Brittle-ductile behavior of a nanocrack in nanocrystalline Ni: A quasicontinuum study

The effects of stacking fault energy, unstable stacking fault energy, and unstable twinning fault energy on the fracture behavior of nanocrystalline Ni are studied via quasicontinuum simulations. Two semi-empirical potentials for Ni are used to vary the values of these generalized planar fault energies. When the above three energies are reduced, a brittle-to-ductile transition of the fracture behavior is observed. In the model with higher generalized planar fault energies, a nanocrack proceeds along a grain boundary, while in the model with lower energies, the tip of the nanocrack becomes blunt. A greater twinning tendency is also observed in the more ductile model. These results indicate that the fracture toughness of nanocrystalline face-centered-cubic metals and alloys might be efficiently improved by controlling the generalized planar fault energies.     

Effects of twin and stacking faults on the deformation behaviors of Al nanowires under tension loading

The effects of twin spacing and temperature on the deformation behavior of nanotwinned Al under tensile loading are investigated using a molecular dynamic(MD) simulation method.The result shows that the yield strength of nanotwinned Al decreases with the increase of twin spacing,which is related to the repulsive force between twin boundary and the dislocation.The result also shows that there is no strain-hardening at the yield point.On the contrary,the stress is raised by strain hardening in the plastic stage.In addition,we also investigate the effects of stacking fault thickness and temperature on the yield strength of the Al nanowire.The simulation results indicate that the stacking fault may strengthen the Al nanowire when the thickness of the stacking fault is below a critical value.     

Effect of alloying element on dislocation cross-slip in γ′-Ni3Al: a first-principles study

The effects of alloying elements Re, Ru, Ta, Ti, and W on the activation enthalpy of dislocation cross-slip in γ′-Ni₃Al are studied combining density functional theory calculations with the classical theory of dislocations. The elements Re and W are found to effectively increase planar fault energies on the (111) plane and decrease the cross-slip activation enthalpy in Ni₃Al. The reduction of activation enthalpy will increase the probabilities of cross-slipping and forming sessile dislocation locks. Therefore, Re and W can inhibit the further motion of dislocations and raise the flow stress of Ni₃Al in the anomalous temperature regime. The underlying electronic mechanism is the strong bonding of Re–Ni and W–Ni and the weak bonding of Re–Al and W–Al in fault areas.     

基于准连续介质方法模拟纳米多晶体Ni中裂纹的扩展

通过准连续介质方法模拟了纳米多晶体Ni中裂纹的扩展过程.模拟结果显示:裂纹尖端的应力场可以导致晶界分解、层错和变形孪晶的形成等塑性形变,在距离裂纹尖端越远的位置,变形孪晶越少,在裂纹尖端附近相同距离处,层错要远多于变形孪晶.这反映了局部应力的变化以及广义平面层错能对变形孪晶的影响.计算了裂纹尖端附近区域原子级局部静水应力的分布.计算结果表明:裂纹前端晶界处容易产生细微空洞,这些空洞附近为张应力集中区,并可能促使裂纹沿着晶界扩展.模拟结果定性地反映了纳米多晶体Ni中的裂纹扩展过程,并与相关实验结果符合得很好     

Ab initio calculation of the phase stability,mechanical properties and electronic structure of ZrCr2 Laves phase compounds

Ab initio calculations have been used to investigate the phase stability, mechanical properties and electronic structure of ZrCr₂ Laves phase compounds, based on the method of augmented plane waves plus local orbitals with the generalized gradient approximation. The calculated lattice constants for the C15, C36 and C14 structures are in good agreement with experimental values. The calculation of heats of formation showed that C15 is a ground-state phase, whereas C36 is an intermediate phase and C14 the high-temperature phase. The elastic constants and elastic moduli for the C15 structure were calculated systematically and compared with experiments and previous theoretical calculations. The intrinsic and extrinsic stacking fault energies are found to be 112 and 98?mJ?m^?2, respectively. The equilibrium separations between Schockley are also predicted using the calculated elastic moduli and stacking fault energies. Finally, the calculated electronic structures of these Laves phases are discussed based on these results.     

