Interaction Of Dislocations Research Articles

Spot–Ladder Selection of Dislocation Patterns in Metal Fatigue

Spontaneous pattern formation by a large number of dislocations is commonly observed during the initial stages of metal fatigue under cyclic straining. It was experimentally found that the geometry of the dislocation pattern undergoes a crossover from a 2D spot-scattered pattern to a 1D ladder-shaped pattern as the amplitude of external shear strain increases. However, the physical mechanism that causes the crossover between different dislocation patterns remains unclear. In this study, we theorized a bifurcation diagram that explains the crossover between the two dislocation patterns. The proposed theory is based on a weakly nonlinear stability analysis that considers the mutual interaction of dislocations as a nonlinearity. It was found that the selection rule among the two dislocation patterns, “spotted” and “ladder-shaped”, can be described by inequalities with respect to nonlinearity parameters contained in the governing equations.

Dislocation Motion Induced by Thermally Driven Phase Transformations

AbstractThe interaction of dislocations with phase boundaries is an interesting aspect of the interplay between phase transformation and plasticity at the nano‐scale. We capture this interaction within a phase field framework coupled to discrete dislocation dynamics. In order to regularize the stress and driving force for phase evolution at the dislocation core, a first strain‐gradient elasticity approach is used, which leads to more physical, discretization‐independent numerical solutions.From a mathematical point of view, this results in a system of coupled partial differential equations (PDEs) and ordinary differential equations (ODEs). The PDEs include an equation analogous to the balance of linear momentum, a second‐order tensor‐valued Helmholtz‐type equation for the true stress as well as a time‐dependent Ginzburg‐Landau equation for the evolution of the phase field. The ODEs are the equations of motion of the dislocations. The dislocations are modeled as lamellae with eigenstrain that can evolve with time; the resulting stress field is an outcome of the numerical solution. A parallel framework was developed in order to solve these coupled dynamics problems using the finite element library FEniCS. We show the effect of dislocations on phase microstructure as well as the influence of phase microstructure on the motion of dislocations using an illustrative example of a thermally‐driven planar phase boundary, and its interaction with a single edge dislocation.

Twin thickness-dependent tensile deformation mechanism on strengthening-softening of Si nanowires

Twin thickness-dependent deformation and the transition from strengthening to softening in twinned silicon nanowires are investigated using molecular dynamics simulations with cylindrical and hexagonal cross sections. The results show that the transition from strengthening to softening occurs at critical twin thicknesses of 8.1 nm (11.0 TB s) with cylindrical cross section and 11.0 nm (8 TBs) with hexagonal cross section with decreasing twin thickness, and that the strongest twin thickness originates from a transition in the initial plasticity mechanism from full dislocation nucleation and interaction with the TBs to partial dislocation nucleation and gliding parallel to the TBs. Moreover, it is found that the relationship between peak stress and twin thickness can be divided into two regions. Several full and partial dislocations are formed in the regions with strengthening twin thickness range. The accumulation and pile-up of these dislocations and their interaction with the TBs at high density cause the Hall-Petch strengthening behavior. In contrast, few full and partial dislocations are formed with softening twin thickness range. These dislocations are nucleated and propagate parallel to the TBs, resulting in TB migration that causes inverse Hall-Petch softening behavior. Our simulation results provide sufficient insight into the mechanical behavior of twinned silicon nanowires with cylindrical and hexagonal cross sections. The study will be helpful to the further understanding of CTB-related mechanical behaviors of non-metallic materials and non-metallic system.

