Effects of void shape and orientation on the elastoplastic properties of spheroidally voided single-crystal and nanotwinned copper

ABSTRACT

Void nucleation, growth and coalescence have been identified as the leading cause of ductile damage in metallic materials. To understand the underlying deformation and damage mechanisms, extensive theoretical, experimental and simulation efforts have been attempted on spherically voided metals. In this work, molecular dynamics simulations are performed to analyze the uniaxial straining deformation behaviours of both single-crystal and nanotwinned copper materials embedded with a preexisting spheroidal void. The coupling effects among twin boundary, spheroidal void aspect ratio and orientation on unidirectional elastoplastic behaviours are systematically examined. The dislocation-induced plastic deformation mechanism is also examined and compared with the one due to a perfectly spherical cavity. Simulation results show that elastic modulus increases with both spheroidal void aspect ratio and orientation. So do the yield stress, the first peak stress and the plasticity index. Another peak stress exists for most cases, except for a prolate void embedded in nanotwinned specimens. The slope between peak stresses decreases with both the spheroidal aspect ratio and orientation. The incorporation of a twin boundary results in lower elastic modulus, higher yield strength and smaller plasticity index. For an oblate void, the twin boundary gives rise to more severe strain softening behaviour. The dislocation extraction algorithm illustrates that the continuous nucleation, propagation and reaction of dislocations emanated from both the void front and twin boundary are responsible for the ductile damage of spheroidally voided crystals. The lower dislocation densities found in nanotwinned specimens indicate the desired suppression effects of twin boundary on dislocation activities.     

Investigation on dislocation-based mechanisms of void growth and coalescence in single crystal and nanotwinned nickels by molecular dynamics simulation

Abstract

Molecular dynamics simulations were conducted to elucidate dislocation mechanisms of the void growth and coalescence in single crystal and nanotwinned nickels subjected to uniaxial tension. The simulation results reveal that twin boundary is capable of decreasing the critical stress, suppressing the emission of dislocations and reducing the overall stiffness of the crystal. A size-scale dependence of critical stress is definitely illustrated through stress–strain response, where the larger void size leads to the lower critical stress and strain. It is the successive emissions of leading partials and the subsequent trailing partials that cause the atoms on the void surfaces to escape from the void surfaces continually, and consequently the voids grow to be larger and larger with increasing strain. The voids in the nanotwinned nickel coalesce earlier than those in the single crystal nickel even though the initiation of dislocations in the former is later than that in the latter. Void fraction remains a constant during elastic deformation, while it presents a linear increase with increasing strain during plastic deformation. Evolution of void fraction during void growth and coalescence is independent on void size.     

α-Fe裂纹的分子动力学研究

通过分子动力学方法，模拟了α-Fe裂纹的单轴拉伸实验中的形变过程.研究了不同晶体取向裂纹的形变特点和断裂机理，观察到各种形变现象，如位错形核和发射，位错运动，堆垛层错或孪晶的形成，纳米空洞的形成与连接等.计算结果表明，裂纹扩展是塑性过程和弹性过程相结合的过程，其中塑性过程表现为由裂尖发射的位错导致的原子切变行为，而弹性过程的发生则是由无位错区中的原子断键所导致.同时还研究了α-Fe裂纹的形变特点和断裂机理与温度场和应力场的依赖关系.     

Molecular dynamics investigation of plastic deformation mechanism in bulk nanotwinned copper with embedded cracks

The plastic deformation of bulk nanotwinned copper with embedded cracks under tension has been explored by using molecular dynamics simulations. Simulation results show that the cracks mainly act as dislocation sources during the plastic deformation and occasionally as sinks at later stage. The dislocation pile-up, accumulation and transformation at twin boundaries (TBs) control the plastic hardening and softening deformations. The TB dislocation pile-up zone is estimated to be 5.6–8 nm, which agrees well with previous experimental and simulation results. Furthermore, it is found that the flow stress vs. dislocation density at the hardening stage follows the Taylor-type relationship.     

Influence of stress state on the evolution of misfit dislocation networks in a Ni‐based single crystal superalloy

The structural evolution of interfacial dislocation networks in a Ni‐based single crystal superalloy under various stress states was simulated by molecular dynamics (MD). From the simulation, we found that the dislocation network exhibits different deformation and damage mechanisms under various stress states. The square dislocation network at the (100) phase interface is the easiest to damage under a [100] uniaxial load, but more difficult to damage when multi‐axial loads are applied. This suggests that the application of a [100] direction axial load is the key factor for the damage of the square dislocation network, which leads to failure of the Ni‐based single crystal superalloy under the [100] axial centrifugal load. Moreover, based on MD simulations, the effects of the stress state on γ′ rafting were explored. The results indicate that the morphology of γ′ raft depends on the damage structures of the dislocation network under various stress states.     

