Strain Energy Of Dislocation Research Articles

Flow behavior and dynamic recrystallization mechanism of a new near-alpha titanium alloy Ti-0.3Mo-0.8Ni-2Al-1.5Zr

A new near-α titanium alloy Ti-0.3Mo-0.8Ni-2Al-1.5Zr was designed based on Ti-0.3Mo-0.8Ni (TA10). The hot compression tests were carried out at temperatures of 800–970 °C and strain rates of 0.01–5 s−1. The results show that the flow softening phenomenon in the α + β phase region is more distinct than that in the single β phase region. The Arrhenius constitutive models based on strain compensation in the α+β phase region and β phase region were established respectively, and the correlation coefficient between the predicted flow peak stress values and the experimental values reached 0.99365. The hot processing map of the alloy was established, the processing parameters of the peak efficiency: 800 ≤ T ≤ 818 °C, 0.01 ≤ ε˙ ≤ 0.0235 s−1, and 960 ≤ T ≤ 970 °C, 0.01 ≤ ε˙ ≤ 0.0213 s−1. The microstructure evolution and deformation mechanism of the compressed specimens were researched by electron backscatter diffraction (EBSD) technique. There were two nucleation mechanisms for dynamic recrystallization (DRX): sub-grains growth nucleation and high angle grain boundaries (HAGBs) bulging nucleation, the former was continuous dynamic recrystallization (CDRX), and the latter was discontinuous dynamic recrystallization (DDRX). The flow stress in the α+β phase region was softened by CDRX and dynamic recovery (DRV), while the principal deformation mechanisms in the β phase region are DRV and DDRX. The dislocation strain energy and recrystallization ability at different temperatures were quantitatively analyzed by the kernel average misorientation (KAM) and the geometrically necessary dislocation (GND), and the results showed that more complete recrystallization occurred at lower temperature in the α + β phase region. The HCP slip was principally completed by prismatic ⟨a⟩ and pyramidal ⟨c+a⟩ slip systems during the hot compression, while BCC was a mixed mode of {110}, {112} and {113} multiple slips.

Influence of magnetic field on the mechanical behavior of friction stir processed paramagnetic alloy

The study investigated the influence of an externally applied static magnetic field (MF) on the mechanical behavior of a friction stir processed paramagnetic 1100 aluminum (Al 1100) alloy. The aim was to take advantage of the solid-state friction stir processing (FSP) technique to modify the microstructure and further improve the properties by testing in the presence of MF. Al 1100 was tested in tension under different static MFs (B = 0, 150, 1000, 1400, 1800, and 2200 Gauss) perpendicular to the stress axis. The strong effect of a comparatively weak static MF was observed on the elongation of both base and processed Al 1100 alloy, in both rolling and transverse directions, attributed to the magneto-plasticity effect (MPE) where the motion of dislocations in crystals is influenced in the presence of magnetic fields. Amongst the different mechanisms associated with MPE, the major effect in the current study was observed from the magnetization force, spin transition, and increase in strain energy of dislocations. This knowledge will open new lanes to improve the properties of a processed sample by exposing it to an MF which is a non-contact, pollution-free route; saving time and cost by avoiding in-between thermo-mechanical steps to break the cast microstructure.

Revealing the acoustic effects on heat transfer and material flow in ultrasonic assisted friction stir welding of dissimilar Al/Mg alloys

Development of a reasonable constitutive equation is critical to realize accurate numerical prediction of ultrasonic vibration-assisted friction stir welding (UVaFSW) of dissimilar Al/Mg alloys and deepen the understanding of the synchronous interaction between the ultrasonic vibration exerted on the tool and the tool induced thermo-mechanical behavior. Considering the thermal activation and dislocation evolution mechanisms, the calculation method of acoustic stress work based on the change of dislocation strain energy is redefined, and a modified acoustic-plastic constitutive equation is developed. The modified constitutive equation was applied to the computational fluid dynamics (CFD) model combined with the volume of fluid (VOF) method and quantitative analysis was conducted on the acoustic effects on heat generation, material flow and intermixing in UVaFSW of Al/Mg alloys. The results indicate that the exerted ultrasonic vibration has a little effect on the total heat due to the multiple effects of acoustic softening, acoustic antifriction and additional acoustic heat, but can promote the material flow around the tool and expand the material intermixed region. The experimental research validates the calculated results, and it is indicated that the flow stress and temperature field calculated by the improved constitutive equation have higher accuracy in UVaFSW of Al/Mg alloys.

