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At least 19 records

Crystal rotation and microstructures in an aluminum single-slip system under tensile loading

Highlights: • The crystal rotation angle with the progression of ductile damage was larger in the vertical plane than that in the horizontal plane. In the measurement along 110, the relative rotation angle was the maximum at the intersection of 111 and 110. • The integrated intensity and the FWHM decreased near the notch (from 0 to 0.3 mm) as well as at the intersection of 110 and 111 in the measurement along 110. • The dislocation cell size and the dislocation density decreased at the intersection of 111 and 110 in the measurement of 110 for ε = 5%. This behavior was attributed to the strain energy being released by the rotation of the dislocation cell. We experimentally investigated the rotation angle of the (220) plane in an aluminum single-slip system in which the angles of 110 and 111 in the single crystal were 45° relative to the tensile loading direction. Crystal rotation was investigated at several spots (50 × 50 μm) along 110 and 111 using synchrotron radiation white X-rays at the BL28B2 beamline of super photon ring-8. In measurements along the 110 axis, at an applied strain of ε = 5%, the relative crystal rotation of (220) in the vertical plane increased from 0.850° to 5.438° in the range of 0.9 to 1.4 mm. We observed the microstructure using a transmission electron microscope and verified the size of the dislocation cells or subgrains at each spot along 110. The fundamental local crystallography revealed in this work should be helpful in establishing a method for evaluating ductile damage in materials.

36 MATERIALS SCIENCE↗

Geometrically projected discrete dislocation dynamics

Three-dimensional discrete dislocation dynamics methods (3D-DDD) have been developed to explicitly track the motion of individual dislocations under applied stress. At present, these methods are limited to plastic strains of about one percent or less due to high computational cost associated with the interactions between large numbers of dislocations. This limitation motivates the construction of minimalistic approaches to efficiently simulate the motion of dislocations for higher strains and longer time scales. In the present study, we propose geometrically projected discrete dislocation dynamics (GP-DDD), a method in which dislocation loops are modeled as geometrical objects that maintain their shape with a constant number of degrees of freedom as they expand. We present an example where rectangles composed of two screw and two edge dislocation segments are used for modeling gliding dislocation loops. We use this model to simulate single slip loading of copper and compare the results with detailed 3D-DDD simulations. We discuss the regimes in which GP-DDD is able to adequately capture the variation of the flow stress with strain rate in the single slip loading condition. In conclusion, a simulation using GP-DDD requires ~40 times fewer degrees of freedom for a copper single slip loading case, thus reducing computational time and complexity.

36 MATERIALS SCIENCE↗

Comparative analysis of plasticity-based GND density estimation methods in crystal plasticity finite element models

In crystal plasticity finite element (CPFE) simulations, accurately quantifying geometrically necessary dislocations (GNDs) is critical for capturing strain gradients in polycrystals. We compare different methods for quantifying GNDs, all of which originate from the Nye tensor, which is computed as the curl of the plastic deformation gradient. The projection technique directly decomposes the Nye tensor onto individual screw and edge dislocation components to compute GNDs. This approach requires converting a nine-component Nye tensor into densities for a larger number of dislocation systems, a fundamentally underdetermined (non-unique) process, which is resolved using L2 minimization. In contrast, when employing CPFE analysis, one could directly compute dislocation densities on each slip system using shear gradients. Projection and slip gradient methods are compared with respect to their prediction of GNDs with changing grain size, strain, and grain neighborhoods, including multigrain junctions. Although these techniques match analytical GND densities for single slip, single crystal deformation, and are consistent with anticipated overall GND trends, we find that the GND densities from projection techniques are significantly lower than those predicted from CPFE-based slip gradients in polycrystals. A suggested improvement of only using the active dislocation systems in the projection technique almost entirely resolved this mismatch.

