Assessment of the thermodynamic dimension of the stacking fault energy

Especially with respect to high Mn and other austenitic TRansformation and/or TWinning Induced Plasticity (TRIP/TWIP) steels, it is a current trend to model the stacking fault energy of a stacking fault that is formed by plastic deformation with an equilibrium thermodynamic formalism as proposed by Olson and Cohen in 1976. In the present paper, this formalism is critically discussed and its ambiguity is stressed. Suggestions are made, how the stacking fault energy and its relation to the formation of hexagonal ?-martensite might be treated appropriately. It is further emphasized that a thermodynamic treatment of deformation-induced stacking fault phenomena always faces some ambiguity. However, an alternative thermodynamic approach to stacking faults, twinning and the formation of ?-martensite in austenitic steels might rationalize the specific stacking fault arrangements encountered during deformation of TRIP/TWIP alloys.     

Generalized stacking fault energy surfaces in the molecular crystal αRDX

The generalized stacking fault (GSF) energy surfaces in the organic energetic molecular crystal, hexahydro-1,3,5-trinitro-s-triazine (RDX), were studied through atomistic simulations. Using a fully flexible molecular potential in highly damped molecular dynamics simulations, we determined quenched 0?K GSF energy surfaces and structures for a set of planes in the α-polymorph RDX crystal and subsequently compare predictions of slip or cleavage with available experimental observations. To account for the steric contributions and elastic shearing due to the presence of flexible molecules, a modified calculation procedure for the GSF energy surface is proposed that enables the distinction of elastic shear energy from the energy associated with the interfacial displacement discontinuity at the slip plane. Comparisons of the unstable stacking fault energy with the surface energy are used to differentiate cleavage planes from likely slip planes, and the calculations are found to be largely in agreement with available experimental data.     

Continuum model for dislocation dynamics in a slip plane

In this paper, we present a continuum model for dislocation dynamics in a slip plane, which accurately incorporates both the long-range interaction and the local line tension effect of dislocations. Unlike the continuum models in the literature using dislocation densities, we use the disregistry across the slip plane to represent the continuous distribution of dislocations in the slip plane, which has the advantage of including the orientation dependence of dislocations in a very simple way. The continuum dislocation dynamics model is validated by linear instability analysis of a uniform dislocation array to small perturbations and comparisons of the results with those of the discrete dislocation dynamics model. Numerical examples for the evolution of distributions of dislocations and plastic slips in a slip plane are presented.     

Crystallographic nature of deformation bands shown in Zn and Mg-based long-period stacking ordered (LPSO) phase

Formation of curious deformation bands has been reported as one of the deformation mechanisms occurring in an Mg-based long-period stacking ordered (LPSO) phase. The origin of the deformation band is still unknown, and the possibility of the deformation kink band and/or the deformation twin has been discussed. To clarify this, the crystallographic nature of deformation bands formed in the LPSO phase was examined by scanning electron microscope–electron backscatter diffraction (SEM-EBSD) pattern analysis. The results were compared to those of the deformation kink bands formed in hcp-Zn and deformation twins formed in hcp-Mg polycrystals. The deformation bands in the LPSO phase was confirmed not to exhibit a fixed crystal orientation relationship with respect to the matrix, different from the case shown in the deformation twin. Instead, the deformation band in the LPSO phase showed three arbitrariness on its crystallographic nature: an ambiguous crystal rotation axis that varied on the [0 0 0 1] zone axis from band to band; an arbitral crystal rotation angle that was not fixed and showed relatively wide distributions; and a variation in crystal rotation angle depending on the position even within a deformation band boundary itself. These features were coincident with those observed in the deformation bands formed in Zn polycrystals, suggesting that the formed deformation bands in LPSO phase crystals are predominantly deformation kink bands.     

Molecular dynamics simulation of the interaction between a mixed dislocation and a stacking fault tetrahedron

A high number-density of nanometer-sized stacking fault tetrahedra are commonly found during irradiation of low stacking fault energy metals. The stacking fault tetrahedra act as obstacles to dislocation motion leading to increased yield strength and decreased ductility. Thus, an improved understanding of the interaction between gliding dislocations and stacking fault tetrahedra are critical to reliably predict the mechanical properties of irradiated materials. Many studies have investigated the interaction of a screw or edge dislocation with a stacking fault tetrahedron (SFT). However, atomistic studies of a mixed dislocation interaction with an SFT are not available, even though mixed dislocations are the most common. In this paper, molecular dynamics simulation results of the interaction between a mixed dislocation and an SFT in face-centered cubic copper are presented. The interaction results in shearing, partial absorption, destabilization or simple bypass of the SFT, depending on the interaction geometry. However, the SFT was not completely annihilated, absorbed or collapsed during a single interaction with a mixed dislocation. These observations, combined with simulation results of edge or screw dislocations, suggest that defect-free channel formation in irradiated copper is not likely by a single dislocation sweeping or destruction process, but rather by a complex mix of multiple shearing, partial absorption and defect cluster transportation that ultimately reduces the size of stacking fault tetrahedra within a localized region.     