Analytical investigation of a grain boundary model that accounts for slip system coupling in gradient crystal plasticity frameworks

In this work, a physically based dislocation theory of plasticity is derived within an extended continuum mechanical context. An orientation-dependent grain boundary flow rule is introduced for the modelling of dislocation pile-up at grain boundaries and dislocation transmission through grain boundaries. With the conventional grain boundary modelling approach according to Gurtin (Gurtin. 2008 J. Mech. Phys. Solids 56 , 640–662. ( doi:10.1016/j.jmps.2007.05. 002 )) the single-crystal consistency check for the limit case of adjacent grains that hold no misorientation is not satisfied. In order to overcome this modelling shortcoming, a slip system coupling based on a geometric measure of slip system compatibility is introduced. In order to investigate the grain boundary modelling approaches, the analytical solution of a three-phase periodic laminate is used to study the interactions of dislocations and grain boundaries within the gradient crystal plasticity framework. With the developed grain boundary model two grain boundary states, i.e. microhard and microcontrolled, are observed for misaligned grains. This allows the modelling of slip activation at grain boundaries based on the dislocation pile-up stress.

Influence of intercritical annealing temperature on microstructure, microtexture, and tensile behavior of TRIP-assisted medium manganese steel

The present work investigates, the effect of intercritical annealing temperature on the microstructure, microtexture, tensile behavior, and mechanical stability of austenite in thermomechanically processed Fe-0.18C-4Al-7Mn (wt.%) medium manganese steel. The steel is subjected to thermomechanical processing (hot forging and hot rolling) followed by intercritical annealing at various temperatures (700, 750 and 800 °C) for 1 hour. The development of a complex microstructure with blocky and lath-type reverted austenite (RA), fine polygonal and blocky type intercritical ferrite (IF), coarse elongated ferrite (EF), and lath martensite (M) is revealed by the scanning electron microscopy (SEM) and transmission electron microscopy (TEM) analyses. The steel annealed at 750 °C exhibits an excellent ultimate tensile strength (UTS) of 802 MPa and total elongation (TE) of 61% owing to its high RA content, high transformation-induced plasticity (TRIP) effect and low mechanical stability of RA. Further, to understand the dislocation phenomena during tensile deformation, the tensile samples are analyzed using TEM, which reveals dislocation interactions, dislocation tangles, and dislocation accumulations at the IF grain boundaries and martensite lath boundaries. The manifestation of the TRIP effect is elucidated by XRD and EBSD studies. In addition, to study the texture evolution and the role of texture components on the TRIP effect, the orientation distribution function is employed. The major texture component, i.e., Ms Brass {011} 〈211〉 indicates the TRIP effect resulting in the deformation-induced martensitic transformation under tensile deformation. Additionally, Ms Brass component shifts towards G/B (Goss/Brass) twin {011} 〈111〉 component by grain rotation to accommodate the deformation.

Microstructures and tensile properties of a grain-size gradient nickel-based superalloy

This work systematically investigated the microstructure characteristics and tensile mechanical properties of a grain-size gradient nickel-based superalloy. The plastically deformation mechanism and the failure behavior of the gradient superalloy at different temperatures (room temperature, 650 °C, 750 °C) were discussed. Results show that the microstructure of nickel-based gradient superalloy is mainly composed of γ matrix phases, γ′ phases and dispersed carbides. The microstructure of the gradient superalloy exhibits equiaxed grains with a few annealing twinning structures. The average grain size changes uniformly from 94.3 µm of the coarse-grain side to 4.9 µm of the fine-grain side. The room temperature tensile strength of the grain-size gradient superalloy is about 1635 MPa, the yield strength is about 1160 MPa and the elongation is around 21%. When testing at 650 °C, the tensile and yield strength of the specimens declined to 1414 MPa and 1034 MPa, respectively, but the elongation raises to 36%. The strength of the specimens continues to decrease at temperature of 750 °C, whereas the elongation decreases back to around 21%, exhibiting intermediate temperature brittle phenomenon (ITB). Analysis concludes that the micro-twinning mechanism dominates at 750 °C in the grain-size gradient nickel-based superalloy. Micro-twins formed by intense interaction of dislocations with γ′ phases lead to the reduction of ductility at 750 °C.

Interaction of O, N, C and H interstitials with screw dislocations in hexagonal titanium

Interaction of interstitial elements and screw dislocations in hexagonal titanium is determined with ab initio calculations. O, N and C are repulsive obstacles while H exhibits attraction to dislocation, especially to pyramidal stacking faults forming the dislocation core. Studied solutes thus provoke different strengthening mechanism, i.e. dislocation cross slip or binding.

