Average Geometrically Necessary Dislocation Density Research Articles

A study of dynamic recovery and recrystallisation mechanisms in aluminium alloy AA7050 at different thermomechanical processing conditions

The effects of hot deformation strain rates and temperatures on aluminium alloys' dynamic recovery and recrystallisation mechanisms have been widely discussed in the literature. However, their influence remains controversial due to a need for comprehensive and detailed thermomechanical testing and characterisation data across a wide range of hot deformation conditions. In this study, hot compression tests of AA7050 were conducted at strain rates of 0.0005–5 s−1 and temperatures of 380–460 °C. The geometrically necessary dislocation (GND), low-angle grain boundary (LAGB) and high-angle grain boundary (HAGB) were acquired by the latest high angular resolution, high-speed EBSD detector (OI Symmetry 2), and their underlying mechanisms were analysed in relation to Zener-Hollomon parameter (Z). It was found that within the tested range of the hot compression condition (ln (Z) between 20.23 and 29.45), continuous dynamic recrystallisation (CDRX) predominates at lower ln (Z) values with its activity being initially increased and then decreased as ln (Z) rises, while discontinuous dynamic recrystallisation (DDRX) becomes dominant at higher ln (Z) levels. This transition of the dominant mechanism is intriguingly reflected in the evolution of HAGB length, which increases, then decreases and finally increases again. The LAGB length shows a relatively linear relationship with ln (Z), and the average GND density exhibits a near-linear correlation until reaching a plateau. Based on the obtained results, the transformation of the dominant microstructural evolution mechanisms with increasing ln (Z) was clarified: from grain growth, to recovery, to CDRX, and then to DDRX, along with the quantitative trend of HAGB length per unit area. This transformation mechanism is believed to encompass the full range of material processing window, providing a basis for justifying the previous controversial proposition in literature and a guide for defining and fabricating microstructures in manufacturing applications.

Dislocation and disclination densities in experimentally deformed polycrystalline olivine

Abstract. We report a comprehensive data set characterizing and quantifying the geometrically necessary dislocation (GND) density in the crystallographic frame (ραc) and disclination density (ρθ) in fine-grained polycrystalline olivine deformed in uniaxial compression or torsion, at 1000 and 1200 ∘C, under a confining pressure of 300 MPa. Finite strains range from 0.11 up to 8.6 %, and stresses reach up to 1073 MPa. The data set is a selection of 19 electron backscatter diffraction maps acquired with conventional angular resolution (0.5∘) but at high spatial resolution (step size ranging between 0.05 and 0.1 µm). Thanks to analytical improvement for data acquisition and treatment, notably with the use of ATEX (Analysis Tools for Electron and X-ray diffraction) software, we report the spatial distribution of both GND and disclination densities. Areas with the highest GND densities define sub-grain boundaries. The type of GND densities involved also indicates that most olivine sub-grain boundaries have a mixed character. Moreover, the strategy for visualization also permits identifying minor GND that is not well organized as sub-grain boundaries yet. A low-temperature and high-stress sample displays a higher but less organized GND density than in a sample deformed at high temperature for a similar finite strain, grain size, and identical strain rate, confirming the action of dislocation creep in these samples, even for micrometric grains (2 µm). Furthermore, disclination dipoles along grain boundaries are identified in every undeformed and deformed electron backscatter diffraction (EBSD) map, mostly at the junction of a grain boundary with a sub-grain but also along sub-grain boundaries and at sub-grain boundary tips. Nevertheless, for the range of experimental parameters investigated, there is no notable correlation of the disclination density with stress, strain, or temperature. However, a broad positive correlation between average disclination density and average GND density per grain is found, confirming their similar role as defects producing intragranular misorientation. Furthermore, a broad negative correlation between the disclination density and the grain size or perimeter is found, providing a first rule of thumb on the distribution of disclinations. Field dislocation and disclination mechanics (FDDM) of the elastic fields due to experimentally measured dislocations and disclinations (e.g., strains/rotations and stresses) provides further evidence of the interplay between both types of defects. At last, our results also support that disclinations act as a plastic deformation mechanism, by allowing rotation of a very small crystal volume.

