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Size Effects in Meso- and Microscaled Forming
Published in Xin Min Lai, Ming Wang Fu, Lin Fa Peng, Sheet Metal Meso- and Microforming and Their Industrial Applications, 2018
Xin Min Lai, Ming Wang Fu, Lin Fa Peng
where τ is the shear flow stress, μ is the shear modulus, b is the magnitude of Burgers vector, α is an empirical coefficient around 0.3, and ρs and ρG are the densities of statistically stored and geometrically necessary dislocations, respectively. The tensile flow stress σflow can be expressed by σflow = Mτ, where M is the Taylor coefficient. M = 3.06 stands for an FCC crystal and body-centered cubic crystal with <110> slip plane [44].
The structure and mechanical properties of nanocrystals
Published in A. M. Glezer, E. V. Kozlov, N. A. Koneva, N. A. Popova, I. A. Kurzina, Plastic Deformation of Nanostructured Materials, 2017
A. M. Glezer, E. V. Kozlov, N. A. Koneva, N. A. Popova, I. A. Kurzina
The dislocation-free grains are observed when their size is smaller than the second critical size which for the pure metals is close to dcr ≤ 100 nm [10]. As a result of grain refining produced by severe plastic deformation, large changes take place in the structure of the polycrystalline aggregate. Firstly the density of the grain boundaries increases. Secondly, the high density of defects at the grain boundaries is retained. These are the defects of the dislocation and disclination type and also grain boundary steps. Thirdly, the defective structure of the body of the grains changes. The scalar dislocation density inside the grains decreases (Fig. 2.27]. Figure 2.27 shows that dcr = 100 nm for pure metals. Fourthly, the fraction of the geometrically necessary dislocations in the dislocation structure increases. The internal stresses increase correspondingly. Fifthly, when reaching some critical grain size the dislocations leave the body of the grain and concentrate at the grain boundaries. Sixthly, the fraction of the ternary junctions of the grains increases and the dislocation density in them also increases. Seventhly, the change of the grain size increases the density of disclinations and their power and also the curvature —torsion of the crystal lattice. When the parameters of the critical grain structure are reached, the main type of defects−dislocations —changes to partial disclinations. When the grain size approaches the critical value, the intragranular dislocation density initially decreases and the grains then become dislocation-free. This is accompanied by an increase of the density of the partial disclinations at the grain boundaries and, in particular, at the triple junctions. At the average grain size of d = 100 nm, the dislocation structure in the nanopolycrystals is completely replaced by the disclination structure. The density of the disclinations reaches the values equal to the dislocation density in the deformed materials. At the grain size of d ≤ 100nm, the dislocation sliding in the nanograins steel takes place about the buildup of dislocation no longer curse. With a further decrease of the grain size the total dislocations are replaced by partial dislocations, twins, stacking faults, semi-symmetric sections of the free and constricted volumes. The investigation of the properties of the nanopolycrystals showed that the different grain sizes, the sizes of their sections in grain boundaries ensure different mechanisms of the deformation processes, phase transitions, achievement of the equilibrium properties and can be critical. The main critical ranges of the grain size and of their areas are presented in Table 2.3 [101,102].
Heterogeneous microstructure and mechanical behaviour of Al-8.3Fe-1.3V-1.8Si alloy produced by laser powder bed fusion
Published in Virtual and Physical Prototyping, 2023
S.J. Yu, P. Wang, H.C. Li, R. Setchi, M.W. Wu, Z.Y. Liu, Z.W. Chen, S. Waqar, L.C. Zhang
Geometrically necessary dislocations (GND) are the key factor to estimate the value of dislocation strengthening, which refers to the force required to form plastic deformation. The relationship between dislocation strengthening and GND can be expressed by the Bailey-Hirsch (or Taylor) relationship as shown (Bailey and Hirsch 1962): where MTaylor is set as 3.33 for both the S350 and the S200 samples according to the data from EBSD analysis (Stoller and Zinkle 2000; Hadadzadeh, Amirkhiz, and Mohammadi 2019) that correlates the yield stress to the critical resolved shear stress for polycrystal metals, α is a material-dependent constant (Al = 0.16) (Hadadzadeh, Amirkhiz, and Mohammadi 2019). G is the shear modulus (G = 26.5 GPa) (Hadadzadeh et al. 2019), b is the value of the Burgers vector (b = 0.286 nm) (Miyajima et al. 2010), and follows the following equation. where V is the volume fraction of each zone and is GND of each zone, which are mentioned above (Figure 4). Based on equation 11, of S200 and S350 are 1.94 × 1014/m2 and 1.84 × 1014/m2, respectively, thereby and σdis of S200 and S350 sample is calculated as 56 and 54 MPa.
Generation and accumulation of atomic vacancies due to dislocation movement and pair annihilation
Published in Philosophical Magazine, 2018
Movement of dislocations realises plastic slip deformation of metallic materials. Dislocations accumulate and annihilate during the plastic deformation and a numerous amount of atomic vacancies are supposed to be generated due to pair annihilation of edge dislocations with positive and negative signs. Essmann and Mughrabi [22] proposed a model for the density evolution of atomic vacancy due to pair annihilation of edge dislocations during slip deformation as follows:where N, Z, , D and γ denote the numbers of atoms and vacancies in unit volume, magnitude of the Burgers vector, dislocation annihilation distance and plastic shear strain, respectively. and ce denote the accumulated density of edge dislocations and the ratio of contribution from the edge component to the plastic shear strain, respectively. Moving dislocations are assumed to sweep up vacancies located within a distance yp above and below the glide plane. The density is considered to be the statistically stored dislocations (SSDs) but not the geometrically necessary dislocations (GNDs) because the density of GNDs originates from the excess of the Burgers vector and individual dislocations are assumed not to be able to find its opponent to annihilate. Essmann and Mughrabi [22] showed saturation values of vacancy for some extreme cases but not their evolution. In this study, we evaluate the evolution of vacancy density by integrating the model by using some additional models for the crystal plasticity analysis.
Particulate metal matrix composites and their fabrication via friction stir processing – a review
Published in Materials and Manufacturing Processes, 2019
Padmakumar A. Bajakke, Vinayak R. Malik, Anand S. Deshpande
Another way of strengthening composites is by the formation of geometrically necessary dislocations (GNDs). This can be achieved by a mismatch in the coefficient of thermal expansion (CTE) and in elastic modulus (EM) between the metal matrix and the reinforcements. The density of GND resulting from CTE and EM mismatch can be estimated by the following mathematical expression (10) and (11) .[124]