超塑性变形晶界效应研究综述

自1934年超塑性现象被发现, 一直以其特殊的塑性变形机制而备受关注.本文以对超塑性变形晶界研究为主线, 从力学角度总结了近年来研究成果. 包括: 基于晶界拓扑构造、统计规律以及能量耗散的力学模型; 论述了由孔洞损伤导致的超塑性沿晶破坏、晶界结构演化与宏观率敏感性之间的关系; 列举了考虑晶界效应的典型超塑性数值模型; 总结并讨论了晶界滑移定量表征的重要实验手段, 指出超塑性研究中需进一步拓展的领域: 多尺度耦合的超塑性力学、材料制备及组合工艺中利用超塑性.      

Grain-boundary sliding and separation in polycrystalline metals: application to nanocrystalline fcc metals

In order to model the effects of grain boundaries in polycrystalline materials we have coupled a crystal-plasticity model for the grain interiors with a new elastic-plastic grain-boundary interface model which accounts for both reversible elastic, as well irreversible inelastic sliding-separation deformations at the grain boundaries prior to failure. We have used this new computational capability to study the deformation and fracture response of nanocrystalline nickel. The results from the simulations reflect the macroscopic experimentally observed tensile stress-strain curves, and the dominant microstructural fracture mechanisms in this material. The macroscopically observed nonlinearity in the stress-strain response is mainly due to the inelastic response of the grain boundaries. Plastic deformation in the interior of the grains prior to the formation of grain-boundary cracks was rarely observed. The stress concentrations at the tips of the distributed grain-boundary cracks, and at grain-boundary triple junctions, cause a limited amount of plastic deformation in the high-strength grain interiors. The competition of grain-boundary deformation with that in the grain interiors determines the observed macroscopic stress-strain response, and the overall ductility. In nanocrystalline nickel, the high-yield strength of the grain interiors and relatively weaker grain-boundary interfaces account for the low ductility of this material in tension.     

Recoverable creep deformation and transient local stress concentration due to heterogeneous grain-boundary diffusion and sliding in polycrystalline solids

Numerical simulations are used to investigate the influence of heterogeneity in grain-boundary diffusivity and sliding resistance on the creep response of a polycrystal. We model a polycrystal as a two-dimensional assembly of elastic grains, separated by sharp grain boundaries. The crystal deforms plastically by stress driven mass transport along the grain boundaries, together with grain-boundary sliding. Heterogeneity is idealized by assigning each grain boundary one of two possible values of diffusivity and sliding viscosity. We compute steady state and transient creep rates as functions of the diffusivity mismatch and relative fractions of grain boundaries with fast and slow diffusion. In addition, our results show that under transient conditions, flux divergences develop at the intersection between grain boundaries with fast and slow diffusivity, which generate high local stress concentrations. The stress concentrations develop at a rate determined by the fast diffusion coefficient, and subsequently relax at a rate determined by the slow diffusion coefficient. The influence of the mismatch in diffusion coefficient, loading conditions, and material properties on the magnitude of this stress concentration is investigated in detail using a simple model problem with a planar grain boundary. The strain energy associated with these stress concentrations also makes a small fraction of the plastic strain due to diffusion and sliding recoverable on unloading. We discuss the implications of these results for conventional polycrystalline solids at high temperatures and for nanostructured materials where grain-boundary diffusion becomes one of the primary inelastic deformation mechanisms even at room temperature.     

Role of grain boundary energetics on the maximum strength of nanocrystalline Nickel

Numerical simulations are used to investigate the competing grain boundary and dislocation mediated deformation mechanisms in nanocrystalline Ni with grain sizes in the range 4-32 nm. We present a 3D phase field model that tracks the evolution of individual dislocations and grain boundaries. Our model shows that the transition from Hall-Petch to inverse Hall-Petch as the grain size is reduced cannot be characterized only by the grain size, but it is also affected by the grain boundary energetics. We find that the grain size corresponding to the maximum yield stress (the transition from Hall-Petch strengthening with decreasing grain size to inverse Hall-Petch) decreases with increasing grain boundary energy. Interestingly, we find that for grain boundaries with high cohesive energy the Hall-Petch maximum is not observed for grains in the range 4-32 nm.     