Geometrically Necessary Dislocation Analysis of Deformation Mechanism for Magnesium under Fatigue Loading at 0 °C

This study focused on the analysis of geometrically necessary dislocation (GND) densities for five selected fine-grained magnesium samples. Among the samples, three were tested under different fatigue-loading conditions at 0 °C, one experienced quasi-static tensile loading at 0 °C, and one represented the as-rolled state. The fatigue-tested samples were chosen according to the relationship between the maximum loading stress of a test and the material’s yield strength. This study provides new insights on the deformation mechanism of fine-grained magnesium at 0 °C. It is observed that the average GND densities were increased by 95~111% for the tested samples when compared with the as-rolled sample. It is especially interesting that there is a significant increase in the average GND density for the sample that experienced the fatigue loading with a low-maximum applied stress, and the maximum applied stress was lower than the material’s yield strength. This observation implies that the grain boundary mediated the dislocation-emission mechanism.

Operating slip modes and inhomogeneous plastic deformation of Mg-10Gd-3Y-0.5Zr alloy during compression

To understand the operating slip modes and inhomogeneous plastic deformation quantitatively and statistically for a high-performance cast Mg−10Gd−3Y−0.5Zr (wt.%, GW103) alloy during room-temperature uniaxial compression, detailed slip trace analysis and electron backscatter diffraction (EBSD) based misorientation analysis of this alloy in aged condition were carried out. After 2% plastic strain, according to relative frequency of identified slip traces, the active slip modes were basal <a> slip (73.3%), followed by prismatic <a> slip (15.8%), then second-order pyramidal <c+a> slip (6.9%), and finally first-order pyramidal <a> slip (4%). Although most of the active slip systems exhibited large Schmid factor (m) values (>0.3), it was worth noting that some hard-oriented (m<0.1) slip systems were also active. For most of the grain boundaries exhibiting extremely large geometrically necessary dislocation (GND) density, at least one of the following conditions was satisfied: large grain boundary misorientation angle (GBMA) and/or large deviation of mmax for particular slip mode between neighboring grains. The plastic heterogeneity of grains (magnitude/distribution of GND density) was independent of the visibility of slip traces. The grain orientation speared (GOS) and/or grain average GND density showed no obvious correlation with mmax (for particular slip mode).

Investigation of accelerated recrystallization behavior via electropulsing treatment in CoCrFeMnNi high-entropy alloy

In this work, the effects of annealed temperatures (700 °C, 800 °C) and heating rates (low heating rate (LR) of 0.17 °C/s, medium heating rate (MR) of 500 °C/s and high heating rate (HR) of 4000 °C/s) on recrystallization behavior in equiatomic CoCrFeMnNi high-entropy alloy (HEA) were investigated. The mechanism of accelerated recrystallization behavior induced by electropulsing treatment (EPT) was elucidated through the evolution analysis of microstructure and geometrically necessary dislocations (GNDs). The results showed that the average GNDs density and grain size of the recrystallized region decreased with increasing annealed heating rate. At 700 °C, the average recrystallized grain size decreased from 6.1 μm to 2.2 μm with increasing annealed heating rate. At 800 °C, the HR material exhibited a higher recrystallization percentage and the corresponding decrease in average grain size from 12.5 μm for LR to 4.7 μm for HR. EPT promoted the recrystallization nucleation rate by reducing the recrystallization nucleation barrier. The better combination of grain refinement and dislocation strengthening due to heterogeneous deformation led to the yield strength (772 MPa) and fracture elongation (0.30) of the MR sample increased by ∼31% and ∼25% respectively compared with LR after annealing at 700 °C. This work provides essential insights into accelerating the recrystallization behavior and further improving the degree of grain refinement of CoCrFeMnNi HEA via EPT under the lower rolling amounts.

Evolution of the microstructure and mechanical properties of interstitial-free steel during multi-axial diagonal forging

In this study, sound workpieces made of interstitial-free (IF) steel were manufactured by performing up to 4 cycles without the occurrence of forging defects via the use of a new multi-axis diagonal forging (MADF-ver2) process at room temperature. The microstructure that was developed in the deformed specimens was experimentally analyzed and compared. As the number of cycles increased, the average grain size gradually decreased, and both the average misorientation angle and the fraction of high-angle grain boundaries (HAGBs) continued to increase. As the number of cycles increased, the change in average geometrically necessary dislocation (GND) density was insignificant due to the occurrence of dynamic recovery. The effects of microstructural factors on the hardness, yield strength, and total elongation of the deformed specimens were investigated. The ultrafine-grained structure formed by MADF-ver2 continuously increased the hardness and yield strength with increases in the number of cycles. On the other hand, total elongation was not dependent on the number of cycles, and this independence was mainly the result of insignificant changes in the average GND density due to the dynamic recovery that occurred throughout the specimen.