堆垛层错和温度对纳米多晶镁变形机理的影响

本文采用分子动力学模拟方法研究了在拉伸载荷下,堆垛层错和温度对纳米多晶镁力学性能的影响,在模拟中,采用嵌入原子势描述镁原子之间的相互作用．计算结果表明：在纳米晶粒中引入堆垛层错能明显增强纳米多晶镁的屈服应力,但堆垛层错对纳米多晶镁杨氏模量的影响很小;温度为300．0K时,孪晶在晶粒交界附近形成,孪晶随着拉伸应变的增加而逐渐生长．当拉伸应变达到0．087时,一种基面与X—Y面成大约35°角且内部包含堆垛层错的新晶粒成核并快速增长．也就是说,孪晶和新晶粒的形成和繁殖是含堆垛层错的纳米多晶镁在300．0K温度下的主要变形机理．模拟结果也显示,当温度为10．0K时,位错的成核和滑移是含堆垛层错的纳米多晶镁拉伸变形的主要形式．     

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.     

First-principles density functional theory study of generalized stacking faults in TiN and MgO

In this paper, the generalized stacking fault (GSF) energies in different slip planes of TiN and MgO are calculated using highly reliable first-principles density functional theory (DFT) calculations. During DFT calculations, the issue of different ways to calculate the GSF energetics in ceramic materials containing more than one element was addressed and applied. For 〈1?1?0〉/{1?1?1} slip, a splitting of saddle point in TiN was observed. For 〈1?1?2〉/{1?1?1} slip, a stable stacking fault at a₀/3〈1?1?2〉 displacement was formed in TiN. For synchroshear mechanism where the slip was accompanied by a cooperative motion of the interfacial nitrogen atoms within the slip plane, a second stable stacking fault was formed at a₀/6〈1?1?2〉 displacement. The energy barrier for the shuffling of nitrogen atoms from one state to another is calculated to be 0.70 eV per atom. In contrast, such features are absent in MgO. These differences highlight the influence of complex bonding nature (mixed covalent, ionic, and metallic bondings) of TiN, which is substantially different than that in MgO (simple ionic bonding) on GSF shapes.     

Effects of stacking fault energy on defect formation process in face-centered cubic metals

To elucidate the effect of stacking fault energies (SFEs) on defect formation by the collision cascade process for face-centred cubic metals, we used six sets of interatomic potentials with different SFEs while keeping the other properties almost identical. Molecular dynamic simulations of the collision cascade were carried out using these potentials with primary knock-on atom energies (E_PKA) of 10 and 20 keV at 100 K. Neither the number of residual defects nor the size distributions for both self-interstitial atom (SIA) type and vacancy type clusters were affected by the difference in the SFE. In the case of E_PKA = 20 keV, the ratio of glissile SIA clusters increased as the SFE decreased, which was not expected by a prediction based on the classical dislocation theory. The trend did not change after annealing at 1100 K for 100 ps. For vacancy clusters, few stacking fault tetrahedrons (SFTs) formed before the annealing. However, lower SFEs tended to increase the SFT fraction after the annealing, where large vacancy clusters formed at considerable densities. The findings of this study can be used to characterise the defect formation process in low SFE metals such as austenitic stainless steels.     

Atomistic simulation of the stacking fault energy and grain shape on strain hardening behaviours of FCC nanocrystalline metals

ABSTRACT

Ultra-fine grained copper with nanotwins is found to be both strong and ductile. It is expected that nanocrystalline metals with lamella grains will have strain hardening behaviour. The main unsolved issues on strain hardening behaviour of nanocrystalline metals include the effect of stacking fault energy, grain shape, temperature, strain rate, second phase particles, alloy elements, etc. Strain hardening makes strong nanocrystalline metals ductile. The stacking fault energy effects on the strain hardening behaviour are studied by molecular dynamics simulation to investigate the uniaxial tensile deformation of the layer-grained and equiaxed models for metallic materials at 300?K. The results show that the strain hardening is observed during the plastic deformation of the layer-grained models, while strain softening is found in the equiaxed models. The strain hardening index values of the layer-grained models decrease with the decrease of stacking fault energy, which is attributed to the distinct stacking fault width and dislocation density. Forest dislocations are observed in the layer-grained models due to the high dislocation density. The formation of sessile dislocations, such as Lomer–Cottrell dislocation locks and stair-rod dislocations, causes the strain hardening behaviour. The dislocation density in layer-grained models is higher than that in the equiaxed models. Grain morphology affects dislocation density by influencing the dislocation motion distance in grain interior.     