Temperature-dependent ideal strength and stacking fault energy of fcc Ni: a first-principles study of shear deformation

Variations of energy, stress, and magnetic moment of fcc Ni as a response to shear deformation and the associated ideal shear strength (τ(IS)), intrinsic (γ(SF)) and unstable (γ(US)) stacking fault energies have been studied in terms of first-principles calculations under both the alias and affine shear regimes within the {111} slip plane along the <112> and <110> directions. It is found that (i) the intrinsic stacking fault energy γ(SF) is nearly independent of the shear deformation regimes used, albeit a slightly smaller value is predicted by pure shear (with relaxation) compared to the one from simple shear (without relaxation); (ii) the minimum ideal shear strength τ(IS) is obtained by pure alias shear of {111}<112>; and (iii) the dissociation of the 1/2[110] dislocation into two partial Shockley dislocations (1/6[211] + 1/6[121]) is observed under pure alias shear of {111}<110>. Based on the quasiharmonic approach from first-principles phonon calculations, the predicted γ(SF) has been extended to finite temperatures. In particular, using a proposed quasistatic approach on the basis of the predicted volume versus temperature relation, the temperature dependence of τ(IS) is also obtained. Both the γ(SF) and the τ(IS) of fcc Ni decrease with increasing temperature. The computed ideal shear strengths as well as the intrinsic and unstable stacking fault energies are in favorable accord with experiments and other predictions in the literature.     

Al纳米线不同晶向力学行为和变形机制的模拟

采用分子动力学模拟计算方法,考察具有较高层错能的Al纳米线沿不同晶向的力学行为和变形机制。在相同计算条件下与具有较低层错能的Ni、Cu、Au和Ag等FCC金属纳米线进行比较。结果表明：在力学行为方面,Al纳米线的弹性模量呈现明显的结构各向异性,满足E_[111] > E_[110] > E_[100]的关系,这一关系在FCC金属纳米线中普遍成立;Al纳米线的屈服应力随晶向呈现σ_y[100] > σ_y[111] > σ_y[110]的关系,这一关系在具有较低层错能的FCC金属纳米线中不具有普遍性,这与体系中位错形成机制密切相关。根据拉伸变形过程微观结构的演变规律,阐明Al纳米线不同晶向的变形机制,并与具有较低层错能的Ni、Cu、Au和Ag等FCC金属纳米线的变形机制进行比较。结果表明,对于尺度较小的高层错能Al纳米线,Schmid因子和广义层错能均难以准确预测其变形机制。     

Effects of atomic size on antiphase boundary energy in solid solutions

The energy of an antiphase boundary has been calculated by means of Pines's elastic spheres method, as modified by incorporating the dependence of atomic size on the neighbors in the first coordination sphere, which represents an advance in the theory of ordered solid solutions. There is a reduction in the elastic strain energy when a nonequilibrium antiphase boundary is formed in CuZn, and if this is incorporated one obtains realistic values for the energies of such boundaries; in AuCu₃ the elastic strain energy increases the energy of an antiphase boundary of octahedral type. The change in the elastic strain energy in a nonequilibrium antiphase boundary constitutes a considerable part of the total energy change given by the quasichemical theory, and it introduces substantial corrections into the antiphase-boundary energy for CuZn and AuCu₃.     

Energy of planar defects in the Ni<Subscript>3</Subscript>Al phase: Theory and experiment

The Ni₃Al phase with an L1₂ surperstructure exhibits a clearly pronounced positive temperature dependence of the yield stress. The nature of this phenomenon is still not clearly understood. The temperature dependence of the yield stress under consideration is determined, in many respects, by the structure of glide superdislocations and planar defects of these superdislocations involved in the L1₂ superstructure. A critical analysis is made of the current state of the art in the solution of the problem regarding the energy of antiphase boundaries in planes of an octahedron and a cube, as well as the energy of stacking faults in the Ni₃Al phase.     

Generalized stacking fault energy in FCC metals with MEAM

The second nearest-neighbor modified embedded atom method (2NN-MEAM) is used to investigate the generalized stacking fault (GSF) energy surfaces of eight FCC metals Cu, Ag, Au, Ni, Pd, Pt, Al and Pb. An offset is observed in all the metals for the displacement δ_us of unstable stacking fault energy from the geometrically symmetric displacement point . The offset value is the greatest for Al and the smallest for Ag. By analyzing the stable stacking fault energy γ_sf and unstable stacking fault energy γ_usf, it can be predicted that stacking fault is more favorable in Cu, Ag, Au, and especially in Pd than the other metals, while it is most preferred to create partial dislocation for Ag and to create full dislocation for Al.     

