Deformation Of Polycrystalline Materials Research Articles

Modeling of the Plastic Deformation of Polycrystalline Materials in Micro and Nano Level Using Finite Element Method

Recent experiments on polycrystalline materials show that nanocrystalline materials have a strong dependency to the strain rate and grain size in contrast to the microcrystalline materials. In this study, mechanical properties of polycrystalline materials in micro and nanolevel were studied and a unified notation for them was presented. To completely understand the rate-dependent stress-strain behavior and size-dependency of polycrystalline materials, a dislocation density based model was presented that can predict the experimentally observed stress-strain relations for these materials. In nanocrystalline materials, crystalline and grain-boundary were considered as two separate phases. The mechanical properties of the crystalline phase were modeled using viscoplastic constitutive equations, which take dislocation density evolution and diffusion creep into account, while an elasto-viscoplastic model based on diffusion mechanism was used for the grain boundary phase. For microcrystalline materials, the surface-to-volume ratio of the grain boundaries is low enough to ignore its contribution to the plastic deformation. Therefore, the grain boundary phase was not considered in microcrystalline materials and the mechanical properties of the crystalline phase were modeled using an appropriate dislocation density based constitutive equation. Finally, the constitutive equations for polycrystalline materials were implemented into a finite-element code and the results obtained from the proposed constitutive equations were compared with the experimental data for polycrystalline copper and good agreement was observed.

Теоретико-полевой подход к описанию деформирования многокомпонентных поликристаллических материалов

Most of inorganic structural materials (metallic alloys, ceramics, minerals etc.) are polycrystalline aggregates, consisted of macroscopically large quantity of single-crystal grains (crystallites). The mechanical behavior of the specimen of polycrystalline material is governed by the physical and mechanical processes in the grains and interaction of the grains. Thus the deformation of polycrystalline material is a cooperative phenomenon typical for condensed matter physics and mechanics of heterogeneous materials. The passing of these processes depends on many parameters, including stress states of individual grains and its evolution during macrodeformation. In this paper we note a mathematical analogy between the equations of the mechanics of heterogeneous polycrystalline materials and the equations of quantum theory of particles scattering. This analogy allows to apply the methods of quantum field theory to solution of the equations of solid mechanics for heterogeneous media. We consider the application of Corringa-Kohn-Rostoker method, used in quantum theory for calculating wave function of electrons in metallic alloys, to elasticity of polycrystals. This approach allows, for instance, to calculate probability distribution density function for stresses in grains under arbitrary macrodeformation of polycrystal. Application of the method to classical problem of homogenization gives new formulae for the effective moduli of disordered polycrystalline medium.

The influence of microstructure on surface strain distributions in a nickel micro-tension specimen

This work presents an integrated experimental and modeling approach for examining the deformation of a pure nickel polycrystal utilizing micro-mechanical testing and a crystal-based elasto-viscoplastic finite-element model (CPFEM). The objective is to study the influence of microstructure on the heterogeneous deformation in polycrystalline materials, and to utilize a modeling framework to explore aspects of the deformation that are difficult or impossible to measure experimentally. To accomplish this, a micro-tension specimen containing 259 grains was created from a pure nickel foil material and deformed in uniaxial tension. After the deformation, the specimen was destructively serial sectioned in concert with electron back scattering diffraction, and these data were used to instantiate a CPFEM simulation. The material parameters in the CPFEM model were calibrated by matching the experimental macroscopic stress-strain response of the micro-tension specimen, and then the simulation results were compared with experimental surface deformations measured with digital image correlation. After validating the simulation results by comparing measured and predicted surface strain distributions, a parametric study of the influence of both crystallographic texture and grain morphology is presented to better understand the influence of microstructure on the development of heterogeneous deformation in the pure nickel polycrystalline material.