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 twin boundary spacing on deformation behavior of nanotwinned magnesium

The effect of twin spacing and temperature on the deformation behavior of nanotwinned magnesium is investigated using molecular dynamics simulation. The results indicate that there is a pronounced shift in the mechanical behavior of nanotwinned magnesium when twin spacing is smaller than 2.9 nm, and that the yield strength decreases with increasing temperature. The results show that at relatively high temperatures, a strength softening can be observed when twin spacing is larger than 7.8 nm. This study demonstrates that the yield strength is associated with the dislocation storage ability of nanotwinned magnesium and the repulsive force between twin boundaries and dislocations.     

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.     

Atomistic simulation study on twin orientation and spacing distribution effects on nanotwinned Cu films

Affected by twin orientation and spacing distribution, different deformation and failure mechanisms of nanotwinned (NT) Cu films are discovered. For films with the same twin spacing, transition from brittle to ductile and ductile to localized necking with the increase of the slanted angle of twin boundary (TB) from 0° to 90° is examined. Two dominant slip mechanisms: (1) slip intersecting with the TBs; (2) slip parallel to the TBs can uncover the transition mechanisms with consideration of twin orientation. To maintain both relatively high strength and good ductility, the slanted angle can be set close to the ductile to localized necking transition border. Besides, the stress–strain curves obtained in this article show that the mechanical responses on both sides of the turning point 45° are asymmetric. On the other hand, the twin spacing distributions affect the ductility of NT Cu films and have almost no contribution to strengthening. The strength of the NT Cu films mainly depends on the twin density. NT Cu films with different twin spacing have worse ductility than equal twin spacing films due to the local twin spacing asymmetry. The failures can be predicted appearing at TBs adjacent to large twin spacing regions, and the failure propagation direction can also be predicted by knowing the obtuse angle decided by stacking faults and TBs.     

Effect of stress state on deformation and fracture of nanocrystalline copper:Molecular dynamics simulation

Deformation in a microcomponent is often constrained by surrounding joined material making the component under mixed loading and multiple stress states. In this study, molecular dynamics(MD) simulation are conducted to probe the effect of stress states on the deformation and fracture of nanocrystalline Cu. Tensile strain is applied on a Cu single crystal,bicrystal and polycrystal respectively, under two different tension boundary conditions. Simulations are first conducted on the bicrystal and polycrystal models without lattice imperfection. The results reveal that, compared with the performance of simulation models under free boundary condition, the transverse stress caused by the constrained boundary condition leads to a much higher tensile stress and can severely limit the plastic deformation, which in return promotes cleavage fracture in the model. Simulations are then performed on Cu single crystal and polycrystal with an initial crack. Under constrained boundary condition, the crack tip propagates rapidly in the single crystal in a cleavage manner while the crack becomes blunting and extends along the grain boundaries in the polycrystal. Under free boundary condition, massive dislocation activities dominate the deformation mechanisms and the crack plays a little role in both single crystals and polycrystals.     

3D DDD modelling of dislocation–precipitate interaction in a nickel-based single crystal superalloy under cyclic deformation

Strain-controlled cyclic deformation of a nickel-based single crystal superalloy has been modelled using three-dimensional (3D) discrete dislocation dynamics (DDD) for both [0?0?1] and [1?1?1] orientations. The work focused on the interaction between dislocations and precipitates during cyclic plastic deformation at elevated temperature, which has not been well studied yet. A representative volume element with cubic γ′-precipitates was chosen to represent the material, with enforced periodical boundary conditions. In particular, cutting of superdislocations into precipitates was simulated by a back-force method. The global cyclic stress–strain responses were captured well by the DDD model when compared to experimental data, particularly the effects of crystallographic orientation. Dislocation evolution showed that considerably high density of dislocations was produced for [1?1?1] orientation when compared to [0?0?1] orientation. Cutting of dislocations into the precipitates had a significant effect on the plastic deformation, leading to material softening. Contour plots of in-plane shear strain proved the development of heterogeneous strain field, resulting in the formation of shear-band embryos.     

