Relations between twin and slip in parent lattice due to kinematic compatibility at interfaces

The relationships between a slip system in the parent lattice and its transform by twinning shear are considered in regards to tangential continuity conditions on the plastic distortion rate at twin/parent interface. These conditions are required at coherent interfaces like twin boundaries, which can be assigned zero surface-dislocation content. For two adjacent crystals undergoing single slip, relations between plastic slip rates, slip directions and glide planes are accordingly deduced. The fulfillment of these conditions is investigated in hexagonal lattices at the onset of twinning in a single slip deforming parent crystal. It is found that combinations of slip system and twin variant verifying the tangential continuity of the plastic distortion rate always exist. In all cases, the Burgers vector belongs to the interface. Certain twin modes are only admissible when slip occurs along an 〈a〉 direction of the hexagonal lattice, and some others only with a 〈c + a〉 slip. These predictions are in agreement with EBSD orientation measurements in commercially pure Ti sheets after plane strain compression.     

The role of grain boundaries on fatigue crack initiation - An energy approach

In this paper, we construct a model for prediction of fatigue crack initiation based on the material’s microstructure. In order to do so, the energy of a persistent slip band (PSB) is monitored and an energy balance approach is taken, in which cracks initiate and the material fails due to stress concentration from a PSB (with respect to dislocation motion). These PSBs are able to traverse low-angle grain boundaries (GB), thus belonging to clusters of grains. As a consequence of the ongoing cyclic slip process, the PSBs evolve and interact with high-angle GBs, the result of which leads to dislocation pile-ups, static extrusions in the form of ledges/steps at the GB, stress concentration, and ultimately crack initiation. Hence, this fatigue model is driven by the microstructure, i.e. grain orientations, widely distributed grain sizes, precipitates, PSB-GB interactions, as well as the affect of neighboring grains. The results predict that cracks initiate near twin boundaries from PSBs spanning a single large grain with a favorable orientation or multiple grains connected by low-angle GBs. Excellent agreement is shown between model predictions and experimental data.     

AN ANALYSIS OF THE EFFECTS OF SYMMETRICAL TILT GRAIN BOUNDARIES ON THE PLASTIC DEFORMATION

A numerical investigation on the simple polycrystals containing threesymmetrical tilt grain boundaries(GBs)is carried out within the framework of crystalplasticity which precisely considers the finite deformation and finite lattice rotation aswell as elastic anisotropy.The calculated results show that the slip geometry and theredistribution of stresses arising from the anisotropy and boundary constraint play animportant role in the plastic deformation in the simple polycrystals.The stress levelalong GB is sensitive to the load level and misorientation,and the stresses along GB aredistributed nonuniformly.The GB may exhibit a softening or strengthening feature,which depends on the misorientation angle.The localized deformation bands usuallydevelop accompanying the GB plastic deformation,the impingement of the localizedband on the GB may result in another localized deformation band.The yield stresseswith different misorientation angles are favorably compared with the experimentalresults.     

含氢原子缺陷晶界的剪切行为

针对4个α-Fe对称倾斜晶界,采用分子静力学考察了4个晶界中H原子偏析能的分布特征,并采用分子动力学方法研究了晶界内植入不同数量H原子对其在室温条件下剪切行为的影响.H原子通过随机方式植入界面内,利用植入H原子数量与晶界面积的比值来定义H原子面密度ρ.在含H原子晶界剪切行为分析过程中,重点考察了在不同H原子密度ρ下,4个晶界的初始塑性临界应力和晶界迁移位移的变化趋势以及4个晶界在加载过程中的微观变形机理.研究表明:晶界内的H原子偏析能明显偏低,4个晶界附近的H原子会自发向晶界内偏析;随着植入H原子数量的逐渐增多,晶界的初始塑性临界应力和后续变形阶段应力均会降低.晶界内植入H原子会从本质上改变晶界的微观变形机理,进而影响晶界在外载荷条件下的迁移属性.与不含H原子晶界的变形机理对比发现,加载过程中晶界的微结构会发生剧烈的演化,H原子的扩散和团簇化效应会导致晶界内出现纳米孔缺陷.     