Effect of microvoids on microplasticity behavior of dual-phase titanium alloy under high cyclic loading (I): Crystal plasticity analysis

A crystal plasticity finite element (CPFE) model was established and 2D simulations were carried out to study the relationship between microvoids and the microplasticity deformation behavior of the dual-phase titanium alloy under high cyclic loading. Results show that geometrically necessary dislocations (GND) tend to accumulate around the microvoids, leading to an increment of average GND density. The influence of curvature in the tip plastic zone (TPZ) on GND density is greater than that of the size of the microvoid. As the curvature in TPZ and the size of the microvoid increase, the cumulative shear strain (CSS) in the primary α, secondary α, and β phases increases. Shear deformation in the prismatic slip system is dominant in the primary α phase. As the distance between the microvoids increases, the interactive influence of the microvoids on the cumulative shear strain decreases.

Quantitative characterization of microstructure in additively manufactured metals with nonlinear ultrasound

Our work employs nonlinear ultrasonic techniques to track microstructural changes in additively manufactured metals. One study is based on the use of the second harmonic generation technique with Rayleigh surface waves used to measure the acoustic nonlinearity parameter, β. Stainless steel specimens made through laser-powder bed fusion and laser engineered net shaping were compared with traditional wrought manufactured specimens. The β parameter is measured through successive steps of an annealing heat treatment intended to decrease dislocation density. In agreement with fundamental material models for the dislocation-acoustic nonlinearity relationship in the second harmonic generation, β drops for each specimen throughout the heat treatment before recrystallization. Geometrically necessary dislocations (GNDs) are measured from electron back-scatter diffraction as a quantitative indicator of dislocations; average GND density and β are found to have a statistical correlation coefficient of 0.852 showing the sensitivity of β to dislocations in additively manufactured metals. Moreover, β shows an excellent correlation with hardness, which is a measure of the macroscopic effect of dislocations. Ongoing work continues trying to characterize additively manufactured stainless steels with nonlinear ultrasound through non-collinear mixing.

Experimental and numerical analysis on bulge forming process of GH4738 thick-walled ring

Ring rolling technology is widely used in the production of GH4738 aerospace rings, but the ring produced by ring rolling often has the phenomenon of uneven stress and unqualified strength. To solve these problems, the thick-walled ring bulge forming technology was proposed. In this paper, a 3D-coupled thermo-mechanical FE model of the GH4738 rectangular ring bulging process was developed, which is verified to be in good agreement with the experimental process. Based on this model, the thermal parameter distribution and evolution of GH4738 rectangular ring during the bulging process were investigated systematically. Then, the evolution of the minimum bulging displacement (BD) required for rings with the change of ring size was obtained by comparing the stress distribution of rings during the bulging process in seven cases. All these provide a theoretical basis for the selection of optimal BD in practical production. Finally, the influence of the bulging process on the microstructure and mechanical properties of GH4738 alloy ring was analyzed by experimental means, and it was verified that the bulging process can play a good role in improving the strength of the ring from the perspective of the average geometrically necessary dislocation (GND) density. The experimental results indicate that with the increase of BD, the grain size of the ring does not change that much, but the average GND density increases gradually, and the yield strength and tensile strength of the ring increase significantly.

Nonlinear ultrasonic technique for the characterization of microstructure in additive materials.

This study employs nonlinear ultrasonic techniques to track microstructural changes in additively manufactured metals. The second harmonic generation technique based on the transmission of Rayleigh surface waves is used to measure the acoustic nonlinearity parameter, β. Stainless steel specimens are made through three procedures: traditional wrought manufacturing, laser-powder bed fusion, and laser engineered net shaping. The β parameter is measured through successive steps of an annealing heat treatment intended to decrease dislocation density. Dislocation density is known to be sensitive to manufacturing variables. In agreement with fundamental material models for the dislocation-acoustic nonlinearity relationship in the second harmonic generation, β drops in each specimen throughout the heat treatment before recrystallization. Geometrically necessary dislocations (GNDs) are measured from electron back-scatter diffraction as a quantitative indicator of dislocations; average GND density and β are found to have a statistical correlation coefficient of 0.852 showing the sensitivity of β to dislocations in additively manufactured metals. Moreover, β shows an excellent correlation with hardness, which is a measure of the macroscopic effect of dislocations.