Anomalous Local Lattice Softening around Kink Boundaries in a Mille-Feuille Structured Dilute Mg–Zn–Y Alloy

We have evaluated local elastic properties at kink boundaries in dilute Mg-Zn-Y alloys based on scanning transmission electron microscopy (STEM), first-principles calculations, and geometrical phase analysis (GPA) by measuring atomic-scale strain fields around dislocation cores. STEM observations showed that dislocations constituting kink boundaries are extended into Shockley partial dislocations by accompanying solute-enriched stacking faults (SESF). Using GPA analysis, we found that strain distributions around the partial dislocation cores are asymmetric across the Mg matrix and the SESF, showing local elastic heterogeneity. Comparison with the calculated strain field model, it is indicated that the observed asymmetric strain profiles are essentially caused by a softening of the Mg matrix. This anomalous elastic softening can be interpreted as a change in strain energy of dislocations at the kink boundary, which may contribute to the unique deformation mechanism of kink in dilute Mg alloys.

Dislocation strain energy based modeling for ultrasonic effect on friction stir lap welding process of dissimilar Mg/Al alloys

Understanding of the ultrasonic effect on the process variables has important significance for the process optimization in ultrasonic vibration enhanced friction stir lap welding (UVeFSLW) of dissimilar Mg/Al alloys. In this study, the dislocation strain energy in both grain interior and grain boundary is considered to improve the formula for determing threshold thermal stress, and the constitutive equation is modified and used to develop the model for Mg/Al UVeFSLW process. The influences of ultrasonic vibration on heat generation, temperature profile, material flow and intermixing are quantitatively analyzed. It is found that the ultrasonic vibration induced the flow stress reduction gets larger, and the interfacial heat generation and viscous dissipation heat generation in the shear layer drop, which results in lower temperature at the tool/workpiece interface, intensifier material flow and larger material intermixed region in Mg/Al UVeFSLW. The interface temperature between the tool/workpiece and the profile of thermo-mechanically affected zone are experimentally measured, and compared with the predicted ones. The results show that the calculation accuracy of the modified model is improved.

Ultra-dense dislocations stabilized in high entropy oxide ceramics

Dislocations are commonly present and important in metals but their effects have not been fully recognized in oxide ceramics. The large strain energy raised by the rigid ionic/covalent bonding in oxide ceramics leads to dislocations with low density (∼106 mm−2), thermodynamic instability and spatial inhomogeneity. In this paper, we report ultrahigh density (∼109 mm−2) of edge dislocations that are uniformly distributed in oxide ceramics with large compositional complexity. We demonstrate the dislocations are progressively and thermodynamically stabilized with increasing complexity of the composition, in which the entropy gain can compensate the strain energy of dislocations. We also find cracks are deflected and bridged with ∼70% enhancement of fracture toughness in the pyrochlore ceramics with multiple valence cations, due to the interaction with enlarged strain field around the immobile dislocations. This research provides a controllable approach to establish ultra-dense dislocations in oxide ceramics, which may open up another dimension to tune their properties.

Rapid fabrication and interface structure of highly faceted epitaxial Ni-Au solid solution nanoparticles on sapphire

Supersaturated Ni-Au solid solution particles were synthesized by rapid solid-state dewetting of bilayer thin films deposited onto c-plane sapphire single-crystals. Rapid thermal annealing above the miscibility gap of the Ni-Au system followed by quenching to room temperature resulted in textured and faceted submicron-sized particles as a function of alloying content in the range of 0–28 at% Au. Morphologically, the observed kinetic crystal shapes are confined by close-packed planes; in addition, high-index facets are identified as a function of alloying content by TEM cross-sectioning and equilibrium crystal shape simulations. All samples exhibit a distinct 〈111〉 out-of-plane as well as in-plane texture along densely packed directions. Lattice parameters extracted from independent orthogonal X-ray and electron diffraction techniques prove the formation of a solid solution without tetragonal distortion imposed by the sapphire substrate. At the particle-substrate interface of highly alloyed particles segregation of Au atoms as well as dislocations in stand-off position are found. These observations are in-line with a semi-coherent interface, where Au segregation is triggered by the reduction of the overall strain energy due to: (i) a lower shear modulus on the particle side of the interface, (ii) the shifting of misfit dislocations in stand-off position further away from the stiffer substrate and (iii) a reduction of intrinsic misfit dislocation strain energy on the tensile side. In addition, the mechanical properties of pure and alloyed particles were characterized by in situ compression experiments in the SEM. Typical force-displacement data of defect-free single-crystals were obtained, reaching the theoretical strength of Ni for particles smaller than 400 nm. Alloying changes the mechanical response from an intermittent and discrete plastic flow behavior into a homogeneous deformation regime at large compressive strain.

