Deformation Of Polycrystalline Materials Research Articles

Investigating grain-resolved evolution of lattice strains during plasticity and creep using 3DXRD and crystal plasticity modelling

Microstructure-informed crystal plasticity finite element models have shown great promise in predicting plastic and creep deformation in polycrystalline materials. These models can provide substantial insight into the design, fabrication and lifetime assessment of critical metallic components during operation, for instance, in thermal power plants. However, to correctly incorporate damage prediction into models, the microstructural strain simulated at the grain level must be accurately predicted with suitable validation. For this reason, a 3D X-ray Diffraction (3DXRD) experiment was carried out on 316H stainless steel, a material commonly used in thermal power plants, to obtain the per-grain strain response during plastic and creep deformation at 550°C. Several hundred grains within a probed X-ray volume were tracked and measured whilst loading in-situ, obtaining per-grain centre-of-mass positions, crystallographic orientations, and average lattice strain over individual grains. These data were used to calibrate a crystal plasticity model to study the plastic and creep deformation using macroscopic stress-strain and stress-relaxation data. Subsequently, the model was used to predict the average elastic strain in different grains during the cyclic creep experiment, which was validated by 3DXRD datasets. The model results reveal that {100} or {311} grain families are strongly sensitive to microstructure, thereby a polycrystal model that describes specific orientation and neighbourhood characteristics is essential to predict the local response of these grain families. Whereas, self-consistent models are suitable for {110} and {111} grain families. This study shows that only with a suitable calibration of subsurface grain behaviour, crystal plasticity models reveal grain characteristic-dependent micromechanical behaviour.

A discrete dislocation dynamics framework for modeling polycrystal plasticity with hardening

A two-dimensional discrete dislocation dynamics (DDD) framework is extended to model plastic deformation in polycrystalline materials having realistic grain morphology in finite geometries. The formulation includes constitutive rules to represent intra-grain dislocation mechanisms as well as dislocation/slip transmission across grain boundaries. Rules for intra-granular interactions mimic key three-dimensional dislocation mechanisms, such as line tension and dynamic junction and source formation, in addition to other short-range dislocation interactions. Various effects of idealized three-dimensional dislocation mechanisms on the mechanical response in tension are explored. The scaling of flow strength with grain size is investigated with and without slip transmission at grain boundaries. To aid in the analysis, spatial mappings of relevant stress components and geometrically necessary dislocation density are produced, which bring out competing dislocation-based strengthening mechanisms leading to the observed grain size effect in polycrystals.

Micromechanical modeling of the elastic-viscoplastic deformation for considering voids and imperfect interfaces in sintered nano-silver under compression

The effects of voids and imperfect interfaces are key issues in the constitutive modeling of porous materials. In the current study, uniaxial compression experiments of short column specimens are performed to investigate the stress–strain relation of porous sintered nano-silver at different temperatures and loading rates. A micromechanical-based constitutive model is proposed to describe the mechanical behaviors of elastic-viscoplastic deformed polycrystalline materials with voids and imperfect interfaces. In the developed model, crystals with different orientations and voids are assumed to be embedded in the homogeneous equivalent medium (HEM). The behavior of single crystal is determined by a crystal plasticity model. A modified self-consistent model is proposed to describe the overall response of HEM by calculating the algorithmic tangent operator and affine strain increment of void and single crystals. The accuracy and rationality of the proposed model is validated by comparing the calculated results with a 3D crystal plasticity finite element (CPFE) model. Influences of the imperfect interface parameter and voids volume fraction on elastic and elastic-viscoplastic deformed media are investigated. The maximum allowable volume fraction of the void is analyzed. The model is applied to simulate the experimental data. The result shows that the proposed model can describe the elastic-viscoplastic deformation of sintered nano-silver with reasonable accuracy.