Effect of twin crystallographic orientation on deformation and growth in Mg alloy AZ31

In this study we present an integrated experimental and computational study of the effect of twin crystallographic orientation on local deformation characteristics that govern its subsequent growth. Experimentally measured intra-twin geometrically necessary dislocations (GND) density and twin-resolved shear stress (TRSS) differences within twins are found to vary with twin crystallographic orientation, which is characterised in terms of inclination angle (that between the loading direction and twin c-axis). Shear transformation modelling of four particular twins with increasing inclination angle shows that the latter dominates both slip and TRSS within the twin. Model predictions and experimental measurements show that intra-twin average GND density increases with inclination angle, and that a reversal in the sign of intra-twin TRSS occurs as the inclination angle increases. This implies that the TRSS (backstress) within a twin is not always negative, which further suggests that the rate of twin growth is influenced by its own crystallographic orientation instead of global Schmid factor (which is based on parent grain orientation).

Precise measurement of strain accommodation in a Mg-Gd-Y-Zn alloy using cross-correlation-based high resolution EBSD

Mg-RE alloys show improved ductility compared to other classical magnesium alloys at room temperature. The present study focused on the strain accommodation mechanism in a wrought Mg-5.4Gd-1.8Y-1.5Zn alloy at the microstructural scale. For this purpose, a tensile specimen was uniaxially strained in-situ in tension up to 6%, and the lattice rotation tensor and geometrically necessary dislocation (GND) density were measured using cross-correlation-based high angular resolution electron backscatter diffraction (HR-EBSD) technique. The strain incompatibility within the Mg-Gd-Y-Zn alloy was accommodated by basal slip together with pyramidal dislocation. The GND measurements via HR-EBSD showed a high occurrence of pyramidal <c + a> dislocation even in well-aligned grains. The orientation dependence of basal <a> and pyramidal <c + a> dislocation was also investigated. It was found that the soft oriented grains had a higher basal <a> density, whereas the average GND density of <c + a> slip appeared to decrease with the Schmid factor of pyramidal dislocation. In addition, slip transfer process of the basal-basal and basal-pyramidal type was observed with high m' factors in this study.

Geometrically necessary dislocations distribution in face-centred cubic alloy with varied grain size

The evolution of geometrically necessary dislocation (GND) distribution in the deformed 6061 alloy is studied with electron back scatter diffraction (EBSD) and transmission electron microscope (TEM). In dynamic recrystallized state, the average GND density is 8.70 × 1014 m−2 with grain size ~30 μm. In annealed state, the average GND density decreases by an order of magnitude, from 6.81 × 1015 to 7.32 × 1013 m−2 (annealing temperature from 200 to 500 °C) accompanied by increasing grain size. Moreover, the sample has greatest ductility with lowest GND density. According to the tendency of dislocations in TEM, GND gradually migrate from near (200) plane to near (220) plane with increasing annealing temperature. Additionally, GND mainly concentrate on the grain boundaries in the deformed state, and the GND distribution is more homogenous after annealing. It is shown that the GND density is related to the grain boundary type and misorientation angle between adjacent grains. The relationship between average GND density and grain size is approximately parabolic.

Effect of strain and strain rate on the development of deformation heterogeneity during tensile deformation of a solution annealed 304 LN austenitic stainless steel: An EBSD study