Influence of high pulsed magnetic field on tensile properties of TC4 alloy**Project supported by the National Natural Science Foundation of China (Grant Nos. 51371091, 51174099, and 51001054) and the Industrial Center of Jiangsu University, China (Grant No. ZXJG201585).

The tensile tests of TC4 alloy are carried on electronic universal testing machine in the synchronous presence of high pulsed magnetic field (HPMF) parallel to the axial direction. The effects of magnetic induction intensity (, 1 T, 3 T, and 5 T) on elongation (δ) of TC4 alloy are investigated. At 3 T, the elongation arrives at a maximum value of 12.41%, which is enhanced by 23.98% in comparison with that of initial sample. The elongation curve shows that 3 T is a critical point. With B increasing, the volume fraction of α phase is enhanced from 49.7% to 55.9%, which demonstrates that the HPMF can induce the phase transformation from β phase to α phase. Furthermore, the magnetic field not only promotes the orientation preference of crystal plane along the slipping direction, but also has the effect on increasing the dislocation density. The dislocation density increases with the enhancement of magnetic induction intensity and the 3-T parameter is ascertained as a turning point from increase to decrease tendency. When B is larger than 3 T, the dislocation density decreases with the enhancement of B. The influence of magnetic field is analyzed on the basis of magneto-plasticity effect. The high magnetic field will enhance the dislocation strain energy and promote the state conversion of radical pair generated between the dislocation and obstacles from singlet into triplet state, in which is analyzed the phenomenon that the dislocation density is at an utmost with T. Finally, the inevitability of optimized 3-T parameter is further discussed on a quantum scale.

A strain energy based damage model for fatigue crack initiation and growth

A strain energy based fatigue damage model is proposed which uses the strain energy from applied loads and the strain energy of dislocations to calculate stress-life, strain-life, and fatigue crack growth rates. Stress ratio effects intrinsic to the model are discussed, and parameterized in terms of the Walker equivalent stress and a fatigue crack growth driving force. The method is then validated using a variety of different metals with strain-life data and fatigue crack growth rate data available on the SAE Fatigue Design & Evaluation subcommittee database.

Effect of Rh content on the mechanical properties of Ir-Rh alloy based on the first principle

Platinum metal Ir-Rh alloy presents a promising candidate as future ultra-high-temperature gas turbine material due to its excellent high-temperature properties. In this paper, the mechanical properties of Ir-xRh (x=0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100) alloys with different rhodium content are investigated. Self-consistent, periodic, density functional theory calculations, Perdew-Burke-Ernzerhof functional, virtual crystal approximation are employed to calculate the elastic constants C11, C12, C44, Cauchy pressure (C12-C44), Young modulus E, shear modulus G, bulk modulus B and the ratio G/B, anisotropic factor A, and strain energy of dislocation per unit length. These parameters are adopted to characterize and assess the effect of Rh content on the mechanical property of Ir-Rh alloy. The results indicate that it is reasonable to use the virtual crystal approximation to calculate the mechanical properties of Ir-Rh alloys. The Young modulus E, shear modulus G and bulk modulus B increase rapidly with the increase of rhodium content, and the maximum value is reached at rhodium content 10%. Then it fast dereases down to a minimum value at 40% after the slowly rises and then slowly drops down. It is found to be in remarkable agreement with the strain energy of dislocation per unit length. This indirectly explains its changing trend. The Cauchy pressure (C12-C44), G/B value and the Poisson's ratio reflect the change of the brittleness of the alloy. Therefore, we can come to a conclusion: the addition of Rh can cause the brittleness of the Ir-Rh alloys. The value of the brittleness first increases and then decreases with the increase of Rh content, and its maximum value is reached at 50%. The charge densities and the densities of states of pure Ir, Ir-10Rh, Ir-50Rh and pure Rh are calculated and compared. At the same time, we also establish a 2 2 1 solid solution supercell structure of Ir-Rh alloy and calculate its differential charge density. The results show that in the Ir-Rh alloys exists a pseudo covalent bond, which leads to the abnormal mechanical properties. The pseudo covalent bond is not a metal bond nor a covalent bond but a kind of transition bond or a mixed type. Finally, the experimental results show that the calculation method is reasonable and it can play an important role in understanding the microscopic mechanism of the abnormal mechanical properties of Ir-Rh alloys.

