textures. Issues like plastic heterogeneities due to grain size dispersion, involving the Hall-Petch relation at the microscale, were not often taken into account in the literature, because only the role of a mean grain size was investigated. Here, the coupled roles of grain orientation and size distributions on the plastic deformation state of grains are examined for a tensile deformed IF steel in the light of EBSD experimental data based on misorientation parameters and of a micromechanics-based modeling regarding grain and overall behaviors.

Residual Stress, Nanohardness, and Microstructure Changes in Whirlwind Milling of GCr15 Steel

Compared to grinding which has low efficiency, serious pollution, and hard turning together with serious tool wear, whirlwind milling (WM) is a more competitive machining process in manufacturing. However, as a technology under development, the complicated mechanism in WM processes has not yet been fully understood. In this paper, surface integrity of a workpiece processed by a computerized numerical control (CNC) WM machine was investigated using a variety of advanced instruments, e.g., Electron Backscatter Diffraction (EBSD), nanoindentation, X-ray diffraction stress analysis, etc. The results show that surface hardening and deep residual compressive stress could be effectively achieved in the WM process. Based on the EBSD analysis and infrared temperature camera, the residual compressive stress was introduced by volume expansion when the phase transformation from austenite to martensite occurred. According to the Hall–Petch (H-P) relationship, it could be concluded that the higher hardness processed by WM is mainly caused by the finer grains, i.e., the average size was 167 × 102 nm2 in the WM zone, which was less than 194 × 102 nm2 in the non-WM zone. These findings were helpful for developing and optimizing the WM process.

Effect of the initial hydrogen concentration and vacuum-annealing modes on the structure, phase composition, and mechanical properties of sheet billets of the VT6 alloy: Part 2. Effect of the phase composition and grain size on mechanical properties of sheet billets of the VT6 alloy

The effect of the size of the α grain and the phase composition on the mechanical properties of sheet billets of the VT6 alloy after hot rolling with the use of reversible alloying by hydrogen is investigated. To evaluate the contribution of various hardening mechanisms to the total hardening of the alloy, the Hall- Petch relationship σ y = σ i + k h d -1/2 is used. The possibility for its use to evaluate the intragrained and grain� boundary hardening of the VT6 α + β alloy in comparison with the Ti-6Al α alloy and commercial titanium is shown.

The effect of heat treatments on the microstructure, texture and mechanical properties of the extruded magnesium alloy ME21

Abstract Heat treatments of the hot extruded magnesium alloy ME21 were performed at 400 °C – 550 °C and various annealing times. The evolution of the microstructure, the texture and the resulting mechanical properties were investigated. The heat treatments result in grain growth and in an intensification of the so-called rare earth texture. The grain coarsening results in a decrease in the yield strength according to the Hall – Petch relationship. The rare earth texture also contributes to a decrease in the yield strength due to the easy activation of basal slip systems. However, this texture improves the ductility at room temperature. The combination of large grain sizes, dissolved Mg12Ce precipitates and the rare earth texture delivers fracture strains up to – 55 % under compression. The elongation under tension is less affected.

The Combined Effect of Grain Size and Strain Rate on the Mechanical Behavior in Ultra-High Purity Aluminum

The effect of grain size on the mechanical properties in ultra-high pure aluminum had been investigated as a function of strain rate. Specimens with average grain diameter sizes of 243, 678 and 1070 m were compressed and elongated at quasi-static and high strain rates by a computer controlled servo-hydraulic testing machine and a Split Hopkinson Pressure (Tension) Bar (SHPB and SHTB). The mechanical properties were found to vary significantly with grain size, and strain rate. The relationship between flow stress and grain size can be expressed by a Hall - Petch relation with the different slope for both compressive tests and tensile tests. The influence of strain rate on the slope of the Hall - Petch relation is such that in compression, the slope does not change much, but in tension, there is an increase in the slope value. The strain hardening rate was seen to increase with increasing strain rate. The strain rate dependence of flow stress is obvious, and is seen to be more significant for the smallest grain size specimens. The 3D fractographs illustrated that the numbers of the dimples decrease with the increase of the grain size.