Abnormal Grain Growth Approached by Sub-Boundary Enhanced Solid-State Wetting

Abnormal grain growth (AGG), which is also called the secondary recrystallization, often takes place after primary recrystallization of deformed polycrystalline materials. A famous example is the evolution of the Goss texture after secondary recrystallization of Fe-3%Si steel. A selective AGG of Goss grains has remained a puzzle over 70 years in the metallurgy community since its first discovery by Goss in 1935. We suggested the sub-boundary enhanced solid-state wetting as a mechanism of selective AGG of Goss grains. According to this mechanism, if Goss grains have sub-boundaries of low energy, they have an exclusively high probability to grow by solid-state wetting along a triple junction compared with other grains without sub-boundaries. This aspect has been confirmed by Monte-Carlo and Phase Field Model simulations. The simulations showed that if the abnormally-growing grain has a high fraction of low energy boundaries with the matrix grains, it favors the sub-boundary enhanced solid-state wetting and produces many island and peninsular grains frequently observed near the growth front of abnormally-growing Goss grains. For example, the {111}<112> orientation has a S9 relationship with a Goss grain. Therefore, grains with the {111}<112> orientation provide a favorable condition for sub-boundary enhanced solid-state wetting. Three or four-sided grains with convex-inward boundaries, which are observed on a two-dimensional section of polycrystalline structures, are not shrinking but are growing, indicating that they are growing by wetting along a triple junction. These and other microstructural evidences of solid-state wetting could be observed relatively easily near the growth front of abnormally-growing Goss grains. The existence of sub-boundaries exclusively in abnormally-growing Goss grains has been experimentally confirmed. In order to understand why only Goss grains have sub-boundaries, the cold rolling process of the hot-rolled Fe-3%Si steel was analyzed by finite element method (FEM). The analysis showed that a small portion of Goss grains formed during hot rolling survives after cold rolling; the survived Goss grains have the lowest stored energy and are expected to undergo only recovery without recrystallization, producing sub-boundaries.

Quantification of dislocation structure heterogeneity in deformed polycrystals by EBSD

Plastic deformation in polycrystalline materials involves a complex interaction of dislocations with defects in the lattice. The geometrically necessary component of the dislocation density can be quantified to some extent using data obtained from automated electron backscatter diffraction scans over planar regions or volumes using the three-dimensional imaging techniques that are currently available. Reliable measurements require that the step size of the orientation data used in determination of geometrically necessary dislocation densities be on the scale of the microstructural information. Measurements were performed in deformed Cu, Al and steel specimens. Geometrically necessary dislocation density in Cu deformed 10% in compression was about 15–30% of the overall estimated dislocation density. Measurements in Al demonstrate that three-dimensional estimates are on the order of 1.2–2 times the values obtained from 2D measurements on the same structures. Analysis of interstitial free steel specimens shows an increase in average geometrically necessary dislocation density by an order of magnitude for specimens deformed to 12% tensile deformation elongation.

Combining Laue Microdiffraction and Digital Image Correlation for Improved Measurements of the Elastic Strain Field with Micrometer Spatial Resolution

The X-ray Laue microdiffraction technique, available at beamline BM32 on the synchrotron ESRF, is ideally suited for probing the field of elastic strain (and associated stress) in deformed polycrystalline materials with a micrometric spatial resolution. We show that using Digital Image Correlation for measuring Laue pattern distortions between two mechanical states improves significantly the estimate of elastic strain increment. The potentiality of this new Laue-DIC method is illustrated on an elastically bent Si single crystal, for which the measured elastic strain deviates not more than 10-5 from the theoretical strain distribution provided by standard solutions.

616 多結晶体における弾塑性変形の粒間および粒内不均一性のモデリング(OS4-4 オーガナイズドセッション《材料・組織と加工》)

616 多結晶体における弾塑性変形の粒間および粒内不均一性のモデリング(OS4-4 オーガナイズドセッション《材料・組織と加工》)

Kinetics of accumulation of scattered damage in polycrystalline materials with various grain sizes under small-scale strain conditions

The paper addresses damage accumulation processes that occur during static deformation in steels 45 and 09G2S and in brass L63 in the initial state and upon “grain annealing.” The authors discuss new experimental evidence on the damage accumulation kinetics during deformation of polycrystalline materials that differ in nature and grain size, including materials in the unloaded state and those under stresses, with small and very small strains (0.05–0.15%). The results obtained have been the necessary physically consistent explanations. Analytical approximations of the correlation between the main mechanical properties of materials (hardness, yield stress, and ultimate strength) and their structure parameters (grain size) are given.

Continuum metrics for deformation and microrotation from atomistic simulations: Application to grain boundaries

Motivated by a desire to incorporate micro- and nanoscale deformation mechanisms into continuum mechanical models of material behavior, we apply recently developed volume-averaged metrics to the results of atomistic simulations to investigate deformation and microrotation in the vicinity of grain boundaries. Three-dimensional bicrystalline structures are employed to study the inelastic deformation behavior under uniaxial tension and simple shear at a temperature of 10 K. Each bicrystal is constructed by molecular statics followed by thermal equilibration under NPT using an embedded atom method potential for copper. Strain is imposed in each simulation cell at a constant 10 9 s −1 strain rate applied perpendicular and parallel to the grain boundary plane for tension and shear, respectively. A variety of grain boundary deformation mechanisms arise and the resulting deformation and microrotation fields are examined. We also include an analysis showing how microrotation varies as a function of distance from the grain boundary with increasing strain for different grain boundary deformation mechanisms. This work demonstrates that critical interface behavior can be extracted from atomistic simulations using volume-averaged metrics, offering a potential avenue for translating fundamental information to continuum theories of grain boundary deformation in polycrystalline materials.