Diffusion-induced stress and strain energy affected by dislocation mechanisms in a cylindrical nanoanode

Based on diffusion kinetics and dislocation theory, this paper describes an analytical model to analyze the effects of mixed dislocation mechanisms on diffusion-induced stress (DIS) and total strain energy when Li-ions insert a cylindrical nanoanode. Electrochemical Biot number (EBN) coupled into diffusion kinetics is analogous to the Biot number in heat-transfer systems and can govern the whole progress of Li-ion diffusion. The results show that diffusion-induced tensile radial stress can be reduced by dislocation work hardening stress and converted to compressive stress near the electrode surface. The presence of dislocations in the diffused electrode reveals that dislocations can be generated by DIS and in turn partially relieve the radial stress. Under small EBN charging, the degree of dislocation work hardening stress relieving the radial stress is obvious and meanwhile the influence of dislocation strain energy upon total strain energy is more significant. To predict the nucleation and propagation of cracks, it is more necessary to consider dislocation strain energy under small EBN control. These quantitative results also indicate that both EBN and dislocation density can be possibly controlled and coordinated based on nanotechnology so as to prolong the cycle life of batteries.

Current transport of the [001]-tilt low-angle grain boundary in high temperature superconductors

Current transport in grain boundary is one of the crucial factors which can affect the macro-supercurrent characteristics of the high temperature superconductors. van der Laan et al. [Phys. Rev. Lett. 103, 027005 (2009)] presented the strain dependence of the critical current density with a power-law fitting function, which has been verified by many experimental measurements. Here, we present a theoretical analysis of current transport in the [001]-tilt low angle grain boundary according to the strain energy of dislocation. An analytical expression is obtained which has the similar form of the fitting function, and in which the physical characteristics of parameters are distinct, and their values are close to the reports in literature.

Surface/interface effects on elastic behavior of an edge dislocation in the shell of a core–shell nanowire

Abstract The elastic behavior of an edge dislocation placed in the shell of a free-standing core–shell nanowire is considered within the theory of surface/interface elasticity. Using the method of complex potential functions the expressions for the stress field of the dislocation, image forces on the dislocation, and the dislocation strain energy are derived and studied in detail. A special attention is paid to non-classical effects revealed within the surface/interface elasticity approach where a characteristic length parameter referred to as surface/interface modulus is introduced. These effects are (i) the stress oscillations along the shell surface and core–shell interface for negative values of the surface/interface elastic moduli; (ii) a strong dependence of image forces on the core size; (iii) extra repelling (attraction) of the dislocation from (to) the shell surface and core–shell interface characterized by positive (negative) interface modulus; and (iv) a decrease of the dislocation strain energy in the central region of the shell and its local increase with an extra maximum in the vicinity of the shell surface for negative values of the surface/interface elastic moduli. These non-classical effects increase with diminishing core radius and shell thickness and are very strong in the layers of 1 nm thickness adjacent to the core–shell interface and shell surface. The effects of the residual surface stress are also addressed.

Interface effects on elastic behavior of an edge dislocation in a core–shell nanowire embedded to an infinite matrix

The elastic behavior of an edge dislocation located inside the core of a core–shell nanowire which is embedded in an infinite matrix is studied within the surface/interface elasticity theory. The corresponding boundary value problem is solved exactly by using complex potential functions. An important parameter so-called interface characteristic parameter which has the dimension of length and is a combination of the interface moduli enters the formulations. The stress field of the dislocation, image force acting on the dislocation, and the dislocation strain energy is calculated by considering the interface effect. The introduced characteristic parameter allows the examination of the core–shell size on the image forces acting on the dislocation. The repelling and attracting effects of the interface parameter on the image force are discussed. The equilibrium position of the dislocation is also studied. The dislocation strain energy in the interface elasticity framework is only slightly different from that of traditional elasticity when the dislocation is placed in the central region of the core and reaches its maximum value when it is located near the core–shell interface.

Is Crystal Growth under Low Supersaturations Influenced by a Tendency to a Minimum of the Surface‐Free Energy?