Dislocation nucleation from bicrystal interfaces and grain boundary ledges: Relationship to nanocrystalline deformation

Molecular dynamics simulations are used to evaluate the primary interface dislocation sources and to estimate both the free enthalpy of activation and the critical emission stress associated with the interfacial dislocation emission mechanism. Simulations are performed on copper to study tensile failure of a planar Σ5 {2 1 0} 53.1° interface and an interface with the same misorientation that contains a ledge. Simulations reveal that grain boundary ledges are more favorable as dislocation sources than planar regions of the interface and that their role is not limited to that of simple dislocation donors. The parameters extracted from the simulations are utilized in a two-phase composite mesoscopic model for nanocrystalline deformation that includes the effects of both dislocation emission and dislocation absorption mechanisms. A self-consistent approach based on the Eshelby solution for grains as ellipsoidal inclusions is augmented by introduction of stress concentration in the constitutive law of the matrix phase to account for more realistic grain boundary effects. Model simulations suggest that stress concentration is required in the standard continuum theory to activate the coupled grain boundary dislocation emission and absorption mechanisms when activation energy of the dislocation source is determined from atomistic calculation on grain boundaries without consideration of impurities or other extrinsic defects.     

Defect redistribution within a continuum grain boundary plasticity model

The mechanical response of polycrystalline metals is significantly affected by the behaviour of grain boundaries, in particular when these interfaces constitute a relatively large fraction of the material volume. One of the current challenges in the modelling of grain boundaries at a continuum (polycrystalline) scale is the incorporation of the many different interaction mechanisms between dislocations and grain boundaries, as identified from fine-scale experiments and simulations. In this paper, the objective is to develop a model that accounts for the redistribution of the defects along the grain boundary in the context of gradient crystal plasticity. The proposed model incorporates the nonlocal relaxation of the grain boundary net defect density. A numerical study on a bicrystal specimen in simple shear is carried out, showing that the spreading of the defect content has a clear influence on the macroscopic response, as well as on the microscopic fields. This work provides a basis that enables a more thorough analysis of the plasticity of polycrystalline metals at the continuum level, where the plasticity at grain boundaries matters.     

Investigating the deformation of nanocrystalline copper with microscale kinematic metrics and molecular dynamics

Atomistic simulations are employed to investigate the deformation of nanocrystalline copper and the associated strain accommodation mechanisms at 10 K as a function of grain size. Volume-averaged kinematic metrics based on continuum mechanics theory are formulated to analyze the results of molecular dynamics simulations. The metrics rely on both reference and current configurations, along with nearest neighbor lists to estimate nanoscale behavior of atomic deformation fields in nanocrystalline copper. Various deformation mechanisms are activated in the structures, and shown to depend on average grain size of the nanocrystalline structure. Furthermore, grain boundaries, along with dislocation glide, become an important source of strain accommodation as grain size is reduced. It is demonstrated that the metrics capture the contributions of various mechanisms, and provide a sense of the history of atomic regions undergoing both elastic and plastic deformation. The significance of this research is that unique kinematic signatures of the mechanisms are uncovered using certain metrics, and we are able to resolve the contributions of the deformation mechanisms to the overall strain of the structure using Green strain.     

Dislocation nucleation in Σ3 asymmetric tilt grain boundaries

Atomistic simulations were used to investigate dislocation nucleation from Σ3 asymmetric (inclined) tilt grain boundaries under uniaxial tension applied perpendicular to the boundary. Molecular dynamics was employed based on embedded atom method potentials for Cu and Al at 10 K and 300 K. Results include the grain boundary structure and energy, along with mechanical properties and mechanisms associated with dislocation nucleation from these Σ3 boundaries. The stress and work required for dislocation nucleation were calculated along with elastic stiffness of the bicrystal configurations, exploring the change in response as a function of inclination angle. Analyses of dislocation nucleation mechanisms for asymmetric Σ3 boundaries in Cu show that dislocation nucleation is preceded by dislocation dissociation from the boundary. Then, dislocations preferentially nucleate in only one crystal on the maximum Schmid factor slip plane(s) for that crystal. However, this crystal is not simply predicted based on either the Schmid or non-Schmid factors. The synthesis of these results provides a better understanding of the dislocation nucleation process in these faceted, dissociated grain boundaries.     

