Physical mesomechanics of grain boundary sliding in a deformable polycrystal

The temperature-rate dependences of strain resistance and the mechanisms of grain boundary sliding in Pb polycrystals and Pb-based alloys under active tension were investigated. The activation energy of plastic deformation and grain boundary sliding was determined. The structural mechanisms of grain boundary sliding were studied in a wide temperature range. The conclusion was made that self-consistency of grain boundary sliding and intragranular plastic flow has its origin in rotational deformation modes, with the grain boundary sliding being a primary process. Theoretical analysis of rotational deformation modes involved in grain boundary sliding was performed. It is shown that the dependence of deforming stress on the polycrystal grain size is impossible to describe by one universal Hall-Petch equation.     

Non-planar grain boundary structures in fcc metals and their role in nano-scale deformation mechanisms

This work presents the results of a comparative molecular dynamics study showing that relaxed random grain boundary structures can be significantly non-planar at the nano-scale in fcc metals characterized by low stacking fault values. We studied the relaxed structures of random [1?1?0] tilt boundaries in a polycrystal using interatomic potentials describing Cu and Pd. Grain boundaries presenting non-planar features were observed predominantly for the Cu potential but not for the Pd potential, and we relate these differences to the stacking fault values. We also show that these non-planar structures can have a strong influence on dislocation emission from the grain boundaries as well as on grain boundary strain accommodation processes, such as grain boundary sliding. We studied the loading response in polycrystals of 40 nm grain size to a level of 9% strain and found that the non-planar grain boundaries favour dislocation emission as a deformation mechanism and hinder grain boundary sliding. This has strong implications for the mechanical behaviour of nano-crystalline materials, which is determined by the competition between dislocation activity and grain boundary accommodation of the strain. Thus, the two interatomic potentials for Cu and Pd considered in this work resulted in the same overall stress–strain curve, but significantly different fractions of the strain accommodated by the intergranular versus intragranular deformation mechanisms. Strain localization patterns are also influenced by the non-planarity of the grain boundary structures.     

Effects of boundary inclination and boundary type on shear-driven grain boundary migration

A series of molecular dynamics simulations was performed on a bicrystal to which a fixed shear rate was applied parallel to the boundary plane. Under some conditions, grain boundary motion is coupled to the relative tangential motion of the two grains. In order to investigate the generality of this type of coupled shear/boundary motion, simulations were performed for both special (low Σ) and general (non-Σ) [010] tilt boundaries over a wide range of grain boundary inclinations. The data point to the existence of two critical stresses: one for coupled shear/boundary motion and the other for grain boundary sliding. For the non-Σ boundaries, the critical stress for coupled shear/boundary motion is typically smaller than that for sliding; coupled shear/boundary motion occurs for all inclinations. For Σ5 boundaries, for which the critical stress is smaller and depends on boundary inclination, coupled shear/boundary motion occurs for some, but not all inclinations.     

Grain boundary sliding during ambient-temperature creep in hexagonal close-packed metals

Even at ambient temperature or less, below their 0.2% proof stresses all hexagonal close-packed metals and alloys show creep behaviour because they have dislocation arrays lying on a single slip system with no tangled dislocation inside each grain. In this case, lattice dislocations move without obstacles and pile-up in front of a grain boundary. Then these dislocations must be accommodated at the grain boundary to continue creep deformation. Atomic force microscopy revealed the occurrence of grain boundary sliding (GBS) in the ambient-temperature creep region. Lattice rotation of 5° was observed near grain boundaries by electron backscatter diffraction pattern analyses. Because of an extra low apparent activation energy of 20 kJ/mol, conventional diffusion processes are not activated. To accommodate these piled-up dislocations without diffusion processes, lattice dislocations must be absorbed by grain boundaries through a slip-induced GBS mechanism.     

Phase-field study of spinodal decomposition under effect of grain boundary

Grain boundary directed spinodal decomposition has a substantial effect on the microstructure evolution and properties of polycrystalline alloys. The morphological selection mechanism of spinodal decomposition at grain boundaries is a major challenge to reveal, and remains elusive so far. In this work, the effect of grain boundaries on spinodal decomposition is investigated by using the phase-field model. The simulation results indicate that the spinodal morphology at the grain boundary is anisotropic bicontinuous microstructures different from the isotropic continuous microstructures of spinodal decomposition in the bulk phase. Moreover, at grain boundaries with higher energy, the decomposed phases are alternating α/β layers that are parallel to the grain boundary. On the contrary, alternating α/β layers are perpendicular to the grain boundary.     

