Dislocation interactions and low-angle grain boundary strengthening

The transmission of an incoming dislocation through a symmetrical low-angle tilt grain boundary (GB) is studied for {1 1 0}〈1 1 1〉 slip systems in body-centered cubic metals using discrete dislocation dynamics (DD) simulations. The transmission resistance is quantified in terms of the different types of interactions between the incoming and GB dislocations. Five different dislocation interaction types are considered: collinear, mixed-symmetrical junction, mixed-asymmetrical junction, edge junction, and coplanar. Mixed-symmetrical junction formation events are found not only to cause a strong resistance against the incident dislocation penetration, but also to transform the symmetrical low-angle tilt GB into a hexagonal network (a general low-angle GB). The interactions between the incident dislocation and the GB dislocations can form an array of 〈1 0 0〉 dislocations (binary junctions) in non-coplanar interactions, or a single 〈1 0 0〉 dislocation in coplanar interaction. We study how the transmission resistance depends on the mobility of 〈1 0 0〉 dislocations. 〈1 0 0〉 dislocations have usually been treated as immobile in DD simulations. In this work, we discuss and implement the mobility law for 〈1 0 0〉 dislocations. As an example, we report how the mobility of 〈1 0 0〉 dislocations affects the equilibrium configuration of a ternary dislocation interaction.     

Wetting of molybdenum grain boundaries by nickel: effect of the boundary structure and energy

The structural effect of the penetration of nickel along symmetrical [101] tilt grain boundaries (GBs) in two different molybdenum bicrystals is investigated. The selection of GBs (Σ=3{121} and Σ=11{323}) is governed by their different energy so that a different penetration behaviour is expected. The temperature of treatment is 1350°C, i.e. above the eutectic temperature. The analysis of the Mo–Ni phase formed on the surface of the bicrystal, the concentration profile along the GB and the identification of the nanophases present at the GB is performed by using several experimental techniques from microscopic to nanoscopic scales. Important differences in the penetration of nickel are found for the two investigated GBs.     

Mechanical behavior of Σ tilt grain boundaries in nanoscale Cu and Al: A quasicontinuum study

Molecular simulations using the quasicontinuum method are performed to understand the mechanical response at the nanoscale of grain boundaries (GBs) under simple shear. The energetics and mechanical strength of 18 Σ 〈1 1 0〉 symmetric tilt GBs and two Σ 〈1 1 0〉 asymmetric tilt GBs are investigated in Cu and Al. Special emphasis is placed on the evolution of far-field shear stresses under applied strain and related deformation mechanisms at zero temperature. The deformation of the boundaries is found to operate by three modes depending on the GB equilibrium configuration: GB sliding by uncorrelated atomic shuffling, nucleation of partial dislocations from the interface to the grains, and GB migration. This investigation shows that (1) the GB energy alone cannot be used as a relevant parameter to predict the sliding of nanoscale high-angle boundaries when no thermally activated mechanisms are involved; (2) the E structural unit present in the period of Σ tilt GBs is found to be responsible for the onset of sliding by atomic shuffling; (3) GB sliding strength in the athermal limit shows slight variations between the different interface configurations, but has no apparent correlation with the GB structure; (4) the metal potential plays a determinant role in the relaxation of stress after sliding, but does not influence the GB sliding strength; here it is suggested that the metal potential has a stronger impact on crystal slip than on the intrinsic interface behavior. These findings provide additional insights on the role of GB structure in the deformation processes of nanocrystalline metals.     

Crossover from grain boundary sliding to rotational deformation in nanocrystalline materials

A theoretical model is suggested which describes cooperative action of grain boundary (GB) sliding and rotational deformation in mechanically loaded nanocrystalline materials. Focuses are placed on the crossover from GB sliding to rotational deformation occurring at triple junctions of GBs. In the framework of the model, gliding GB dislocations at triple junctions of GBs split into dislocations that climb along the adjacent boundaries. The splitting processes repeatedly occurring at triple junctions give rise to climb of GB dislocation walls that carry rotational deformation accompanied by crystal lattice rotation in grains of nanocrystalline materials. The role of GB sliding, rotational deformation and conventional dislocation slip in high-strain-rate superplastic flow in nanocrystalline materials is discussed.     