In-situ study of anisotropic strain-hardening and grain boundary mediated deformation in commercially pure titanium

In this study, we investigated the anisotropy in tensile deformation behaviour of CP-Ti plate in the rolling (RD) and transverse direction (TD), using in-situ SEM-EBSD testing and stress-relaxation method. The EBSD-assisted slip trace analysis was conducted to examine the slip systems activated within individual grains. It was found that the prismatic slip is dominant in the RD sample, whilst the activity of non-prismatic slip systems is higher in the TD sample. The slip transfer significantly occurred in the TD sample, thereby promoting the activity of multiple slips and dislocation interactions at the grain interiors. However, the limited occurrence of slip transfer in the RD sample indicates the strong dislocation pinning at the grain boundaries (GBs). Combined with the EBSD analysis, the SEM observations revealed that the GBs with ledge character are formed in the slip-favourable and -unfavourable grain pairs, and the GBs with sink character are created in the grain pairs whose c-axes are equally inclined to the loading direction, but the sign of c-axis inclination angles is opposite with each other. The formation of GB ledges and GB sinks was pronounced in the RD and TD sample, respectively. The GB-dislocation interactions and GB-mediated deformation arising from the orientation relationship between the particular grain pairs led to the anisotropy in strain-hardening behaviour of polycrystalline α-Ti.

Temperature and Strain Rate Dependence on the Tensile Mechanical Properties, Constitutive Equations, and Fracture Mechanisms of MarBN Steel.

The effect of strain rate and temperature on the thermomechanical behavior and microstructure of MarBN steel is studied with the strain rates of 5 × 10-3 and 5 × 10-5 s-1 from room temperature (RT) to 630 °C. At high strain rates of 5 × 10-3 s-1, the Holloman and Ludwigson equations can better predict tensile plastic properties. In contrast, under low strain rates of 5 × 10-5 s-1, coupling of the Voce and Ludwigson equations appears to predict the flow relationship at RT, 430, and 630 °C. However, the deformation microstructures have the same evolution behavior under strain rates and temperatures. Geometrically necessary dislocations appear along the grain boundaries and increase the dislocation density, which results in the formation of the low-angle grain boundaries and a decrease in the number of twinning. The strengthening sources of MarBN steel include grain boundary strengthening, dislocation interactions, and multiplication. The fitted R2 values of these models (JC, KHL, PB, VA, ZA) to plastic flow stress at 5 × 10-5 s-1 are greater than 5 × 10-3 s-1 for MarBN steel. Due to the flexibility and minimum fitting parameters, the phenomenological models of JC (RT and 430 °C) and KHL (630 °C) give the best prediction accuracy under both strain rates.

The three-dimensional elastodynamic solution for dislocation plasticity and its implementation in discrete dislocation dynamics simulations

An analytical solution for the elastodynamic displacement field of non-uniformly moving Volterra dislocations is derived using the Green’s function approach. The elastodynamics strain and stress fields can then be evaluated by numerically differentiating the displacement field. Qualitative comparisons are made with molecular dynamic simulations, and the analytical solution is shown to capture the same features. The plane waves that emanate from, and are parallel to, the slip plane during the instantaneous injection process of edge or screw dislocations are captured by the analytical solution. This was not captured by previously proposed elastodynamic solutions. A computationally efficient swept-area-tracking algorithm is then developed and implemented into three-dimensional discrete dislocation dynamics simulations to compute the elastodynamic field induced by dislocation movements and interactions. This approach provides a way forward for modeling deformation of materials under shock loading or quantifying the dynamics effects that dominate during dislocation avalanches during deformation of metals.