Effect of grain refinement by severe plastic deformation on the next-neighbor misorientation distribution

Next-neighbor misorientation distributions (NNMD) in severely deformed polycrystalline materials are commonly measured by orientation imaging. A procedure is proposed which enables the separation of NNMD of ultrafine-grained materials into two parts: the distribution of misorientations between newly emerged grains within the original (“parent”) grain interior (“internal daughter grains”) and the distribution of misorientations between grains adjacent to an original grain boundary on its opposite sides (“grain boundary daughter grains”). The procedure is based on electron backscatter diffraction orientation map analyses carried out on different planes of deformed samples considering the evolution of the grain size and shape during severe plastic deformation. It was applied to copper processed by up to three passes of equal-channel angular pressing. A characteristic feature of the measured NNMD is the occurrence of a double peak, which is clearly due to the differences between the NNMD of the two distinct populations of new grains defined above. The peak at low angles represents mainly the continual grain subdivision process in the interior of a parent grain (and is associated with internal daughter grains), while the peak at large angles is due to the high angle misorientations of the grain boundary daughter grains.

Superglide at an Internal Incommensurate Boundary

The intriguing possibility of frictionless gliding of one solid surface on another has been predicted for certain incommensurate interfaces in crystals, based on Aubry's solution to the Frenkel-Kontorova model of a harmonic chain in a periodic potential field. Here we test this prediction for grain boundaries by comparing atomistic simulations with direct experimental observations on the structure and load-deformation behavior of gold nanopillars containing a root-two incommensurate grain boundary. The simulations show supergliding at this boundary limited by finite-size effects which cause edges to act as defects of the incommensurate structure. Structural relaxation at the edges generates stacking faults, dislocations, and asymmetric surface steps. These features as well as the related load-displacement behavior are replicated by experimental observations on the compression of nanopillars using a quantitative nanoindentation device inside a transmission electron microscope. The good agreement between the observed and predicted behavior suggests that incommensurate interfaces could play an important role in the deformation of polycrystalline materials.

A novel yield function for single crystals based on combined constraints optimization

A novel yield function representing the overall plastic deformation in a single crystal is developed using the concept of optimization. Based on the principle of maximum dissipation during a plastic deformation, the problem of single crystal plasticity is first considered as a constrained optimization problem in which constraints are yield functions for slip systems. To overcome the singularity that usually arises in solving the above problem, a mathematical technique is used to replace the above constrained optimization problem with an equivalent problem which has only one constraint. This single constraint optimization problem, the so-called combined constraints crystal plasticity (CCCP) model, is implemented into a finite element code and the results of modeling the uniaxial tensions of the single crystal copper along different crystallographic directions and also hydroforming of aluminum tubes proved the capability of the proposed CCCP model in accurately predicting the deformation in polycrystalline materials.

Probing intra-granular deformation by micro-beam Laue diffraction

Deformation in polycrystalline materials does not occur uniformly in the constituent grains, but shows strong inter- and intra-granular variations. The local deformation response depends on lattice orientation, anisotropic elastic-plastic properties, hardening and damage behaviour and the microstructural neighbourhood. Understanding of these complex interactions is vital for the construction and validation of crystal plasticity models, the introduction of mesoscopic deformation effects into polycrystal models and the fundamental understanding of the material’s deformation behaviour.Micro-beam Laue diffraction provides an excellent tool for the study of inter- and intra-granular deformation, allowing, unlike other microscopy methods, measurements within the bulk of the material. A focused “pink” beam is used to probe the interior of individual grains within a polycrystalline sample. The diffracted radiation forms a pattern of Laue spots which is captured by an area detector. From the spot positions, lattice orientation and elastic strains can be deduced. The intensity distribution within individual spots, can be interpreted in terms of the dislocation arrangement within the gauge volume.In this paper we present a novel setup for microbeam Laue diffraction recently developed on the B16 test-beamline at the Diamond Light Source, UK, with the aim of collecting a high quality dataset characterising mesoscopic deformation behaviour within a polycrystal containing a small number of large grains. Such a dataset was collected from a large grained Ni sample in which a number of maps covering several grains were recorded for a sequence of deformation steps. In this paper some first results from this investigation are presented. Ultimately the dataset is intended to allowe a direct comparison between crystal plasticity models and experimental behaviour.

Dislocation interactions with tilt walls

The flow of plastic deformation in polycrystalline materials can be due to activation of sources in adjacent grains due to the effect of pile up dislocations against the grain boundary and also through the transmission of dislocations across the grain boundary. In this paper, we focus on these two issues by studying the evolution of resolved shear stress as a result of pile up dislocations against the boundary and understanding the basic phenomena of dislocation transmission through grain boundary. We also investigated the relaxed structures a grain boundary acquires after the process of dislocation transmission.