Evolution of the microstructure and geometrically necessary dislocation (GND) structure was studied during tensile deformation of a solution annealed 304 LN austenitic stainless steel. Microstructures of the steel at varying engineering strains and strain rates (i.e., 1x10-4 s-1, 1x10-3 s-1 and 1x10-2 s-1) were analyzed using electron back scatter diffraction (EBSD) and electron channelling contrast imaging (ECCI) at ambient temperature. EBSD was used to quantify the evolution of the GND structure and the martensite formed during tensile straining to reveal the deformation mechanisms in the presence of microstructural heterogeneities. The average GND density and the amount of deformation induced martensite increased with increasing plastic strain at a faster rate than expected, following a concave up pattern that accelerated GND formation as strain increased. ECCI was used to examine the dislocation storage arrangements with plastic strain. Various strain rates were imposed on the steel specimens and the results show that the average GND density increased only slightly with increasing engineering strain rate. This substantiates the small decrease in strain rate sensitivity of the steel that was observed as the plastic strain increased. Therefore, the steel is tolerant to a change in the strain rate during forming. This study provides an understanding for the way in which the plastic deformation behavior of the steel is influenced by the evolution of GND density in the presence of microstructural heterogeneities, and by deformation induced martensitic transformations.

Evolution and Distribution of Geometrically Necessary Dislocations for TA15 Titanium Alloy Sheets During the Hot Tensile Process

A thorough understanding of the behavior of geometrically necessary dislocations (GNDs) for titanium alloys during the thermo-mechanical process is very important for effectively guiding the forming process and controlling the property of finial products. The current work seeks to provide valuable insights into the evolution and distribution of GNDs for TA15 titanium alloy sheet during the hot tensile process through the experimental study and numerical simulation. Based on EBSD analyses, the overall GND densities increased with the imposed macroscopic strain and saturated after a true strain of 0.4. A modified model for the prediction of average GND density with the imposed strain was proposed according to the mixed mechanism of texture, crystalline orientation, grain size, dynamic restoration and imposed strain. Moreover, GNDs were commonly distributed near grain boundaries, and some band-liked GND structures took triple junctions as starting points and extended linearly into grains nearly along a 45° angle toward the tensile direction. According to the result of a crystal plasticity finite element model, the mechanism of GND distribution was revealed.

Microstructure and mechanical properties variations of pure aluminum subjected to one pass of ECAP-Conform process

Aluminum rod (AA1100) is severely plastic-deformed by one pass of the ECAP-Conform method. Optical and electron backscatter diffraction (EBSD) methods are used for microstructural characterizations. EBSD examinations of in process and processed samples reveal that grain sizes are not changed appreciably and they are mostly elongated by the plastic deformation. The EBSD data shows an increase in the number of subgrains and inhomogeneous dislocation distributions. Estimation of the geometrically necessary dislocation (GND) densities is done by using EBSD data. Estimated average GND density of the annealed material is as low as 5 × 107 m−2. For severely deformed Al specimen, the estimated GNDs and SSDs densities are 2.9 × 1014 m−2 and 4.6 × 1014 m−2 respectively with an averaged total dislocation density of 7.5 × 1014 m−2. Mechanical properties of samples at different stages of deformation are examined through hardness and tensile tests. Microhardness results show the inhomogeneous distribution of hardness at these sections due to the complex and varied loading conditions. Despite hardness inhomogeneity, macro tensile test results show that ECAP-Conform process is very effective in increasing the strength of the material at least by the factor of three. This increase in strength can be well interpreted by an increase in dislocation densities and formation of subgrains.

The failure mechanism at adiabatic shear bands of titanium alloy: High-precision survey using precession electron diffraction and geometrically necessary dislocation density calculation

The difficulty of obtaining key information, such as the crystal orientation and geometrically necessary dislocation (GND) density distribution, from a large deformation region in an adiabatic shear band (ASB) has hindered further study of the ASB failure mechanism in titanium alloys. In this work, the crystal orientation information of the failure position and surrounding region in ASB of a Ti-5Al-2.5Cr-0.5Fe-4.5Mo-1Sn-2Zr-3Zn alloy was obtained via transmission electron microscopy (TEM) and precession electron diffraction (PED) with a high spatial resolution. The GND density distribution was calculated and the adiabatic shear failure mechanism was revealed from the collected data. ASBs (original width: ∼3–4 µm) formed in the cylinder sample during dynamic compression (strain rate: ∼3000 s−1). In the transition region at the edge of ASB, the grains were severely elongated along the direction parallel to the ASB boundaries with an average grain size on the order of μm and an average GND density of 5.5374 × 1015/m2 in the α phase. Relatively strong < 0001 > textures and weak < -12–10 > textures were observed. However, significant dynamic-recrystallization-dominated grain refinement in ASB, especially at the crack tip, resulted in many ultrafine equiaxed recrystallized grains (10 nm level) and weakened textures. The highest average GND density (8.6242 × 1015/m2, in α phase) occurred in the crack tip region. Moreover, the vicinity of the "primary microcracks" in the main crack extension line was characterized by combinations of an extremely high GND density work hardening region and a group of low GND density recrystallized grains. This indicates that cracks in the ASB were initiated by the deformation incompatibility between the antecedent recrystallization region and the surrounding high work hardening region.

