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The orientation and strain dependence of dislocation structure evolution in monotonically deformed polycrystalline copper
... Consideration of the latent hardening assumes that dislocation accumulation on intersecting slip planes also affects the CRSS on Using Eq. 3.21, the mean dislocation density of the RVE calculated from the Voce law is 3.07 × 10 14 m −2 while the mean dislocation density estimated by the DD law is 2.58 × 10 14 m −2 at 30% true strain. For polycrystalline copper, [26] reported mean dislocation density of 5.70 × 10 14 m −2 after 30% tensile deformation, while, [98] reported mean geometrical necessary dislocation density of 5.30 × 10 14 m −2 after 40% tensile deformation. Thus, in comparison to the experimental observations, both the laws slightly under-predict the mean dislocation density. ...
... Moreover, X-ray peak broadening characterization by [102] revealed that the stored energy of the grains with the < 111 > component is nearly 5 times that of the grains with the < 001 > component. In terms of the geometrically necessary dislocations also, it has been observed that grains with the < 111 > orientations have higher dislocation density than the grains with the < 001 > orientation during tensile deformation of polycrystalline copper [98]. Hence, we conclude that the functional form of the inplane recovery (Eq. ...
... Hence, irrespective of the microstructure, material, anisotropy of the dislocation strengthening or the differences in the dynamic recovery, average dislocation density accumulation of the dislocations is higher for the < 001 > grains. As discussed earlier, previous experimental results [98,102] have contrasting observations to our results. ...
... It is apparent that the subject of orientation-dependent substructure evolution, especially under different solute content and deformation temperatures, is an applied topic with significant basic science involved. [4,25,26,[31][32][33][34] This has been the focus of the present study. ...
... Dillamore et al. [28] proposed a relationship between the Taylor factor (which depends on crystallographic orientation) and the stored energy of cold work. Past experimental research, from different groups, [16,20,27,31,32,[72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88] brought out extensive experimental evidences on orientation-dependent substructure evolution in polycrystalline metallic materials. Our study did the same but extended the orientation dependence to both solute (Mg) content and working temperatures. ...
... Past explanations were often qualitative. These include explanations from Taylor or Schmid factors [17,19,23,24,31] to arguments on orientation stability. For example, an unstable orientation may experience textural softening or rotations to softer crystallographic orientations. ...
Role of magnesium (Mg) solute and deformation temperature on the orientation-dependent substructure evolution in aluminum (Al) was investigated experimentally. The mechanistic origin of the experimental orientation dependence was then explored with numerical modelling. In experiments, the Al–Mg showed more geometrically necessary dislocation density and residual strain but had insignificant differences between hard and soft crystallographic orientations. Increased Mg-content led to the conversion of dislocation cell structures to dislocation tangles. On the other hand, an increase in deformation temperature appeared to nullify the role of solute, and irrespective of Mg content, the substructures were not orientation dependent. Molecular dynamics (MD) simulations provided temperature and solute dependence of dislocation drag coefficient and probability of cross slip. These appeared to be orientations independent. Discrete dislocation dynamics (DDD) simulations were then conducted by incorporating relevant parameters from MD and fitting DDD simulated stress-strain behavior with experimental data. Further, the solute was modelled as static obstacles to dislocation movement, hindering easy glide and short-range dislocation–dislocation interactions. Disloca- tion interactions at the slip plane intersections generated dynamic obstacles and sources—their ratio being determined by the probability of cross-slip. The DDD simulations indicated that evolving density of dynamic obstacles and sources determined the orientation dependence of substructure evolution.
... Because the TEM technique samples only a tiny area, more recently, researchers have turned to EBSD to collect data from more expansive areas for a more quantitative and statistical significant examination. Jiang et al. claimed the grain size-GND density relation largely depends on the strain values [49,50]. At lower strains, smaller grains present a higher average GND density, but this trend diminishes as strain value exceeds 10 %. ...
... However, all the above-mentioned studies ignored the GND distribution and density within the starting materials [46,[48][49][50][51]. A recent study has shown that the average GND density in annealed state can decrease by an order of magnitude as grain size increases [52], consistent with results presented in Fig. 9(c). ...
... In mesoscale reverse extrusion and microscale molding experiments, the materials' deformation conditions differ vastly from those under simple deformation configuration, such as uniaxial tensile test utilized in Refs. [46,[48][49][50][51]. For instance, in mesoscale reverse extrusion experiments, surfaces of extruded Cu were mostly constrained between the die and the punch, and deformation conditions varied by location. ...
Meso-/micro-scale metal forming offers problems in which the characteristic deformation length scale can approach the grain size of the material being formed. In this regime, the mechanical response of the deformed material exhibits various deviations from conventional continuum plasticity. This paper shows two such examples involving polycrystalline Cu with different grain sizes. In mesoscale axisymmetric reverse extrusion, Cu with a larger grain size requires a higher scaled pressure to extrude. In microscale double-punch molding, Cu with a larger grain size flows less into micron sized gaps as compared to Cu with a smaller grain size. In both cases, the trend expected from ranking of the bulk flow stress is reversed. To understand these phenomena, we quantitatively analyze crystallographic orientation data obtained from electron backscatter diffraction scans on thin material slices extracted from as-extruded and as-molded Cu specimens. The results show that, for both deformation geometries, Cu with the larger grain size stored more geometrically necessary dislocations under the same deformation geometry. The influence of grain size on geometrically necessary dislocation storage during forming offers a unified, structure-based rationale for the observed anomalous mechanical behavior. This storage is likely influenced by an interplay between the deformation geometry, the characteristic deformation length scale, and the grain size.
... Thus, TEM observation is essential to achieve a complete description of the material strain hardening via dislocation mechanisms. Finally, others authors have used this approach to show relationships between dislocation density evolution and strain [39,[41][42][43], as they considered the GND densities obtained from EBSD analyses to be reliable (provided that measurements are made in comparable conditions). ...
... It can clearly be seen that the GND density changed with the deformation; the more this increased, the more the GND density increased too. This observation has already been made by different authors [39,[41][42][43] for different materials (IF steel or OFHC copper) deformed under tension or for aluminum deformed under compression. As shown in Figure 18b, in this study a linear dependency is shown between the ρ GND and local deformation; energy level similar to as-built L-PBF specimens. ...
... It can clearly be seen that the GND density changed with the deformation; the more this increased, the more the GND density increased too. This observation has already been made by different authors [39,[41][42][43] for different materials (IF steel or OFHC copper) deformed under tension or for aluminum deformed under compression. As shown in Figure 18b, in this study a linear dependency is shown between the ρGND and local deformation; Finally, three trapezoidal samples deformed under the same conditions were heattreated at 1100 °C over 9, 12, and 24 min (these durations corresponded to the critical recrystallization times trec identified for the warm, mild, and cold process conditions, respectively, as shown in Figure 14. ...
The microstructures induced by the laser-powder bed fusion (L-PBF) process have been widely investigated over the last decade, especially on austenitic stainless steels (AISI 316L) and nickel-based superalloys (Inconel 718, Inconel 625). However, the conditions required to initiate recrystallization of L-PBF samples at high temperatures require further investigation, especially regarding the physical origins of substructures (dislocation densities) induced by the L-PBF process. Indeed, the recrystallization widely depends on the specimen substructure, and in the case of the L-PBF process, the substructure is obtained during rapid solidification. In this paper, a comparison is presented between Inconel 625 specimens obtained with different laser-powder bed fusion (L-PBF) conditions. The effects of the energy density (VED) values on as-built and heat-under microstructures are also investigated. It is first shown that L-PBF specimens created with high-energy conditions recrystallize earlier due to a larger density of geometrically necessary dislocations. Moreover, it is shown that lower energy densities offers better tensile properties for as-built specimens. However, an appropriate heat treatment makes it possible to homogenize the tensile properties.
... Several dislocation characterization techniques can be used to quantify the dislocation density, such as TEM [32,34], X-ray diffraction (XRD) [40], neutron diffraction (ND) [41], chemical pitting [42], EBSD [14,43]. TEM is a well-established method, which enabled the development of the plasticity theories by directly observing the localized dislocation structures. ...
... This technique has been compared and validated by various other dislocation density measurement techniques such as TKD-TEM [45] and Pitting [46] on various materials. EBSD sensitivity study was also reported in Ultramiscropy [47], confirming its reliability on misorientation and grain boundary measurements, especially for metals [14,18,43,45,48]. By measuring the misorientations of the material, geometrical necessary dislocations (GND) can be estimated based on the rotation of grain orientations [14,48]. ...
... Note that there exist some dark blue clusters, especially apparently presented in Fig. 4 (B). These correspond to the non-indexed area from EBSD maps due to the unindexed diffraction patterns [14,43]. These non-indexed areas (i.e. the dark blue cluster) are likely to contain much higher GND densities [14], where the significant disorientations in crystal structures may exist. ...
Physically based constitutive equations incorporating the key microstructural mechanisms e.g. dislocations, grain size, etc, have been used widely to predict the stress-strain behaviour of alloys at plastic and viscoplastic conditions. This enables an accurate prediction of the formed geometry as well as the final underlying microstructures. However, these physically based constitutive equations have not been practically validated due to the lack of systematic experimental data at microscopic scale. This leads to a large number of unknown constants required to be determined through various optimization algorithms. The aim of this paper is to provide direct and systematic experimental data by revealing the dislocation (geometrically necessary one) density and grain size evolution of AA6082, which is a widely used high-strength aluminium alloy for automobile structural panels, as functions of strain, strain rate and temperature, and is the first-time using Electron Back Scattering Diffraction (EBSD) technique to visualize the microstructures during the hot deformation. The evolution of the dislocation accumulation during the hot tensile deformation at 300, 450, 530 ˚C using various strain rates (i.e. 1/s, 0.1/s, 0.01/s) was achieved. EBSD maps were analysed on samples submitted to a true strain level of ∼0.1 and ∼0.3 under each condition. These maps cover >3000 grains and enable to capture the statistical nature of the geometrically necessary dislocation densities during hot deformation. Despite the rapidly plateaued flow stress curves at high temperatures, a continuously increased average GND density was observed in AA6082 with the imposed true strain levels under all conditions. Dislocation channel structures were observed in the hot deformed samples. Dynamic recrystallization was also observed, which coupled with the GNDs and affects the hardening behaviour of the flow stress-strain curves. This work is the first study, using EBSD, to visualize the high temperature and high strain rate induced dislocation distributions over a relatively large area, providing valuable data that may be used for subsequently improving and calibrating the physically based material models.
... Numerous investigations have highlighted the significant influence of applied strain on GND characteristics. It has been observed that the average density of GNDs tends to rise with increasing applied strain [14][15][16]. For instance, Kundu et al. [17] revealed a gradual increase followed by saturation of GND density during quasi-static tensile deformation. ...
... By employing EBSD analysis, we obtain the GND characteristics of the deformed specimens at different strain rates, as well as the variations in characteristics globally and locally. For pure copper, in contrast to existing studies that mainly focus on GND characteristics at low strain rates [16,26,34], the present study investigates the GND characteristics at higher strain rates and explores the underlying microscopic mechanisms; this provides a robust experimental foundation for modeling and theoretical research. ...
Geometrically necessary dislocations (GNDs) play a pivotal role in polycrystalline plastic deformation, with their characteristics notably affected by strain rate and other factors, but the underlying mechanisms are not well understood yet. We investigate GND characteristics in pure copper polycrystals subjected to tensile deformation at varying strain rates (0.001 s−1, 800 s−1, 1500 s−1, 2500 s−1). EBSD analysis reveals a non-linear increase in global GND density with the strain rate rising, and a similar trend is also observed for local GND densities near the grain boundaries and that in the grain interiors. Furthermore, GND density decreases from the grain boundaries towards the grain interiors and this decline slows down at high strain rates. The origin of these trends is revealed by the connections between the GND characteristics and the behaviors of relevant microstructural components. The increase in grain boundary misorientations at higher strain rates promotes the increase of GND density near the grain boundaries. The denser distribution of dislocation cells, observed previously at high strain rates, is presumed to increase the GND density in the grain interiors and may also contribute to the slower decline in GND density near the grain boundaries. Additionally, grain refinement by higher strain rates also promotes the increase in total GND density. Further, the non-linear variation with respect to the strain rate, as well as the saturation at high strain rates, for grain boundary misorientations and grain sizes align well with the non-linear trend of GND density, consolidating the intimate connections between the characteristics of GNDs and the behaviors of these microstructure components.