Theory of grain boundary motion during high-temperature DIGM

A theory of diffusion induced grain boundary migration (DIGM) is presented for high temperatures where volume diffusion of solute atoms out of the grain boundary is important. It is shown that due to the presence of a gradient term in the expression for the free energy of solid solution, even a relatively small discontinuity in the solute distribution across the gain boundary provides enough driving force for grain boundary migration. From the expression obtained for the grain boundary velocity the coefficient for the Ni diffusion across the grain boundaries in a Cu(Ni) polycrystal has been estimated.     

晶界对纳米多晶铝中冲击波阵面结构影响的分子动力学研究

用分子动力学方法研究了纳米多晶铝在冲击加载下的冲击波阵面结构及塑性变形机理.模拟研究结果表明:在弹性先驱波之后,是晶界间滑移和变形主导了前期的塑性变形机理;然后是不全位错在界面上成核和向晶粒内传播,然后在晶粒内形成堆垛层错、孪晶和全位错的过程主导了后期的塑性变形机理.冲击波阵面扫过之后留下的结构特征是堆垛层错和孪晶留在晶粒内,大部分全位错则湮灭于对面晶界.这个由两阶段塑性变形过程导致的时序性塑性波阵面结构是过去未见报道过的. 关键词： 晶界 塑性变形 冲击波阵面 分子动力学     

Cooperative grain boundary sliding in nanocrystalline materials

Superplastic behaviour of microcrystalline materials is now believed to be controlled by cooperative grain boundary sliding (CGBS). An increasing role of grain boundary mediated plasticity with decreasing grain size down to the nanoscale was predicted leading to the prospect of enhanced superplasticity in nanocrystalline materials. Nevertheless, materials with nanosized grains have revealed a significant decrease in plasticity contrary to theoretical prediction. Direct evidence of CGBS in nanocrystalline Ni₃Al alloy from SEM surface analysis and in-situ TEM tensile testing was detected, confirming one similarity in the rheology of deformation processes between micro- and nanomaterials. Thus, differences in deformation behaviour of materials at these two length scales are related to the probability of sliding surface formation, sliding distance and related accommodation mechanisms.     

Strain induced grain boundary premelting in bulk copper bicrystals

In bulk bicrystals strain induced grain boundary premelting (SIGBPM) occurs when heavy screw dislocation pileup can be held up to a certain high temperature, approximately 0.6T _M, where T _M is the melting point of bulk material in Kelvin. SIGBPM occurs at grain boundaries to which new twist component is added due to the rotation of both component crystals toward opposite direction about the axis perpendicular to the grain boundary plane. At the original grain boundary, grain boundary sliding takes place due to this relative rotation. In f.c.c. metals with relatively low stacking fault energies such as copper, nickel, brass(30Zn) and silver, dislocations dissociate into partials. Therefore high density tangled dislocations introduced during plastic deformation hardly loose. If these dislocations can be held to high temperatures, SIGBPM is promoted. Formation of static or dynamic recrystallized grains suppresses SIGBPM itself and the propagation of grain boundary cracks formed by SIGBPM.     

Rate of creep due to grain-boundary diffusion in polycrystalline solids with grain-size distribution

For steady-state deformation caused by grain-boundary diffusion, the macroscopic creep rate is analysed for a three-dimensional polycrystal consisting of space-filling grains, by taking into account the effects of diffusional interaction between grains, viscous grain-boundary sliding and grain-size distributions. For regular polyhedral grains, the grain–grain interactions increase the degree of symmetry of diffusional field, resulting in a decrease of the effective diffusion distance. Meanwhile, both the viscous grain-boundary sliding and the grain-size distribution are found to decrease the creep rate. At decreasing grain sizes, the influence of the viscous grain-boundary sliding becomes increasingly important, which explains the recent experimental observations that the creep rates of nanosized grains are much lower than those predicted by grain-boundary diffusion. On the effect of the grain-size distribution, the upper-bound and lower-bound creep rates are estimated.     

Damage mechanism of nickel-based creep-resistant alloys strengthened by the Laves phase at the grain boundary

ABSTRACT

This study proposes a design guideline for polycrystal Ni-based model alloys with high ductility and 100-MPa creep rupture strength beyond 800°C and 10^5?h. These alloys are strengthened by both the precipitation of fine γ′ particles inside the grain and the Laves phase at the grain boundary. For investigating the damage mechanism, transformation from the non-equilibrium Laves phase to the σ phase at the grain boundary and formation of the equilibrium needle-like Laves phase inside the grain are promoted by increasing the Fe concentration. The rupture time of Fe-free alloys significantly increases because of the equilibrium Laves phase at the grain boundary owing to a suitable Mo equivalent. In particular, W addition can help achieve high-temperature creep strength. The precipitate-free zone (PFZ) is predominantly formed by prior migration at the grain boundary without precipitation. Creep rupture occurs at the precipitation/matrix interface in the PFZ. Therefore, transformation control from the Laves to the σ phase at the grain boundary suppresses creep degradation. Consequently, a Ni-based alloy with strength >100?MPa and rupture elongation >20% at 800°C and 10^5?h is fabricated using Larson–Miller parameter conversion, and the alloy design guideline’s validity is confirmed.     