小角度非对称倾侧晶界形貌和变形的晶体相场模拟

采用双模晶体相场模型,计算了二维正方相相图,并以正方相为研究对象,在原子尺度上,模拟了小角度非对称倾侧晶界结构及变形过程。结果表明,小角度非对称倾侧晶界由刃型位错和刃型位错组构成;在外加应力作用下,位错先于位错组滑移并进行短程的攀移,最后合并,位错组分离为滑移方向相反的2个刃型位错并最终与其它晶界位错组分离出的异号刃型位错合并,完成晶粒的合并。     

Tracer diffusion of Au and Cu in a series of near Σ=5 (310)[001] symmetrical Cu tilt grain boundaries

Grain boundary diffusion of Au and Cu was measured in a series of Cu bicrystals with symmetrical near Σ=5, Θ=36.9° (310)[001] CSL tilt grain boundaries (GBs) using the radiotracer and the serial sectioning technique. The orientations of the bicrystals were very precisely determined with the Kossel technique where all three macroscopic parameters describing the orientations of the grains in the bicrystal were evaluated. The tilt angles ranged from 33.21° to 39.26°. The GB diffusion of the radiotracers ¹⁹⁵Au and ⁶⁴Cu was measured as a function of tilt angle and temperature. In the investigated temperature range 1030–661 K the orientation dependence of both radiotracers shows a characteristic cusp not exactly at but slightly below the ideal Σ=5 CSL GB. The Arrhenius parameters, activation enthalpy and frequency factor, determined from lower temperature data adopt a maximum, again slightly before the ideal Σ=5 CSL GB. These features are discussed with respect to the accidental small twist and second tilt orientations and the corresponding dislocation network inherent in the investigated real GBs. With increasing temperature a negative deviation from a straight Arrhenius behaviour is observed. This result indicates a certain change in the GB structure in the temperature range above 800 K.     

Effect of crystallographic orientation and grain boundary character on fatigue cracking behaviors of coaxial copper bicrystals

Four coaxial copper bicrystals were employed to study the slip morphologies and fatigue cracking behaviors during cyclic deformation. Three of them had high-angle grain boundaries (GBs) with nearly the same misorientation and one bicrystal had a twin boundary (TB). Different slip bands (SBs) operated near the GBs and TB, generating different dislocation arrangements, which are mainly determined by the crystallographic orientations of the component grains. The GBs suffered impingement or shear damage caused by slip difference from both sides. It is suggested that there is an energy increase in the interfaces between matrix and persistent slip bands (PSBs), GBs and TBs per cycle during cyclic deformation due to the accumulation of lattice defects, which would make the interface unstable. After a certain number of cycles, fatigue cracks initiated firstly at GBs for some bicrystals while fatigue cracking occurred preferentially at PSBs for the others. It is confirmed that the energy growth rate is an increasing function of the shear stress, strain amplitude and strain incompatibility, which results from slip differences on both sides of the interfaces. Interfaces with different energies and strain incompatibilities have different fatigue cracking resistance. It is found that GBs with defective and complex structure, and hence high interfacial energy accompanied by high modulus of the residual GB dislocation (GBD), are preferential sites for fatigue cracking, while the fatigue cracking appeared predominantly at PSBs when the modulus of the residual GBD is lower than that of a perfect dislocation with simple GB structure and low interfacial energy. The present model for the energy can predict well which kind of interface would form cracks preferentially during cyclic deformation in one coaxial bicrystal and which GB would need more cycles to initiate fatigue cracking between coaxial bicrystals with different GB characters.     

Molecular dynamics simulation on mechanisms of plastic anisotropy in nanotwinned polycrystalline copper with {111} texture during tensile deformation

Based on molecular dynamics (MD) simulation, the mechanisms of plastic anisotropy in nanotwinned polycrystalline copper with {111} texture during tensile deformation were systematically studied from the aspects of Schmid factor of the dominant slip system and the dislocation mechanism. The results show that the Schmid factor of dominated slip system is altered by changing the inclining angle of the twin boundaries (TBs), while the yield stress or flow stress does not strictly follow the Schmid law. There exist hard and soft orientations involving different dislocation mechanisms during the tensile deformation. The strengthening mechanism of hard orientation lies in the fact that there exist interactions between the dislocations and the TBs during plastic deformation, which leads to the dislocation blocking and reactions. The softening mechanism of soft orientation lies in the fact that there is no interaction between the dislocations and the TBs because only the slip systems parallel to the TBs are activated and the dislocations slip on the planes parallel to the TBs. It is concluded that the plastic anisotropy in the nanotwinned polycrystalline copper with {111} texture is aroused by the combination effect of the Schmid factor of dominated slip system and the dislocation mechanism.     