Crack-stimulated generation of deformation twins in nanocrystalline metals and ceramics

A theoretical model is proposed that describes the generation of deformation twins near brittle cracks of mixed I and II modes in nanocrystalline metals and ceramics. In the framework of the model, a deformation twin nucleates through stress-driven emission of twinning dislocations from a grain boundary distant from the crack tip. The emission is driven by both the external stress concentrated by the pre-existent crack and the stress field of a neighbouring extrinsic grain boundary dislocation. The ranges of the key parameters, the external shear stress, τ, and the crack length, L, are calculated within which the deformation-twin formation near pre-existent cracks is energetically favourable in a typical nanocrystalline metal (Al) and ceramic (3C-SiC). The results of the proposed model account for experimental data on observation of deformation twins in nanocrystalline materials reported in the literature. The deformation-twin formation is treated as a toughening mechanism effectively operating in nanocrystalline metals and ceramics.     

不同对称性下晶界结构演化及微观机理的晶体相场法研究

采用晶体相场法研究了单轴拉伸下三角相双晶变形过程及机理, 并重点分析了小角对称与非对称晶界和大角对称与非对称晶界在变形过程中的演化及微观机理, 变形过程中应力方向与初始晶界方向平行. 结果表明, 小角对称晶界由柏氏矢量夹角呈60°的两种刃型位错组成, 变形过程中不同类型的位错运动方向相反, 并各自与另一晶界上同一类型位错相互吸引以致部分位错发生湮没; 小角非对称晶界上的位错类型单一, 在应力作用下先沿水平方向攀移, 后各自分解成柏氏矢量约呈120°的两位错, 并通过位错运动和湮没最终形成理想单晶; 大角晶界在应力的作用下先保持水平状态而后锯齿化并发射位错, 伴随着位错运动和湮没, 最终大角非对称晶界发生分解, 而大角对称晶界则重新平直化, 表明大角对称晶界比大角非对称晶界更稳定, 这与实验和分子动力学模拟结果一致. 关键词： 晶体相场 双晶 晶界 对称性     

Evaluating the effects of loading parameters on single-crystal slip in tantalum using molecular mechanics

This study is aimed at developing a physics-based crystal plasticity finite element model for body-centred cubic (BCC) metals, through the introduction of atomic-level deformation information from molecular dynamics (MD) investigations of dislocation motion at the onset of plastic flow. In this study, three critical variables governing crystal plasticity mediated by dislocation motion are considered. MD simulations are first performed across a range of finite temperatures up to 600K to quantify the temperature dependence of critical stress required for slip initiation. An important feature of slip in BCC metals is that it is not solely dependent on the Schmid law measure of resolved shear stress, commonly employed in crystal plasticity models. The configuration of a screw dislocation and its subsequent motion is studied under different load orientations to quantify these non-Schmid effects. Finally, the influence of strain rates on thermal activation is studied by inducing higher stresses during activation at higher applied strain rates. Functional dependence of the critical resolved shear stress on temperature, loading orientation and strain rate is determined from the MD simulation results. The functional forms are derived from the thermal activation mechanisms that govern the plastic behaviour and quantification of relevant deformation variables. The resulting physics-based rate-dependent crystal plasticity model is implemented in a crystal plasticity finite element code. Uniaxial simulations reveal orientation-dependent tension–compression asymmetry of yield that more accurately represents single-crystal experimental results than standard models.     

Uniaxial deformation of nanotwinned nanotubes in body-centered cubic tungsten

We perform large-scale molecular dynamics simulations to delve into tensile and compressive loading of nanotubes containing {112} nanoscale twins in body-centered cubic tungsten, as a function of wall thickness, twin boundary spacing, and strain rate. Solid nanopillars without the interior hollow and/or nanotubes without the nanoscale twins are also investigated as references. Our findings demonstrate that both stress-strain response and deformation behavior of nanotwinned nanotubes and nanopillars exhibit a strong tension-compression asymmetry. The yielding of the nanotwinned nanotubes with thick walls is governed by dislocation nucleation from the twin boundary/surface intersections. With a small wall thickness, however, the failure of the nanotwinned nanotubes is dominated by crack formation and buckling under tensile and compressive loading, respectively. In addition, the strain rate effect, which is more pronounced in compressive loading than in tensile loading, increases with a decreasing twin boundary spacing.     

