Dislocation Annihilation Research Articles

A general physics-based hardening law for single phase metals

A simple exponential strain hardening model (ESH) has been developed in the framework of the Kocks-Mecking-Estrin formalism with a new microstructure-based parameter that accounts for the effect of yield strength. The relevant parameters reflecting the effect of the composition (or dislocation annihilation distance) and the microstructure type (or strengthening technology) are comprehensively analyzed. The application scope of the model is then briefly discussed, and several significant advantages are enumerated including the clear derivation processes and the explicit physical meaning of the various parameters. Finally, the ESH model is verified extensively by systematic tensile tests on six groups of Cu-Al alloys having more than one hundred microstructural states. In addition, significant and quantitative revelations of strength and uniform elongation for ductile metals are elaborated in the following manuscript. The present ESH model is of significant theoretical value in providing a detailed understanding of the tensile performance of metallic materials.

Relationship between strength and uniform elongation of metals based on an exponential hardening law

An exponential strain-hardening (ESH) model for single phase metals was established and well verified by systematic experiments on Cu-Al alloys in an earlier study. In this report, several additional significant revelations will be documented for the tensile behaviors of several typical metals. Firstly, a unified interpretation of the well-known five strain-hardening stages is developed by correlating the characteristics of each stage with the parameter n that relates to the dislocation annihilation behavior. Secondly, quantitative relationships among the yield strength (YS), ultimate tensile strength (UTS) and uniform elongation (UE) are established and verified using the tensile experimental results for Cu-Al alloys. Thirdly, the two general principles of the synchronous improvement of strength and uniform elongation (SISUE) effect, such as the composition adjustment and microstructure optimization, are quantitatively revealed by the composition parameter n and a microstructure type parameter η. Two typical trends of the true UTS-UE curves and two kinds of characteristic strengths are quantitatively revealed and confirmed by the relevant experimental data. Finally, a prediction model of tensile properties is proposed and a corresponding procedure is displayed, which is further verified by the tensile experimental results for Cu-Al alloys. These applications further support the validity and significance of the ESH model.

Nanoindentation of nanoporous tungsten: A molecular dynamics approach

Nanoporous metals, also known as metallic nanofoams, offer a wide range of functionalities and improved mechanical properties enabled by nanoscale effects. In particular, tungsten nanofoams are a novel class of materials with potential applications as radiation-resistant coating, and they share some similarities with the fuzz structure arising in fusion devices. We approach their study by nanoindentation tests using molecular dynamics simulations, for a single crystal nanofoam. To help understanding the foam mechanical behavior we also carry out simulations of W nanowire compression, finding elastic moduli of 375–450 GPa, and plastic yielding at ≈15 GPa. For the nanofoam, we obtain an elastic modulus of 64 GPa, in reasonable agreement with experiments, but our hardness value of ∼15 GPa is higher, likely due to nanocrystalline effects in the experiment. Atomistic simulations reveal that plastic deformation is caused by a combination of 12〈111〉 dislocations and twinning in the neighborhood of the indenter surface. It was found that twins also promote complete amorphization of some thin filaments in contact with the indenter tip. Dislocation activity also produces vacancies in the plastic region. Besides, the displacement induced by the indenter also drives changes of the network topology mainly due to densification, filament bending and twisting. Dislocation density is lower in the foam than in bulk indentation, due to the dislocation annihilation on the filament surfaces, but also because of changes in network topology help accommodate strain. Based on the simulation results, a nanoporous bcc foam behaves differently than a fcc foam, but still displays excellent mechanical properties for a low density material, and also offer additional technological advantages.