... Initially, with a small amount of plastic deformation, dislocations formed in the moderately deformed grains and the other area of these grains was occupied by low GND density points without specific structure as seen in the near-equiaxed grains in the GND map for the 0.03 strain. The present data are consistent with previous results showing the developed GND structure in various grains characterised by high-resolution EBSD in deformed copper samples [23]. As the plastic deformation increased, the number of GND density points increased. ...
... Some preferentially oriented grains with similar neighbours are likely to be deformed and forming GND and LAGB structure first, while those 'hard' grains will be subsequently deformed, forming the GND network and later LAGBs. These findings confirmed the correlation between the deformation-GND-LAGB and grain orientations as found in previous studies of aluminium [33] and copper [23], respectively. Generally, LAGBs are believed to be low-energy, stable dislocation structures, acting as effective dislocation barriers and responding to the strain hardening [34]. ...
Understanding dynamic recrystallisation mechanism has significant scientific and practical importance for controlling the microstructure of AA7050 alloy during hot forging process. In this study, interrupted hot compression was conducted using Gleeble to the strain levels of 0.03, 0.15, 0.40 and 0.58 respectively, at 420 °C and strain rate of 0.05 s−1. The grain orientation, geometrically necessary dislocations (GND) density, low-angle grain boundary (LAGB) and high-angle grain boundary (HAGB) at various strain levels were characterised by electron backscatter diffraction (EBSD) and their evolutions as a function of strain were analysed qualitatively and quantitatively. The correlations of GND density, LAGB and HAGB with strain and stress were examined, and the evolution processes of these variables at grain scale were revealed. It was found that dislocations were firstly formed in some of the grains when the deformation started, and the saturation point for the average GND density was 13.5 in log10 scale at the strain of 0.15. Some dislocations transformed into LAGB which could transform to HAGBs and form recrystallised grains in further deformation, demonstrating continuous dynamic recrystallisation (CDRX) behaviour. During this process, the areas of LAGB and HAGB per unit volume increased from 1.2 × 105 to 1.9 × 105 m−1 and from 2.8 × 104 to 7.1 × 104 m−1 respectively, meanwhile the misorientation angles of LAGB and HAGB did not vary markedly with increasing strain level. Based on the direct observation and the statistical analysis, the detailed dynamic recrystallisation mechanisms have been proposed and discussed.
... Figure 1 (a3-c3) are the Taylor factor maps of samples. The Taylor factor M is a geometric factor used in analysis of plastic deformation in polycrystals [6]. The researchers used the Taylor factor to define "hard grain" and "soft grains" [7]. ...
... It was found that the points with high GND (geometrically necessary dislocation) preferentially gather in the grains with high Taylor factor ("hard" grains) in the plastic deformation samples [6,7]. Because the grains with high Taylor factor need more stress to apply uniform geometry change and more work in the deformation process, which leads to the generation of dislocation on different slip surfaces and higher GND density, so the dislocation density is higher. ...
... Work by Humphrey [18] shows that plotting of correlated data is far more precise relative to uncorrelated data as uncorrelated data may produce numerous false boundaries in a structure. This is due to correlated data having the ability to identify changes in orientations that result in grain boundaries between neighbouring pixels, but with uncorrelated data is taken from random pixels in the structure. ...
... The presence of low angle grain boundaries is not usually found in the cast, as shown by Modak [5], therefore the formation of low angle grain boundaries is through the mechanism of CDRX. Longer interpass times show a greater degree of high angle grain boundary intensity relative to shorter interpass times correlating to work by numerous authors [11,18]. The correlated misorientation angle distribution diagrams illustrate that newly formed, recrystallised grains have a greater degree of misorientation relative to the parent grain with the misorientation being more pronounced in grains strained at lower strain rates. ...
The following article looks at using scanning electron microscopy-electron back scatter diffraction techniques to study recrystallisation structures produced through hot rolling of 436 ferritic stainless steel. Characterisation of recrystallisation textures was undertaken through analysis of misorientation angle distribution diagrams, orientation distribution function maps, inverse pole figures and Taylor factor maps. These techniques were applied in a case study where typical industrial hot rolling conditions were simulated through uniaxial compression tests in a Bähr Dilatometer 850D, whereby the effect of strain rate and interpass time on recrystallisation structures was investigated.
... The Taylor's theory is based on the assumption that dislocation slip is solely responsible for deformation and the strains induced in the grains are identical to macroscopic strain [74]. Taylor factor (M) represents the yielding response of overall distribution of grain orientation with respect to the direction of applied stress state [75,76]. In other words, it represents the propensity of crystals to deform based on their orientation relative to macroscopic stress state, by the activation of slip systems [44,47]. ...
... It is clearly observed in Fig. 14(d) that fraction of grains having Taylor factor M ~ 3-5 has increased during deformation as compared to AR specimen (illustrated in Fig. 13). This signifies that grains have work hardened during the course of deformation [75,78]. The fraction of grains within Taylor factor M ~ 3-4 is higher as compared to M ~ 2-3 after deformation in EBD specimen, whereas a reverse trend is observed in the other two deformation modes ( Fig. 14(d)). ...
A detailed investigation on the microstructure and micro-texture evolution in Al–Li alloy has been carried out following deformation at various strain paths. The stretch forming tests have been conducted to achieve three distinct strain paths, viz. close to uniaxial, plane strain and equi-biaxial. A correlation has been established between the microstructural and micro-textural developments with the various strain paths. The development of Brass {110}<112> and Cube {001}<100> components during uniaxial deformation and evolution of Goss component {110}<001> with development of <011 //ND fiber during equi-biaxial deformation have been observed as stable orientations. Meanwhile, a marginal strengthening of R {214}<112> and S component {123}<634> is noticed during plane strain deformation. The deformation micro-texture and associated active number of slip systems under different deformation modes are simulated using visco-plastic self-consistent (VPSC) polycrystalline model. During uniaxial deformation, the availability of the least number of active slip systems leads to the development of a relatively stronger micro-texture. Moreover, a detailed insight into the Taylor factor has been performed to elucidate its distribution based on the micro-textural developments along the three deformation paths. The higher fraction of grains in Taylor factor range M ∼ 2–3 during uniaxial and plane strain deformation is associated with the presence of Cube component {001}<100>. On the contrary, the higher fraction of grains in Taylor factor range M ∼ 3–4 during equi-biaxial deformation is related to the strengthening of <011 //ND fiber. The fewer number of grains in Taylor factor range M ∼ 4–5, as observed during plane strain deformation, is attributed to the evolution of Brass texture {110}<112>.
... For example, the harder (111) grains had higher than softer (100). This is not unexpected (Jiang et al., 2015). ...
... Detailed deformed microstructure was analyzed by transmission-EBSD (t-EBSD) method, using JEOL 7000F SEM. Kernel Average Misorientation (KAM) maps of the grain interior and GB zone are separately extracted by defining the minimum Euclidean distance [33]. Considering the distribution characteristics of Al 2 O 3 in Al-5CuO as well as the sharp contrast between the GND concentration at distances up to 100 nm from GB and that closer to the grain interior, the 100 nm distance was selected as a threshold of the minimum Euclidean distance in this work. ...
... A direct consequence of a difference between the external and internal plastic energies is an effect on the Taylor factor. The Taylor factor is extensively used to link microscopic and macroscopic stress and strain quantities Bieler and Semiatin, 2002;Follansbee and Gray, 1991;Jiang et al., 2015;Kopacz et al., 1999;Masui, 2008;Mecking et al., 1996;Miller and Turner, 2001;Tome et al., 1984;Van Houtte, 2001;Zhang et al., 2019]. They can be obtained only by simulation of the mechanical behaviour of the polycrystal. ...
... This grain splitting is described with specific terminology as deformation bands and transition bands, etc [49]. Geometrical necessary dislocations are often generated to accommodate strain gradient over a range of scales [50][51][52]. Within each characteristic domain, the orientation is substantially the same and it has to be one slip system in operation at one time in the domain during deformation. However, the dominant slip system can change due to unequal hardening among slip systems. ...
A von Mises criterion for compatible deformation states that five independent slip systems must operate for polycrystals to deform uniformly and without failure at the grain boundaries, which is supported by the Taylor–Bishop–Hill theory or simply the Taylor model, defining the laws of plastic deformation of polycrystalline aggregates and being one of the key cornerstones of crystal plasticity theory. However, the criterion has fundamental flaws as it is based on an unfounded correlation between phenomenological material flow behaviour in continuum mechanics and crystal structure dependent dislocation slip, and there has been no experimental evidence to show simultaneous operation of five independent slip systems. In this paper, the Von Mises criterion and the Taylor model are revisited and examined critically, and the fundamental issues related to the requirement of independent slip systems for compatible deformation and the selection of the active slip systems are addressed. Detailed analysis is performed of the stress state that eliminates the possibility of the simultaneous operation of five independent slip systems, and of the relative displacement vector due to the dislocation slip which defines the quantity of the strain that can be expressed by a strain tensor, instead of individual strain components. Discussions are made to demonstrate that although three linearly independent slip systems are essentially sufficient for compatible deformation, one slip system, being selected according to Schmidt law, dominates at a time in a characteristic domain as deformation accommodation occurs between grains or characteristic domains rather than at each point.
... Size effect may be approached by several strategies concerning meso-scale models of plasticity such as strain gradient plasticity [8][9][10], mixture models [11][12][13][14], statistical-based models [15][16][17]. The present study aims to develop a simple framework to simulate the deformation of grains in an aggregate and study the plasticity of miniature specimens, which have a long history in the literature [18][19][20][21][22][23][24][25]. The developed model is operable in many commercial finite element codes, without the requirement of any further coding. ...
In this study, by combining crystal plasticity notions developed by Taylor and the mathematical expression of Hill’s yield criterion for anisotropic materials, a model is introduced to describe the flow behavior of grains in a grain aggregate. In this model, Hill’s yield criterion coefficients are calculated in terms of Taylor factors for different straining conditions for each grain. The convexity of the proposed model is proved by sign determination of the eigenvalues of the associated Hessian matrix. It is found that the experimental load-displacement curves of specimens showing the size effect are enveloped by the bounds obtained from simulations using the proposed model, which to some extent verifies the applicability of the developed model. Using the developed model, the microforging of miniature rods consisting of 50 and 200 grains in their cross-section are simulated. In agreement with the literature, the results showed that due to the difference in the mechanical behavior of grains, the distribution of strain abruptly changes from one grain to another. Moreover, it is shown that as the number of grains in the cross-section of the specimen increases, the plastic equivalent strain tends toward that predicted by the classical plasticity theories, proving the applicability of the proposed model. Finally, the results suggest that the successful production of microparts by forming processes requires raw materials in microforming to be the products of the severe plastic deformation techniques, where the microstructure is scaled down to the nanometer.
... During the rolling process, a matrix with nondeformable particles will experience strain incompatibility. This local strain incompatibility accommodates the generation of the extra dislocations at the particle-matrix interfaces around these non-deformable particles, which are known as geometrically necessary dislocations (GNDs) (De Siqueira et al., 2013;Hatherly and Humphreys, 2012;Jiang et al., 2015;Zhu et al., 2021). Randomly oriented SRX grains were observed near the Cu 2 O particles (magnified IPF view of particles 1, 2 and 3 appear in Fig. 11(c-e)), which suggested the occurrence of DSRX. ...