Observation of bulk plasticity in a polycrystalline titanium alloy by diffraction contrast tomography and topotomography

The mechanical properties of polycrystalline metals are governed by the interaction of defects that are generated by deformation within the 3D microstructure. In materials that deform by slip, the plasticity is usually highly heterogeneous within the microstructure. Many experimental tools can be used to observe the results of slip events at the free surface of a sample; however, there are only a few methods for imaging these events in the bulk. In this article, the imaging of bulk slip events within the 3D microstructure are enabled by the combined use of X-ray diffraction contrast tomography and topotomography. Correlative measurements between high-resolution digital image correlation, X-ray diffraction contrast tomography, topotomography and phase contrast tomography are performed during deformation of Ti-7Al to investigate the sensitivity of the X-ray topotomography method for the observation of slip events in the bulk. Much larger neighborhoods of grains were able to be mapped than in previous studies, enabling quantitative measurements of slip transmission. Significant differences were observed between surface and bulk grains, indicating the need for 3D observations of plasticity to better understand deformation in polycrystalline materials.

Theoretical Considerations for Transitioning the Grid Method Technique to the Microscale

As new applications demand the synthesis and validation of materials with specific mechanical performance targets, there is a need for improved characterization and understanding of reduced length-scale deformation processes which govern mechanical behavior (i.e., dislocation slip and twinning). The heterogeneous nature of deformation in polycrystalline materials makes it essential to employ length-scale-independent and material agnostic full-field measurement techniques during mechanics of materials studies. The intention of the current work is to demonstrate the fundamental steps of transitioning the Grid Method (GM), a macro-scale full-field measurement technique used in mechanics of materials studies, to the microscale. Two obstacles overcame when transitioning the technique are reported. The first is the deposition of ultra-fine grids with a pitch of 500nm using a focused ion beam. The second is the characterization and correction of equipment-dependent raster-based image distortions inherent to scanning electron microscope (SEM) image acquisition. The SEM-induced distortions are simulated using a closed-form model which more accurately represents the Fast Fourier Transform modulus obtained from SEM micrographs. The proposed model is validated against synthetic deformation cases, specifically uniaxial tension, uniaxial compression, pure shear, simple shear, and heterogeneous deformation. A two-step filtering procedure informed by the newly introduced closed-form model, consisting of a notch and frame filter is proposed in order to remove distortions observed in SEM micrographs. After correcting the SEM-induced distortions on the stationary microgrid micrographs using the proposed two-step filtering, the extracted strain distortion level is reduced from 0.02 to 0.005 strain. Combined, the efforts presented in the current work demonstrate the initial development and promise of the microscale scanning electron microscope grid method (SEM-GM) to capture distortion corrected strain maps in reduced length-scale.

Why is local stress statistics normal, and strain lognormal?

In the present study we elucidate the nature of local strain statistics evolution during tensile deformation in polycrystalline materials. A rate-independent formulation was implemented within a crystal plasticity framework by the means of representative volume element (RVE) analysis. Local elastic strain, as well as stress, were found to obey a normal distribution, whereas the statistics of local plastic strain conforms to a lognormal distribution. In line with experimental observations, the plastic strain becomes progressively localised and the local regions of large strains make significant contribution to the overall average strain increase. The results reveal the nature of strain inhomogeneity at the microscale and emphasize the fact that in metallic materials the elastic strain accumulation represents an additive process, whereas plastic deformation is a multiplicative process.

A study on anomalous yield drop behaviour in modified beta titanium alloys

ABSTRACTThe yield drop phenomenon observed in the Ti–15V-3Al–3Sn-3Cr (Ti–15–3) beta-titanium alloy and its anomalous behaviour in the boron and carbon added Ti–15–3 alloys have been studied. While the base and the carbon containing alloys exhibit yield drop, the boron containing alloy with smaller grain size than base alloy does not appear to show this phenomenon. Tensile tests were interrupted at different stress levels followed by analyses of slip lines and sub-structural characteristics using scanning and transmission electron microscopes to understand this anomalous yield point phenomenon. Infrared thermal imaging technique was used to map the strain localisation and the spatiotemporal evolution of deformation along the gauge length of the specimens during the tensile tests. Deformation in these alloys initiates only in a few grains. Pile-up of dislocations in these grains subsequently triggers the formation of dislocations in other grains and their rapid multiplications. The spreading of deformation by the generation of dislocations from pile up dislocations in one grain to neighbouring un-deformed grains and their rapid multiplication to new regions influence the yield drop phenomenon and its characteristics. It is shown in this study that microscopic instability in the grain level is a necessary, but not the sufficient condition for the manifestation of macroscopic instability during tensile deformation in polycrystalline materials. The presence of boride particles at grain boundaries restricts the slip transfer across the grains as well as the spreading of deformation to new regions, which causes the suppression of yield drop in the boron containing alloy.