Experimental characterization and crystal plasticity modeling for predicting load reversals in AA6016-T4 and AA7021-T79

The detailed contribution of microstructural-level phenomena, such as dislocation structure development and annihilation, as well as inter-granular and intra-granular backstress fields, to reverse loading behavior in metal alloys remains an area of active research and debate. The ability to predict unloading nonlinearities, the Bauschinger effect (BE), and changes in hardening rates during reverse loading is necessary for accurate modeling of deformation and springback in forming operations that involve strain path changes. This paper applies a recently developed elasto-plastic self-consistent (EPSC) crystal plasticity model to predict and interpret reverse loading in two commercially sensitive aluminum alloys (AA): 6016-T4 and 7021-T79. Model calibration and verification was enabled by an extensive experimental campaign of cyclic loading applied to the two alloys. The experimental data included hardening rates during monotonic tension, linear followed by non-linear unloading, the BE, and hardening rate changes during reverse loading that induce permanent softening. By considering anisotropic elasticity, dislocation density-based hardening, intra-granular slip system-level backstress fields, and inter-granular stress fields, the model predicted and quantified the contribution of different micro-scale phenomena to the observed behavior. The ability of the model to capture contrasting characteristics of the two alloys, particularly the distinct permanent softening and reloading yield stresses, demonstrated its ability to account for the co-dependent nature of crystallographic glide and the sources of hardening originating from the deformation history-dependent dislocation density evolution and backstress fields. Comparison of the experimental and modeling results revealed that the unloading behavior is primarily driven by backstress, the BE is governed by backstress and inter-granular stresses, and the hardening rates upon load reversals are controlled primarily by the strain-path sensitive evolution of dislocation density.

Investigating Nanoscale Contact Using AFM-Based Indentation and Molecular Dynamics Simulations

In this work we study nanocontact plasticity in Au thin films using an atomic force microscope based indentation method with the goal of relating the changes in surface morphology to the dislocations created by deformation. This provides a rigorous test of our understanding of deformation and dislocation mechanisms in small volumes. A series of indentation experiments with increasing maximum load was performed. Distinct elastic and plastic regimes were identified in the force-displacement curves, and the corresponding residual imprints were measured. Transmission electron microscope based measured dislocation densities appear to be smaller than the densities expected from the measured residual indents. With the help of molecular dynamics simulations we show that dislocation nucleation and glide alone fail to explain the low dislocation density. Increasing the temperature of the simulations accelerates the rate of thermally activated processes and promotes motion and annihilation of dislocations under the indent while transferring material to the upper surface; dislocation density decreases in the plastic zone and material piles up around the indent. Finally, we discuss why a significant number of cross-slip events is expected beneath the indent under experimental conditions and the implications of this for work hardening during wear.

An investigation on microstructure and mechanical properties of 316 stainless steel: a comparison between ultrasonic treatment and thermal annealing

ABSTRACT The effect of ultrasonic treatment (UST) and thermal annealing (THA) post-processes on the mechanical properties and the related microstructural mechanisms of the tensile pre-strained 316 stainless steel was investigated. It was shown that both processes reduce the microhardness and the yield point as well as increasing the elongation of the pre-deformed alloy. A 10% reduction of the yield point and 28% increase in the elongation was observed after the higher power UST (500 W), while an enhanced ductility of 56% and 41% reduction of the yield point was measured for the high-temperature THA (800°C) treated steel. The increased ductility was related to de-twinning and dislocation annihilation mechanisms, which increase the mean free path distance of dislocations. The de-twinning mechanism was proposed as the boundary migration mechanism and reverse gliding of the partial dislocations by cyclic shear stress for the THA and UST processes, respectively. Unlike the UST process, the high-temperature thermal annealing was associated with the formation of M23C6 precipitates, which causes depletion of alloying elements from the vicinity of grain boundaries and makes the alloy more prone to intergranular corrosion. Compared with THA, the advantages of the UST process are as follows: a rapid and straightforward process, low energy consumption, enhanced ductility without significant reduction in strength, and inhibition of grain boundary precipitation.

In-situ TEM investigation of dislocation loop evolution in Al-forming austenitic stainless steels during Fe+ irradiation: Effects of irradiation dose and pre-existing dislocations