Strengthening at nanoscaled coherent twin boundary in f.c.c. metals

This paper analyses slip transfer at the boundary of nanoscaled growth twins in face-centred cubic (f.c.c.) metals for strengthening mechanism. The required stress for slip transfer, i.e. inter-twin flow stress, is obtained in a simple expression in terms of stacking fault energy and/or twin boundary (TB) energy, constriction energy and activation volume. For nanotwinned Al, Cu and Ni, inter-twin flow stress versus twin thickness remarkably shows Hall–Petch relationship. The Hall–Petch slope is rationalized for various reactions of screw and non-screw dislocations at the TB. Additionally, strengthening at the boundary of nanoscaled deformation twins in f.c.c. metals is analysed by evaluating required twinning stress. At small nanograin size, the prediction of deformation twin growth stress shows inverse grain-size effect on twinning, in agreement with recent experimental finding.     

Generalized stacking faults in model lattice of ordered Fe-Si alloys

The energies of the generalized stacking faults lying on {110} and {112} planes are calculated for Fe-Si alloys with the DO₃ long-range order for concentrations 10–25 at. % Si. In the used model, the interaction between atoms is described by the series of three central interatomic potentials fitted to experimental data. The lattice relaxations perpendicular to the stacking fault plane are considered. The displacement vectors corresponding to stable antiphase boundaries are found and some consequences for the structure of superdislocations in the DO₃ superlattice are mentioned.The author is indebted to Dr. F.Kroupa and Dr. L.Lejek for valuable discussion.     

fcc金属层错能的EAM法计算

采用嵌入原子法(EAM)计算了Cu，Ag，Au，Ni，Al，Rh，Ir，Pd，Pt和Pb等10种面心立方(fcc)金属的层错能，除Rh和Ir两种金属外，其他金属的计算结果和实验结果基本一致. 关键词： 面心立方金属 层错能 EAM     

The theory of equilibrium antiphase boundaries in ordered solid solutions of the AuCu3 type

The Gorsky-Bragg-Williams approximation gives expressions which determine the equilibrium values of the long-range-order parameter and the concentrations of components in the vicinity of the antiphase boundary 1/2 (110) {111} in an L1₂ super-structure of stoichiometric composition AB₃. On the assumption that the changes in the alloy due to the presence of an antiphase boundary are distributed over a great number of planes on both sides of the boundary, the long-range-order parameter and the concentration of components in these planes have been calculated. It is found that the long-range-order parameter at the antiphase boundary is considerably lower than it is in the matrix over a wide temperature range. The concentration of the components at the antiphase boundary under conditions of thermodynamic equilibrium is somewhat lower than the mean concentration in the alloy.Estimates are made of the critical stress for the start of superdislocations with equilibrium antiphase boundaries, the equilibrium width of the superdislocations, and the defect in the elastic modulus due to the reversible movement of the superparticle dislocations.     

Inverse grain-size effect on twinning in nanocrystalline Ni

A long-standing controversy exists between molecular dynamics simulations and experiments on the twinning propensity of nanocrystalline (NC) face-centered-cubic metals. For example, three-dimensional molecular dynamics simulations rarely observed twins in NC Ni, whereas experiments readily observed them. Here this discrepancy is resolved by experimental observation of an inverse grain-size effect on twinning. Specifically, decreasing the grain size first promotes twinning in NC Ni and then hinders twinning due to the inverse grain-size effect. Interestingly, no inverse grain-size effect exists on stacking fault formation. These observations are explained by generalized planar fault energies and grain-size effect on partial emissions.     

Emission of dislocations from grain boundaries by grain boundary dissociation

In this article, we examine the conditions that favour the emission of Shockley partial dislocations (SPDs) that standoff from a grain boundary (GB) plane by a few lattice parameters as part of the atomic structure of some GBs. To do so, we consider GBs to be formed by the operation of arrays of intrinsic grain boundary dislocations (GBDs) that create the tilt and twist misorientation, and the lattice mismatch between the two crystal grains adjoining the GB. The conditions to be considered that favour SPDs are the following: (1) Frank’s rule, (2) the proper sequential arrangement of partial dislocations to bound an intrinsic stacking fault and (3) the equilibrium stand-off distance (ESD). We apply an isotropic elasticity analysis to compute the ESD, in the absence of an applied stress, for SPDs emerging from asymmetric tilt GBs in two FCC metals, Cu and Al. The ESD is shown to be dependent on the glide plane orientation relative to the GB plane and on the position of the glide planes, relative to the position of the GBDs. An applied stress increases the ESD up to a critical stress that removes the SPDs without limit from the GB. We examine the effect of the stacking fault energy on the ESD and critical stress. The critical stress is effectively linearly dependent on the stacking fault energy. Finally, we present results of atomistic simulations of asymmetric tilt Σ11[1?0?1]{4?1?4}||{2?5?2} GBs in Cu bicrystal models subject to shock loading that behave in a manner similar to the elasticity predictions. The atomistic simulations reveal additional behaviour associated with elastic incompatibility between the two grains in the bicrystal models.     