Role of discrete intra-granular slip bands on the strain-hardening of polycrystals

This work investigates a new micromechanical modeling of polycrystal plasticity, accounting slip bands for physical plastic heterogeneities considered as periodically distributed within grains. These intra-granular plastic heterogeneities are modeled by parallel flat ellipsoidal sub-domains, each of them may have a distinct uniform plastic slip. To capture the morphology of slip bands occurring in plastically deforming polycrystals, these interacting sub-domains are considered as oblate spheroids periodically distributed and constrained by spherical grain boundaries. In this paper, we focus the study on the influences of internal length scale parameters related to grain size, spatial period and thickness of slip bands on the overall material’s behavior. In a first part, the Gibbs free energy accounting for elastic interactions between plastic heterogeneities is calculated thanks to the Green function’s method in the case of an isolated spherical grain with plastic strain occurring only in slip bands embedded in an infinite elastic matrix. In a second part, the influence of discrete periodic distributions of intra-granular slip bands on the polycrystal’s behavior is investigated considering an aggregate with random crystallographic orientations. When the spatial period of slip bands is on the same order as the grain radius, the polycrystal’s mechanical behavior is found strongly dependent on the ratio between the spatial period of slip bands and the grain size, as well as the ratio between the slip band thickness and the grain size, which cannot be captured by classic length scale independent Eshelby-based micromechanics.     

Plastic Strain Mapping with Sub-micron Resolution Using Digital Image Correlation

Digital image correlation (DIC) of images obtained using scanning electron microscopy has been used to study, quantitatively, the plastic deformation of stainless steel at the microstructural scale. An artificial speckle pattern was generated by the remodelling of a deposited gold layer. A new experimental setup was shown to accelerate the remodelling process and promote the formation of finer nano-scale speckles with sizes ranging 30 nm to 150 nm and of similar spacing. The effects of surface preparation on speckle morphology are discussed. The high density of speckles enabled displacement mapping with resolution of one displacement vector each 0.2?×?0.2 μm² of surface area. It is shown that sub-micron resolution is necessary to capture the plastic deformation associated with the formation of slip bands in stainless steel, which are an important component of the deformation of these materials at the microscale. Electron backscatter diffraction (EBSD) was used to reconstruct the surface grain boundaries and enabled these deformation features to be linked to the microstructure.     

Simulations of thermal conductance across tilt grain boundaries in graphene

Non-equilibrium molecular dynamics (MD) method was performed to simulate the thermal transportation process in graphene nanoribbons (GNRs). A convenient way was conceived to introduce tilt grain boundaries (GBs) into the graphene lattice by repetitive removing C atom rows along certain directions. Comprehensive MD simulations reveal that larger-angle GBs are effective thermal barriers and substantially reduce the average thermal conductivity of GNRs. The GB thermal conductivity is ～10 W·m 1 ·K 1 for a bicrystal GNR with a misorientation of 21.8, which is ～97% less than that of a prefect GNR with the same size. The total thermal resistance has a monotonic dependence on the density of the 5-7 defects along the GBs. A theoretical model is proposed to capture this relation and resolve the contributions by both the reduction in the phonon mean free path and the defect-induced thermal resistance.     

A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation

This work is an attempt to answer the question:

Is there a physically natural method of characterizing the possible interactions between the slip systems of two grains that meet at a grain boundary—a method that could form the basis for the formulation of grain-boundary conditions?

Here we give a positive answer to this question based on the notion of a Burgers vector as described by a tensor field G on the grain boundary [Gurtin, M.E., Needleman, A., 2005. Boundary conditions in small-deformation single-crystal plasticity that account for the Burgers vector. J. Mech. Phys. Solids 53, 1-31]. We show that the magnitude of G can be expressed in terms of two types of moduli: inter-grain moduli that characterize slip-system interactions between the two grains; intra-grain moduli that for each grain characterize interactions between any two slip systems of that grain.We base the theory on microscopic force balances derived using the principle of virtual power, a version of the second law in the form of a free-energy imbalance, and thermodynamically compatible constitutive relations dependent on G and its rate. The resulting microscopic force balances represent flow rules for the grain boundary; and what is most important, these flow rules account automatically—via the intra- and inter-grain moduli—for the relative misorientation of the grains and the orientation of the grain boundary relative to those grains.     