Alumina-forming austenitic (AFA) stainless steel with excellent properties has been regarded as a promising candidate of fuel claddings in Supercritical carbon dioxide (S-CO2) gas cooled nuclear reactor. In current work, in-situ irradiation with 400 keV Fe+ in transmission electron microscope were performed on AFA stainless steel to investigate the influences of irradiation dose and pre-existing dislocation lines on loop evolution at 773 K. The irradiation damage caused by irradiation-induced loops was also analyzed. In-situ TEM observation displayed the evolution and characteristics of dislocation loops, including initiation, migration, aggregation, growth, annihilation, and combination. Both Frank loops with b = 1/3<111> and perfect loops with b = 1/2<110> were formed, and at 0.54 dpa, 1/2<110> loops accounted for the majority and was up to 64.6%. Pre-existing dislocation lines obviously affected not only the evolution and distribution of dislocation loops, but also the degree of irradiation hardening. At the same irradiation dose, not only the size and number density of dislocation loops in the region with dislocation lines were smaller than those in the region without dislocation lines, but also the increment of yield strength and irradiation damage was lower before the formation of dislocation network. Increasing pre-existing dislocation density should be beneficial to improve the irradiation resistance of materials, but it needed to be comprehensively considered with the mechanical properties of the material. Al component played an important role in irradiation behavior of AFA steels and the corresponding mechanism was discussed subsequently.

Effect of Si on bainitic transformation kinetics in steels explained by carbon partitioning, carbide formation, dislocation densities, and thermodynamic conditions

The effect of Si addition on the evolution of bainitic transformation, carbon diffusion, carbide formation, and dislocation density in steel was investigated using in-situ high-energy X-ray diffraction (HEXRD). Alloys Fe-0.4C-1.7Mn (in wt%) with 1–4 wt% Si were austenitized at 1273 K and then isothermally heat treated at 573, 623, and 673 K. According to the HEXRD results, increasing Si content reduces the bainitic transformation kinetics and causes the incompleteness of the bainitic transformation to occur at lower bainite volume fraction. This is because i) Si retards carbide formation, impeding the eutectoid bainitic transformation, and leads to the accumulation of carbon at the migrating interface; ii) Si leads to higher strain energy and more dislocations in the austenite that also hinders the migration of the interface. Carbide formation was observed to occur prior to the incomplete transformation stage. During further isothermal holding, the decrease in dislocation density due to dislocation annihilation had little effect on carbide formation or carbon diffusion. Finally, the Si content has a minor effect on the calculated T 0 , T 0 ’, and WBs lines. The measured carbon content in carbon enriched austenite agrees well with WBs and T 0 but not with T 0 ’. • Bainitic transformation was systematically studied by in-situ HEXRD and microscopy. • Si affects transformation by solute hardening and retardation of carbide formation. • Carbide formation is observed prior to incomplete transformation stage. • Dislocation annihilation has insignificant effect on carbide formation. • The final carbon content in retained austenite agrees with T 0 and WBs predictions.

Dislocation transport using a time-explicit Runge–Kutta discontinuous Galerkin finite element approach

A time-explicit Runge–Kutta discontinuous Galerkin (RKDG) finite element scheme is proposed to solve the dislocation transport initial boundary value problem in 3D. The dislocation density transport equation, which lies at the core of this problem, is a first-order unsteady-state advection–reaction-type hyperbolic partial differential equation; the DG approach is well suited to solve such equations that lack any diffusion terms. The development of the RKDG scheme follows the method of lines approach. First, a space semi-discretization is performed using the DG approach with upwinding to obtain a system of ordinary differential equations in time. Then, time discretization is performed using explicit RK schemes to solve this system. The 3D numerical implementation of the RKDG scheme is performed for the first-order (forward Euler), second-order and third-order RK methods using the strong stability preserving approach. These implementations provide (quasi-)optimal convergence rates for smooth solutions. A slope limiter is used to prevent spurious Gibbs oscillations arising from high-order space approximations (polynomial degree ⩾ 1) of rough solutions. A parametric study is performed to understand the influence of key parameters of the RKDG scheme on the stability of the solution predicted during a screw dislocation transport simulation. Then, annihilation of two oppositely signed screw dislocations and the expansion of a polygonal dislocation loop are simulated. The RKDG scheme is able to resolve the shock generated during dislocation annihilation without any spurious oscillations and predict the prismatic loop expansion with very low numerical diffusion. These results indicate that the proposed scheme is more robust and accurate in comparison to existing approaches based on the continuous Galerkin finite element method or the fast Fourier transform method.