纳米单晶与多晶铜薄膜力学行为的数值模拟研究

通过对不同温度下单晶薄膜的拉伸性能的分子动力学模拟，从微观角度揭示了温度效应对材料性能的影响. 结果表明温度效应对材料的变形机理影响很大.0K温度下由于缺乏热激活软化的影响, 粒子运动所受到的阻碍较大, 薄膜的强度较高, 塑性变形主要来自于粒子的短程滑移.温度升高，粒子的热运动加剧，屈服强度降低, 塑性变形将主要来自于大范围的位错长程扩展.多晶薄膜的模拟结果表明, 虽然其晶粒形状较为特殊, 但是它仍然遵循反Hall-Petch关系.在模拟过程中，侧向应力最大值比拉伸方向应力的最大值滞后出现.位错只会从晶界产生并向晶粒内部传播，晶粒间界滑移是多晶薄膜塑性变形的主要来源. 关键词： 纳米薄膜 变形机理 温度效应 分子动力学     

金属切削变形与显微高速摄影分析

运用显微高速摄影技术分析了切削过程中金属显微组织塑性变形规律。结果指出,切削中金属晶粒变形具有不均匀性和多晶体变形协调性,以晶粒为单元发生了波浪式起伏立体型变化,但受到晶界的制约。     

Lattice-diffusion-controlled rotation of crystals about a common interface

During the high-temperature deformation of polycrystalline materials, the interaction between neighbouring grains gives rise to grain shape changes, grain-boundary sliding and grain rotation. There is debate on whether sliding makes a direct contribution to strain or whether it merely accommodates the shape changes. In principle, it is possible to deduce any direct sliding contribution, by comparing the overall strain with grain strain. Such attempts are often confounded, however, by the existence of grain rotation. In a previous paper, by Burton, rotation occurring by interfacial diffusion was anaIysed. It may also occur by lattice diffusion and this is the subject of the present paper, where a numerical method is used to treat the rotation of a bicrystal configuration. The method is validated by adapting it to solve a related problem, that of lattice diffusion creep, and predictions are shown to agree with known analytical solutions. The rate of rotation is calculated as a function of bending moment, grain dimensions and grain aspect ratio. The steady-state vacancy concentration and diflusion fluxes within the bicrystal are determined. The fluxes at the free surfaces are shown to lead to apparent boundary ‘grooving’ and ‘mounding’ effects at the tensile and compressive ends of the interface. The method can be further adapted to solve the diffusion creep problem for a ‘bamboo’ structure and this has given important new results. It allows diffusion fluxes at the free surfaces to be calculated for the first time and the variation in the creep constant to be determined as a function of the grain aspect ratio. Reported measurements of enhanced grain-boundary grooving may be explained by these results.     

Analysis of creep due to grain-boundary diffusion in hexagonal microstructures

For steady-state deformation caused by grain-boundary diffusion in hexagonal microstructures, the stress distribution on grain boundaries and the macroscopic strain rates are analysed by taking the effects of viscous grain-boundary sliding into account. The maximum normal stress and the extent of stress concentration are shown to decrease as the grain-boundary viscosity increases. For infinite viscosity and/or extremely small grain sizes, the distribution of the normal stress becomes uniform on grain boundaries. The strain rates are predicted by both the stress analysis and the energy balance method, and the two strain rates are consistent with each other. The predicted strain rates also decrease as the grain-boundary viscosity increases. The present analysis reveals that the grain-size exponent is dependent on the grain size and the grain-boundary viscosity: the exponent becomes unity for small grain sizes and/or high viscosity, while it is three for large grain sizes and/or low viscosity. Recent experimental observations that the strain rates of nano-sized grain are much lower than those predicted by grain-boundary diffusion are explained by the increasing contribution of viscous grain-boundary sliding with decreasing grain size.     