The present study addresses the evolution of microstructural and crystallographic texture in room-temperature-rolled (RTR) and cryogenic-rolled (CR) electrolytic tough-pitch (ETP) copper. Copper specimens were subjected to 20, 40, 60, and 80% reductions via RTR and CR processing. The microstructure evolution of the severely deformed RTR and CR specimens revealed deformed and recrystallized grains. Static recrystallization (SRX) at room temperature (RT) was observed in the severely deformed RTR and CR specimens. Both discontinuous SRX (DSRX) and continuous SRX (CSRX) were responsible for the nucleation of small grains at RT. Particle-stimulated nucleation (PSN) was also responsible for small-grain formations around the Cu2O particles. The initial ETP copper specimen showed a weak texture whose intensity increased after the RTR and CR deformation. The texture intensity of the severely deformed specimens was affected by both deformation and the SRX phenomena. The CR specimens showed texture that was stronger than that of the RTR specimens up to the point of an intermediate reduction (60%), whereas at higher deformation (80%), the RTR specimens showed stronger texture intensity compared with that of the CR specimens. The texture weakening in the CR80 specimen was due to the formation of strain localizations (SLs) and to the nucleation at SLs. Large amounts of stored energy and SL formation in severely deformed CR specimens led to a different recrystallization texture compared with that of RTR specimens. A Cube component was dominant in the RTR80, whereas Goss, Copper and S components were observed in the CR80 specimen for SRX grains. The CR specimen showed a relatively high hardness value compared with the RTR specimen. Time-dependent decay in the hardness values for both the RTR and the CR specimens were attributed to room-temperature recovery (SRV) and recrystallization (SRX).
... A high Taylor factor in grain A observed in the experiments [43] also seems to correlate very well with the observed high GND density distributions in grain A in our atomistic simulations (Fig. 5). This can be attributed to several aspects: First, it is known that a grain with high Taylor factor requires a relatively high stress to accommodate the resulting shape change and thus, more work is performed in such grains [80]. Thus, more GNDs can be accumulated in these grains. ...
In this work, atomistic simulations are performed to investigate the dislocation activity during plain strain compression in a face centered cubic (FCC) Cu bicrystal. Analysis techniques involving the use of discrete atomic coordinates to characterize the change in lattice orientations of individual crystals and the resulting dislocation patterns are exploited. Compression induces dislocation activities in the abutting crystals and the grain boundary (GB) poses a significant barrier to dislocation motion. Heterogeneous deformation in the crystals due to the presence of GB instigates appreciable differences in the grain orientation distributions at different stages of deformation. The observed local lattice rotation fields are found to correlate well with the calculated geometrically necessary dislocation distributions computed from per-atom Nye tensor. A close comparison of the obtained results with the corresponding experiments published in the literature on same Cu bicrystal provides unique insights into the operative nanoscale deformation mechanisms. The ramifications of such modeling approaches in bridging the traditional gap existing between experiments and simulations are discussed.
... Predictions of both the Voce and the DD law are shown.of polycrystalline copper(Jiang et al., 2015). Hence, we conclude that the functional form of the 411 inplane recovery (Eq. ...
Crystal plasticity modelling and simulation is an important predictive tool for understanding the deformation of polycrystalline materials under diverse loading conditions. The validity and accuracy of these simulations depend on the choice of the constitutive law. One of the main components of the constitutive law for plastic deformation is the hardening law. This study, therefore, focuses on understanding the effect of the phenomenological Voce hardening law and the dislocation density based hardening law on full field predictions of crystal plasticity simulations. The crystal plasticity simulations were performed using a three dimensional (3D) fast Fourier transform-based elasto-viscoplastic (EVP-FFT) micromechanical solver for the tensile deformation of copper. Simulation results show that the local distribution of stress strongly depends on the hardening rule. Average texture characteristics predicted by both the laws do not vary significantly. However, spatial orientation evolution (micro-texture) varies with increasing strain. For the Voce law, spatial distribution of the dislocation density calculated from the threshold stress is more homogeneous than the predictions of the dislocation density based hardening law. Finally, our results highlight that a simple dislocation density based storage-recovery model is insufficient to explain the orientation dependence of the stored energy distribution. Hence, careful choice of the hardening law is important for the prediction of localized micromechanical fields.
... Cette dépendance à l'orientation est également rencontrée pour les matériaux CFC notamment l'aluminium (Driver et al., 1994;Huang et Hansen, 1997;Hurley et Humphreys, 2003;Huang et Winther, 2007;Lin et al., 2009;Le et al., 2012), le cuivre (Huang, 1998;Huang et Winther, 2007;Jiang et al., 2015) et le nickel Wu et al., 2011). Pour les matériaux CFC, trois morphologies de sous-structures ont été très souvent observées et semblent indépendantes du matériau étudié et du mode de déformation utilisé (figure 2.8) (Huang et Winther, 2007). ...
Du fait de sa grande ductilité à température ambiante, le tantale pur est idéal pour la mise en forme à froid de pièces à géométries complexes avec des risques de rupture minimes. L’objectif de cette thèse est de comprendre et proposer une description des mécanismes physiques qui se déroulent lors d’une déformation plastique suivie d’un traitement thermique. Différents échantillons de tantale pur ont été déformés à froid par compression et laminage. Les microstructures déformées ont été ensuite caractérisées par microscopie électronique à balayage à l’échelle des grains et des sous-structures. Ces caractérisations ont révélé que le développement de sous-structures est fortement influencé par l’orientation cristallographique des grains et également par la texture de l’état initial. En particulier, les grains de la fibre gamma forment plus de sous-structures que ceux de la fibre thêta. Ces différences ne peuvent pas être correctement retranscrites uniquement par les valeurs de densité de dislocations. D’autres paramètres permettant de quantifier les sous-structures ont été proposés et leurs évolutions ont été décrites par des modèles. La recristallisation est très impactée par la dépendance de l’état déformé à l’orientation cristallographique. La germination est favorisée dans les grains de la fibre gamma en raison du développement de sous-structures plus important lors de la déformation. Cette hétérogénéité de comportement peut être bien décrite par l’énergie stockée lorsqu’elle est estimée à l’échelle des sous-structures. La restauration a été étudiée de manière directe et indirecte à travers ses effets sur la recristallisation avec différents pré-traitements de restauration. Deux effets opposés sur la recristallisation ont été observés. Un premier effet défavorable est lié à l’annihilation des dislocations, ce qui implique une diminution de la force motrice pour la recristallisation. Un second effet favorable est lié à l’amélioration de l’aptitude à migrer des sous-joints, ce qui favorise la germination. L’effet global de la restauration sur la recristallisation est conditionné par l’équilibre entre ces deux effets. Cet équilibre varie en fonction du niveau de déformation, de l’orientation cristallographique et des conditions du pré-traitement de restauration (temps et température).
... • Pour ces matériaux, la contribution des déformations élastiques dans le calcul des densités de dislocations géométriquement nécessaires est apparue négligeable devant celle des courbures, ce qui est en accord avec la littérature [145,146]. A l'inverse, les déformations élastiques doivent être prises en compte quand les désorientations sont faibles (~0,2°), comme dans l'échantillon de GaN où la sensibilité sur les densités de dislocations est voisine de 2,5×10 -3 µm -1 (8×10 12 m -2 ). ...
La compréhension des mécanismes de déformation dans les matériaux cristallins passe par la caractérisation fine des microstructures. Dans le cadre de la microscopie électronique à balayage, la mesure précise des gradients d’orientation et des déformations élastiques du cristal est l’objectif des méthodes dites à haute résolution angulaire. Pour cela, elles emploient des techniques de corrélation d’images numériques afin de recaler les clichés de diffraction électronique. Cette thèse propose une méthode de recalage originale. Le champ de déplacement à l’échelle du scintillateur est décrit par une homographie linéaire. Il s’agit d’une transformation géométrique largement utilisée en vision par ordinateur pour modéliser les projections. L’homographie entre deux clichés est mesurée à partir d’une grande et unique région d’intérêt en utilisant un algorithme de Gauss-Newton par composition inverse numériquement efficace. Une correction des distorsions optiques causées par les lentilles de la caméra lui est intégrée et sa convergence est assurée par un pré-recalage des clichés. Ce dernier repose sur des algorithmes de corrélation croisée globale basés sur les transformées de Fourier-Mellin et de Fourier. Il permet de rendre compte des rotations allant jusqu’à une dizaine de degrés avec une précision comprise typiquement entre 0,1 et 0,5°. La détermination de l’homographie est indépendante de la géométrie de projection. Cette dernière n’est considérée qu’à l’issue du recalage pour déduire analytiquement les rotations et les déformations élastiques. La méthode est validée numériquement sur des clichés simulés distordus optiquement, désorientés jusqu’à 14° et présentant des déformations élastiques équivalentes jusqu’à 5×10⁻². Cette étude montre que la mesure précise de déformations élastiques comprises entre 1×10⁻⁴ et 2×10⁻³ nécessite de corriger la distorsion optique radiale, même lorsque la désorientation est faible. Finalement, la méthode est appliquée à des clichés acquis par diffraction des électrons rétrodiffusés (EBSD) et en transmission en utilisant la nouvelle configuration TKD on-axis (transmission Kikuchi diffraction). Des métaux polycristallins déformés plastiquement ainsi que des semi-conducteurs sont caractérisés. La méthode retranscrit des détails fins de la microstructure d’un acier martensitique trempé et revenu et d’un acier sans interstitiels déformé de 15% en traction, malgré la détérioration du contraste de diffraction induit par la déformation plastique. Les structures de déformation sont également analysées dans de l’aluminium nanostructuré obtenu par déformation plastique sévère grâce au couplage de la méthode de recalage et de la configuration TKD on-axis. Ce couplage permet d’atteindre simultanément une haute résolution spatiale (3 à 10 nm) et une haute résolution angulaire (0,01 à 0,05°). Des cartes de déformation élastiques sont obtenues à l’échelle de quelques nanomètres dans une lame mince de SiGe et les densités de dislocations dans un monocristal de GaN sont déterminées avec une résolution voisine de 2,5×10⁻³ µm⁻¹ (soit 8×10¹² m⁻²).
... In this paper, we use High Resolution EBSD (HR-EBSD) to experimentally map the lattice rotation field in the vicinity of nanoindentation and nanoscratch experiments [32,[52][53][54][55] . Scratch and indentations were generated under the same normal force (3 mN) using a Berkovich indenter, in single crystal copper. ...
In this paper, we investigate the residual deformation field in the vicinity of nanoscratch tests using two orientations of a Berkovich tip on an (001) Cu single crystal. We compare the deformation with that from indentation, in an attempt to understand the mechanisms of deformation in tangential sliding. The lattice rotation fields are mapped experimentally using high-resolution electron backscatter diffraction (HR-EBSD) on cross-sections prepared using focused ion beam (FIB). A physically-based crystal plasticity finite element model (CPFEM) is used to simulate the lattice rotation fields, and provide insight into the 3D rotation field surrounding a nano-scratch experiment, as it transitions from an initial static indentation to a steady-state scratch. The CPFEM simulations capture the experimental rotation fields with good fidelity, and show how the rotations about the scratch direction are reversed as the indenter moves away from the initial indentation.
... With reduction in step size (or Burgers' circuit size) the fraction of dislocations that appear as GNDs increases (more dipoles are resolved as GNDs) until finally, for Burgers' circuit smaller than the dipole size, every dislocation appears as a GND. Thus the density of GNDs increases with decreasing step size, as shown by Jiang et al. in simulations of a deformed copper polycrystal (Jiang et al., 2015(Jiang et al., , 2013. The mesh size in CPFE was chosen to ensure there is no mesh dependence, with a smallest element size of 50 nm near the indenter tip. ...