Laser powder bed fusion of M789 maraging steel on Cr–Mo N709 steel: Microstructure, texture, and mechanical properties

In this work, M789 steel was deposited (printed) onto wrought N709 steel by a laser powder bed fusion (LPBF) process to fabricate a hybrid M789-N709 alloy. The microstructure of the as-printed, new hybrid material consists of melt pool boundaries in the M789 region. Direct aging treatment was then applied, which allowed the annihilation of dislocations as well as the formation of the η-phase (Ni3(Ti, Al)) in the M789 section. Electron backscatter diffraction (EBSD) revealed essentially random orientations of the martensitic grains (in both as-printed and heat-treated states) with traces of reverted austenite that formed after heat treatment. Nanoindentation results (hardness profile across the interface) showed that the post-processing treatment increased the mechanical properties of M789 steel to comparable to that of wrought N709 steel. This assessment was validated through tensile testing, where the as-printed material failed in the M789 section, while the heat-treated sample fractured in the N709 section. This can be attributed to the presence of the η-phase after heat treatment. Since the fracture location is in the base alloy, a strong metallurgical bond is formed between M789 and N709. Thus, the new hybrid alloy can be employed without a compromised strength due to the interface.

Microstructure evolution and cyclic deformation behavior of Ti-6Al-4 V alloy via electron beam melting during low cycle fatigue

Low cycle fatigue (LCF) behavior of Ti-6Al-4 V alloy constructed via electron beam melting (EBM) was investigated. The relationship among fatigue property, internal stress and microstructure was established to characterize cyclic-deformation behavior and LCF life of EBM Ti-6Al-4 V alloy. The LCF life of EBM Ti-6Al-4 V is almost comparable to the wrought counterparts under low strains and higher than that of selective laser melted Ti-6Al-4 V reported. Tension-compression asymmetry and cyclic softening behavior were found at various strains. Considering the asymmetry of hysteresis loops, internal stresses during tension and compression were distinguished. The anisotropy of tension-compression enhances with increasing strain due to the increase of back stress and the decrease of friction stress. Sub-grain boundaries along with fragmented β phase were observed. The formation of sub-grains and dislocation annihilation in α grains reduce the friction stress, resulting in cyclic softening.

Annihilation dynamics of a dislocation pair in graphene: Density-functional tight-binding molecular dynamics simulations and first principles study

The time evolution of a dislocation pair in graphene is investigated by performing subnanosecond-scale molecular dynamics simulations based on the density-functional tight-binding method. The simulations show the self-healing behavior of the graphene lattice, resulting in complete annihilation of dislocations, that is, the formation of the pristine graphene structure. To understand the mechanism of the structural developments, first principles calculations are performed for the principal dislocation structures observed in the density-functional tight-binding/molecular dynamics simulations. We reveal the characteristic bonding states in the area around the dislocation structures by bond analyses based on the Wiberg bond index and crystal orbital Hamilton population approaches. The unusual local bonding states mainly originate from geometrical features of the out-of-plane deformation of the dislocation structures. The annihilation processes of dislocations in graphene are discussed in relation to the local bonding states of the dislocation structures.

Effects of elasticity and dislocation core structure on the interaction of dislocations with embedded CNTs in aluminium: An atomistic simulation study

The interaction between edge dislocations and carbon nanotubes (CNTs) embedded into an Al matrix is investigated. Both pristine and Ni-coated CNTs are considered. It is demonstrated that the embedded CNTs lead to a yield stress contribution equivalent to that of an array of non-shearable inclusions that are by-passed via the Orowan mechanism. The strain hardening mechanism associated with multiple dislocation passes shows, however, strong effects of atomistic core structure such as crystallographic and non-crystallographic cross slip of near-screw segments on the CNT-metal interface, dislocation lock formation and annihilation, jog formation and shedding of prismatic dislocation loops.

Nucleation of Frank Dislocation during the Squeeze-Out Process in Boundary Lubrication: A Molecular Dynamics Study.