Crystal plasticity↗

Hierarchical 3D Nanolayered Duplex-Phase Zr with High Strength, Strain Hardening, and Ductility

Nanolayered, bimetallic composites are receiving increased attention due to an exceptional combination of strength and thermal stability not possible from their coarse-layered counterparts or constituents alone. Yet, due to their 2D planar, unidirectional arrangement, they are highly anisotropic, which results in limited strain hardening and ductility. Therefore, like many high-performance, ultrastrong materials of our time, they succumb to the usual strength-ductility trade-offs. Here we present the formation of a novel hierarchical microstructure, comprised of crystals consisting of 3D nanolayered α/β–Zr networks. By direct comparison with coarse-layered material of the same chemistry, we show that the unusual hierarchical 3D structure gives rise to high strain hardening, high strength, and high ductility. Using TEM analysis and hysteresis testing, we discovered that the 3D randomly oriented biphase boundaries result in progressively dispersive rather than localized slip with increasing strain. Dislocation activity in the α–Zr lamellae transitions from single slip to multislip and eventually to multimodal slip as strain increases. Furthermore, the diffusive slip-promoting properties of 3D layered networks can potentially invoke simultaneous high strength, strain hardening, and ductility, and reveal a new target in the microstructural design of high performance structural materials.

36 MATERIALS SCIENCE↗

Effect of neighboring grain orientation on strain localization in slip bands in HCP materials

Particularly in plastically anisotropic crystals, such as hexagonal close packed (HCP) materials, plastic deformation is realized by slip acting in the small volumes within individual crystals. Here we extend a full field fast Fourier transform (FFT)-based elasto-viscoplastic formulation to simulate the development of a single slip band on either prismatic or basal planes spanning a crystal. Calculations of the strain and stress fields induced locally within the band and parent crystal, and ahead of the band/grain boundary junction in the neighboring crystal are analyzed as the slip band intensifies under increasing applied strain. We report a substantial influence of the crystallographic orientation of the nearest neighboring grain on the rate of slip band localization. Performing the analysis on two materials, CP-Ti and Mg, indicates that the strength of the material affects the rate of localization, with stronger materials tending to localize more easily. A slip band tip stress-based criterion is proposed for identifying the nearest neighbor orientations in which slip band transmission is possible and the likely slip system for which it occurs. This indicator is validated against experimental studies on commercially pure Ti, an Mg–Y alloy, and Ti–6Al–4V. Finally, we show that for low GB misorientations, the slip band is likely to transmit into another slip band of the same type in the neighbor grain, while for high GB misorientations, it is likely to transmit into one of a different type or to not transmit at all.

36 MATERIALS SCIENCE↗

Enabling high resolution strain mapping in zirconium alloys

Highlights: • Optimisation of speckle patterns suitable for high resolution digital image correlation in a zirconium alloy • Evidence of distinct strain patterning at the macro and micro scale • Analysis of strain heterogeneity in a neighbouring low and high strain band • Paved the way for future studies on strain localization in zirconium alloys subjected to hydriding and irradiation damage - Abstract: High Resolution Digital Image Correlation (HRDIC) has been established recently as a novel displacement mapping technique during mechanical loading experiments to quantify strain localisation down to the level of individual slip traces. This is achieved by the creation of a nano-scale gold pattern naturally formed during remodelling of a thin gold layer that was sputtered onto the region of interest. To date, the gold remodelling is carried out in a water vapourisation environment, which excludes the technique to be applied to materials that readily form noticeable oxide layers in such environments. The current paper describes a recently developed gold remodelling technique using a styrene-argon environment at substantially lower temperatures than the water-vapour based technique. The material used in the present work is a zirconium alloy where we first demonstrate the problem of oxide formation during remodelling in water vapour and the benefit of the modified remodelling procedure. The error associated with the spatial drift was assessed for different interrogation window sizes followed by detailed analysis of the subsequent strain maps produced using the styrene remodelled patterns after tensile deformation to nominal applied strains of ~3.5% and ~7.0%. The level of detail captured demonstrate the suitability of styrene-argon-based remodelling for materials like Zr alloys with the strain maps showing clear strain patterning on both a transgranular and single grain scale with the possibility of quantifying strain across a single slip trace.