Predicting the dramatic changes in mechanical and physical properties caused by irradiation damage is key for the design of future nuclear fission and fusion reactors. Self-ion irradiation provides an attractive tool for mimicking the effects of neutron irradiation. However, the damaged layer of self-ion implanted samples is only a few microns thick, making it difficult to estimate macroscopic properties. Here we address this challenge using a combination of experimental and modelling techniques. We concentrate on self-ion-implanted tungsten, the front-runner for fusion reactor armour components and a prototypical bcc material. To capture dose-dependent evolution of properties, we experimentally characterise samples with damage levels from 0.01 to 1 dpa. Spherical nano-indentation of <001> grains shows hardness increasing up to a dose of 0.032 dpa, beyond which it saturates. Atomic force microscopy (AFM) measurements show pile-up increasing up to the same dose, beyond which large pile-up and slip-steps are seen. Based on these observations we develop a simple crystal plasticity finite element (CPFE) model for the irradiated material. It captures irradiation-induced hardening followed by strain-softening through the interaction of irradiation-induced-defects and gliding dislocations. The shear resistance of irradiation-induced-defects is physically-based, estimated from transmission electron microscopy (TEM) observations of similarly irradiated samples. Nano-indentation of pristine tungsten and implanted tungsten of doses 0.01, 0.1, 0.32 and 1 dpa is simulated. Only two model parameters are fitted to the experimental results of the 0.01 dpa sample and are kept unchanged for all other doses. The peak indentation load, indent surface profiles and damage saturation predicted by the CPFE model closely match our experimental observations. Predicted lattice distortions and dislocation distributions around indents agree well with corresponding measurements from high-resolution electron backscatter diffraction (HR-EBSD). Finally, the CPFE model is used to predict the macroscopic stress-strain response of similarly irradiated bulk tungsten material. This macroscopic information is the key input required for design of fusion armour components.
... A better statistical analysis of twins can be provided by the use of electron diffraction [15][16][17][18]. For this purpose, the high angular resolution electron back scatter diffraction (HR-EBSD) technique is mainly used [19][20][21]. ...
Understanding the deformation mechanisms of hexagonal close-packed (HCP) polycrystals at the grain scale is crucial for developing both macro and micro scale predictive models. Slip and twinning are the two main deformation mechanisms of HCP polycrystals at room temperature. In this paper, the development of grain-level stress tensors during nucleation and growth of twins is investigated. A pure zirconium specimen with HCP crystals is deformed in-situ while the centre-of-mass, orientation, elastic strain, and stress of individual grains are measured by three-dimensional synchrotron X-ray diffraction (3D-XRD). The observed microstructure is subsequently imported into a crystal plasticity finite element (CPFE) model to simulate the deformation of the polycrystal. The evolution of stress in twin-parent pairs at the early stages of plasticity, further into plasticity zone, and unload is studied. It is shown that twins do not relax very much at the nucleation step, but the difference between the measured stress in the twin and parent increases further into plastic zone where twins relax. While at the early stages of plasticity all six twin variants are active, a slightly better estimation of active variants is obtained using the measured grain-resolved stress tensors.
... In this paper, we use High Resolution EBSD (HR-EBSD) to experimentally map the lattice rotation field in the vicinity of nanoindentation and nanoscratch experiments [32,[52][53][54][55] . Scratch and indentations were generated under the same normal force (3 mN) using a Berkovich indenter, in single crystal copper. ...
... In this paper, we use High Resolution EBSD (HR-EBSD) to experimentally map the lattice rotation field in the vicinity of nanoindentation and nanoscratch experiments [32,52,53,54,55]. Scratch and indentations were generated under the same normal force (3mN) using a Berkovich indenter, in single crystal copper. ...
In this paper, we investigate the residual deformation field in the vicinity of nano-scratch tests using two orientations of a Berkovich tip on an (001) Cu single crystal. We compare the deformation with that from indentation, in an attempt to understand the mechanisms of deformation in tangential sliding. The lattice rotation fields are mapped experimentally using high-resolution electron backscatter diffraction (HR-EBSD) on cross-sections prepared using focused ion beam (FIB). A physically-based crystal plasticity finite element model (CPFEM) is used to simulate the lattice rotation fields, and provide insight into the 3D rotation field surrounding nano-scratch experiments, as it transitions from an initial static indentation to a steady-state scratch. The CPFEM simulations capture the experimental rotation fields with good fidelity, and show how the rotations about the scratch direction are reversed as the indenter moves away from the initial indentation.
To achieve a desired microstructure and minimize the thickness variation in rolled foils, researchers must understand the effects of foil fabrication process variables on microstructure evolution. We developed an integrated simulation of deformation and recrystallization that employs the finite element method (FEM) and the kinetic Monte Carlo (KMC) Potts model, respectively, to investigate microstructure evolution during multiple-pass hot rolling and heat treatment in polycrystalline U-10Mo fuel. Scanning electron microscopy and electron backscatter diffraction images of microstructures were directly used as input in FEM calculation of deformation, and the calculated strains were used to determine the driving force of nucleation and growth of recrystallized grains in the Potts model. Grain structures predicted by the Potts model were used to update the grain structure and material properties for FEM. Simulation alternated between FEM and the Potts model to simulate grain structure evolution during multiple rolling and heat treatments. The initial model parameters were determined by benchmarking the recrystallization kinetics against experimental data. Then, the model was applied to predict the grain structure evolution. Results showed that our model can capture the coupling between deformation and recrystallization and can quantitatively reproduce the observed U-10Mo recrystallization and grain growth kinetics. The simulation results demonstrated that the developed model can predict U-10Mo grain structures as a function of initial microstructure and foil fabrication parameters.
In the present study, MXene-reinforced Mg matrix composites were manufactured via the electrostatic self-assembly protocol and spark plasma sintering (SPS) process to develop lightweight materials with high mechanical performance. Uniform dispersion of MXene sheets was achieved in MXene/AZ91 composites. A unique interfacial structure was confirmed in these composites, which exhibited an ultrafine MgO interlayer (grain size of ∼10 nm) coherently incorporated or intercalated into MXene layers. The unique interfacial structure contributed to robust interfacial bonding between MXene sheets and Mg matrix, resulting in a substantial mechanical performance enhancement. The yield strength of 325.3 ± 7.9 MPa and elongation of 8.8 ± 0.2% were achieved in 0.3vol% MXene/AZ91 composites, showing a significantly high strengthening efficiency of 159.1 without sacrificing ductility. Quantitatively investigation of strengthening behavior manifested that the load-transfer effect was the primary strengthening mechanism in MXene/AZ91 composites, and the simulated strength was well-matched with experimental results due to the special interfacial structure and excellent dispersion properties. This study could offer significant guidance for developing novel lightweight materials with high mechanical performance for structural applications.
Geometrically necessary dislocations (GNDs) play a key role in accommodating strain incompatibility between neighboring grains in polycrystalline materials. One critical step toward accurately capturing GNDs in deformation models involves studying the microstructural features that promote GND accumulation and the resulting character of GND fields. This study utilizes high-resolution electron backscatter diffraction to map GND populations in a large polycrystalline sample of pure tantalum, under simple tension. A total of 1,989 grains, 3,518 grain boundaries (GBs), and 3,207 triple junctions (TJs) were examined in a subsurface region of the sample. Correlations between GND density and GB character, and to some extent, TJ character, are investigated. Statistical geometrical relationships between these entities are quantified, and also visualized, using a novel application of two-point statistics. The nature of GNDs across the sample is also visualized and assessed using a recently developed method of mapping the local net Burgers vectors. The different approaches to characterizing GND distribution are compared in terms of how they quantify the size of near boundary gradient zones.
The proposed global HR-EBSD/TKD method is applied to semiconductors and plastically deformed metals. The importance of the disorientation axis as well as the relative contribution of elastic strains and lattice curvatures to geometrically necessary dislocation (GND) densities are discussed. For each kind of material, both the EBSD (electron backscatter diffraction) and the on-axis TKD (transmission Kikuchi diffraction) techniques are used. More specifically, ability of scanning electron microscopy to simultaneously achieve high-spatial and high-spatial resolutions is investigated. Finally, a general discussion and perspectives conclude this series of five chapters.
The coefficient of thermal expansion (CTE) mismatch between the reinforcement and the matrix results in thermal residual stresses and defects within metal-matrix composites (MMCs) upon cooling from the processing temperature to ambient temperature. The residual stresses and thermally induced defects play an important role in the mechanical properties of MMCs, it is critical to understand the mechanism of defect formation and evolution. This study provides atomistic simulations to reveal the generation of thermal residual stresses, dislocation and incomplete stacking fault tetrahedron (ISFT) during cooling in the idealized Cu/SiC composites. We found that dislocations are generated explosively in a certain temperature range during cooling, which results in a non-linear relationship between dislocation density and temperature. The combined effect of the stresses induced by CTE mismatch and the thermodynamic state of the metal leads to the rapid generation of dislocations. The Shockley partial and the highly stable stair rod are the two dominant dislocation structures. The immobile stair-rod dislocations and the highly stable ISFTs formed in the initial high temperature stage inhibit further development of plastic deformation. The present results provide new insights into the defect formation mechanism and the dislocation strengthening mechanism of MMCs caused by thermal mismatch between constituents.
Ultrasonic vibration-assisted (UVA) forming is expected to be an effective way to improve the forming ability of Ni-based superalloy thin-walled sheet. However, the deformation characteristics and mechanism of this material under ultrasonic field keep unclear. To this end, experiments of UVA tension followed by quasi-in-situ EBSD were conducted. The tensile mechanical properties under different amplitudes were investigated, and the quasi-in-situ microstructure evolutions of the feature areas on non-UVA/UVA tensile specimens were compared. Experimental results show that ultrasonic vibration reduces the stress response, but the fracture may occur in advance under excessive ultrasonic amplitude. During the UVA deformation, the easy-to-deform grains with initial orientation close to<101>along the tensile direction rotate to<111>and<001>orientations, which then have a tendency to rotate back to<101>orientation in subsequent deformation. In addition, low-angle grain boundaries and dislocation density are also promoted. Based on the experimental results, a new perspective of the acoustic softening mechanism considering grain rotation and dislocation slip was proposed. The ultrasonic vibration facilitates grain rotation to coordinate plastic deformation. Meanwhile, the superposition of the ultrasonic field intensifies the atomic inherent vibration. The lattice resistance required for dislocation slip decreases accordingly.
Plastic deformation and static recrystallization of pure tantalum are studied using Electron BackScatter Diffraction (EBSD) technique. Recrystallization kinetics are discussed in light of stored energy estimation from EBSD data acquired on deformed microstructures. Characterization of deformed state reveals the influence of crystallographic orientation on the plastic deformation. Dislocation substructures are formed in the γ-fiber grains and almost no substructures are observed in the θ-fiber grains. Subsequent recrystallization directly inherits this orientation dependence of deformed state. Nucleation is promoted in the γ-fiber grains because of substructure development whereas nucleation is more sluggish to occur in the θ-fiber grains. Thus, a microstructure composed mostly of γ-fiber grains recrystallizes faster than a microstructure with a less strong texture, despite a strain nearly three times lower. At the polycrystalline scale (step size of 1.20 μm in the present case), recrystallization kinetics are better described with stored energy estimated through substructures than through dislocation density. At the substructure scale (step size of 90 nm), Geometrically Necessary Dislocation (GND) density seems to be correctly estimated; still recrystallization kinetics cannot be accounted for by this density because it does not account for the substructure formation.