A screw dislocation nucleated from a triple junction

Dislocation mechanism is still considered to be an effective way in plastic deformation of nanocrystalline materials. The possible nucleation of a screw dislocation from the triple junction is explored. The nucleation of a screw dislocation is found to be rather difficult from the triple junction with well-bonded grain boundaries due to the small singularity (0 to −1/3) introduced by the elasticity anisotropy. For the triple junction with a free sliding grain boundary, the stress singularity is higher than −0.5 and dislocations can be spontaneously nucleated for grain sizes less than 100 nm.     

Constitutive modeling for nanocrystalline metals based on cooperative grain boundary mechanisms

In nanocrystalline metals, the plastic deformation is accommodated primarily at the grain boundaries. Yang and Wang (J. Mech. Phys. Solids, 2003) suggested a deformation model based on clusters consisting of nine grains and incorporating both the Ashby-Verrall mechanism and a 30° rotation of closely linked pairs of grains. In the present article, the insertion and rotation processes are considered together as a cooperative deformation mechanisms, and the degree to which each process contributes is determined by the application of the principle of maximum plastic work. Plane strain and three-dimensional constitutive relations based on this concept are derived for which a general stress state drives the orientation evolution of various grain clusters under the Reuss assumption. Detailed calculation shows that the strain rate depends linearly on the stress, with the values of the coefficients in this linear relationship dictated by the microscopic energy dissipation. The deformation contributed to the overall response by the grain boundary mechanism is discussed in the spirit of the Hashin-Shtrikman bounds.     

Size effects and dislocation patterning in two-dimensional bending

We perform atomistic Monte Carlo simulations of bending a Lennard-Jones single crystal in two dimensions. Dislocations nucleate only at the free surface as there are no sources in the interior of the sample. When dislocations reach sufficient density, they spontaneously coalesce to nucleate grain boundaries, and the resulting microstructure depends strongly on the initial crystal orientation of the sample. In initial yield, we find a reverse size effect, in which larger samples show a higher scaled bending moment than smaller samples for a given strain and strain rate. This effect is associated with source-limited plasticity and high strain rate relative to dislocation mobility, and the size effect in initial yield disappears when we scale the data to account for strain rate effects. Once dislocations coalesce to form grain boundaries, the size effect reverses and we find that smaller crystals support a higher scaled bending moment than larger crystals. This finding is in qualitative agreement with experimental results. Finally, we observe an instability at the compressed crystal surface that suggests a novel mechanism for the formation of a hillock structure. The hillock is formed when a high angle grain boundary, after absorbing additional dislocations, becomes unstable and folds to form a new crystal grain that protrudes from the free surface.     

Discrete dislocation dynamics simulations to interpret plasticity size and surface effects in freestanding FCC thin films

Strong size effects have been experimentally observed when microstructural features approach the geometric dimensions of the sample. In this work experimental investigations and discrete dislocation analyses of plastic deformation in metallic thin films have been performed. Columnar grains representative of the film microstructure are here considered. Simulations are based on the assumptions that sources are scarcely available in geometrically confined systems and nucleation sites are mainly located at grain boundaries. Especially, we investigated the influence on the mesoscopic constitutive response of the two characteristic length scales, i.e., film thickness and grain size. The simulated plastic response qualitatively reproduces the experimentally observed size effects while the main deformation mechanisms appear to be in agreement with TEM analyses of tested samples. A new interpretation of size scale plasticity is here proposed based on the probability of activating grain boundary dislocation sources. Moreover, the key role of a parameter such as the grain aspect ratio is highlighted. Finally, the unloading behavior has been investigated and a strong size dependent Bauschinger effect has been found. An interpretation of these phenomena is proposed based on the analysis of the back stress distribution within the samples.     