36 MATERIALS SCIENCE↗

On the measurement of dislocations and dislocation substructures using EBSD and HRSD techniques

The accumulation of the dislocations and development of dislocation structures in plastically deformed Ni201 is examined using dedicated analyses of Electron Back-Scatter Diffraction (EBSD) acquired orientation maps, and High-Resolution Synchrotron Diffraction (HRSD) acquired patterns. The results show that the minimum detectable microstructure-averaged (bulk) total dislocation density ($ρ_T$) measured via HRSD is approximately 1E13 m -2 , while the minimum GND density ($ρ_G$) measured via EBSD is approximately 2E12 m -2 - the EBSD technique being more sensitive at low plastic strain. This highlights complementarity of the two techniques when attempting to quantify amount of plastic deformation (damage) in a material via a measurement of present dislocations and their structures. Furthermore, a relationship between EBSD-measured $ρ_G$ and the size of HRSD-measured Coherently Scattering Domains (CSDs) has been mathematically derived - this allows for an estimation of the size of CSDs from EBSD-acquired orientation maps, and conversely an estimation of $ρ_G$ from HRSD-measured size of CSDs. The measured evolution of ($ρ_T$), and $ρ_G$ is compared with plasticity theory models - the current results suggest that Ashby's single-slip model underestimates the amount of ONDs ($ρ_G$), while Taylor's model is correctly predicting the total amount of dislocation ($ρ_T$) present in the material as a function of imparted plastic strain.

36 MATERIALS SCIENCE↗

Sessile dislocations by reactions in NiAl severely deformed at room temperature

B2 ordered NiAl is known for its poor room temperature (RT) ductility; failure occurs in a brittle like manner even in ductile single crystals deforming by single slip. In the present study NiAl was severely deformed at RT using the method of high pressure torsion (HPT) enabling the hitherto impossible investigation of multiple slip deformation. Methods of transmission electron microscopy were used to analyze the dislocations formed by the plastic deformation showing that as expected dislocations with Burgers vector a(100) carry the plasticity during HPT deformation at RT. In addition, we observe that they often form a(110) dislocations by dislocation reactions; the a(110) dislocations are considered to be sessile based on calculations found in the literature. It is therefore concluded that the frequently encountered 3D dislocation networks containing sessile a(110) dislocations are pinned and lead to deformation-induced embrittlement. In spite of the severe deformation, the chemical order remains unchanged.

36 MATERIALS SCIENCE↗

Determining heterogeneous slip activity on multiple slip systems from single crystal orientation pole figures

A new experimental method to determine heterogeneity of shear strains associated with crystallographic slip in the bulk of ductile, crystalline materials is outlined. The method quantifies the time resolved evolution of misorientation within plastically deforming crystals using single crystal orientation pole figures (SCPFs) measured in-situ with X-ray diffraction. A multiplicative decomposition of the crystal kinematics is used to interpret the distributions of lattice plane orientation observed on the SCPFs in terms of heterogeneous slip activity (shear strains) on multiple slip systems. Here, to show the method’s utility, the evolution of heterogeneous slip is quantified in a silicon single crystal plastically deformed at high temperature at multiple load steps, with slip activity in sub-volumes of the crystal analyzed simultaneously.