Tunable band structures of polycrystalline graphene by external and mismatch strains

Lacking a band gap largely limits the application of graphene in electronic devices. Previous study shows that grain boundaries (GBs) in polycrystalline graphene can dramatically alter the electrical properties of graphene. Here, we investigate the band structure of polycrystalline graphene tuned by externally imposed strains and intrinsic mismatch strains at the GB by density functional theory (DFT) calculations. We found that graphene with symmetrical GBs typically has zero band gap even with large uniaxial and biaxial strain. However, some particular asymmetrical GBs can open a band gap in graphene and their band structures can be substantially tuned by external strains. A maximum band gap about 0.19 eV was observed in matched-armchair GB (5, 5) | (3, 7) with a misorientation of θ = 13° when the applied uniaxial strain increases to 9%. Although mismatch strain is inevitable in asymmetrical GBs, it has a small influence on the band gap of polycrystalline graphene.     

An experimental study on grain deformation and interactions in an Al-0.5%Mg multicrystal

Heterogeneous plastic deformation behavior of a coarse-grained Al-0.5%Mg multicrystal was investigated experimentally at the individual grain level. A flat uniaxial tensile specimen consisting of a single layer of millimeter-sized grains was deformed quasi-statically up to an axial strain of 15% at room temperature. The initial local crystallographic orientations of the grains and their evolutions after 5, 12, and 15% plastic strains were measured by electron backscattered diffraction pattern analysis in a scanning electron microscope. The local in-plane plastic strains and rigid body rotations of the grains were measured by correlation of digital optical video images of the specimen surface acquired during the tensile test. It is found that both intergranular and intragranular plastic deformation fields in the aluminum multicrystal specimen under uniaxial tension are highly heterogeneous. Single or double sets of slip-plane traces were predominantly observed on the electro-polished surfaces of the millimeter-sized grains after deformation. The active slip systems associated with these observed slip-plane traces were identified based on the grain orientation after deformation, the Schmid factor, and grain interactions in terms of the slip-plane trace morphology at grain boundaries. It is found that the aluminum multicrystal obeys neither the Sachs nor the Taylor polycrystal deformation models but deforms heterogeneously to favor easy slip transmission and accommodation among the grains.     

Yield stress strengthening in ultrafine-grained metals: A two-dimensional simulation of dislocation dynamics

The effect of grain size on the tensile plastic deformation of ultrafine-grained copper polycrystals is investigated using a two-dimensional simulation of dislocation dynamics. Emphasis is put on the elementary mechanisms governing the yield stress in multislip conditions. Whatever the grain size, the yield stress is found to follow a Hall-Petch law. However, the elementary mechanism controlling slip transmission through the grain boundaries at yield is observed to change with the grain size. For the larger grain sizes, the stress concentrations due to dislocations piled-up at grain boundaries are responsible for the activation of plastic activity in the poorly stressed grains. For the smaller grain sizes, the pile-ups contain less dislocations and are less numerous, but the strain incompatibilities between grains become significant. They induce high internal stresses and favor multislip conditions in all grains. Based on these results, simple interpretations are proposed for the strengthening of the yield stress in ultrafine grained metals.     

Sub-Grain Scale Digital Image Correlation by Electron Microscopy for Polycrystalline Materials during Elastic and Plastic Deformation

Damage during loading of polycrystalline metallic alloys is localized at or below the scale of individual grains. Quantitative assessment of the heterogeneous strain fields at the grain scale is necessary to understand the relationship between microstructure and elastic and plastic deformation. In the present study, digital image correlation (DIC) is used to measure the strains at the sub-grain level in a polycrystalline nickel-base superalloy where plasticity is localized into physical slip bands. Parameters to minimize noise given a set speckle pattern (introduced by chemical etching) when performing DIC in a scanning electron microscope (SEM) were adapted for measurements in both plastic and elastic regimes. A methodology for the optimization of the SEM and DIC parameters necessary for the minimization of the variability in strain measurements at high spatial resolutions is presented. The implications for detecting the early stages of damage development are discussed.     