Interactions between non-screw lattice dislocations and coherent twin boundaries in face-centered cubic metals

In a first report [Jin ZH, Gumbsch P, Ma E, Albe K, Lu K, Hahn H, et al. Scripta Mater 2006;54:1163], interactions between screw dislocation and coherent twin boundary (CTB) were studied via molecular dynamics simulations for three face-centered cubic (fcc) metals, Cu, Ni and Al. To complement those preliminary results, purely stress-driven interactions between 60° non-screw lattice dislocation and CTB are considered in this paper. Depending on the material and the applied strain, slip has been observed to interact with the boundary in different ways. If a 60° dislocation is forced by an external stress into a CTB, it dissociates into different partial dislocations gliding into the twin as well as along the twin boundary. A sessile dislocation lock may be generated at the CTB if the transited slip is incomplete. The details of the interaction are controlled by the material-dependent energy barriers for the formation of Shockley partial dislocations from the site where the lattice dislocation impinges upon the boundary.     

柱状晶Al在冷轧过程中微观组织演变的定量表征Ⅱ.微观分裂

摘要原始取向为{001)(uv0)的柱状晶Al样品分别冷轧到10％，30％和50％，采用EBSP技术定量表征了不同取向晶粒基带内的微观分裂．结果表明晶粒均都分裂为胞块组织，不同取向晶粒变形后的微观组织结构不同．随应变量的增加GNBs取向差增加，并满足2／3指数关系．Frank公式分析表明，胞块界面中的位错主要来自由Schmid因子决定的激活滑移位错．     

Application of the Peierls-Nabarro Model to Symmetric Tilt Low-Angle Grain Boundary with Full <a> Dislocation in Pure Magnesium

Three types of symmetric (11\(\bar{2}\)0) tilt low-angle grain boundaries (LAGBs) with array of basal, prismatic, and pyramidal edge full dislocations in pure Mg have been studied by using the improved Peierls-Nabarro model in combination with the generalized stacking fault energy curve. The results show that with decreasing distance between the dislocations in all the three types of tilt LAGBs, the stress and strain fields are gradually suppressed. The reduction extent of the stress and strain fields decreases from the prismatic to basal to pyramidal dislocations. The variation of dislocation line energy (DLE) for all tilt LAGBs is divided into three stages: DLE changes slightly and linearly when the distance is larger than 300 Å, ~10%; DLE declines exponentially and quickly when the distance goes from 300 to 100 Å, ~70%; and finally, the descent speed lowers when the distance is smaller than 100 Å and the dislocation core energy is nearly half of the DLE. The grain boundary energy (GBE) decreases when the tilt angle of LAGB increases from 1° to 2° for all cases. The tilt LAGB consists of pyramidal dislocations always has the largest GBE, while that with array of prismatic dislocations has the smallest one in the whole range. The Peierls stress of dislocation in tilt LAGB is nearly unchanged, the same as that of single dislocation. This work is useful for further study of dissociated dislocation, solute segregation, precipitate nucleation in tilt LAGB and its interaction with single dislocations.     

Formation of Face-Centered Cubic Phase in Ti35 Alloy Under In Situ Heating Transmission Electron Microscopy

A thermally induced hexagonal close-packed (HCP) to face-centered cubic (FCC) phase transition was investigated in an α-type Ti35 alloy with twinned structure by in situ heating transmission electron microscopy (TEM) and ab initio calculations. TEM observations indicated that the HCP to FCC phase transition occurred both within matrix/twin and at the twin boundaries in the thinner region of the TEM film, and the FCC-Ti precipitated as plates within the matrix/twin, while as equiaxed cells at twin boundaries. The crystallographic orientation relationship between HCP-Ti and FCC-Ti can be described as: $\left\{ {111} \right\}_{{{\text{FCC}}}} //\left\{ {0002} \right\}_{{{\text{HCP}}}} \;{\text{and}}\; < 110 >\,_{{{\text{FCC}}}} //\, <1\overline{2} 10>\,_{{{\text{HCP}}}}$. The HCP to FCC phase transition was accomplished by forming an intermediate state with a BB stacking sequence through the slip of partial dislocations. The formation of such FCC-Ti may be related to the thermal stress and temperature. Ab initio calculations showed that the formation of FCC-Ti may also be related to the contamination of interstitial atoms such as oxygen.     