Strengthening and softening in gradient nanotwinned FCC metallic multilayers

Plastic-deformation behaviors of gradient nanotwinned (GNT) metallic multilayers are investigated in nanoscale via molecular dynamics simulation. The evolution law of deformation behaviors of GNT metallic multilayers with different stacking fault energies (SFEs) during nanoindentation is revealed. The deformation behavior transforms from the dislocation dynamics to the twinning/detwinning in the GNT Ag, Cu, to Al with SFE increasing. In addition, it is found that the GNT Ag and GNT Cu strengthen in the case of a larger twin gradient based on more significant twin boundary (TB) strengthening and dislocation strengthening, while the GNT Al softens due to more TB migration and dislocation nucleation from TB at a larger twin gradient. The softening mechanism is further analyzed theoretically. These results not only provide an atomic insight into the plastic-deformation behaviors of certain GNT metallic multilayers with different SFEs, but also give a guideline to design the GNT metallic multilayers with required mechanical properties.     

Crystallographic variant selection of martensite during fatigue deformation

Metastable austenitic stainless steels are prone to form deformation-induced martensite under the influence of externally applied stress. Crystallographic variant selection during martensitic transformation of metastable austenite has been investigated thoroughly with respect to the interaction between the applied uniaxial cyclic stress and the resulting accumulated plastic strain during cyclic plastic deformation. The orientation of all the Kurdjomov–Sachs (K-S) variants has been evaluated extensively and compared with the measured orientation of martensite with their corresponding interaction energies by applying the elegant transformation texture model recently developed by Kundu and Bhadeshia. Encouraging correlation between model prediction and experimental data generation for martensite pole figures at many deformed austenite grains has been observed. It has been found that both the applied uniaxial cyclic stress and the accumulated plastic strain are having strong influence on crystallographic variant selection during cyclic plastic deformation. Patel and Cohen’s classical theory can be utilized to predict the crystallographic variant selection, if it is correctly used along with the phenomenological theory of martensite crystallography.     

Twin boundary and grain boundary effects on cyclic responses of tensile pre-deformed highly oriented nanotwinned Cu: Molecular dynamics simulation

Molecular dynamics method is performed for analyzing the relationship of the twin boundary and grain boundary on the cyclic response of nanotwinned Cu. Results show that the strength difference among the grain boundary, the twin boundary and the variation of dislocation density are nearly 2-2.5 times. We predict twin boundary is only a factor that affects the stable response, however, the dislocation form and the time to reach stability is caused by the grain boundary. Furthermore, the phenomenon of cyclic hardening is found in all the nanotwinned Cu samples.     

FeCoCrCuNi高熵合金裂纹及孔洞结构力学与微观构象演化机理的分子动力学模拟研究

本文采用分子动力学方法研究了FeCoCrCuNi高熵合金裂纹及孔洞模型结构在不同轴向拉伸应变速率下的力学与微观结构演化机理. 结果表明：应变速率越高FeCoCrCuNi裂纹结构对应更高的过冲应变和过冲应力，其主要原因是高拉伸速率会导致高强度的BCC结构及孪晶结构的生成，而BCC结构及孪晶结构的产生进而会抑制应力的下降，通过应力-应变曲线，可知FeCoCrCuNi裂纹模型在轴向应力作用下表现为塑性形变. 对于不同尺寸的孔洞FeCoCrCuNi裂纹模型的应力模拟与结构分析，可以得出：孔洞尺寸越大, FeCoCrCuNi裂纹结构对应的过冲应变和过冲应力越小，其主要原因是大尺寸的孔洞造成孔洞之间产生裂纹的，进而会影响这个材料的屈服应变和屈服强度.     

Deformation induced microtwins and stacking faults in aluminum single crystal

Microtwins and stacking faults in plastically deformed aluminum single crystal were successfully observed by high-resolution transmission electron microscope. The occurrence of these microtwins and stacking faults is directly related to the specially designed crystallographic orientation, because they were not observed in pure aluminum single crystal or polycrystal before. Based on the new finding above, we propose a universal dislocation-based model to judge the preference or not for the nucleation of deformation twins and stacking faults in various face-centered-cubic metals in terms of the critical stress for dislocation glide or twinning by considering the intrinsic factors, such as stacking fault energy, crystallographic orientation, and grain size. The new finding of deformation induced microtwins and stacking faults in aluminum single crystal and the proposed model should be of interest to a broad community.