High strain-rate modeling of the interfacial effects of dispersed particles in high strength aluminum alloys

The interfacial effects of dispersed particles on the dynamic deformation of high strength aluminum alloys have been investigated using an eigenstrain-based formulation coupled with dislocation-density based crystalline plasticity and a microstructurally based finite element framework. This accounts for the unrelaxed plastic strains associated with the interfacial behavior of dispersed particles, such as Orowan looping. Particle spacing had a significant effect on the distribution of plastic shear slip, with localization occurring between the particles for smaller particle spacing. The eigenstress field associated with larger particles led to longer-range interaction of pressure fields, which can promote void coalescence for nucleated voids at the particle-matrix interface. Grain orientation also had a significant effect on the behavior associated with the particles, with plastic shear slip localizing at the particle-matrix interfaces for low angle grain-boundary (GB) misorientations, and at GBs and GB junctions for high angle GB misorientations.     

基于微纳米压入法的高熵合金柏氏矢量研究

采用微纳米压入法对CoCrFeNiMn高熵合金进行多种应变率下的压入测试研究,实验获得了材料硬度与压深之间的关系并通过计算分析得到了其不同工况下的柏氏矢量值,探究了压入深度和应变率对柏氏矢量的影响．实验结果表明,所测材料柏氏矢量值在一定范围内呈现出一定的波动性,随着压深的增大,柏氏矢量表现出尺寸效应,即柏氏矢量随压深呈增加趋势;并且在同等压深下,柏氏矢量存在率效应,随着应变率的增加,柏氏矢量值先减小后增加,柏氏矢量从滑移主导向原子失配主导的转变是其率效应转变的主要原因．     

Cylindrical void in a rigid-ideally plastic single crystal III: Hexagonal close-packed crystal

The analytical solution is derived for the plane strain stress field around a cylindrical void in a hexagonal close-packed single crystal with three in-plane slip systems oriented at the angle π/3 with respect to one another. The critical resolved shear stress on each slip system is assumed to be equal. The crystal is loaded by both internal pressure and a far-field equibiaxial compressive stress. The deformation field takes the form of angular sectors, called slip sectors, within which only one slip system is active; the boundaries between different sectors are radial lines. The stress fields are derived by enforcing equilibrium and a rigid, ideally plastic constitutive relationship, in the spirit of anisotropic slip line theory. The results show that each slip sector is divided into smaller regions denoted as stress sectors and the stress state valid within each stress sector is derived. It is shown that stresses are unique and are continuous within stress sectors and across stress sector boundaries, but the gradient of stresses is not continuous across the boundaries between stress sectors. The solution shows self-similarity in that the stresses over the entire domain can be determined from the stresses within a small region adjacent to the void by invoking certain scaling and symmetry properties. In addition, the stress state exhibits periodicity along logarithmic spirals which emanate from the void. The results predict that the mean value of in-plane pressure required to activate plastic deformation around a void in a single crystal can be higher than that necessary for a void in an isotropic material and is sensitive to the orientation of the slip systems relative to the void.     

Grain boundary interface mechanics in strain gradient crystal plasticity

Interactions between dislocations and grain boundaries play an important role in the plastic deformation of polycrystalline metals. Capturing accurately the behaviour of these internal interfaces is particularly important for applications where the relative grain boundary fraction is significant, such as ultra fine-grained metals, thin films and micro-devices. Incorporating these micro-scale interactions (which are sensitive to a number of dislocation, interface and crystallographic parameters) within a macro-scale crystal plasticity model poses a challenge. The innovative features in the present paper include (i) the formulation of a thermodynamically consistent grain boundary interface model within a microstructurally motivated strain gradient crystal plasticity framework, (ii) the presence of intra-grain slip system coupling through a microstructurally derived internal stress, (iii) the incorporation of inter-grain slip system coupling via an interface energy accounting for both the magnitude and direction of contributions to the residual defect from all slip systems in the two neighbouring grains, and (iv) the numerical implementation of the grain boundary model to directly investigate the influence of the interface constitutive parameters on plastic deformation. The model problem of a bicrystal deforming in plane strain is analysed. The influence of dissipative and energetic interface hardening, grain misorientation, asymmetry in the grain orientations and the grain size are systematically investigated. In each case, the crystal response is compared with reference calculations with grain boundaries that are either ‘microhard’ (impenetrable to dislocations) or ‘microfree’ (an infinite dislocation sink).     