Grain Boundary Segregation of Interstitial and Substitutional Impurity Atoms in Alpha-Iron

The macroscopic behavior of polycrystalline materials is influenced by the local variation of properties caused by the presence of impurities and defects. The effect of these impurities at the atomic scale can either embrittle or strengthen grain boundaries (GBs) within. Thus, it is imperative to understand the energetics associated with segregation to design materials with desirable properties. In this study, molecular statics simulations were employed to analyze the energetics associated with the segregation of various elements (helium, hydrogen, carbon, phosphorous, and vanadium) to four 〈100〉 (Σ5 and Σ13 GBs) and six 〈110〉 (Σ3, Σ9, and Σ11 GBs) symmetric tilt grain boundaries in α-Fe. This knowledge is important for designing stable interfaces in harsh environments. Simulation results show that the local atomic arrangements within the GB region and the resulting structural units have a significant influence on the magnitude of binding energies of the impurity (interstitial and substitutional) atoms. These data also suggest that the site-to-site variation of energies within a boundary is substantial. Comparing the binding energies of all 10 boundaries shows that the Σ3(112) boundary possesses a much smaller binding energy for all interstitial and substitutional impurity atoms among the boundaries examined in this study. Additionally, based on the Rice–Wang model, our total energy calculations show that V has a significant beneficial effect on the Fe grain boundary cohesion, while P has a detrimental effect on grain boundary cohesion, much weaker than H and He. This is significant for applications where extreme environmental damage generates lattice defects and grain boundaries act as sinks for both interstitial and substitutional impurity atoms. This methodology provides us with a tool to effectively identify the local as well as the global segregation behavior that can influence the GB cohesion.     

Effect of grain boundary character on sink efficiency

The dependence of the width of void-denuded zones (VDZs) on grain boundary (GB) characters was investigated in Cu irradiated with He ions at elevated temperature. Dislocation loops and voids formed near GBs during irradiation were characterized by transmission electron microscopy, and GB misorientations and normal planes were determined by electron back-scatter diffraction. The VDZ widths at Σ3〈1 1 0〉 tilt GBs ranged from 0 to 24 nm and increased with the GB plane inclination angle. For non-Σ3 GBs, VDZ widths ranged from 40 to 70 nm and generally increased with misorientation angle. Nevertheless, there is considerable scatter about this general trend, indicating that the remaining crystallographic parameters also play a role in determining the sink efficiencies of these GBs. In addition, the VDZ widths at two sides of a GB show different values for certain asymmetrical GBs. Voids were also observed within GB planes and their density and radius also appeared to depend on GB character. We conclude that GB sink efficiencies depend on the overall GB character, including both misorientation and GB plane orientation.     

Atomistic simulations of grain boundary segregation in nanocrystalline yttria-stabilized zirconia and gadolinia-doped ceria solid oxide electrolytes

Hybrid Monte Carlo–molecular dynamics simulations are carried out to study defect distributions near Σ5(3 1 0)/[0 0 1] pure tilt grain boundaries (GBs) in nanocrystalline yttria-stabilized zirconia and gadolinia-doped ceria. The simulations predict equilibrium distributions of dopant cations and oxygen vacancies in the vicinity of the GBs where both materials display considerable amounts of dopant segregation. The predictions are in qualitative agreement with various experimental observations. Further analyses show that the degree of dopant segregation increases with the doping level and applied pressure in both materials. The equilibrium segregation profiles are also strongly influenced by the microscopic structure of the GBs. The high concentration of oxygen vacancies at the GB interface due to lower vacancy formation energies triggers the dopant segregation, and the final segregation profiles are largely determined by the dopant–vacancy interaction.     

Temperature dependence of faceting in Σ5(310)[001] grain boundary of SrTiO3

Using high-resolution electron microscopy (HREM), temperature dependence of faceting of an asymmetric Σ5 grain boundary (GB) in SrTiO₃ is observed. The bicrystal samples have been fabricated by ultra-high vacuum diffusion bonding and heat-treated between 1100 and 1600 °C. Below 1300 °C, this GB facets into symmetric (310) and asymmetric (100)//(430) GB planes. At 1300 °C, in addition to the asymmetric facet, the symmetric {210} facet appears: three different facets are thus observed at this temperature. At 1400 and 1500 °C, the asymmetric facet disappears and the two kinds of symmetric facets remain. At 1600 °C, faceting disappears and the GB becomes defaceted. The faceting/defaceting transition behavior of the GB is interpreted in terms of the Wulff plot and its corresponding equilibrium crystal shape.     