X-ray diffraction studies on asymmetrically broadened peaks of heavily deformed zirconium-based alloys

The diffraction peaks of Zircaloy-2 and Zr–2.5% Nb alloys at various deformations are found to be asymmetric in nature. In order to characterize the microstructure from these asymmetric peaks of these deformed alloys, X-ray diffraction line profile analysis like Williamson–Hall technique, Variance method based on second- and fourth-order restricted moments and Stephens model based on anisotropic strain distribution have been adopted. The domain size and dislocation density have been evaluated as a function of deformation for both these alloys. These techniques are useful where the dislocation structure is highly inhomogeneous inside the matrix causing asymmetry in the line profile, particularly for deformed polycrystalline materials.

Grain boundary sliding revisited: Developments in sliding over four decades

It is now recognized that grain boundary sliding (GBS) is often an important mode of deformation in polycrystalline materials. This paper reviews the developments in GBS over the last four decades including the procedures available for estimating the strain contributed by sliding to the total strain, ξ, and the division into Rachinger GBS in conventional creep and Lifshitz GBS in diffusion creep. It is shown that Rachinger GBS occurs under two distinct conditions in conventional creep depending upon whether the grain size, d, is larger or smaller than the equilibrium subgrain size, λ. A unified model is presented leading to separate rate equations for Rachinger GBS in power-law creep and superplasticity. It is demonstrated that these two equations are in excellent agreement with experimental observations. There are additional recent predictions, not fully resolved at the present time, concerning the role of GBS in nanostructured materials.

Multiscale Total Lagrangian Formulation for Modeling Dislocation-Induced Plastic Deformation in Polycrystalline Materials

Multiscale mathematical and computational formulation for coupling mesoscale dislocation mechanics and macroscale continuum mechanics for prediction of plastic deformation in polycrystalline materials is presented. In this development a total Lagrangian multiscale variational formulation for materials subjected to geometric and material nonlinearities is first introduced. By performing scale decomposition of kinematic variables and the corresponding dislocation kinematic variables, several leading-order equations, including a scale-coupling equation, a mesoscale dislocation evolution equation, and a homogenized macroscale equilibrium equation, are obtained. By further employing the Orowan relation, a mesoscopic plastic strain is obtained from dislocation velocity and its distribution, and a homogenized elastoplastic stress-strain relation for macroscale is constructed. The macroscale, mesoscale, and scale-coupling equations are solved interactively at each macroscopic load increment, and information on the two scales is passed through the macroscale integration points. In this multiscale approach the phenomenological hardening rule and flow rule in the classical plasticity theory are avoided, and they are replaced by a homogenized mesoscale material response characterized by dislocation evolution and their interactions.

2224 多結晶体の変形に及ぼす内部拘束の影響(S03-1 材料の塑性挙動の構成式のモデル化とシミュレーション(1),S03 材料の塑性挙動の構成式のモデル化とシミュレーション)

2224 多結晶体の変形に及ぼす内部拘束の影響(S03-1 材料の塑性挙動の構成式のモデル化とシミュレーション(1),S03 材料の塑性挙動の構成式のモデル化とシミュレーション)

Plasticity goes supercriticial

The notion that plasticity is governed not by the steady flow of a material under an applied stress, but by the occurrence of intermittent avalanches of defects moving through the material, is gaining increasing acceptance. A new study of plastic deformation in polycrystalline materials suggests that the situation could be even more complex than once thought.

Simulation of grain-boundary diffusion creep: analysis of some new numerical techniques

We consider the simulation of deformation of polycrystalline materials by grain–boundary diffusion creep. For a given network of grain boundaries intersecting at nodes, with appropriate boundary conditions, we can calculate the rate at which material will be dissolved or deposited along each grain boundary and hence predict the rate at which each grain will move to accommodate this dissolution/deposition. We discuss two numerical methods for simulating the network changes over a finite time–interval, based on using the movement of adjacent grain boundaries over a small time–interval to estimate the velocities of the nodes. (The second of these methods has enabled us to speed up solution by 100 times in typical experiments compared with a naive forward–Euler approach.) We show that the accuracy with which the node velocities can be estimated is dependent only on the precision of the machine with which they are computed and deduce that, for all practical purposes, the lack of precise node velocity values does not detract from the quality of our solution. Finally, we consider the underlying stability of the problem under various different boundary conditions and conclude that our methods have the potential for providing useful insight into the effect of grain size and shape on deformation in polycrystalline materials.