Liquid–vapor molecular dynamics (LVMD) simulations are performed to reinvestigate the phase transition and solvation force oscillation behavior of a simple argon liquid film confined between two solid surfaces. Our simulations present a novel scenario in which the n → n − 1 layering transitions are accompanied by the formation, climb, and annihilation of Frank partial dislocations during the squeeze-out process under compression. This is indicated by the splitting of the repulsive peaks in the solvation force profile. The detailed analysis reveals that the formation–climb–annihilation mechanism of Frank dislocation occurs during approach and disappears during receding, which would result in force hysteresis. In combination with our recent works, this study provides new insights into the physical property of nanoconfined lubricant films in boundary lubrication.

Enhancing surface integrity of titanium alloy through hybrid surface modification (HSM) treatments

The current study investigates the development of a novel hybrid surface modification (HSM) technique to improve the surface integrity of Ti–6Al–4V alloy. The approach combines the mechanical shot peening (SP) and the deposition by Physical Vapour Deposition (PVD) of a tungsten-doped diamond-like carbon coating (WC/C) on Ti–6Al–4V surfaces. The mechanical shot peening induced high surface roughness increasing the metallurgical bonding sites for the PVD deposition, whereas mainly the grain growth during the deposition, was successfully eliminated. The mechanical SP process induced the high strain lattice misorientations evident for increasing the dislocation density in the crystalline structure. The Electron Backscatter Diffraction (EBSD) results suggest that subjecting the SP specimens to a temperature of 240 °C for more than 3 h during coating deposition, results in a reduction of dislocation densities, presumably as a result of dislocation annihilation by heat-activated dislocation mobilisation. Hence, the presented Grain Orientation Spread maps suggest that some degree of macro and micro stress relaxation may have occurred during the coating deposition treatment. Further, the Raman spectroscopy confirms the existence of beneficial compressive residual stresses on both PVD and hybrid (HY) coated surfaces. Comparatively, the HY surfaces show a high hardness of 12.08 GPa and high elasticity indices (H/E ratios) of 0.1.

The Three-Level Elastoviscoplastic Model and Its Application to Describing Complex Cyclic Loading of Materials with Different Stacking Fault Energies.

The development of new technologies for thethermomechanical processing of metals and the improvement of the existing ones would be unattainable without the use of mathematical models. The physical and mechanical properties of alloys and the performance characteristics of the products made of these alloys are generally determined by the microstructure of materials. In real manufacturing processes, the deformation of metals and alloys occurs when they undergo complex (non-proportional) loading. Under these conditions, the formation of defect substructures, which do not happen at simple (proportional) loading, can take place. This is due to the occurrence of a great number of slip systems activated under loading along complex strain paths, which leads, for instance, to the more intense formation of barriers of different types, including barriers on split dislocations. In these processes, the formation and annihilation of dislocations proceed actively. In this paper, we present a three-level mathematical model that is based on an explicit description of the evolution dislocations density and the formation of dislocations barriers. The model is intended for the description of arbitrary complex loads with an emphasis on complex cyclic deformation.The model is composed of macrolevel (a representative macrovolume of the material that can be considered as an integration point in the finite-element modeling of real constructions), and mesolevel-1 (description of the mechanical response of a crystallite) and mesolevel-2 (description of the defect structure evolution in a crystallite) submodels. Using the model, we have performed a series of numerical experiments on simple and complex, monotonic and cyclic deformations of materials with different stacking fault energies, analyzed the evolution of defect densities, and analyzed the challenges of a relationship between the complexity of loading processes at a macrolevel and the activation of slip systems at low scale levels.

Abnormal strain rate strengthening and strain hardening with constitutive modeling in body-centered cubic {332} TWIP titanium alloy

Metastable body-centered cubic titanium alloys exhibiting {332}<113> twinning-induced plasticity (TWIP) have attracted extensive attention owing to their remarkable strain hardenability and unprecedented impact performance. However, the intrinsic correlation between the strain rate, {332}<113> twinning, and flow stress remains to be fully elucidated. In this study, the instantaneous strain rate sensitivity (ISRS) and strain rate sensitivity of strain hardening (SRSS) corresponding to strain rate strengthening and strain hardening, respectively, were systematically clarified in {332}<113> Ti-15Mo alloy exhibiting TWIP effect by conducting strain-rate-jump tests and constitutive modeling analyses. The positive ISRS with an increasing trend correlated well with the change in the dislocation activation volume, which was mainly controlled by local obstacles of interstitial O atoms, and was affected by geometrically necessary dislocations due to twin formation. The negative SRSS with a decreasing trend correlated well with the evolution of deformation microstructures, which was mainly due to the decrease in the twinning rate and an increase in the dislocation annihilation rate. The established constitutive model reasonably described not only the abnormal strain rate strengthening from the thermal activation of dislocation but also the abnormal strain hardening from concurrent back stress strengthening due to twin formation and dislocation strengthening.