Theory of diffusional rotation about the common boundary of a bicrystal

During the creep of polycrystals, individual grains may undergo shape changes, grain boundary sliding and grain rotation. Theoretical studies have focused on the first two of these processes but only recently has the theory of rotation received detailed attention. Diffusional rotation was analysed by Burton [Phil. Mag. A 82 51 (2002); Phil. Mag. 83 2715 (2003)], for a bicrystal with orthorhombic grains of dimensions X, Y and Z with the common boundary in the yz plane and with Z???X,Y. Rate equations were derived and the stress profile over the common boundary predicted, for cases where grain boundary and lattice diffusion predominate. In this paper, the analyses are extended using numerical methods, to the full two- and three-dimensional cases for boundary and lattice diffusion, respectively. For boundary diffusion, the results for Z/Y???1 reproduce those obtained by analytical means and this is regarded as a verification of the numerical method. When Z/Y?=?1, the rotation rates are shown to be about 30% faster, due to the additional diffusion contribution in the z direction. This contribution increases with decreasing values of Z/Y. The stress patterns at the rotating boundary are derived. For lattice diffusion, the stress pattern at the boundary, the shapes of the vacancy potential contours and the variation of the rotation rate with the ratios X/Y and Z/Y are presented.     

Non-conservation of grain volume during diffusion creep and its effect on denuded zones

It is reasoned in this paper that the traditional assumption of grain volume conservation during diffusion creep is correct only for special grain configurations. An analysis is presented that illustrates this, using a hypothetical arrangement of grains specifically chosen to be stable against both grain boundary sliding and grain rotation, so that the extent of grain volume non-conservation can be illustrated in the absence of these factors. The influence on the development of the ‘denuded’ zones that characterize diffusion creep in particle-containing materials is addressed. The analysis contributes to an explanation for the discrepancies between the creep strain estimated from zone sizes and the overall specimen strain, a discrepancy that has been used in the past as counter evidence for the diffusion creep mechanism. Suggestions are made for the improved modelling of diffusion creep in polycrystalline materials and duplex structures.     

Grain boundary interdiffusion in the case of concentration-dependent grain boundary diffusion coefficient

The grain boundary diffusion in a binary system which exhibits a grain boundary phase transition is considered in the framework of Fisher's model. The kinetic law of the growth of the grain boundary phase and the distribution of the diffusant near the grain boundary are calculated. The method of determining of the concentration dependence of the grain boundary diffusion coefficient from the experimentally measured penetration profiles of the diffusant along the grain boundaries is suggested. The experimental results on Zn diffusion in Fe(Si) bicrystals, Ni diffusion in Cu bicrystals and grain boundary grooving in Al in the presence of liquid In are discussed in light of the suggested model.     

Effect of High-Temperature Structure and Diffusion on Grain-Boundary Diffusion Creep in fcc Metals

Molecular dynamics simulations of high-energy twist and tilt bicrystals of fcc palladium reveal a universal, liquid-like, isotropic high-temperature diffusion mechanism, characterized by a rather low self-diffusion activation energy that is independent of the boundary type or misorientation. Medium-energy grain boundaries exhibit the same behavior at the highest temperatures; however, at lower temperatures the diffusion mechanism becomes anisotropic, with a higher, misorientation-dependent activation energy. Our simulations demonstrate that the lower activation energy at elevated temperatures is caused by a structural transition, from a solid boundary structure at low temperatures to a liquid-like structure at high temperatures. We demonstrate that the existence of such a transition has important consequences for diffusion creep in nanocrystalline fcc metals. In particular, our simulations reveal that in the absence of grain growth, nanocrystalline microstructures containing only high-energy grain boundaries exhibit steady-state diffusion creep with a creep rate that agrees quantitatively with that given by the Coble-creep formula. Remarkably, the activation energy for the high-temperature creep rate is the same as that characterizing the universal high-temperature diffusion in high-energy energy bicrystalline grain boundaries.     

Molecular-Dynamics Simulation of Grain-Boundary Diffusion Creep

Molecular-dynamics (MD) simulations are used, for the first time, to study grain-boundary diffusion creep of a model polycrystalline silicon microstructure. Our fully dense model microstructures, with a grain size of up to 7.5 nm, were grown by MD simulations of a melt into which small, randomly oriented crystalline seeds were inserted. In order to prevent grain growth and thus to enable steady-state diffusion creep to be observed on a time scale accessible to MD simulations (of typically 10^-9s), our input microstructures were tailored to (i) have a uniform grain shape and a uniform grain size of nm dimensions and (ii) contain only high-energy grain boundaries which are known to exhibit rather fast, liquid-like self-diffusion. Our simulations reveal that under relatively high tensile stresses these microstructures, indeed, exhibit steady-state diffusion creep that is homogenous (i.e., involving no grain sliding), with a strain rate that agrees quantitatively with that given by the Coble-creep formula.