Cyclic deformation mechanism and fracture behaviour of 316L stainless steel under thermomechanical fatigue loading

Thermomechanical fatigue (TMF) behaviour of 316L is investigated based on the internal stress and microstructural characterization at various cyclic stages. Results reveal that the cyclic stress response shows initial hardening followed by cyclic softening at a high strain amplitude, while presenting continuous cyclic hardening as the strain amplitude decreases. Among these, Out-of-phase TMF always shows cyclic softening irrespective of strain amplitude. It is important to note that the hardening of back stress and friction stress contribute to the initial and subsequent cyclic hardening. In contrast, the subsequent cyclic softening is mainly dominated by the reduced friction stress. It is observed that the proliferation of dislocations at grain boundaries and the enhanced dislocation interactions within the grains are primarily responsible for the hardening of back stress and friction stress, respectively. Specifically, the cyclic softening of friction stress is attributed to the annihilated dislocations as a result of cross-slip. It is also found from the hysteresis curves that the intensity of dynamic strain ageing is related to strain amplitude, loading history and phase angle, which correlates to the occurrence of cross-slip, the diffusion rate of the solute atom, the density of point defect and the mobility of vacancies. Finally, the effect of loading conditions on fracture behaviour is demonstrated from the point view of crack sources, secondary cracks, creep cavities and oxidation damage.

Grain boundary softening from stress assisted helium cavity coalescence in ultrafine-grained tungsten

The formation of helium cavities in coarse-grained materials produces hardening proportional to the number density and size of the cavities and due to the interaction of dislocations with intragranular helium defects. In nanostructured metals containing a high density of interfacial sinks, preferential cavity formation in the grain boundaries instead produces softening that is often attributed to enhanced interfacial plasticity. Employing two grades of ultrafine-grained tungsten, we explore this effect using targeted implantation studies to map cavity evolution as a function of the irradiation conditions and quantify its impact on the mechanical response through nanoindentation. Softening is reported at implantation temperatures above the threshold for preferential grain boundary cavity formation but at a sufficiently low fluence prior to the growth of intragranular cavities. Collective changes in the mean cavity size, density, and morphology beneath a residual impression on an implanted surface indicate that cavity coalescence accompanied the reduction in hardness. Complementary atomistic simulations demonstrate that, in tungsten grain structures exhibiting softening, grain boundary bubble coalescence is driven by stress concentrations that further act to localize strain in the grain boundaries through cooperative deformation processes involving local atomic shuffling and sliding, dislocation emission, and even the nucleation of unstable twinning events.

Hydrogen-induced intergranular cracking of pure nickel under various strain rates and temperatures in gaseous hydrogen environment

Industrial-grade pure nickel, NI-201, was tensile tested in high-pressure hydrogen gas at various testing temperatures and strain rates. The degree of hydrogen embrittlement (HE) was strongly affected by the testing temperature and strain rate, and elevating the strain rate and lowering the temperature result in suppressed HE. While hydrogen trapped at GBs via local equilibrium dominated the HE degree in hydrogen-charged cases, hydrogen supply to GBs during the tests was required in gaseous hydrogen cases. Although hydrogen–dislocation interaction was one of candidates for the hydrogen supply, the lattice hydrogen, which can interact with dislocations, hardly existed and related behaviors such as increase in flow stress and serrated yielding were not observed in the gaseous hydrogen cases; therefore, the contribution of the hydrogen–dislocation interaction was speculated to be minor. Alternatively, we proposed an HE model considering hydrogen diffusion along grain boundaries (GBs) from the crack tip, which successfully demonstrated the experimental results.

In Situ Study of the Microstructural Evolution of Nickel-Based Alloy with High Proportional Twin Boundaries Obtained by High-Temperature Annealing.

In this paper, we report an in situ study regarding the microstructural evolution of a nickel-based alloy with high proportional twin boundaries by using electron backscatter diffraction techniques combined with the uniaxial tensile test. The study mainly focuses on the evolution of substructure, geometrically necessary dislocation, multiple types of grain boundaries (especially twin boundaries), and grain orientation. The results show that the Cr20Ni80 alloy can be obtained with up to 73% twin boundaries by annealing at 1100 °C for 30 min. During this deformation, dislocations preferentially accumulate near the twin boundary, and the strain also localizes at the twin boundary. With the increasing strain, dislocation interaction with grain boundaries leads to a decreasing trend of twin boundaries. However, when the strain is 0.024, the twin boundary is found to increase slightly. Meanwhile, the grain orientation gradually rotates to a stable direction and forms a Copper, S texture, and α-fiber <110>. Above all, during this deformation process, the alloy is deformed mainly by two deformation mechanisms: mechanical twinning and dislocation slip.