The substitution of a precipitation-hardenable alloy of Cu-0.5wt.%Cr for the widely adopted pure Cu has been proposed for infiltration into the pre-sintered concrete skeleton of particulate and fibrous W. By the reinforcement of a concrete skeleton of particulate and fibrous W along with coherent Cr precipitates in the Cu matrix, the composite exhibited superior comprehensive properties. Specifically, the proposed composite here exhibited a high tensile strength of 601.2 MPa improved by 22.7%, a low friction coefficient of 0.567 decreased by 27.3% and high electrical breakdown strength of 9.07 × 10⁷ V/m increased by 101.5%. Notably, due to the precipitation of the coherent Cr particles to lower the solute content in the Cu matrix, the composite exhibited rather good electrical conductivity of 51.4%IACS. The proposed strategy by infiltration of precipitation-hardenable Cu-based alloys into the W skeleton here provides a new clue for the microstructure design and performance enhancement of novel WCu composites.
Laser cladding deposition (LCD) is widely used to remanufacture/repair workpieces because of its high design freedom to rebuild areas of damage. However, the process often introduces a columnar grain structure in the cladding layer, resulting in a large variation of microstructure and hardness across the cladding layer, welding interface, and base metal. Under fatigue and tensile loading, fractures can initiate in the lower hardness cladding layer. This study explores the feasibility of a new hybrid remanufacturing method integrating the LCD with a subsequent hot deformation process to refine grain structure, reduce hardness variations, and enhance mechanical properties. The effects of deformation temperatures and imposed plastic strains were studied by examining the microstructural and stress-strain behaviour of laser cladded 316L stainless steel. After LCD, compressive deformation was imposed at temperatures of 900 and 1100 °C, with engineering strain levels of 0.1 and 0.5. A high-quality metallurgical joint was achieved, with the optimal ultimate tensile strength and yield strength under process conditions of an engineering strain level of 0.5 imposed at 900°C (35% improvement compared to the directly laser cladding remanufacturing process). Dynamic recrystallization process was observed by the electron back scatter diffraction technique to reveal the underlying mechanism.
The role of microstructure and strain rate on the development of geometrically necessary dislocation (GND) density in polycrystalline copper subjected to compression is assessed via crystal plasticity modelling and electron microscopy. Micropolar crystal plasticity finite element (MP-CPFE) simulations show that GND density is strongly dependent on crystal orientation, with the highest values in grains with a <101> direction parallel to the compression axis. Experimental analysis shows that this relationship breaks down and demonstrates that orientation is only one of many microstructural features that contributes to dislocation density evolution. Texture development as a function of strain rate is also considered, and it is found that the commonly observed <101> compression texture is delocalized from that pole at high strain rate. Furthermore, quantitative analysis of the role of grain boundaries in GND density evolution highlights their role as strong dislocation sources.
Physicallybased constitutive equations are increasingly used for finite element simulations of metal forming processes due to the robust capability of modelling of underlying microstructure evolutions. However, one of thelimitations of current models is the lack of practical validation using real microstructure data due to the difficulties in achieving statistically meaningful data at a sufficiently large microstructure scale. Particularly, dislocation density and grain size governing the hardening in sheet deformation are of vital importance and need to be precisely quantified. In this paper, a set of dislocation mechanics-based plane stress material model is constructed for hot forming aluminum alloy. This material model is applied to high strength 7075 aluminum alloy for the prediction of the flow behaviorsconditioned at 300–400°C with various strain rates. Additionally, an electron backscatter diffraction (EBSD) technique was applied to examine the average grain size and geometrical necessary dislocation (GND) density evolutions, enabling both macro- and micro- characteristics to be successfully predicted. In addition, to simulate the experienced plane stress states in sheet metal forming, the calibrated model is further extended to a plane stress stateto accuratelypredict the forming limits under hot conditions.The comprehensively calibrated material model could be used for guidinga better selection of industrial processing parameters and designing process windows, taking into account both the formed shape as well as post formed microstructure and, hence, properties.
Electron backscatter diffraction (EBSD) in the scanning electron microscope is routinely used for microstructural characterisation of polycrystalline materials. Maps of EBSD data are typically acquired at high stage tilt and slow scan speed, leading to tilt and drift distortions that obscure or distort features in the final microstructure map. In this paper, we describe TrueEBSD, an automatic postprocessing procedure for distortion correction with pixel-scale precision. Intermediate images are used to separate tilt and drift distortion components and fit each to a physically-informed distortion model. We demonstrate TrueEBSD on three case studies (titanium, zirconium and hydride containing Zr), where distortion removal has enabled characterisation of otherwise inaccessible microstructural features.
The present work examined the anisotropy magnitudes obtained from different elastic models of cubic metals (Cu, 5383 Al alloy, FCC austenite steel and BCC steel) to explore the origin of strain anisotropy. The results showed that stable intersections were observed from the modeled and experimental plots of the reciprocal elastic modulus (1/Ehkl) and orientation parameter (Γ). The effectiveness of quasi elasto-plastic model based method in correcting strain anisotropy was further verified in cold-worked specimens. For the important input parameters in dislocation model based diffraction line profile analysis methods, the average diffraction contrast factors of dislocations were observed to depend on elastic constants. Interesting intersections were found from linear dependence of on Γ. The conventional input values indicated distinct dependencies on given elastic constants in diffraction line profile analysis. Accordingly, a refined approach was proposed by adopting the optimized intersections as input values, by which more reliable results could be obtained in practical applications.
Herein, annealing experiments were performed on Cu-filled through silicon via (Cu-TSV) samples in the temperature range of 250–550°C and the relevant microstructural aspects were examined using scanning electron microscope, electron back-scattered diffraction (EBSD) and crystal plasticity (CP) simulations to study the role of grain boundary sliding in Cu on the structural integrity of Cu-TSV. Grain boundary sliding induced non-uniform extrusion of the Cu, as recognized by the formation of vertical steps at the boundaries of Cu grains, was observed in all samples. EBSD of the Cu surface revealed that a group of randomly oriented grains slid relative to each other. CP simulations indicated generation of large shear stresses along the grain boundaries of Cu during annealing that can drive grain boundary sliding. Furthermore, CP simulations also suggested a limited effect of the crystallographic texture of Cu on the plasticity induced extrusion of Cu relative to Si. Finally, grain boundary sliding induced non-uniform extrusion of Cu continued to occur at the highest annealing temperature; however, it could not efficiently relax the thermal stresses and micro-cracks nucleated in Si. This study, therefore, confirms the important role of grain boundary sliding in the stress relaxation and the structural integrity of Cu-TSV samples.
In this study, for the first time, the evolution of geometrically necessary dislocation (GND) and statistically stored dislocation (SSD) densities, as well as their roles in strain hardening during mechanical twinning, was experimentally investigated in a tensile-deformed Fe-22Mn-0.6C twinning-induced plasticity (TWIP) steel. GND and SSD densities were estimated via EBSD-acquired orientation data and a modified strain hardening model, respectively. The analysis demonstrates that the GND density increases non-linearly due to mechanical twinning. The SSD density increases much faster than the GND density, which shows that multiplication of the SSDs is heavily dependent on the imposed strain level. It is revealed that the GND density is higher at early strain stages (below 0.14 true strain), dominating dislocation hardening, but thereafter the SSD density contributes more. It is also found that the GND density is several times higher in this TWIP steel than in metals or alloys, which deform through dislocation slip only. We attribute this difference to the planar slip of dislocations and the occurrence of mechanical twinning, which leads to much more pile-ups of the GNDs at/near boundaries. Mechanical twinning directly contributes less than 100 MPa to flow stress increment in the studied true strain range of 0 to 0.34. Consequently, depending on dislocation types, dislocation multiplication governs strain hardening at all deformation ranges. The findings provide insight into the evolution behaviors of GNDs and SSDs in TWIP steels, which are particularly important for further understanding of the dynamic Hall-Petch effect and useful for TWIP alloy design efforts.
We present an archival format for electron back-scatter diffraction (EBSD) data based on the HDF5 scientific file format. We discuss the differences between archival and data work flow file formats, and present details of the archival file layout for the implementation of h5ebsd, a vendor-neutral EBSD-HDF5 format. Information on sample and external reference frames can be included in the archival file, so that the data is internally consistent and complete. We describe how the format can be extended to include additional experimental modalities, and present some thoughts on the interactions between working files and archival files. The complete file specification as well as an example h5ebsd formatted data set are made available to the reader.
A configurable business process model (sometimes referred to as a reference business process model) may be configured to meet the specific requirements of an organization. The configuration activity is required to automatically determine the variability of a configurable process model and ensure the correctness of a specific process model. However, few approaches solve the problem. In this paper, we propose an innovative approach for automatically separating a configurable process model into atomic and correct sub-process models (sub-process models without abnormal behavioral problems). The atomic sub-process models that fulfill specific requirements are merged into specific process models that are provided for organizations. Compared with existing approaches, since the configuration activity is incorporated into the verification process of a process model at design time and can obtain all feasible configurations, our approach avoids independently handling the configuration activity and does not suffer from computational complexity. Moreover, our approach is language-independent. We have developed a prototype tool for configuring these process models.
In the orthodontic treatment and manufacture of complete dentures, the most important steps are designing and generating a dental arch curve which adapts to the requirements of the patient according to their jaw arch form. The traditional way of acquiring the dental arch curve form is based on manual operation, which will randomly generate a lot of errors caused by human factors. The purpose of this paper is to automatically acquire the dental arch curve and implement the coordinated control of the dental arch generator of the multi‐manipulator tooth‐arrangement robot, which can be used in full denture manufacturing. According to the work principle, motion planning method of the dental arch generator will be analysed. A collaborative simulation of the dental arch generator is realized based on Matlab and ADAMS. Controlled experimentation of the dental arch generator and preliminary tooth‐arrangement experimentation are performed using the multi‐manipulator tooth‐arrangement robot system in order to verify the feasibility of the motion planning method and the technical route. It will lay an
important theoretical foundation for quantitative research on oral restoration and also provide a way to standardize the manufacturing process of full dentures and orthodontic treatments.
The response of polycrystals to plastic deformation is studied at the level of variations within individual grains, and comparisons are made to theoretical calculations using crystal plasticity (CP). We provide a brief overview of CP and a review of the literature, which is dominated by surface observations. The motivating question asks how well does CP represent the mesoscale behavior of large populations of dislocations (as carriers of plastic strain). The literature shows consistently that only moderate agreement is found between experiment and calculation. We supplement this with a current example of microstructure evolution in the interior of a copper sample subjected to tensile deformation. Nondestructive measurements of orientation fields were performed using the near-field high-energy X-ray diffraction microscopy (nf-HEDM) technique at the Advanced Photon Source (APS). Starting at highly ordered grains, a single two-dimensional slice of microstructure containing ∼150 grains was followed through multiple strain states, where it tracked lattice rotations and defect accumulation of up to 14% elongation. In accord with the literature, at the scale of individual grains, comparison of observations with CP models indicates reasonable qualitative agreement but significant variations between simulation and experiment are apparent. The conclusion is that in order to be able to quantify the effects of microstructure on the distributions of slip, orientation change, and damage accumulation, the empirically derived constitutive relations used in continuum-scale simulations need to be improved. Equally important will be the development of large-scale simulations of polycrystals that directly model dislocations.
Consideration is given to the resolution of dislocation density afforded
by EBSD-based scanning electron microscopy. Comparison between the
conventional Hough- and the emerging high-resolution cross-correlation-based approaches
is made. It is illustrated that considerable care must be exercised in selecting
a step size (Burger’s circuit size) for experimental measurements. Important
variables affecting this selection include the dislocation density and the physical
size and density of dislocation dipole and multi-pole components of the structure.
It is also illustrated that simulations can be useful to the interpretation of experimental
recoveries.