The long-standing problem of face morphology is discussed. Special emphasis is put on macroscopically flat faces, whose growth, under low supersaturations, is driven by dislocations possessing some screw component. The most general case, where the crystal face is pierced by more than one screw dislocation, is considered. If performed under sufficiently low supersaturation, the growth leads to the formation of the face morphology corresponding to the minimum of the surface-free energy. The thermodynamic driving force for face flattening is the difference in the surface-free energy of the vicinal faces of the hillocks (emanating from screw dislocations) and that of a singular face, which can truncate the valley between the growth hillocks. The hillock slope gives the quantitative relation between energetics and kinetics. The result of the considerations is that the lower the supersaturation, the more important is the role of the surface-free energy in face flattening. Another factor, particularly under sufficiently low supersaturations, is the effective increase in the local supersaturation at the valley separating two growth hillocks. The reason is that the dislocation strain energy vanishes there. (This is most evident when two dislocations of opposite sign are considered.) Besides, the valley floors are concave regions on the crystal surface, where the building blocks are bound more strongly. Thus, the kinetic reason for face flattening is the relative preference for incorporation of atoms, arriving from the ambient phase, at the valley floor. Note that accelerated step annihilation in the valley floor should be a universal factor, which favors face flattening under any supersaturation. The amount of flattening in the growth situation is determined by the interplay between supersaturation and thermodynamics.

The effects of couple stresses on dislocation strain energy

The correspondence theorem which relates the solutions of displacement boundary value problems in classical and couple stress elasticity is formulated and applied to derive the solutions for edge and screw dislocations in an infinite medium. The effects of couple stresses on the dislocation strain energy is evaluated for both types of dislocations. It is shown that within a radius of influence of each dislocation in a metallic crystal with dislocation density of 10 10 cm −2, the strain energy contribution from couple stresses (excluding the core energy) is about 15% in the case of an edge dislocation, and about 11% in the case of a screw dislocation. It is then shown that couple stresses make large effect on the total work of tractions acting on the dislocation core surface.

The elastic interaction of screw dislocations and a star crack with a central hole

The elastic interaction of screw dislocations and a star crack with a central hole was investigated. The complex potential of the present problem was obtained from that of an internal crack in an infinite medium using the conformal mapping technique. The stress field, image force and strain energy of dislocation, and stress intensity factor at the crack tip were derived. The critical stress intensity factor for dislocation emission was calculated based on the spontaneous dislocation emission criterion. The influence of the ratio of crack length to hole radius, crack number, and dislocation source on the above mechanical variables were studied. The present solution was reduced to several special cases previously reported in the literature.

Dislocations near a sliding interface

The system of a dislocation near a sliding interface has been investigated. The stress field arising from a dislocation of Burgers vector ( b x , b y , b z ) was obtained from a point force using the Moutier cycle. Stress contours were plotted to show the validity of the solution. The strain energy of dislocation near the sliding interface was derived based on the imaginary cutting method and was differentiated with respect to the coordinate to obtain the image force. The effect of elastic constants of the second medium on the stress field, strain energy and image force was studied. A comparison of the results for an edge dislocation near a sliding interface and those near a perfectly bonded interface was made. Some special cases were illustrated to compare with the results given in the literature.

On the elastic properties of grain boundary dislocations

The stress field and the strain energy of a screw grain boundary dislocation (GBD) are evaluated using the image stress solution of Chou ( Physica status solidi (a) 17, 509, 1966). The results show that to a good approximation, a GBD of Burgers vector g can be treated as a crystal dislocation but with a reduced Burgers vector ƒ where ƒ = 1 + 0.21 log α α is the ratio of the elastic constants of the “grain boundary phase” to that of the bulk crystal. The approximation is generally valid for the strain energy of the dislocation, and for stresses with α > 0.5. In addition, it is shown that GBDs in metals remain localised; the stress fields of which are comparable to that of a crystal dislocation. In glassy phase containing ceramics, however, the stress field of a crystal dislocation at the grain boundary can be relaxed significantly. Implications of above findings are discussed.

Plastic deformation mechanisms in tungsten carbide

Transmission electron microscopy studies of dislocations formed by plastic deformation in tungsten carbide have confirmed a slip deformation mechanism involving the {1 0 ¯1 0} 〈0 0 0 1〉 system. Direct visual evidence also confirmed the existence of extended dislocations formed by a suggested dissociation 1/3〈1 1 ¯2 3〉=1/6〈2 0 ¯2 3〉+1/6〈0 2 ¯2 3〉 which can further interact with other extended dislocations on pairs of intersecting {1 1 ¯2 2} pyramidal planes. The proposed interaction is suggested as a means of reducing both dislocation strain energy and atomic misfit strains due to antiphase boundary formation and leads to a form of sessile dislocation arrangement similar to the Lomer Cottrell lock.