Additively manufactured Ti55511 alloy: Microstructure and residual stress effect on mechanical properties

Stress relief (SR) is an effective heat treatment process that potentially changes microstructure and enhances the mechanical properties of additively manufactured parts. In this study, the influence of SR on the microstructure and mechanical properties of Ti-5Al-5Mo-5V-1Cr-1Fe alloy (Ti-55511), a near-β alloy fabricated by laser powder bed fusion (LPBF), was investigated. LPBF-built Ti-55511 samples were characterized and tested under tensile and low cycle fatigue loading in the as-built (AB) and SR conditions. The obtained results show that the LPBF sample was composed of columnar grains in a single bcc β-phase in the AB condition. In contrast, the SR condition resulted in a bi-modal microstructure comprising of α + β phases. This led to significant grain refinement of the β phase and reduced the residual stress (RS) up to 91 % compared to the AB condition. At the same time, the SR treatment increased the yield strength, ultimate tensile strength, and fatigue life at the expense of ductility. The improvement in mechanical properties is attributed to the grain refinement and phase transformation resulting in complex dislocation interactions during deformation.

Atomistic simulation of the dislocation interactions with the Al2Ca Laves phase in Mg–Al–Ca alloy

The mechanical properties of Mg–Al–Ca alloys are significantly affected by their Laves phases, including the Al2Ca phase. Laves phases are generally considered to be brittle and have a detrimental effect on the ductility of Mg. Recently, the Al2Ca phase was shown to undergo plastic deformation in a dilute Mg-Al-Ca alloy to increase the ductility and work hardening of the alloy. In the present study, we investigated the extent to which the deformation of Al2Ca is driven by dislocations in the Mg matrix by simulating the interactions between the basal edge dislocations and Al2Ca particles. In particular, the effects of the interparticle spacing, particle orientation, and particle size were considered. Shearing of small particles and dislocation cross-slips near large particles were observed. Both events contribute to strengthening, and accommodate to plasticity. The shear resistance of the dislocation to bypass the particles increased as the particle size increased. The critical resolved shear stress (CRSS) for activating dislocations and stacking faults was easier to reach for small Al2Ca particles owing to the higher local shear stress, which is consistent with the experimental observations. Overall, this work elucidates the driving force for Al2Ca particles in Mg–Al–Ca alloys to undergo plastic deformation.

Achieving high strength and ductility in high-entropy alloys via spinodal decomposition-induced compositional heterogeneity

The compositional heterogeneity in high-entropy alloys (HEAs) has been reported to be an inherent entity, which significantly alters the mechanical properties of materials by tuning the variation of lattice resistance for dislocation motion. However, since the body-centered cubic (BCC) structure is not close-packed, the change of lattice resistance is less sensitive to the normal concentration wave compared to that in face-centered cubic (FCC) structured materials. In this work, we selected a refractory bcc HEAs TiZrNbTa for the matrix and added a small amount of Al to facilitate the special spinodal decomposition structure. In particular, (TiZrNbTa)98.5Al1.5 displayed a typical basket-weave fabric morphology of spinodal decomposition structure with a characteristic periodicity of ∼8 nm and had an optimal combination of strength and ductility (the yield strength of 1123 ± 9 MPa and ductility of ∼20.7% ± 0.6%). It was determined that by doing in situ TEM mechanical testing, the plastic deformation was dominated by the formation and operation of dislocation loops which provided both edge and screw components of dislocations. The synergetic effect of the remarkable chemical heterogeneity created by the spinodal decomposition and the spreading lattice distortion in high entropy alloys is quite effective in tuning the mobility of different types of dislocations and facilitates dislocation interactions, enabling the combination of high strength and ductility.