When a single crystal deforms by glide which is unevenly distributed over the glide surfaces the lattice becomes curved. The constant feature of distortion by glide on a single set of planes is that the orthogonal trajectories of the deformed glide planes (the c-axes in hexagonal metals) are straight lines. This leads to the conclusion that in polygonisation experiments on single hexagonal metal crystals the polygon walls are planes, while the glide planes are deformed into cylinders whose sections are the involutes of a single curve. The analysis explains West's observation that the c-axes in bent crystals of corundum are straight lines. For double glide on two orthogonal sets of planes there is a complete analogy between the geometrical properties of the distorted glide planes and those of the "slip-lines" in the mathematical theory of plasticity. More general cases are discussed and formulae are derived connecting the density of dislocations with the lattice curvatures. For a three-dimensional network of dislocations the "state of dislocation" of a region is shown to be specified by a second-rank tensor, which has properties like those of a stress tensor except that it is not symmetrical.
An extension to a previously published, novel stereological method is reported which infers experimentally inaccessible components of the Nye GND tensor. Limitations imposed by electron-opacity of metals prevent direct measurement of four components of the Nye tensor, but it is possible to use additional experimentally-obtainable information in connection with underlying field equilibrium equations to estimate these additional components. This approach uses derivatives to the infinitesimal elastic distortion tensor to reduce error imposed by pattern center inaccuracy.
Cross-correlation-based analysis of electron backscatter diffraction patterns has been used to map the distribution of geometrically necessary dislocation (GND) density in deformed polycrystalline copper. Patterning of the dislocations into high-density cell walls and low-density cell interiors was readily observed at the micron scale. Patterning at the longer length scale of the grain size was also evident with high-density regions (GND hot spots) tending to be in clusters, often found close to some but not all grain boundaries and triple junctions.
This study combines nanoindentation, electron backscatter diffraction (EBSD) and crystal plasticity finite element analysis to examine the anisotropy in the indentation behaviour of individual grains within an alpha-Ti polycrystal. Nanoindentation is utilized to mechanically probe small volumes of material within grains for which orientations are known from prior EBSD mapping. Both indentation modulus and hardness decrease significantly as the indentation axis is inclined further from the c-axis; the plastic response showing the more marked anisotropy. Recently developed high angular resolution EBSD has been utilized to examine selected indents, providing maps of elastic strain variations and lattice rotations. From such maps lower bound solutions for the density of geometrically necessary dislocations (GNDs) have been established. Crystal plasticity modelling showed promise in capturing correctly the orientation dependence of load-displacement response and in lattice rotations local to the indenter, particularly for indentation into a basal plane which generated threefold rotational symmetry about an axis parallel with the indentation direction which was also observed in experiments.
The angular resolution of electron backscatter diffraction (EBSD) measurements can be significantly improved using an analysis based on determination of small shifts in features from one pattern to the next using cross-correlation functions. Using pattern shift measurements at many regions of the pattern, errors in the best fit strain and rotation tensors can be reduced. The authors show that elements of the strain tensor and small misorientations can be measured to ± 10?4 and ±0·006° for rotations. We apply the technique to two quite different materials systems. First, we determine the elastic strain distribution near the interface in a cross-sectioned SiGe epilayer, Si substrate semiconductor heterostructure. The plane stress boundary conditions at the sample surface are used to separate every term in the strain tensor. Second, the applicability to structural materials is illustrated by determining the lattice curvature caused by dislocations within the plastic zone associated with the wake and tip of a fatigue crack in a Ni based superalloy. The lattice curvatures are used to calculate the geometrically necessary dislocation content in the plastic zone.
In a large number of industrially important metals and alloys, a fraction of the dislocations generated during deformation remain trapped and arranged into well-defined dislocation boundaries (Bay et al. 1992; Hansen and Juul Jensen 1999; Hughes and Hansen 2000; Li et al. 2004). Extensive investigations using the transmission electron microscope have established that these dislocation boundaries separate volumes of different crystal orientations, and that two classes of dislocation boundaries can be defined (Liu et al. 1998; Hansen 2001). Individual cells are delineated by boundaries referred to as incidental dislocation boundaries (IDBs). These dislocation cells are grouped into cell-blocks, delineated by long planar dislocation boundaries, referred to either as extended planar boundaries or geometrically necessary boundaries. Two of the key quantitative parameters for describing the deformed microstructure are therefore the misorientation angle across each boundary, and the spacing between adjacent dislocation boundaries. This description of the deformed microstructure has proved very useful both in providing information to understand the underlying processes taking place during plastic deformation, and in providing quantitative data that can be used to assess both the mechanical properties and the thermal stability of a deformed sample. © Springer Science+Business Media, LLC 2009. All rights reserved.
We study the link between the indentation size effect and the density of geometrically necessary dislocations (GNDs) through the following approach: four indents of different depth and hardness were placed in a Cu single crystal using a conical indenter with a spherical tip. The deformation-induced lattice rotations below the indents were monitored via a three-dimensional electron backscattering diffraction method with a step size of 50 nm. From these data we calculated the first-order gradients of strain and the GND densities below the indents. This approach allowed us to quantify both the mechanical parameters (depth, hardness) and the lattice defects (GNDs) that are believed to be responsible for the indentation size effect. We find that the GND density does not increase with decreasing indentation depth but rather drops instead. More precisely, while the hardness increases from 2.08 GPa for the largest indent (1230 nm depth) to 2.45 GPa for the smallest one (460 nm depth) the GND density decreases from %2.34 Â 10 15 m À2 (largest indent) to %1.85 Â 10 15 m À2 (smallest indent). Crown
We study the link between the indentation size effect and the density of geometrically necessary dislocations (GNDs) through the following approach: four indents of different depth and hardness were placed in a Cu single crystal using a conical indenter with a spherical tip. The deformation-induced lattice rotations below the indents were monitored via a three-dimensional electron backscattering diffraction method with a step size of 50 nm. From these data we calculated the first-order gradients of strain and the GND densities below the indents. This approach allowed us to quantify both the mechanical parameters (depth, hardness) and the lattice defects (GNDs) that are believed to be responsible for the indentation size effect. We find that the GND density does not increase with decreasing indentation depth but rather drops instead. More precisely, while the hardness increases from 2.08 GPa for the largest indent (1230 nm depth) to 2.45 GPa for the smallest one (460 nm depth) the GND density decreases from %2.34 Â 10 15 m À2 (largest indent) to %1.85 Â 10 15 m À2 (smallest indent). Crown
When a metal is deformed cold, a small fraction of the energy expended in its deformation is stored in the crystal lattice associated with crystal defects and their elastic strain fields. There is evidence that grains having different orientations store different amounts of strain energy, although the data available are restricted to just a few grain orientations or are averages over a zone of orientations. A method is described which allows a more complete measurement of the orientation dependence of the stored strain energy of cold work, and is illustrated for the case of 50% cold rolled copper.
In the present study the relative angular resolution of an electron backscatter diffraction system based on Hough transform analysis has been determined with a silicon single crystal wafer. The resolution is found to be better than 0.1° and can be easily improved by repetition of measurements. A test measurement on a BaFe2As2 thin film, where disorientations of 0.1° and less are present, was performed using the cross correlation electron backscatter diffraction technique. The same measurement is evaluated with the Hough transform technique. Comparing both techniques give evidence of a relative resolution of better than 0.1°. However, in specimen areas with strain inhomogeneities a deviation along one rotation axis can be observed. In the present study the relative angular resolution of an electron backscatter diffraction system based on Hough transform evaluation was determined and compared with high resolution electron backscatter diffraction. A test measurement on a BaFe2As2 thin film provides clear evidence that the angular resolution is better than 0.1°. Only in some specimen areas with strain inhomogeneities deviations are observable.
Microstructure plays a key role in fatigue crack initiation and growth. Consequently, measurements of strain at the microstructural level are crucial to understanding fatigue crack behavior. The few studies that provide such measurements have relatively limited resolution or areas of observation. This paper provides quantitative, full-field measurements of plastic strain near a growing fatigue crack in Hastelloy X, a nickel-based superalloy. Unprecedented spatial resolution for the area covered was obtained through a novel experimental technique based on digital image correlation (DIC). These high resolution strain measurements were linked to electron backscatter diffraction (EBSD) measurements of grain structure (both grain shape and orientation). Accumulated plastic strain fields associated with fatigue crack growth exhibited inhomogeneities at two length scales. At the macroscale, the plastic wake contained high strain regions in the form of asymmetric lobes associated with past crack tip plastic zones. At high magnification, high resolution DIC measurements revealed inhomogeneities at, and below, the grain scale. Effective strain not only varied from grain to grain, but also within individual grains. Furthermore, strain localizations were observed in slip bands within grains and on twin and grain boundaries. A better understanding of these multiscale heterogeneities could help explain variations in fatigue crack growth rate and crack path and could improve the understanding of fatigue crack closure and fracture in ductile metals.
A novel method of micromechanical stereoinference is reported which yields components and gradients of Nye’s GND tensor which are inaccessible by surface EBSD. In particular, it determines the Nye’s tensor gradients going into the sample bulk. The method overcomes limitations imposed by metal’s electron opacity by combining experimentally-accessible Nye’s tensor components and measured infinitesimal elastic distortion tensors with a solution to the underlying stress equilibrium equations. The full Nye’s tensor can be transformed into a crystal coordinate frame and interpreted in the context of slip systems, a more physical sense than in the sample or experimental frame. A demonstration of the method is given for a simulated microstructure. The method is largely robust to random experimental noise but may be sensitive to pattern-center errors.
The evolution of dislocation storage in deformed copper was studied with cross-correlation-based high-resolution electron backscatter diffraction. Maps of 500 mu m x 500 mu m areas with 0.5 mu m step size were collected and analysed for samples deformed in tension to 0%, 6%, 10%, 22.5% and 40% plastic strain. These. maps cover similar to 1500 grains each while also containing very good resolution of the geometrically necessary dislocation (GND) content. We find that the average GND density increases with imposed macroscopic strain in accord with Ashby's theory of work hardening. The dislocation density distributions can be described well with a log-normal function. These data sets are very rich and provide ample data such that quantitative statistical analysis can also be performed to assess the impact of grain morphology and local crystallography on the storage of dislocations and resultant deformation patterning. Higher GND densities accumulate near grain boundaries and triple junctions as anticipated by Ashby's theory, while lower densities are rather more spread through the material. At lower strains (<= 6%) the grain-averaged GND density was higher in smaller grains, showing a good correlation with the reciprocal of the grain size. When combined with a Taylor hardening model this last observation is consistent with the Hall-Petch grain size effect for the yield or flow stress.
The objective of this experimental study is to recognize the roles of several quantities like grain size and orientation distributions on the development of plastic heterogeneities. The measurements are performed on an interstitial free (IF) steel by Electron Back Scattered Diffraction (EBSD) at different states of deformation (from 0% to 17% tensile deformation). For each level of deformation, EBSD maps are performed before and after the deformation on exactly the same area. Several parameters as the Grain Orientation Spread (GOS), the Grain Orientation Spread over the grain Diameter (GOS/D) and the Geometrically Necessary Dislocation (GND) densities can thus be determined for different subpopulations of grains ranked as a function of individual grains sizes to follow the evolution of the deformed-induced microstructure. It appears that none of these grain scale measures are deciding and that grain neighborhood interactions play an important role.
In this study, high resolution ex situ digital image correlation (DIC) was used to measure plastic strain accumulation with sub-grain level spatial resolution in uniaxial tension of a nickel-based superalloy, Hastelloy X. In addition, the underlying microstructure was characterized with similar spatial resolution using electron backscatter diffraction (EBSD). With this combination of crystallographic orientation data and plastic strain measurements, the resolved shear strains on individual slip systems were spatially calculated across a substantial region of interest, i.e., we determined the local slip system activity in an aggregate of ∼600 grains and annealing twins. The full-field DIC measurements show a high level of heterogeneity in the plastic response with large variations in strain magnitudes within grains and across grain boundaries (GBs). We used the experimental results to study these variations in strain, focusing in particular on the role of slip transmission across GBs in the development of strain heterogeneities. For every GB in the polycrystalline aggregate, we have established the most likely dislocation reaction and used that information to calculate the residual Burgers vector and plastic strain magnitudes due to slip transmission across each interface. We have also used molecular dynamics simulations (MD) to establish the energy barriers to slip transmission for selected cases yielding different magnitudes of the residual Burgers vector. From our analysis, we show an inverse relation between the magnitudes of the residual Burgers vector and the plastic strains across GBs. Also, the MD simulations reveal a higher energy barrier for slip transmission at high magnitudes of the residual Burgers vector. We therefore emphasize the importance of considering the magnitude of the residual Burgers vector to obtain a better description of the GB resistance to slip transmission, which in turn influences the local plastic strains in the vicinity of grain boundaries.