Plastic deformation behavior of ultrafine grained CoCrFeNiMn high entropy alloy with nanoparticles

High strength ultrafine grained CoCrFeNiMn high entropy alloys (HEAs) containing TiO(C) nanoparticles were fabricated by thermomechanical consolidation of a mechanically milled powder at 950 and 1000 °C, respectively. The sample consolidated at 950 °C with an average grain size of 417 nm had a high yield strength (YS) of 1457 MPa, but exhibited necking immediately after yield drop, leading to a limited elongation to fracture of 1.3%. In contrast, the sample consolidated at 1000 °C with an average grain size of 489 nm had a clearly lower YS of 1236 MPa, but exhibited yield drop, Lüders deformation, work hardening and then necking, with a significant elongation to fracture of 10.0%. Our work shows that by introducing intragranular Ni–Ti nanoparticles in the coarser grained sample through quenching to liquid nitrogen and aging, the YS of the sample was brought back to 1449 MPa, and still kept a substantial elongation to fracture of 4.2%. The transition of the plastic deformation behavior with grain refinement is analyzed based on dislocation dynamics theory. Based on this analysis, it is proposed that to maintain the uniform deformation, the grain sizes should be larger than a critical value, above which maximum flow stress of the material is higher than the upper yield stress. Introducing intragranular Ni–Ti nanoparticles is an effective strategy to further enhance yield strength without losing work hardening ability due to the synergistic effect with intragranular TiO(C) nanoparticles to inhibiting dislocation annihilation at grain boundaries.

Deformation behavior and microstructure in the low-frequency vibration upsetting of titanium alloy

Low-frequency vibration-assisted metal plastic forming is a novel promising technology, adopting a high-pressure-capability device compared to the ultrasonic vibration system. This work focuses on the low-frequency vibration assisted upsetting (LFVAU) process of Ti45Nb, to reduce the flow stress and crack initialization in the cold deformation of titanium alloy. The results show that the flow stress is significantly reduced by applying the vibration, and this stress reduction phenomenon becomes more obvious with larger frequency and amplitude. The vibration promotes the dislocation movement and grain rotation, resulting in dislocation annihilation in the shear band but dislocation concentration and low-angle grain boundary formation near the grain boundary in the large deformation zone. Therefore, more homogenous deformation occurred in LFVAU compared to the conventional quasi static upset (QUS) specimen, though the grain size is similar in the cylinders after QSU and LFVAU. Based on the above research results, the application of low-frequency vibration assisted processing technology in the field of aerospace will help to improve the plastic deformation quality, especially the riveting quality for Ti45Nb.

Microstructure Evolution in Nano-sized Wiredrawing Process:

By using molecular dynamics (MD) simulation, the mechanism of nanometer-sized wiredrawing is studied. The possibility of nano-sized plastic working process and predictive microstructures are investigated. As a drawn material, pure iron (α-Fe) and magnesium (Mg) single crystals are compared. The MD models are constructed by utilizing many-body-type (FS or EAM) interatomic potentials with adequate modification for lubrication between wire and die. Dislocation slip is a principal mechanism of plastic deformation in the case of α-Fe in any drawing direction of single crystal. Besides, dislocation densities increases with increase of the wire diameter, where nucleation, annihilation and mutual behavior of dislocations are observed in detail. On the other hand, in Mg single crystal, mechanism of plastic deformation depends strongly on crystal orientation as to drawing direction. Twinning and twin boundaries can be identified by detecting a network of interface dislocations. When the c-axis of hcp lattice is inclined by 45 degrees from the drawing direction, dislocations on basal plane occur, but no twin, and therefore the minimum dislocation density is obtained.