Thermodynamically consistent phase field approach to dislocation evolution at small and large strains

A thermodynamically consistent, large strain phase field approach to dislocation nucleation and evolution at the nanoscale is developed. Each dislocation is defined by an order parameter, which determines the magnitude of the Burgers vector for the given slip planes and directions. The kinematics is based on the multiplicative decomposition of the deformation gradient into elastic and plastic contributions. The relationship between the rates of the plastic deformation gradient and the order parameters is consistent with phenomenological crystal plasticity. Thermodynamic and stability conditions for homogeneous states are formulated and satisfied by the proper choice of the Helmholtz free energy and the order parameter dependence on the Burgers vector. They allow us to reproduce desired lattice instability conditions and a stress-order parameter curve, as well as to obtain a stress-independent equilibrium Burgers vector and to avoid artificial dissipation during elastic deformation. The Ginzburg–Landau equations are obtained as the linear kinetic relations between the rate of change of the order parameters and the conjugate thermodynamic driving forces. A crystalline energy coefficient for dislocations is defined as a periodic step-wise function of the coordinate along the normal to the slip plane, which provides an energy barrier normal to the slip plane and determines the desired, mesh-independent height of the dislocation bands for any slip system orientation. Gradient energy contains an additional term, which excludes the localization of a dislocation within a height smaller than the prescribed height, but it does not produce artificial interface energy. An additional energy term is introduced that penalizes the interaction of different dislocations at the same point. Non-periodic boundary conditions for dislocations are introduced which include the change of the surface energy due to the exit of dislocations from the crystal. Obtained kinematics, thermodynamics, and kinetics of dislocations at large strains are simplified for small strains and rotations, as well.     

Grain–boundary interactions and orientation effects on crack behavior in polycrystalline aggregates

A dislocation-density grain–boundary interaction scheme has been developed to account for the interrelated dislocation-density interactions of emission, absorption and transmission in GB regions. The GB scheme is based on slip-system compatibility, local resolved shear stresses, and immobile and mobile dislocation-density accumulation at critical GB locations. To accurately represent dislocation-density evolution, a conservation law for dislocation-densities is used to balance dislocation-density absorption, transmission and emission from the GB. The behavior of f.c.c. polycrystalline copper, with different random low and high angle GBs, are investigated for different crack lengths. For aggregates with random low angle GBs, dislocation-density transmission dominates at the GBs, which can indicate that the low angle GB will not significantly change crack growth directions. For aggregates with random high angle GBs, extensive dislocation-density absorption and pile-ups occur. The high stresses associated with this behavior, along the GBs, can result in intergranular crack growth due to potential crack nucleation sites in the GB.     

Multiscale strain measurements of plastically deforming polycrystalline titanium: Role of deformation heterogeneities

The purpose of this work was to characterize the spatial distribution of residual deformation at the mesoscale (a few grains) and at the macroscale (hundreds of grains) in titanium subjected to cyclic tensile loading. Using ex situ digital image correlation, we compared the axial residual strain fields obtained at optical magnifications ranging from 3.2× to 50×. To compare the results obtained at different optical magnifications, numerous images at higher magnification had to be assembled to encompass the same field-of-view observed at lower magnifications. The strain fields at the highest optical magnification revealed deformation patterns that were not detectable at lower magnifications. These deformation patterns appeared as inclined slip bands near grain boundaries and grain boundary triple points, with the bands sometimes crossing into neighboring grain interiors. Measurements made at optical magnifications greater than 10× captured an underlying deformation pattern, however, considerably more detail within grains was obtained at 50× magnification. The strain fields obtained at 10× and 50× magnifications were subsequently used to estimate the length scale of a representative volume element (RVE) based on the standard deviation of the average residual strain. The estimated RVE length scale was nearly three times the average grain diameter if extracted from the 50× results. The estimate of the RVE length scale was smaller at lower magnification which was due to a homogenizing effect caused by the low measurement resolution. Thus, care must be taken when experimentally obtaining RVE length scale estimates.