A general relationship between stress and plastic strain in a polycrystalline aggregate is derived for any metal in which individual crystals deform by slipping over preferred planes under a critical shear stress. Full account is taken of the non-uniform distortion due to mutual constraints between the grains of an aggregate. It is shown that a plastic potential exists which is identical with the yield function. Upper and lower bounds are obtained for an approximate calculation of this function for any applied system of combined stresses.
Reported here is a study of the pattern of lattice curvature near the interface of deformed high-purity aluminium (99.9999%) bicrystals of specified crystallographic character (large-angle random). Curvature data are obtained from electron back-scattering diffraction pattern observations using orientation imaging microscopy. The concept of geometrically necessary dislocations (GNDs) is used as the central tool in the description of the observations. The samples studied were channel-die compressed perpendicular to the interface to plastic strain levels of 0.1 and 0.3. At a strain level of 0.1 the primary observation is the development of a pile-up of GNDs (i.e. lattice curvature) near the interface. At the higher strain level of 0.3, however, a dramatic change in the distribution is observed. The nature of this change suggests that the interface has absorbed (or emitted) some components of the nearby GND field, with an accompanying change in the local character of the interface towards a broader dispersion of misorientation character.
Halloysite nanotubes (HNTs) were used as nano-adsorbents for removal of the cationic dye, Malachite Green (MG), from aqueous solutions. The adsorption of the dye was studied with batch experiments. The natural HNTs used as adsorbent in this work were initially characterized by FT-IR and TEM. The effects of adsorbent dose, initial pH, temperature, initial dye concentration and contact time were investigated. Adsorption increased with increasing adsorbent dose, initial pH, and temperature. Equilibrium was rapidly attained after 30min of contact time. Pseudofirst-order, pseudo-second-order and intraparticle diffusion models were considered to evaluate the rate parameters. The adsorption followed pseudo-second-order kinetic model with correlation coefficients greater than 0.999. The factors controlling adsorption process were also calculated and discussed. The maximum adsorption capacity of 99.6mgg−1 of MG was achieved in pH=9.5. Thermodynamic parameters of ΔG°, ΔH° and ΔS° indicated the adsorption process was spontaneous and endothermic.
Experimental studies on indentation into face-centered cubic (FCC) single crystals such as copper and aluminum were performed to reveal the spatially resolved variation in crystal lattice rotation induced due to wedge indentation. The crystal lattice curvature tensors of the indented crystals were calculated from the in-plane lattice rotation results as measured by electron backscatter diffraction (EBSD). Nye's dislocation density tensors for plane strain deformation of both crystals were determined from the lattice curvature tensors. The least L-norm solutions to the geometrically necessary dislocation densities for the case in which three effective in-plane slip systems were activated in the single crystals associated with the indentation were determined. Results show the formation of lattice rotation discontinuities along with a very high density of geometrically necessary dislocations.
Plastic deformation in polycrystalline materials involves a complex interaction of dislocations with defects in the lattice. The geometrically necessary component of the dislocation density can be quantified to some extent using data obtained from automated electron backscatter diffraction scans over planar regions or volumes using the three-dimensional imaging techniques that are currently available. Reliable measurements require that the step size of the orientation data used in determination of geometrically necessary dislocation densities be on the scale of the microstructural information. Measurements were performed in deformed Cu, Al and steel specimens. Geometrically necessary dislocation density in Cu deformed 10% in compression was about 15–30% of the overall estimated dislocation density. Measurements in Al demonstrate that three-dimensional estimates are on the order of 1.2–2 times the values obtained from 2D measurements on the same structures. Analysis of interstitial free steel specimens shows an increase in average geometrically necessary dislocation density by an order of magnitude for specimens deformed to 12% tensile deformation elongation.
In continuation of a previous paper (Bishop and Hill 1951) it is conjectured that the work done in plastically deforming a polycrystal is approximately equal to that which would be done if the grains were free to deform equally. In conjunction with the principle of maximum plastic work, this enables the yield function of an aggregate to be calculated. This is done for an isotropic aggregate of face-centred cubic crystals, following a determination of the stresses needed to produce multi-slip. The theoretical yield criterion lies between those of Tresca and von Mises, in good agreement with observaton for copper and aluminum. It is shown further that the work-hardening of an aggregate would be a function only of the total plastic work if the grains hardened equally ; the departure from this functional relation is expressed explicitly in terms of the non-uniform hardening.
Characterizing the content of geometrically necessary dislocations (GNDs) in crystalline materials is crucial to understanding plasticity. Electron backscatter diffraction (EBSD) effectively recovers local crystal orientation, which is used to estimate the lattice distortion, components of the Nye dislocation density tensor (α), and subsequently the local bulk GND density of a material. This paper presents a complementary estimate of bulk GND density using measurements of local lattice curvature and strain gradients from more recent high resolution EBSD (HR-EBSD) methods. A continuum adaptation of classical equations for the distortion around a dislocation are developed and used to simulate random GND fields to validate the various available approximations of GND content.
Eagerly awaited, this second edition of a best-selling text comprehensively describes from a modern perspective the basics of x-ray physics as well as the completely new opportunities offered by synchrotron radiation. Written by internationally acclaimed authors, the style of the book is to develop the basic physical principles without obscuring them with excessive mathematics. The second edition differs substantially from the first edition, with over 30% new material, including: A new chapter on non-crystalline diffraction - designed to appeal to the large community who study the structure of liquids, glasses, and most importantly polymers and bio-molecules. A new chapter on x-ray imaging - developed in close cooperation with many of the leading experts in the field. Two new chapters covering non-crystalline diffraction and imaging. Many important changes to various sections in the book have been made with a view to improving the exposition. Four-colour representation throughout the text to clarify key concepts. Extensive problems after each chapter. There is also supplementary book material for this title available online (http://booksupport.wiley.com). Praise for the previous edition: "The publication of Jens Als-Nielsen and Des McMorrow's Elements of Modern X-ray Physics is a defining moment in the field of synchrotron radiation... a welcome addition to the bookshelves of synchrotron-radiation professionals and students alike. ... The text is now my personal choice for teaching x-ray physics..." - Physics Today, 2002.
Recent advances using cross-correlation analysis of full resolution high quality electron backscatter diffraction (EBSD) patterns have provided a method for quantitatively mapping the stored dislocation density at high spatial resolution. Larger areas could be mapped with image binning or coarser step sizes. We have studied the effects of image binning and step size on the recovery of GND density. Our results suggest that: (i) the measured lower bound GND density noise floor broadly agrees with Wilkinson and Randman's 2009 prediction, where a decrease in step size or an increase in misorientation uncertainty increases the noise floor; (ii) increasing the step size results in a lower GND density being recovered as some dislocations are now considered as statistically stored dislocations (SSDs); (iii) in deformed samples the average GND density stays relatively constant as the degree of pattern binning is increased up to 8×8. Pattern binning thus provides a means of increasing the data acquisition and analysis rate without unduly degrading the data quality.
The deformation around a 500-nm deep Berkovich indent in a large grained Fe sample has been studied using high resolution electron back scatter diffraction (EBSD). EBSD patterns were obtained in a two-dimensional map around the indent on the free surface. A cross-correlation-based analysis of small shifts in many sub-regions of the EBSD patterns was used to determine the variation of elastic strain and lattice rotations across the map at a sensitivity of similar to +/- 10(-4). Elastic strains were smaller than lattice rotations, with radial strains found to be compressive and hoop strains tensile as expected. Several analyses based on Nye's dislocation tensor were used to estimate the distribution of geometrically necessary dislocations (GNDs) around the indent. The results obtained using different assumed dislocation geometries, optimisation routines and different contributions from the measured lattice rotation and strain fields are compared. Our favoured approach is to seek a combination of GND types which support the six measurable (of a possible nine) gradients of the lattice rotations after correction for the 10 measurable elastic strain gradients, and minimise the total GND line energy using an L(1) optimisation method. A lower bound estimate for the noise on the GND density determination is similar to +/- 10(12) m(-2) for a 200-nm step size, and near the indent densities as high as 10(15) m(-2) were measured. For comparison, a Hough-based analysis of the EBSD patterns has a much higher noise level of similar to +/- 10(14) m(-2) for the GND density.
We have used EBSD orientation mapping and digital image correlation-based strain mapping to investigate inhomogeneous deformation of Ti-6Al-4V in tension, fatigue and cold-dwell fatigue. Strong strain inhomogeneities were found in all loading modes and in each case the pattern of high and low strain is established relatively early in the tests. Comparing the orientation and strain maps shows that grain-grain interactions are the primary cause of strain concentration. Surface grains with the crystallographic c-axis parallel to the loading direction showed very low strain levels, and neighbouring grains showed exceptionally high strain levels. In both fatigue and dwell fatigue, these regions of high strain concentration were observed to act as sites for crack nucleation. Strain evolution was found to be significantly different in each loading mode: in particular, deformation in dwell fatigue appears to have similarities with creep deformation. (C) 2012 Elsevier Ltd. All rights reserved.
Cross-correlation-based electron backscattering diffraction analysis has been used to map lattice rotations in Ti-6Al-4V polycrystals deformed by load-controlled fatigue and dwell fatigue including a hold at maximum load. The lattice curvatures were used to form lower bound estimates of the geometrically necessary dislocation (GND) density distributions. In all cases the density of < a >-type GNDs was much higher than for < c + a >-type GNDs. As for tensile deformation the GND density histograms were significantly skewed toward the high density side. Observations of interrupted fatigue tests suggested that the density of < a >-type GNDs decreases during continued cyclic loading, presumably due to the formation of tightly bound dipoles and multipole structures. As has been proposed in models of facet fatigue formation, an example is presented of the accumulation, within a soft grain, of GNDs in a diffuse pile-up against a grain boundary with a hard grain. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
We have used cross-correlation-based analysis of electron backscatter diffraction patterns to map lattice rotations in polycrystalline samples of Ti-6Al-4V before and after moderate (6%) tensile deformation. The sensitivity is improved compared to conventional Hough-based indexing and allows the density of geometrically necessary dislocations (GNDs) to be determined to similar to 3 x 10(12) m(-2) at a step size of 250 nm. In the undeformed sample there were a few grains with GND density significantly higher than the background level. These tended to be of small area and associated with neighbouring regions of beta-phase exhibiting the Burgers relation. After deformation the overall GND density increased, with < a > dislocations some 20 times more frequent than < c + a > ones. Evidence is given of elevated GND densities close to some, but not all, grain boundaries after deformation. This was also the most likely reason for the trend for the grain-averaged GND density to be higher for grains with small area on the section plane. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
We have examined the interaction of a blocked slip band and a grain boundary in deformed titanium using high-resolution electron backscatter diffraction and atomic force microscopy. From these observations, we have deduced the active dislocation types and assessed the dislocation reactions involved within a selected grain. Dislocation sources have been activated on a prism slip plane, producing a planar slip band and a pile-up of dislocations in a near screw alignment at the grain boundary. This pile-up has resulted in activation of plasticity in the neighbouring grain and left the boundary with a number of dislocations in a pile-up. Examination of the elastic stress state ahead of the pile-up reveals a characteristic "one over the square root of distance" dependence for the shear stress resolved on the active slip plane. This observation validates a dislocation mechanics model given by Eshelby, Frank and Nabarro in 1951 and not previously directly tested, despite its importance in underpinning our understanding of grain size strengthening, fracture initiation, short fatigue crack propagation, fatigue crack initiation and many more phenomena. The analysis also provides a method to measure the resistance to slip transfer of an individual grain boundary in a polycrystalline material. For the boundary and slip systems analysed here a Hall-Petch coefficient of K = 0.41 MPa m(1/2) was determined. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Mapping of residual stresses at the mesoscale is increasingly practical thanks to technological developments in electron backscatter diffraction (EBSD) and X-ray microdiffraction using high brilliance synchrotron sources. An analysis is presented of a Cu single crystal deformed in compression to about 10% macroscopic strain. Local orientation measurements were made on sectioned and polished specimens using EBSD and X-ray microdiffraction. In broad strokes, the results are similar to each other with orientations being observed that are on the order of 5° misoriented from that of the original crystallite. At the fine scale it is apparent that the X-ray technique can distinguish features in the structure that are much finer in detail than those observed using EBSD even though the spatial resolution of EBSD is superior to that of X-ray diffraction by approximately two orders of magnitude. The results are explained by the sensitivity of the EBSD technique to the specimen surface condition. Dislocation dynamics simulations show that there is a relaxation of the dislocation structure near the free surface of the specimen that extends approximately 650 Å into the specimen. The high spatial resolution of the EBSD technique is detrimental in this respect as the information volume extends only 200 Å or so into the specimen. The X-rays probe a volume on the order of 2 µm in diameter, thus measuring the structure that is relatively unaffected by the near-surface relaxation.