EBSD Study of Delamination Fracture in Al–Li Alloy 2090

Aluminum–lithium (Al–Li) alloys offer attractive combinations of high strength and low density for aerospace structural applications. However, a tendency for delamination fracture has limited their use. Identification of the metallurgical mechanisms controlling delamination may suggest processing modifications to minimize the occurrence of this mode of fracture. In the current study of Al–Li alloy 2090 plate, high quality electron backscattered diffraction (EBSD) information has been used to evaluate grain boundary types exhibiting delamination fracture and characterize microtexture variations between surrounding grains. Delamination was frequently observed to occur between variants of the brass texture component, along near-Σ3, incoherent twin boundaries. EBSD analyses indicated a tendency for intense deformation along one side of the fractured boundary. A through-thickness plot of grain-specific Taylor factors showed that delaminations occurred along boundaries with the greatest difference in Taylor factors. Together, these suggest a lack of slip accommodation across the boundary, which promotes significantly higher deformation in one grain, and stress concentrations that result in delamination fracture.     

Effect of microstructure on the nucleation of deformation twins in polycrystalline high-purity magnesium: A multi-scale modeling study

A multi-scale, theoretical study of twin nucleation from grain boundaries in polycrystalline hexagonal close packed (hcp) metals is presented. A key element in the model is a probability theory for the nucleation of deformation twins based on the idea that twins originate from a statistical distribution of defects in the grain boundaries and are activated by local stresses at the grain boundaries. In this work, this theory is integrated into a crystal plasticity constitutive model in order to study the influence of these statistical effects on the microstructural evolution of the polycrystal, such as texture and twin volume fraction. Recently, a statistical analysis of exceptionally large data sets of {101?2} deformation twins was conducted for high-purity Mg (Beyerlein et al., 2010a). To demonstrate the significantly enhanced accuracy of the present model over those employing more conventional, deterministic approaches to twin activation, the model is applied to the case of {101?2} twinning in Mg to quantitatively interpret the many statistical features reported for these twins (e.g., variant selection, thickness, numbers per grain) and their relationship to crystallographic grain orientation, grain size, and grain boundary misorientation angle. Notably the model explains the weak relationship observed between crystal orientation and twin variant selection and the strong correlation found between grain size and the number of twins formed per grain. The predictions suggest that stress fluctuations generated at grain boundaries are responsible for experimentally observed dispersions in twin variant selection.     

Atomistic simulations of elastic deformation and dislocation nucleation during nanoindentation

Nanoindentation experiments have shown that microstructural inhomogeneities across the surface of gold thin films lead to position-dependent nanoindentation behavior [Phys. Rev. B (2002), to be submitted]. The rationale for such behavior was based on the availability of dislocation sources at the grain boundary for initiating plasticity. In order to verify or refute this theory, a computational approach has been pursued. Here, a simulation study of the initial stages of indentation using the embedded atom method (EAM) is presented. First, the principles of the EAM are given, and a comparison is made between atomistic simulations and continuum models for elastic deformation. Then, the mechanism of dislocation nucleation in single crystalline gold is analyzed, and the effects of elastic anisotropy are considered. Finally, a systematic study of the indentation response in the proximity of a high angle, high sigma (low symmetry) grain boundary is presented; indentation behavior is simulated for varying indenter positions relative to the boundary. The results indicate that high angle grain boundaries are a ready source of dislocations in indentation-induced deformation.     