First-principles study of the effects of selected interstitial atoms on the generalized stacking fault energies,strength, and ductility of Ni

We analyze the influences of interstitial atoms on the generalized stacking fault energy （GSFE）, strength, and ductility of Ni by first-principles calculations. Surface energies and GSFE curves are calculated for the （112） （111） and / 101） （ 1 1 1） systems. Because of the anisotropy of the single crystal, the addition of interstitials tends to promote the strength of Ni by slipping along the （10T） direction while facilitating plastic deformation by slipping along the （115） direction. There is a different impact on the mechanical behavior of Ni when the interstitials are located in the slip plane. The evaluation of the Rice criterion reveals that the addition of the interstitials H and O increases the brittleness in Ni and promotes the probability of cleavage fracture, while the addition of S and N tends to increase the ductility. Besides, P, H, and S have a negligible effect on the deformation tendency in Ni, while the tendency of partial dislocation is more prominent with the addition of N and O. The addition of interstitial atoms tends to increase the high-energy barrier γmax, thereby the second partial resulting from the dislocation tends to reside and move on to the next layer.     

Effects of stacking fault energies on formation of irradiation-induced defects at various temperatures in face-centred cubic metals

ABSTRACT

By using the six sets of interatomic potentials for face-centred cubic metals that differ in the stacking fault energy (SFE) while most of the other material parameters are kept almost identical, we conducted molecular dynamics simulations to evaluate the effects of SFE on the defect formation process through collision cascades. The simulations were performed at 100, 300 and 600?K, with a primary knock-on atom energy of 50 keV. The number of residual defects is not dependent on the SFE at all the temperatures. For clusters of self-interstitial atoms (SIAs), their clustering behaviour does not depend on the SFE, either. However, the ratio of glissile SIA clusters tends to decrease with increasing SFE. This is because perfect loops, the edges of which split into two partial dislocations with stacking fault structures between them in most cases, prefer to form at lower SFEs. The enhanced formation of glissile SIA clusters at lower SFEs can also be observed even at increased temperature. Because most large vacancy clusters have stacking fault structures, they preferentially form at lower SFE; however, it is observed only at the lowest temperature, where the mean size increases with decreasing SFE. At higher temperatures, because of their extremely low number density, the vacancy clustering behaviour does not depend on the SFEs.     

A study of the hot and cold deformation of twin-roll cast magnesium alloy AZ31

Recent advances in twin-roll casting (TRC) technology of magnesium have demonstrated the feasibility of producing magnesium sheets in the range of widths needed for automotive applications. However, challenges in the areas of manufacturing, material processing and modelling need to be resolved in order to fully utilize magnesium alloys. Despite the limited formability of magnesium alloys at room temperature due to their hexagonal close-packed crystalline structure, studies have shown that the formability of magnesium alloys can be significantly improved by processing the material at elevated temperatures and by modifying their microstructure to increase ductility. Such improvements can potentially be achieved by processes such as superplastic forming along with manufacturing techniques such as TRC. In this work, we investigate the superplastic behaviour of twin-roll cast AZ31 through mechanical testing, microstructure characterization and computational modelling. Validated by the experimental results, a novel continuum dislocation dynamics-based constitutive model is developed and coupled with viscoplastic self-consistent model to simulate the deformation behaviour. The model integrates the main microstructural features such as dislocation densities, grain shape and grain orientations within a self-consistent viscoplasticity theory with internal variables. Simulations of the deformation process at room temperature show large activity of the basal and prismatic systems at the early stages of deformation and increasing activity of pyramidal systems due to twinning at the later stages. The predicted texture at room temperature is consistent with the experimental results. Using appropriate model parameters at high temperatures, the stress–strain relationship can be described accurately over the range of low strain rates.     

A stochastic theory for clustering of quenched-in vacancies—IV. Continuum model applied to the formation of stacking fault tetrahedra and vacancy loops

The continuum model for the growth of clusters developed in the previous paper (paper III) is applied to the formation of stacking fault tetrahedra in quenched gold and the formation of faulted vacancy loops in quenched aluminium. The results of the theory namely the distribution of the clusters as a function of their size and time, and the average size and the total density of the clusters as a function of time and the ageing temperature are shown to be in good agreement with the experimental results.     

Dislocation formation and twinning from the crack tip in Ni3Al: molecular dynamics simulations

The mechanism of low-temperature deformation in a fracture process of L12 Ni3Al is studied by molecular dynamic simulations.Owing to the unstable stacking energy,the [01ˉ1] superdislocation is dissociated into partial dislocations separated by a stacking fault.The simulation results show that when the crack speed is larger than a critical speed,the Shockley partial dislocations will break forth from both the crack tip and the vicinity of the crack tip;subsequently the super intrinsic stacking faults are formed in adjacent {111} planes,meanwhile the super extrinsic stacking faults and twinning also occur.Our simulation results suggest that at low temperatures the ductile fracture in L12 Ni3Al is accompanied by twinning,which is produced by super-intrinsic stacking faults formed in adjacent {111} planes.