Subgrains, Texture Evolution, and Dynamic Abnormal Grain Growth in a Mo Rod Material

The roles of subgrains, texture, and surface energy during dynamic abnormal grain growth (DAGG) were examined in a commercial-purity Mo rod material. DAGG was observed in this material during tensile deformation at 2023 K (1750 °C). Cooling of specimens after tensile testing was sufficiently rapid to preserve both subgrain structures developed during deformation and several abnormal grains at early stages of growth. These and other microstructural features were characterized to evaluate how subgrains and boundary character influence the early stages of DAGG. Subgrains were observed in the deformed polycrystalline material but were generally absent in newly formed abnormal grains. This was identified as the cause of the sudden drop in flow stress observed at the initiation of DAGG. It is proposed that subgrain intersections with abnormal grain boundaries provide a driving pressure for DAGG. Subgrains within the deformed polycrystals were observed to locally change the boundary curvature at their intersections with abnormal grain boundaries, which likely encouraged growth of the abnormal grains into the deformed polycrystals. Abnormal grains produced by DAGG retained crystallographic orientations and boundary characters that closely resembled those of the polycrystalline material from which they grew. This suggests that neither differences in orientation nor boundary character were important to DAGG in this material.

Comparison of self-consistent and crystal plasticity FE approaches for modelling the high-temperature deformation of 316H austenitic stainless steel

The present article examines the predictive capabilities of a crystal plasticity model for inelastic deformation which captures the evolution of dislocation structure, precipitates and solute atom distributions at the microscale, recently developed by Hu and Cocks (2015) and Hu et al. (2013). The model is implemented within a self-consistent framework and a crystal plasticity finite element (CPFE) scheme. Through direct comparison between the two CP schemes and with an extensive material database for Type 316H stainless steel, the different types of information and the degree to which the models are consistent with experimental observations are assessed. The study demonstrates an agreement between the SCM and the CPFE schemes, providing confidence in the micromechanical deformation model employed. The multi-scale approach also allows the effects of micro-scale deformation processes, related to dislocation-obstacle interactions, on the global deformation response to be captured. Modelling results from this study and their comparison to experimental observations show that deformation of polycrystalline materials, such as 316H stainless steel, is controlled by the evolution of microstructural state of the material and the redistribution of stress between individual grains. The study suggests that the SCM is a feasible tool to simulate and explain the deformation behaviour of complex alloys under industrially-relevant thermo-mechanical operating histories. The CPFE framework captures the effects of the variation in grain geometry and provides more detailed information about the variation of stress and strain within the individual grains, particularly their distribution near grain boundaries and triple points – which are important to understand in the context of damage development and failure. The SCM predicts a “stiffer”, more creep-resistant response than a CPFE model for a given set of material parameters due to the more highly-constrained deformation modes allowed in the model. As a result, material parameters calibrated using one modelling approach are not necessarily suitable for use in another approach – although parameters obtained when fitting the different models should not vary significantly.

In-plane and out-of-plane deformation at the sub-grain scale in polycrystalline materials assessed by confocal microscopy

High-resolution digital image correlation (HR-DIC) techniques have become essential in material mechanics to assess strain measurements at the scale of the elementary mechanisms responsible of the deformation in polycrystalline materials. The purpose of this study is to demonstrate the use of laser scanning confocal microscopy (LSCM) coupled with DIC techniques to deepen knowledge on the deformation process of a polycrystalline nickel-based superalloy at room temperature. The LSCM technique is capable of detecting both in-plane and out-of-plane strain localization within slip bands at the sub-grain level. The LSCM observations are consistent with previous in-situ scanning electron microscopy (SEM) studies: The onset of crystal plasticity occurs primarily near Σ3 twin boundaries with macroscopic loading in the elastic domain (macroscopic stress as low as 80% of the 0.2% offset yield strength (Y.S.0.2%)). This intense irreversible strain localization occurs with either a high Schmid factor (μ > 0.43) or a significant elastic modulus difference between the pair of twins (ΔΕ > 100 GPa). In the plastic deformation domain, transgranular slip activity following slip systems with the highest Schmid factor is mostly responsible for the deformation at the grain level, thus leading to strain percolation. The simultaneous in-plane and out-of-plane deformation assessment via the HR-LSCM-DIC technique was found to be essential for the identification of active slip systems. Finally, the HR-LSCM-DIC technique enabled the quantification of the glide amplitude involved in the three-dimensional shearing process at the grain level that solely in-plane measurements cannot provide.