γ-TiAl中<110>倾斜晶界断裂行为的分子动力学模拟(英文)

采用分子动力学(MD)方法研究γ-Ti Al合金中<110>对称倾斜界面的断裂行为,模拟在不同温度与应变速率下垂直界面方向的拉伸变形。结果表明:晶粒的相对取向及晶界特定的原子结构是影响位错形核临界应力的两个主要因素。取向差角度大于90°的Σ3(111)109.5°、Σ9(221)141.1°和Σ27(552)148.4°界面,位错在晶界处形核和扩展;取向差角度小于90°的Σ27(115)31.6°和Σ11(113)50.5°界面,无位错在晶界处形核,当应力达到峰值后界面直接断裂。γ-Ti Al双晶的断裂机制为微裂纹在界面处的形核及沿界面扩展;不同取向差界面的区别在于裂纹前端有无塑性区增韧。     

Fatigue cracking at twin boundaries: Effects of crystallographic orientation and stacking fault energy

The combined effects of crystallographic orientation and stacking fault energy (SFE) on the cracking behaviors of twin boundaries (TB) under low-cycle fatigue (LCF) tests were studied in pure Cu, Cu–Al and Cu–Zn alloys. A new approach, called the slipping morphology method, based on the crystallographic characteristics of Σ3 TB in face-centered cubic materials, was developed to determine the grain orientations by studying the twin-slip morphology characteristics on the sample surfaces after LCF tests. Through analyzing the dislocation–TB interaction and the damage this causes to TBs, a new parameter, defined as the difference of Schmid factors (DSF), was proposed to describe the effects of crystallographic orientation on the LCF cracking behaviors of TBs. A semi-quantitative relationship was established among DSF, SFE, dislocation slip mode and the critical conditions of TB cracking by systematically studying more than a hundred post-fatigue surface morphologies of pure Cu, Cu–Al and Cu–Zn alloys. It is interesting to find that the TB cracking relies strongly on the cooperation of both DSF and SFE. Furthermore, taking into account the interactions between slip dislocations and different boundaries, the fatigue cracking possibilities of several typical interfaces were compared and discussed. The results demonstrate that low-angle grain boundaries (GBs) are the strongest in resisting fatigue cracking, high-angle GBs are the weakest, and TBs are in between, which contributes the most to the final fatigue performance of materials. This new finding will help understanding of the interfacial properties under cyclic loading and may be beneficial to the design of high-performance materials with optimal fatigue properties in the future.     

Why is the slip direction different in different B2 alloys?

The dominant slip directions in different intermetallic alloys with B2 structure are different, either 〈0 0 1〉 or 〈1 1 1〉. The elastic energy of 〈1 1 1〉 dislocations is usually significantly higher than that of 〈0 0 1〉 dislocations and it is commonly assumed that 〈1 1 1〉 slip occurs if 〈1 1 1〉 dislocations can dissociate on {1 1 0} planes into 1/2〈1 1 1〉 superpartials. However, we show in this paper that 1/2〈1 1 1〉 anti-phase boundaries may not be metastable faults on {1 1 0} planes and the displacement vectors of metastable stacking-fault-like defects on these planes vary from material to material. This analysis involves calculations of {1 1 0} γ-surfaces for eight B2 alloys (CuZn, FeAl, NiAl, FeTi, CoTi, NiTi, FeGa, PdAl) using a density functional theory-based method. Since both 〈1 1 1〉 and 〈0 0 1〉 screw dislocations may possess non-planar cores if undissociated and will then control plastic properties analogously as 1/2〈1 1 1〉 screw dislocations in body-centered cubic metals, the dissociations have been analyzed for screw dislocations. Subsequently, we assume that if the width of splitting in {1 1 0} planes exceeds the Burgers vector of the corresponding dislocation, the dislocation spreads in this plane and is glissile while undissociated dislocation is sessile. The ability to glide is then regarded as the determining factor for the choice of the slip direction. If no planar spreading occurs the dominant dislocations are determined by their energy. This analysis predicts the slip directions for all alloys studied and demonstrates that an interplay of elastic anisotropy, displacement vectors of metastable stacking-fault-like defects and their energies govern the choice of the slip direction in any specific B2 alloy.