Strength Weakening by Nanocrystals in Ceramic Materials

A key question in nanomechanics concerns the grain size effects on materials' strength. Correct solution to this question is critical to design and tailor the properties of materials for particular applications. The full map of grain sizes-hardness/yield stress relationship in metals has been built. However, for ceramic materials, the similar studies and understandings are really lacking. Here we employed a novel technique to comparatively study the mechanical features of titanium dioxide (TiO(2)) with different crystallite sizes. On the basis of peak profile analysis of the X-ray diffraction data, we determined yield strength for nanocrystalline and bulk TiO(2). Our results reveal a remarkable reduction in yield strength as the grain size decreases from 30-40 microm to approximately 10 nm, providing the only evidence of a strength weakening by nanocrystals relative to their bulk counterparts. This finding infers an inverse Hall-Petch effect, the first of its kind for ceramic materials, and a dramatic strength weakening after the breakdown of classic Hall-Petch relation below a characteristic grain size.

Grain Refinement of AZ31 Magnesium Alloy by Titanium and Low-Frequency Electromagnetic Casting

The grain-refinement effects of titanium (Ti) additions and a low-frequency electromagnetic casting (LFEC) process on the AZ31 magnesium alloy have been investigated. It is shown that Ti has no effect on the formation and distribution of secondary phases in the AZ31 alloy. The results suggests that the grain size decreases with an increasing cooling rate for the AZ31 alloy; it decreases first, however, then increases slightly for Ti-containing AZ31 alloys, indicating that the grain-refinement effect of Ti decreases with an increasing cooling rate. However, the grain size decreases first, and then increases with increasing Ti for a given cooling rate. The lowest grain size is obtained at the addition of about 0.01% Ti and the cooling rate of about 6 K/s. The grain refinement effect is explained in terms of the growth restriction factor (GRF) due to the constitutional undercooling generated by the Ti solute elements, which produces grain refinement up to a critical GRF value corresponding to about 0.01% Ti addition. The yield strength of a conventional-cast AZ31 alloy can be improved by grain refinement and expressed as σy = 39.31 + 142.53 d−1/2 according to the Hall−Petch relationship. The combination of the Ti grain refiner and the LFEC process during direct-chill (DC) casting of an AZ31 alloy can produce high-quality magnesium alloy billets with uniform and equiaxed grains of less than 40 μm across the billet section up to at least a 100-mm diameter, which further improves the yield strength of the alloy, resulting in σy = 51.53 + 90.85 d−1/2.

On the Orowan stress in intermetallic ODS alloys and its superposition with grain size and solid solution hardening

Abstract The intermetallic trialuminide Al67Ti25Cr8 was strengthened by nano-scaled dispersions of up to 3 vol.% yttrium and aluminum oxide via mechanical milling. Subsequent powder consolidation, heat treatment, and thermo-mechanical treatment yielded grain growth to an increasing degree, resulting in grain sizes ranging from sub-µm level to about 0.5 mm. Consequently, the room-temperature yield strength σ0, as determined by constant compression rate tests, increases due to three different hardening contributions, namely dispersion strengthening σOR due to Orowan bypassing, fine-grain strengthening σHP due to Hall – Petch relation, and, finally, as virtually always present, some solid-solution strengthening σs. The analysis of the particle parameters was done using TEM as well as focused ion beam (FIB) imaging. The latter provides the opportunity to directly determine the mean radius rs of planar intersections with spherical particles and their nearest-neighbour spacing L since it displays a plane sectio...

Prediction of ferrite grain size and tensile properties of a low carbon steel

A relationship between ferrite grain size, cooling rate from austenitising temperature, austenitising time, and austenitising temperature is developed to predict the ferrite grain size of a low carbon steel. The coefficients of that relationship are determined experimentally. A Hall - Petch relationship is used to predict the yield stress and fracture stress from the predicted ferrite grain size. Considering the experimental results, maximum errors of 12.5% and 6.5% were found in the prediction of ferrite grain size and strengths, respectively.

Elastic and Inelastic Properties of Electroplated Nickel Used in LIGA Techniques

ABSTRACTThe aim of this paper is a wide investigation at the micro scale of the elastic and inelastic properties of electroplated Nickel, which is extensively used in the LIGA techniques. Using a nano-indentation set-up, we have obtained the Berkovitch's hardness HB and the Young's modulus E. These mechanical properties are affected by the current densities used during the electroplating as well as the nature of the substrates. The roughness Ra was obtained thanks to confocal microscopy and a linear behavior of HB versus 1/ Ra corresponds to a Hall and Petch relation. The yield stress Y0 and the ultimate strength Q have been deduced from the experimental measurements using a Finite Element Method (FEM).Q has been found sensitive to the deposition conditions. Moreover (Y0+Q) has shown a linear dependence versus the hardness HB. Finally, Nickel microbeams fabricated by LIGA technique have been characterized with a bending test. The data deduced from this method, i.e. E and Y0+Q, are in good agreement with the results obtained by nano-indentation.