36 MATERIALS SCIENCE↗

Hydrogen effects on the deformation and slip localization in a single crystal austenitic stainless steel

Hydrogen is known to embrittle austenitic stainless steels, which are widely used in high-pressure hydrogen storage and delivery systems, but the mechanisms that lead to such material degradation are still being elucidated. The current work investigates the deformation behavior of single crystal austenitic stainless steel 316L through combined uniaxial tensile testing, characterization and atomistic simulations. Thermally precharged hydrogen is shown to increase the critical resolved shear stress (CRSS) without previously reported deviations from Schmid’s law. Molecular dynamics simulations further expose the statistical nature of the hydrogen and vacancy contributions to the CRSS in the presence of alloying. Slip distribution quantification over large in-plane distances (> 1 mm), achieved via atomic force microscopy (AFM), highlights the role of hydrogen increasing the degree of slip localization in both single and multiple slip configurations. The most active slip bands accumulate significantly more deformation in hydrogen precharged specimens, with potential implications for damage nucleation. For $\langle$110$\rangle$ tensile loading, slip localization further enhances the activity of secondary slip, increases the density of geometrically necessary dislocations and leads to a distinct lattice rotation behavior compared to hydrogen-free specimens, as evidenced by electron backscatter diffraction (EBSD) maps. Finally, the results of this study provide a more comprehensive picture of the deformation aspect of hydrogen embrittlement in austenitic stainless steels.

36 MATERIALS SCIENCE↗

Coupled elasticity, plastic slip, and twinning in single crystal titanium loaded by split-Hopkinson pressure bar

Here coupled elasticity, plastic slip, and twinning in high-purity single crystal titanium loaded by split-Hopkinson pressure bar (SHPB) are investigated, in the framework of large deformation and by utilizing the finite element method (FEM). A thermodynamically consistent system of equations for combined plastic slip and twinning is formulated. Novel kinematics is proposed to develop the driving forces for slip and twinning processes and to consider plastic slip in twins. Dislocation based crystal plasticity is proposed, with an emphasis on the interactions among all slip modes in multi-variant/multiphase heterogeneous materials. A mechanism for dislocation density evolution during twinning is proposed. The impact loading along the [0001] and [1$0\bar{1}$1] directions of single crystal high purity titanium is investigated. The evolution of stress-strain field, dislocation density, and volume fraction for each variant in the sample during the entire loading process are obtained and discussed in detail. Results in simulations show that for the [0001] specimen due to the existence of six symmetry primary twin variants with respect to the loading direction and fifteen different slip systems in each variant, the fields of stress and dislocation density are very homogenous in the sample. The simulation results are compared with experimental data for the [0001] and [1$0\bar{1}$1] specimens. The experimental results are explained and interpreted for both specimens, which include the pole figures, the stress-strain curves, and volume fraction of variants. The simulation results provide an important insight into mechanical responses of high-purity single crystal titanium under high rate loading, and this paper advances the mesoscale modeling and simulations in coupled plastic slip and twinning.

36 MATERIALS SCIENCE↗

Maximum strength and dislocation patterning in multi–principal element alloys

Multi–principal element alloys (MPEAs) containing three or more components in high concentrations render a tunable chemical short-range order (SRO). Leveraging large-scale atomistic simulations, we probe the limit of Hall-Petch strengthening and deformation mechanisms in a model CrCoNi alloy and unravel chemical ordering effects. The presence of SRO appreciably increases the maximum strength and lowers the propensity for faulting and structure transformation, accompanied by intensification of planar slip and strain localization. Deformation grains exhibit notably different microstructures and dislocation patterns that prominently depend on their crystallographic orientation and the number of active slip planes. Grain of single-planar slip attains the highest volume fraction of deformation-induced structure transformation, and grain with double-slip planes develops the densest dislocation network. These results advancing the fundamental understanding of deformation mechanisms and dislocation patterning in MPEAs suggest a mechanistic strategy for tuning mechanical behavior through simultaneously tailoring grain texture and local chemical order.