DISLOCATION STRUCTURE AND WORK-HARDENING OF COPPER SINGLE CRYSTALS WITH [100] AXIS ORIENTATIONI. DISLOCATION ARRANGEMENT AND CELL STRUCTURE OF CRYSTALS DEFORMED IN TENSIONCopper single crystals with [100] axis orientation are deformed in tension at room temperature and after load-removal are irradiated with neutrons to stabilize the dislocation arrangement before the preparation of thin foils. TEM investigations of {111}-, {110}- and {100}-foils and the analysis of Burgers vectors and lino vectors yield the essential information about the dislocation arrangement. A cell structure is observed which is, in principle, the same in all stages of deformation. This cell structure consists of nearly dislocation free regions of varying sizes surrounded by walls of dislocation networks without preferred orientation.The most important parameters of this dislocation structure are measured as a function of stress: Dislocations of all 6 Burgers vectors—including those which do not operate under the external stress—occur with equal frequency. The same is true for the different characters of dislocations.Total dislocation density ρ: τ = 0·30 Gb√rH. Mean diameter of cells D = 4·2 Gb/τ. Ratio of dislocation free areas to the total area of the glide plane p(τ) = 0·55 = constant. The average diameter of the walls is nearly proportional to 1/τ.The results are compared with other measurements.
To clarify the effect of grain orientation on the evolution of dislocation structures in metals of medium-to-high stacking fault energy, detailed TEM characterization of structures was carried out for more than 350 individual grains in Al and Cu deformed in tension or by cold rolling up to moderate strain levels (ϵvM ≤ 0.8). Efforts were made to obtain a precise description of the three-dimensional arrangement of the dislocation structures and to determine the crystallographic plane of extended dislocation boundaries (geometrically necessary boundaries). A universal pattern of structural evolution characterized by a formation of three types of structure was found in both metals, irrespective of material parameters (stacking fault energy, grain size and impurity) and deformation conditions (deformation mode, strain and strain rate). The key parameter controlling the formation of the different structural types was found to be grain orientation with respect to the deformation axis (axes) and a clear relationship between the structural type and the grain orientation was established. A review of single crystal data shows a similar relationship. The grain orientation dependence of the structural type and similar structural types observed in tension and rolling suggest a common cause. Part II explores this by relating the structural types to the active slip systems.
From local orientation measurements on planar surfaces by means of electron backscattering diffraction, six components of the lattice curvature tensor can be identified. They allow determination of five components of the dislocation density tensor (thus two more than hitherto reported) and, additionally, one difference between two other components. With this information improved lower bounds for the geometrically necessary dislocation content are obtained by linear optimization. (c) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Cross-correlation-based analysis of electron back-scatter diffraction (EBSD) patterns has been used to obtain high angular resolution maps of lattice rotations and elastic strains near carbides in a directionally solidified superalloy MAR-M-002. Lattice curvatures were determined from the EBSD measurements and used to estimate the distribution of geometrically necessary dislocations (GNDs) induced by the deformation. Significant strains were induced by thermal treatment due to the lower thermal expansion coefficient of the carbide inclusions compared to that of the matrix. In addition to elastic strains the mismatch was sufficient to have induced localized plastic deformation in the matrix leading to a GND density of 3 × 1013 m–2 in regions around the carbide. Three-point bending was then used to impose strain levels within the range ±12% across the height of the bend bar. EBSD lattice curvature measurements were then made at both carbide-containing and carbide-free regions at different heights across the bar. The average GND density increases with the magnitude of the imposed strain (both in tension and compression), and is markedly higher near the carbides particles. The higher GND densities near the carbides (order of 1014 m–2) are generated by the large strain gradients produced around the plastically rigid inclusion during mechanical deformation with some minor contribution from the pre-existing residual deformation caused by the thermal mismatch between carbide and nickel matrix.
A well-organized dislocation structure forms in many polycrystalline metals during plastic deformation. This structure is described qualitatively with no explanation of the quantitative characterization. In this work, the evolution of dislocation structure in commercial purity aluminum is described by means of the excess dislocation density and by quantitative characterization of the cell structure as seen on a plane surface. The measurements were performed on a pseudo-internal surface of a split specimen deformed by channel die deformation. The results show a clear dependence of cell structure formation on orientation of the crystallite with respect to the imposed deformation gradient with the largest excess dislocation density occurring in grains of {0 1 1}[1 2 2] orientation for plane strain deformation. Neighboring grain and non-local effects are shown to be of importance in the type of dislocation structures that evolve.
A single nickel crystal is indented with a wedge indenter such that a two-dimensional deformation state with three effective plane strain slip systems is induced. The in-plane lattice rotation of the crystal lattice is measured with a three micrometer spatial resolution using Orientation Imaging Microscopy (OIM). All non-zero components of the Nye dislocation density tensor are calculated from the lattice rotation field. A rigorous analytical expression is derived for the lower bound of the total Geometrically Necessary Dislocation (GND) density. Existence and uniqueness of the lower bound are demonstrated, and the apportionment of the total GND density onto the effective individual slip systems is determined. The lower bound solution reduces to the exact solution under circumstances in which only one or two of the effective slip systems are known to have been activated. The results give insight into the active slip systems as well as the dislocation structures formed in the nickel crystal as a result of the wedge indentation.
Classical plasticity has reached its limit in describing crystalline material behavior at the micron level and below. Its inability to predict size-dependent effects at this length scale has motivated the use of higher-order gradients to model material behavior at the micron level. The physical motivation behind the use of strain gradients has been based on the framework of geometrically-necessary dislocations (GNDs). A new but equivalent definition for Nye's dislocation tensor, a measure of GND density, is proposed, based on the integrated properties of dislocation lines within a volume. A discrete form of the definition is applied to redundant crystal systems, and methods for characterizing the dislocation tensor with realizable crystallographic dislocations are presented. From these methods and the new definition of the dislocation tensor, two types of three-dimensional dislocation structures are found: open periodic networks which have long-range geometric consequences, and closed three-dimensional dislocation structures which self-terminate, having no geometric consequence. The implications of these structures on the presence of GNDs in polycrystalline materials lead to the introduction of a Nye factor relating geometrically-necessary dislocation density to plastic strain gradients.
Recent advances in high-resolution electron backscatter diffraction (EBSD)-based microscopy are applied to the characterization of elastic fields and incompatibility structures near the grain boundaries (GBs) in polycrystals. Two main recoveries are reported here: surface geometrically necessary dislocation (density) tensors, as described by Kröner, and the elastic fields near cracks (unconsolidated portions of interface) in loaded samples. Context for the application of these recoveries is described, using Green’s function solutions for combined heterogeneity and dislocation. Featured recoveries required the cross-correlation based determination of the elastic distortion tensor, aided by application of the simulated pattern method, and determination of the absolute pattern center utilizing the expected pattern properties in a spherical Kikuchi reference frame. High-resolution data obtained along an ultrasonically consolidated nickel boundary of varying amalgamation indicates that the imposed traction free boundary condition at free surfaces is well observed in the data structure. Further, high-resolution data acquired near a single grain boundary in well-annealed, low content steel suggests that it may be possible to measure the intrinsic elastic properties of GBs.
In this paper we explore methods of measuring elastic strain variations in the presence of larger lattice rotations (up to -11°) using high resolution electron backscatter diffraction. We have examined the fundamental equations which relate pattern shifts to the elastic strain tensor and modified them to a finite deformation framework from the original infinitesimal deformation one. We incorporate the traction free boundary condition into the minimisation problem for the finite deformation case (i.e. large rotations and small elastic strains). Numerical experiments show that this finite deformation kinematic analysis continues to work well, while the infinitesimal analysis fails, when the misorientation between test and reference pattern is made increasingly high. However, measurements on patterns simulated using dynamical diffraction theory indicated that this formulation is not sufficient to recover elastic strains accurately because the pattern shifts are not determined accurately when large rotations are present. To overcome this issue we remap the test pattern to an orientation that is close to that of reference pattern. This remapping was defined by a finite rotation matrix, which was estimated from the infinitesimal rotation matrix measured using cross-correlation. A second cross-correlation analysis between the reference pattern and the remapped test pattern allows the elastic strains to be recovered using the much simpler infinitesimal deformation theory. We have also demonstrated that accurate recovery of elastic strains requires accurate knowledge of the pattern centre if this remapping algorithm is used.
This book explains concepts of transmission electron microscopy (TEM) and x-ray diffractometry (XRD) that are important for the characterization of materials. The third edition has been updated to cover important technical developments, including the remarkable recent improvement in resolution of the TEM. This edition is not substantially longer than the second, but all chapters have been updated and revised for clarity. A new chapter on high resolution STEM methods has been added. The book explains the fundamentals of how waves and wavefunctions interact with atoms in solids, and the similarities and differences of using x-rays, electrons, or neutrons for diffraction measurements. Diffraction effects of crystalline order, defects, and disorder in materials are explained in detail. Both practical and theoretical issues are covered. The book can be used in an introductory-level or advanced-level course, since sections are identified by difficulty. Each chapter includes a set of problems to illustrate principles, and the extensive Appendix includes laboratory exercises.
A set of dynamically simulated electron backscatter patterns (EBSPs) for α-Ti crystals progressively rotated by 1° steps were analysed using cross-correlation to determine image shifts from which strains and rotations were calculated. At larger rotations the cross-correlation fails in certain regions of the EBSP where large shifts are generated. These incorrect shifts prevent standard least square error procedures from obtaining a valid solution for the strain and rotation, where the applied rotation exceeds ∼ 8°. Using a robust iterative fitting routine reliable strains and rotations can be obtained for applied rotations of up to and including ∼ 11° even though some image shifts are measured incorrectly. Finally, high resolution electron backscatter diffraction has been used to analyse the residual elastic strain, lattice rotations and density of stored geometrically necessary dislocations in a sample of copper deformed to 10% total strain. The robust iterative fitting analysis allows reliable analysis of a larger proportion of the map, the difference being most obviously beneficial in regions where significant lattice rotations have been generated.
"A revised version of the last part of Théorie et technique de la radiocristallographie." First ed. published in 1945 under title: Radiocristallographie. Incluye bibliografía