Thermodynamic description of the plastic work partition into stored energy and heat during deformation of polycrystalline materials

• Thermodynamic description of plastic deformation of polycrystals is presented. • We present the stored energy as an additive component in Gibb's potential. • This description gives a method of stored energy determination. • Experiments show that the energy storage rate is dependent on plastic strain. • Two components of energy storage rate are identified and determined.

Applied machine learning to predict stress hotspots II: Hexagonal close packed materials

Stress hotspots are regions of stress concentrations that form under deformation in polycrystalline materials. We use a machine learning approach to study the effect of preferred slip systems and microstructural features that reflect local crystallography, geometry, and connectivity on stress hotspot formation in hexagonal close packed materials under uniaxial tensile stress. We consider two cases: a hypothetical HCP material without any preferred slip systems with a critically resolved shear stress (CRSS) ratio of 1:1:1, and a second with CRSS ratio 0.1:1:3 for basal: prismatic: pyramidal slip systems. Random forest based machine learning models predict hotspot formation with an AUC (area under curve) score of 0.82 for the Equal CRSS and 0.81 for the Unequal CRSS cases. The results show how data driven techniques can be utilized to predict hotspots as well as pinpoint the microstructural features causing stress hotspot formation in polycrystalline microstructures.

Instantiation of crystal plasticity simulations for micromechanical modelling with direct input from microstructural data collected at light sources

Novel non-destructive characterization techniques performed at light sources provide previously inaccessible 3-D mesoscopic information on the deformation of polycrystalline materials. One major difficulty for interpretation of these experiments through micromechanical modelling is the likelihood that processing and/or mounting the sample introduce residual stresses in the specimen. These stresses need to be incorporated into crystal plasticity formulations, for these models to operate directly from microstructural images and be predictive. To achieve this, the initial micromechanical state of each voxel needs to be specified. In this letter we present a method for incorporating grain-averaged residual stresses for instantiation of crystal plasticity simulations.

Deformation compatibility in a single crystalline Ni superalloy.

Deformation in materials is often complex and requires rigorous understanding to predict engineering component lifetime. Experimental understanding of deformation requires utilization of advanced characterization techniques, such as high spatial resolution digital image correlation (HR-DIC) and high angular resolution electron backscatter diffraction (HR-EBSD), combined with clear interpretation of their results to understand how a material has deformed. In this study, we use HR-DIC and HR-EBSD to explore the mechanical behaviour of a single-crystal nickel alloy and to highlight opportunities to understand the complete deformations state in materials. Coupling of HR-DIC and HR-EBSD enables us to precisely focus on the extent which we can access the deformation gradient, F, in its entirety and uncouple contributions from elastic deformation gradients, slip and rigid body rotations. Our results show a clear demonstration of the capabilities of these techniques, found within our experimental toolbox, to underpin fundamental mechanistic studies of deformation in polycrystalline materials and the role of microstructure.

Laue-DIC: a new method for improved stress field measurements at the micrometer scale.

A better understanding of the effective mechanical behavior of polycrystalline materials requires an accurate knowledge of the behavior at a scale smaller than the grain size. The X-ray Laue microdiffraction technique available at beamline BM32 at the European Synchrotron Radiation Facility is ideally suited for probing elastic strains (and associated stresses) in deformed polycrystalline materials with a spatial resolution smaller than a micrometer. However, the standard technique used to evaluate local stresses from the distortion of Laue patterns lacks accuracy for many micromechanical applications, mostly due to (i) the fitting of Laue spots by analytical functions, and (ii) the necessary comparison of the measured pattern with the theoretical one from an unstrained reference specimen. In the present paper, a new method for the analysis of Laue images is presented. A Digital Image Correlation (DIC) technique, which is essentially insensitive to the shape of Laue spots, is applied to measure the relative distortion of Laue patterns acquired at two different positions on the specimen. The new method is tested on an in situ deformed Si single-crystal, for which the prescribed stress distribution has been calculated by finite-element analysis. It is shown that the new Laue-DIC method allows determination of local stresses with a strain resolution of the order of 10(-5).