36 MATERIALS SCIENCE↗

Laws of evolution of slip trace pattern and its parameters with deformation in [1.8.12] – single crystals of Ni{sub 3}Fe alloy

The slip trace pattern of Ni{sub 3}Fe alloy single crystals with the short range order oriented for a single slip were investigated on replica at different stages of deformation using the transmission diffraction electron microscopy method. The connection of staging with the formation of slip trace pattern and the change of its parameters were established. The number of local areas where two or more slip systems work is increased with the change of stages. In these conditions the character of slip localization in the primary slip system is changed from the packets to the homogeneous distribution. The distributions of the distances between slip traces and the shear power in slip traces were plotted. The correlation between the average value of the shear power in the primary slip traces and the average distance between them was revealed in this work. It was established that the rates of the average value growth of the relative local shear and the shear power in the slip traces reach the largest values at the transition stage.

36 MATERIALS SCIENCE↗

Spatial organization of plastic deformation in single crystals with different structure of slip dislocation

It is established that different structure of slip dislocation at the end of the linear hardening stage results in different distribution of dislocation charges in the volume of a single crystal. In the alloy with a near atomic order the slip of single dislocations leads to formation of planar structures—layers with the excess density of dislocations. In the alloy with long-range atomic order the slip of superdislocations brings the formation of the system of parallel rod-like charged dislocation linking.

36 MATERIALS SCIENCE↗

A High-Rate, Single-Crystal Model including Phase Transformations, Plastic Slip, and Twinning

An anisotropic, rate-­dependent, single-­crystal approach for modeling materials under the conditions of high strain rates and pressures is provided. The model includes the effects of large deformations, nonlinear elasticity, phase transformations, and plastic slip and twinning. It is envisioned that the model may be used to examine these coupled effects on the local deformation of materials that are subjected to ballistic impact or explosive loading. The model is formulated using a multiplicative decomposition of the deformation gradient. A plate impact experiment on a multi-­crystal sample of titanium was conducted. The particle velocities at the back surface of three crystal orientations relative to the direction of impact were measured. Molecular dynamics simulations were conducted to investigate the details of the high-­rate deformation and pursue issues related to the phase transformation for titanium. Simulations using the single crystal model were conducted and compared to the high-­rate experimental data for the impact loaded single crystals. The model was found to capture the features of the experiments.

36 MATERIALS SCIENCE↗

Assessment of surface and bulk-dominated methodologies to measure critical resolved shear stresses in hexagonal materials

We present that crystallographic slip in hexagonal metals involves a number of geometrically distinct slip families characterized by their slip direction and slip plane (basal, prismatic, and pyramidal). Owing to the low symmetry of hexagonal lattices, each of these slip families only have a few symmetrically equivalent slip systems (family members). Furthermore, different slip families become active at different resolved shear stress, i.e., they have different critical resolved shear stress values (CRSS). The plastic anisotropy of hexagonal materials makes the numerical prediction of their plastic behavior challenging and depends critically on the knowledge of CRSS values. The present contribution assesses the reliability of three proposed methods (with additional variations) to quantify CRSS values of the different hexagonal slip families. Those methods (a to c) rely on: (a) the statistics of observed surface slip traces in a (slightly) deformed polycrystal; (b) an iterative adjustment of CRSS values until a simulated single crystal indentation matches the corresponding experiment in terms of load–displacement response and residual surface topography of the indent; (c) in-situ high-energy X-ray diffraction to measure the evolution of resolved stress (from lattice strains) in grains for which single-family slip is probable based upon specific lattice reorientation conditions. Virtual experiments are performed on synthetic microstructures such that the (extracted) CRSS values resulting from simulating the different methodologies can be rigorously compared against the (target) CRSS values that are installed in the phenomenological constitutive material description used in the simulations. The resulting CRSS values of methods (a) exhibit a strong dependence on, and deterioration with, decreasing level of slip trace observability, which is an uncertain quantity in experimental measurements. For the inverse indentation method (b), the predicted CRSS values are within 8 % of their reference CRSS values for the two investigated cases. Lastly, the high-energy X-ray diffraction method (c) most reliably determines CRSS values for basal and prism slip, but lacks a strict grain selection criterion to assess pyramidal slip.

36 MATERIALS SCIENCE↗