Analyses of tensile deformation of nanocrystalline α-Fe2O3+fcc-Al composites using molecular dynamics simulations

The tensile deformation of nanocrystalline α-Fe₂O₃+fcc-Al composites at room temperature is analyzed using molecular dynamics (MD) simulations. The analyses focus on the effects of variations in grain size and phase volume fraction on strength. For comparison purposes, nanostructures of different phase volume fractions at each grain size are given the same grain morphologies and the same grain orientation distribution. Calculations show that the effects of the fraction of grain boundary (GB) atoms and the electrostatic forces between atoms on deformation are strongly correlated with the volume fractions of the Al and Fe₂O₃ phases. In the case of nanocrystalline Al where electrostatic forces are absent, dislocation emission initiates primarily from high-angle GBs. For the composites, dislocations emits from both low-angle and high-angle GBs due to the electrostatic effect of Al-Fe₂O₃ interfaces. The effect of the interfaces is stronger in structures with smaller average grain sizes primarily because of the higher fractions of atoms in interfaces at smaller grain sizes. At all grain sizes, the strength of the composite lies between those of the corresponding nanocrystalline Al and Fe₂O₃ structures. Inverse Hall-Petch (H-P) relations are observed for all structures analyzed due to the fact that GB sliding is the dominant deformation mechanism. The slopes of the inverse H-P relations are strongly influenced by the fraction of GB atoms, atoms associated with defects, and the volume fractions of the Al and Fe₂O₃ phases.     

Modeling dynamic plasticity and spall fracture in high density polycrystalline alloys

The dynamic thermomechanical response of a tungsten heavy alloy is investigated via modeling and numerical simulation. The material of study consists of relatively stiff pure tungsten grains embedded within a more ductile matrix alloy comprised of tungsten, nickel, and iron. Constitutive models implemented for each phase account for finite deformation, heat conduction, plastic anisotropy, strain-rate dependence of flow stress, thermal softening, and thermoelastic coupling. The potentially nonlinear volumetric response in tungsten at large pressures is addressed by a pressure-dependent effective bulk modulus. Our framework also provides a quantitative prediction of the total dislocation density, associated with cumulative strain hardening in each phase, and enables calculation of the fraction of plastic dissipation converted into heat energy. Cohesive failure models are employed to represent intergranular fracture at grain and phase boundaries. Dynamic finite element simulations illustrate the response of realistic volume elements of the polycrystalline microstructure subjected to compressive impact loadings, ultimately resulting in spallation of the material. The relative effects of mixed-mode interfacial failure criteria, thermally-dependent fracture strengths, and grain shapes and orientations upon spall behavior are weighed, with interfacial properties exerting a somewhat larger influence on the average pressure supported by the volume element than grain shapes and initial lattice orientations within the bulk material. Spatially resolved profiles of particle velocities at the free surfaces of the volume elements indicate the degree to which the incident and reflected stress waves are altered by the heterogeneous microstructure.     

Mechanics of very fine-grained nanocrystalline materials with contributions from grain interior, GB zone, and grain-boundary sliding

In this paper, we formulated an atomically-equivalent continuum model to study the viscoplastic behavior of nanocrystalline materials with special reference to the low end of grain size that is typically examined by molecular dynamic (MD) simulations. Based on the morphology disclosed in MD simulations, a two-phase composite model is construed, in which three distinct inelastic deformation mechanisms disclosed from MD simulations are incorporated to build a general micromechanics-based homogenization scheme. These three mechanisms include the dislocation-related plastic flow inside the grain interior, the uncorrelated atomic motions inside the grain-boundary region (the GB zone), and the grain-boundary sliding at the interface between the grain and GB zone. The viscoplastic behavior of the grain interior is modeled by a grain-size dependent unified constitutive equation whereas the GB zone is modeled by a size-independent unified law. The GB sliding at the interface is represented by the Newtonian flow. The development of the rate-dependent, work-hardening homogenization scheme is based on a unified approach starting from elasticity to viscoelasticity through the correspondence principle, and then from viscoelasticity to viscoplasticity through replacement of the Maxwell viscosity of the constituent phases by their respective secant viscosity. The developed theory is then applied to examine the grain size- and strain rate-dependent behavior of nanocrystalline Cu over a wide range of grain size. Within the grain-size range from 5.21 to 3.28 nm, and the strain rate range from 2.5 × 10⁸ to 1.0 × 10⁹/s, the calculated results show significant grain-size softening as well as strain-rate hardening that are in quantitative accord with MD simulations [Schiotz, J., Vegge, T., Di Tolla, F.D., Jacobsen, K.W., 1999. Atomic-scale simulations of the mechanical deformation of nanocrystalline metals. Phys. Rev. B 60, 11971–11983]. We have also applied the theory to investigate the flow stress, strain-rate sensitivity, and activation volume over the wider grain size range from 40 nm to as low as 2 nm under these high strain rate loading, and found that the flow stress initially displays a positive slope and then a negative one in the Hall–Petch plot, that the strain-rate sensitivity first increases and then decreases, and that the activation volume first decreases and then increases. This suggests that the maximum strain rate sensitivity and the lowest activation volume do not occur at the smallest grain size but, like the maximum yield strength (or hardness), they occur at a finite grain size. These calculated results also confirm the theoretical prediction of Rodriguez and Armstrong [Rodriguez, P., Armstrong, R.W., 2006. Strength and strain rate sensitivity for hcp and fcc nanopolycrystal metals. Bull. Mater. Sci. 29, 717–720] on the basis of grain boundary weakening and the report of Trelewicz and Schuh [Trelewicz, J.R., Schuh, C.A., 2007. The Hall–Petch breakdown in nanocrystalline metals: a crossover to glass-like deformation. Acta Mater. 55, 5948–5958] on the basis of hardness tests. In general the higher yield strength, higher strain rate sensitivity, and lower activation volume on the positive side of the Hall–Petch plot are associated with the improved yield strength of the grain interior, but the opposite trends displayed on the negative side of the plot are associated with the characteristics of the GB zone which is close to the amorphous state.     