A Matlab toolbox to analyze slip transfer through grain boundaries

Slip transmission across grain boundaries is an essential micromechanical processes during deformation of polycrystalline materials. Slip transmission processes can be characterized based on the geometrical arrangement of active slip systems in adjacent grains and the value of the critical resolved shear stress acting on the incoming and possible outgoing slip systems. We present a Matlab toolbox which enables quantification of grain boundary slip transfer properties and comparison with experiments. Using a graphical user interface, experimental grain boundary data can be directly exported as input files for crystal plasticity finite element simulation of bicrystal experiments.

Accumulation of Defects During Plastic Deformation of Polycrystals of the Meso- and Microscale Grain Size

The results obtained from an experimental study on the structure of deformed polycrystalline materials of the meso- and microscale grain size, using transmission electron microscopy, are presented. The slip line pattern, accumulation of the scalar dislocation density and dislocation density components, lattice curvature-torsion, and internal stresses are investigated. The difference between the characteristics of the defect polycrystalline structure at the micro- and mesoscale levels is established.

Quantifying the mesoscopic shear strains in plane strain compressed polycrystalline zirconium

An algorithm is used to estimate mesoscopic strains in a deformed polycrystalline material. This requires comparison of microstructures before and after imposed macroscopic plastic deformations, in order to estimate the local/mesoscopic strains from the displacements of identifiable grain boundary segments. The algorithm was applied to lightly plane strain compressed (PSC) polycrystalline zirconium. Very large (up to 1.2) near-boundary mesoscopic shear strains were estimated. These were well above the estimated measurement uncertainties and remarkably larger than the extremely small (0.01–0.04) PSC strains imposed. Opposing local shears, on both sides of a grain boundary, appeared to compensate each other. Direct correlations were noted, in the same grain, between mesoscopic shear strains and (i) in-grain misorientations and (ii) subsequent grain fragmentation.

Crystallographic Effects on Microscale Machining of Polycrystalline Brittle Materials

This paper studies the effects of crystallography on the microscale machining characteristics of polycrystalline brittle materials on a quantitative basis. It is believed that during micromachining of brittle materials, plastic deformation can occur at the tool-workpiece interface due to the presence of high compressive stresses which leads to chip formation as opposed to crack propagation. The process parameters for such a machining process are comparable to the size of the grains, and hence crystallography assumes importance. The crystallographic effects include grain size, grain boundaries (GB), and crystallographic orientation (CO) for polycrystalline materials. The size of grains (crystals), whose distribution is analyzed as a log-normal curve, has an effect on the yield stress of a material as described by the Hall–Petch equation. The effects of grain boundary and orientation have been considered using the principles of dislocation theory. The microstructural anisotropy in a deformed polycrystalline material is influenced by geometrically necessary boundaries (GNB) and incidental dislocation boundaries (IDB). The dislocation theory takes both types of dislocations into account and relates the material flow stress to the dislocation density. The proposed analysis is compared with previously reported experimental data on polycrystalline germanium (p-Ge). This paper aims to provide a deeper physical insight into the microstructural aspects of polycrystalline brittle materials during precision microscale machining.

Estimation of Local Plastic Deformation of Polycrystalline Materials

Final properties of formed steel or another alloy pieces are affected even by plastic deformation of material. Therefore it is needful to know detail structure changes of material under conditions of plastic deformation caused by forming, grinding, drilling etc. Estimation of the deformation based on its observable macroscopic effects doesn’t correspond fully with microscopic structural changes in whole volume of deformed parts and such estimation is quite impossible in case if only surface layers are deformed. It is possible to obtain value of strain by measurement of grain boundary deformation. Effect of grains boundaries self-orientation caused by grains deformation can be identified on metallographic cut. Stereological measurement of degree of grain boundary orientation is relatively simple if axes of orientation are known (as it is in most of deformation processes). Preferred direction of grains boundaries orientation is the same as direction of deformation; however orientation is not the same thing as deformation. Therefore model of conversion of degree of grain boundary orientation to deformation based on an idealized shape of grains has been proposed. This conversion model is independent on an initial grain size – strain depends only on the shape of the grain and does not depend on its dimension. It allows experimental estimation of local plastic deformation by means of measurement of grain boundary orientation in various areas of plastically deformed parts.