Microstructural Evolution of Mechanically Deformed Polycrystalline Silicon for Kerfless Photovoltaics

Silicon wafers for photovoltaics could be produced without kerf loss by rolling, provided sufficient control of defects such as dislocations can be achieved. A study using mainly high resolution electron backscatter diffraction (HR‐EBSD) of the microstructural evolution of Siemens polycrystalline silicon feedstock during a series of processes designed to mimic high temperature rolling is reported here. The starting material is heavily textured and annealing at 1400 °C results in 90% recrystallization and a reduction in average geometrically necessary dislocation (GND) density from &gt;1014 to 1013 m−2. Subsequent compression at 1150 °C – analogous to rolling – produce sub‐grain boundaries seen as continuous curved high GND content linear features spanning grain interiors. Post‐deformation annealing at 1400 °C facilitates a secondary recrystallization process, resulting in large grains typically of 100 μm diameter. HR‐EBSD gives the final average GND density in as 3.2 × 1012 m−2. This value is considerably higher than the dislocation density of 5 × 1010 m−2 from etch pit counting, so the discrepancy is investigated by direct comparison of GND maps and etch pit patterns. The GND map from HR‐EBSD gives erroneously high values at the method's noise floor (≈1012 m−2) in regions with low dislocation densities.

Geometrically Necessary Dislocation Density Evolution in Interstitial Free Steel at Small Plastic Strains

Measurement of geometrically necessary dislocation (GND) density using electron backscatter diffraction (EBSD) has become rather common place in modern metallurgical research. The utility of this measure as an indicator of the expected flow behavior of the material is not obvious. Incorporation of total dislocation density into the Taylor equation relating flow stress to dislocation density is generally accepted, but this does not automatically extend to a similar relationship for the GND density. This is discussed in the present work using classical equations for isotropic metal plasticity in a rather straight-forward theoretical framework. This investigation examines the development of GND structure in a commercially produced interstitial free steel subject to tensile deformation. Quantification of GND density was carried out using conventional EBSD at various strain levels on the surface of a standard dog-bone-shaped tensile specimen. There is linear increase of the average GND density with imposed macroscopic strain. This is in agreement with the established framework.

Determination of geometrically necessary dislocations in large shear strain localization in aluminum

In this paper, a systematic approach is presented to quantifying shear band evolution by quantifying geometrically necessary dislocations (GND) associated with morphological anisotropy in 7039-aluminum alloy using the compact forced-simple shear (CFSS) design. A statistically motivated approach, i.e. the line averaged GND density profile, has been developed to investigate the GND density near heavily deformed, shear band regions. Our study shows that: i) line average GND density profiles for the Al samples machined in the A-direction (transverse to pancake-shaped grains), B-direction (parallel to longitudinal pancake-shaped grains, shearing in through-thickness direction), C-direction (parallel to pancake-shaped grains, shearing in the in-plane direction) and D-direction (parallel and through the pancake-shaped grains) are nominally similar; ii) apart from 7039-aluminum alloy C-direction that has a uniform GND distribution in the direction normal to shear due to a grain-sliding mechanism, GND profiles for other samples decrease steadily away from the shear band as plastic strain diminishes, in agreement with Ashby's theory of work hardening, iii) anisotropy in damage evolution and shear-stress shear-strain response of 7039-aluminum alloy is associated with the grain structure of the material, i.e. morphological anisotropy creating variations in grain boundary interactions; iv) microbands formation in D-direction is associated with local GND peaks; v) stress-relief crack propagating along grain boundaries due to the presence of voids or inclusions generates a ‘shielding effect’ on neighboring grains; and vi) the line average GND density profile within a single grain usually varies inversely with the width of the grain for A-, B- and D-directions, leading to generally pronounced higher GND density near triple junctions.