On the simulation of cohesive fatigue effects in grain boundaries of a piezoelectric mesostructure

Ferroelectric materials offer a variety of new applications in the field of smart structures and intelligent systems. Accordingly, the modelling of these materials constitutes an active field of research. A critical limitation of the performance of such materials is given when electrical, mechanical, or mixed loading fatigue occurs, combined with, for instance, microcracking phenomena. In this contribution, fatigue effects in ferroelectric materials are numerically investigated by utilisation of a cohesive-type approach. In view of finite element-based simulations, the geometry of a natural grain structure, as observed on the so-called meso-level, is represented by an appropriate mesh. While the response of the grains themselves is approximated by coupled continuum elements, grain boundaries are numerically incorporated via so-called cohesive-type or interface elements. These offer a great potential for numerical simulations: as an advantage, they do not result in bad-conditioned systems of equations as compared with the application of standard continuum elements inhering a very high ratio of length and height. The grain boundary behaviour is modelled by cohesive-type constitutive laws, designed to capture fatigue phenomena. Being a first attempt, switching effects are planned to be added to the grain model in the future. Two differently motivated fatigue evolution techniques are applied, the first being appropriate for low-cycle-fatigue, and a second one adequate to simulate high-cycle-fatigue. Subsequent to a demonstration of the theoretical and numerical framework, studies of benchmark boundary value problems with fatigue-motivated boundary conditions are presented.     

Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation

A strain gradient dependent crystal plasticity approach is used to model the constitutive behaviour of polycrystal FCC metals under large plastic deformation. Material points are considered as aggregates of grains, subdivided into several fictitious grain fractions: a single crystal volume element stands for the grain interior whereas grain boundaries are represented by bi-crystal volume elements, each having the crystallographic lattice orientations of its adjacent crystals. A relaxed Taylor-like interaction law is used for the transition from the local to the global scale. It is relaxed with respect to the bi-crystals, providing compatibility and stress equilibrium at their internal interface. During loading, the bi-crystal boundaries deform dissimilar to the associated grain interior. Arising from this heterogeneity, a geometrically necessary dislocation (GND) density can be computed, which is required to restore compatibility of the crystallographic lattice. This effect provides a physically based method to account for the additional hardening as introduced by the GNDs, the magnitude of which is related to the grain size. Hence, a scale-dependent response is obtained, for which the numerical simulations predict a mechanical behaviour corresponding to the Hall-Petch effect. Compared to a full-scale finite element model reported in the literature, the present polycrystalline crystal plasticity model is of equal quality yet much more efficient from a computational point of view for simulating uniaxial tension experiments with various grain sizes.