Shape memory behavior in Fe3Al-modeling and experiments

The Fe₃Al alloy with D0₃ structure exhibits large recoverable strains due to reversible slips. Tension and compression experiments were conducted on single crystals of Fe₃Al, and the onset of slip in forward and reverse directions were obtained utilizing high-resolution digital image correlation technique. The back stress provides the driving force for reversal of deformation upon unloading, resulting in a superelastic phenomenon as in shape memory alloys. Using density functional theory simulations, we obtain the energy barriers (GSFE – generalized stacking fault energy) for {1?1?0}〈1?1?1〉 and {1?1?2}〈1?1?1〉 slips in D0₃ Fe₃Al and the elastic moduli tensor, and undertake anisotropic continuum calculations to obtain the back stress and the frictional stress responsible for reversible slip. We compare the theoretically obtained slip stress magnitudes (friction and back stress) with the experimental measurements disclosing excellent agreement.     

Doping effects on the stacking fault energies of the γ’ phase in Ni-based superalloys

The doping effects on the stacking fault energies(SFEs),including the superlattice intrinsic stacking fault and superlattice extrinsic stacking fault,were studied by first principles calculation of the/phase in the Ni-based superalloys.The formation energy results show that the main alloying elements in Ni-based superalloys,such as Re,Cr,Mo,Ta,and W,prefer to occupy the Al-site in Ni3 AI,Co shows a weak tendency to occupy the Ni-site,and Ru shows a weak tendency to occupy the Al-site.The SFE results show that Co and Ru could decrease the SFEs when added to fault planes,while other main elements increase SFEs.The double-packed superlattice intrinsic stacking fault energies are lower than superlattice extrinsic stacking fault energies when elements(except Co) occupy an Al-site.Furthermore,the SFEs show a symmetrical distribution with the location of the elements in the ternary model.A detailed electronic structure analysis of the Ru effects shows that SFEs correlated with not only the symmetry reduction of the charge accumulation but also the changes in structural energy.     

New deformation twinning mechanism generates zero macroscopic strain in nanocrystalline metals

Macroscopic strain was hitherto considered a necessary corollary of deformation twinning in coarse-grained metals. Recently, twinning has been found to be a preeminent deformation mechanism in nanocrystalline face-centered-cubic (fcc) metals with medium-to-high stacking fault energies. Here we report a surprising discovery that the vast majority of deformation twins in nanocrystalline Al, Ni, and Cu, contrary to popular belief, yield zero net macroscopic strain. We propose a new twinning mechanism, random activation of partials, to explain this unusual phenomenon. The random activation of partials mechanism appears to be the most plausible mechanism and may be unique to nanocrystalline fcc metals with implications for their deformation behavior and mechanical properties.     

Dislocation modeling in bcc lithium: A comparison between continuum and atomistic predictions in the modified embedded atoms method

In this study, the modified embedded-atom method (MEAM) was applied to compare the predictions of dislocation core properties obtained by molecular statics with the continuum predictions obtained in the framework of the simplified 1D-Peierls–Nabarro model. To this end, a set of four fictive Li potentials in the MEAM framework was proposed with the condition that all four potentials reproduce the same elastic constants, the same transition energies between bcc and fcc crystal structures, and between bcc and hcp crystal structures, while the unstable stacking fault energy on the plane {110} in the direction <111> was varied around the value predicted by first-principles. Within these potentials, direct atomistic calculations were performed to evaluate dislocation core properties such as dislocation half width and Peierls stress and the results were compared with continuum predictions. We found that the trends predicted by the Peierls–Nabarro model, i.e. (i) a decrease of the dislocation half width with increasing unstable stacking fault energy, and (ii) an increase of the Peierls stress with increasing the magnitude of the unstable stacking fault energy, were recovered using atomic calculations in the MEAM framework. Moreover, the magnitude of the dislocation half width and the Peierls stress calculated in the MEAM framework are in good agreement with the Peierls–Nabarro predictions when the dislocation half width is determined using a generic strategy. Specifically, the dislocation half width is defined as the distance for which the disregistery is included between b/4 and 3b/4. It was, therefore, demonstrated herein that the set of fictive potentials could be parameterized in the MEAM framework to validate or to disprove the continuum theory using atomistic methods.