Synergistic effects of Ta and Mo on the hydrogen embrittlement resistance in ultra-high strength hot stamping steel

Hydrogen embrittlement (HE) is a major problem that restricts the application of ultra-high strength hot stamping steels. This paper proposes a novel strategy for against HE via Ta–Mo multi-microalloying, and systematically analyzes the synergistic effects of Ta and Mo. The results show that a major fraction of Ta and a small fraction of Mo generated high-density semicoherent nanosized (Ta, Mo) C precipitates and further refined the prior-austenite-grain/martensite structure. Ta–Mo multi-microalloying resulted in significantly higher precipitate and grain boundary (GB)-induced H trap densities and a higher H trapping capacity of the precipitates than Ta alloying, thereby reducing the H diffusivity. Additionally, Ta–Mo alloying significantly increased the HE resistance through the following mechanisms: (i) Ta–Mo hindered H enrichment at the GBs by providing numerous additional H traps and increasing the GB cohesive strength through Mo segregation, inhibiting hydrogen-enhanced decohesion (HEDE); and (ii) Ta reduced the proportion of Σ3 boundaries, Mo increased the binding force of Σ3 boundaries, and (Ta, Mo) C precipitates hindered the H–dislocation interactions, suppressing hydrogen-enhanced localized plasticity (HELP). In summary, Ta–Mo multi-microalloying combines the advantages of Ta and Mo and synergistically hinders the HELP and HEDE, thereby significantly increasing the HE resistance.

High temperature plasticity at twin boundary in Al: An in-situ TEM perspective

Coherent twin boundaries are of special importance in structural materials due to their strengthening ability by impeding dislocation motion while maintaining possible glide along their plane. Interactions of lattice dislocations with twin boundaries have been extensively studied experimentally and numerically but relaxation and deformation processes at high temperature are not fully understood. The reason is related to complex mechanisms of dislocation decompositions into disconnections, their further motion and possible reactions. Moreover, as in shear-coupled grain boundary (GB) mechanisms, motion of disconnections in the interface plane is expected to lead to twin motion perpendicular to its plane. Here, shear-coupled motion of a coherent twin in pure Al is explored during in situ straining in a transmission electron microscope (TEM) in a favorable geometrical configuration. Surprisingly, the twin boundary does not couple to shear but slightly migrates by propagating nanoscale incoherent facets. Although, disconnections of Burgers vector 1/6〈112〉 have been extensively observed moving in the interface plane, their motion did not lead to migration as expected but presumably to GB sliding. This was interpreted by the motion of disconnections with opposite single and double steps in the [111] direction. Extensive dislocation/GB interactions were observed and reactions following absorption are interpreted by contrast analysis and motion observations. Incoming dislocations do not always decompose but often react with the GB disconnection microstructure which may lead to intergranular motions or dislocation emissions in the adjacent grain. As these processes usually involve disconnection climb in the interface plane, direct transmission, i.e. spatially and temporally correlated absorption/emission processes, is not observed as revealed by large scale observations. Finally, the internal disconnection microstructure of the twin boundary often forms networks which although flexible are found to slow down intergranular plasticity. Such networks should strongly control stress induced mechanisms in realistic GBs.

Formation of helical dislocations mediated by interstitials in ion irradiated FeCrAl alloy

Unraveling the interaction of the pre-existing dislocations with irradiation defects is crucial to understanding the microstructural evolution and the strength-ductility trade-off of iron-based alloys under service in an irradiation environment. In this work, the formation of helical dislocations was analyzed by combining an in-situ experiment of 400 keV Fe+ irradiated Fe-13.2Cr-5.6Al alloy at 823 K with molecular dynamics (MD) simulations. A mechanism that irradiation induced interstitial defects would mediate the pre-existing screw dislocation to produce the helical dislocations was revealed. The in-situ formation of helical dislocations and the absence of dislocation loop in the vicinity of helical dislocations were observed. The helical dislocations more likely form in the region with higher pre-existing screw dislocation density, but it will be suppressed by the dislocation loops nucleating near the screw dislocations.