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Unraveling kinking: A plasticity enhancing failure mode in high strength nano metallic laminates
Kinking is an important and plasticity-enhancing deformation/failure mode in numerous mechanically anisotropic materials including high-strength nano metallic laminates (NMLs). However, our current limited understanding of the mechanics of kinking and its dependence on microstructural attributes is insufficient for thoroughly comprehending and eventually being able to control failure behaviors of materials. In this study, we investigate kinking dependencies on microstructural attributes in NMLs via in situ micropillar compression, multiscale microstructure characterization, dislocation dynamic simulations, and crystal plasticity modeling. Additionally, by examining several NML systems (Cu/Fe, Ag/Fe, Al-4Mg/Fe), we demonstrate that the development of internal stresses during loading activates local layer-parallel glide triggering kinking in NMLs. Furthermore, this work reveals the effect of key microstructural features including layer thickness, layer waviness, interface barrier strength, and work hardening capacity on kink band formation in NMLs. More broadly, our efforts represent a generically applicable approach for probing large-strain deformation behavior of complex materials via synergetic modeling and experimental efforts.
Self-equilibrated backstresses induce compensation between hardening and softening: Micromechanical and microstructural features
For crystal plasticity formulation neglecting the strain gradients at the dislocation scale, backstresses are necessary to satisfy the mesoscopic stress equilibrium and strain compatibility requirements. Backstresses in a material point and those between neighboring points are treated separately. Physically backstresses can dynamically induce either hardening or softening effects to adjust the dislocation hardening of slip systems, whereas the sum of the stresses resulting in backstresses in the representative volume element (RVE) is zero. Backstress hardening suppresses certain slip activities, while backstress softening triggers excess dislocations. A two-phase brass is studied. Backstresses make the hard phase deform smaller and the soft phase deform more than those without employing backstresses in a model. In the former, more homogeneous lattice strain and higher yield stress are obtained. Backstress has limited effects on the evolution of the critical resolved shear stress and crystallographic texture. Furthermore, it is a major cause of the banded structures featuring sharp crystallographic contrasts which are not parallel to the slip planes. Tests indicate that backstress induces a serrated behavior at the early stages of deformation and induces the geometrically necessary bands (GNBs), which are parallel to the macroscopic axes.
Numerical Simulation of Irradiation Induced Swelling for STAR 4.1 Blanket
Here, this article presents the preliminary results of FEM implementation of irradiation-induced swelling, hardening, and creep effect using ANSYS user programmable features (UPFs) applied to material properties. The first liquid metal breeding blanket model for STAR 4.1 tokamak as a part of the virtual prototyping system is under development at Princeton Plasma Physics Laboratory (PPPL). Intense neutron irradiation produces significant changes in the physical and mechanical properties of Fe-(8%–9%)Cr-based reduced activation ferritic martensitic (RAFM) steels. An ANSYS model of the breeding blanket was built to involve these irradiation-induced material property changes with neutron fluence distribution mapped from the MCNP model. Simulation results show that significant structure deformation forms from nuclear swelling, stress, and plastic strain arising from DPA gradient through wall thickness. The material degradation effect is not negligible. This modeling feature can either assist in analyzing the structural behaviors with the influence of nuclear swelling or provide guidance to design the structure to withstand irradiation.
A predictive strain-gradient model with no undetermined constants or length scales
A general meso–scale (GM) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc numerical techniques were employed. It uses general stress field equations for GND content and a novel harmonization technique to enforce consistency of elastic long-range singular defect fields with applied elastic-plastic fields. The model facilitates implementation in commercial finite element programs without requiring special elements, special boundary conditions, or access to element shape functions. GM simulations confirmed, with improved accuracy, previously published predictions of the Hall-Petch effect, Bauschinger effect, and anelasticity. Previously unpredicted phenomena were also predicted: anelasticity and hysteresis for single Ta crystals and strain-hardening stagnation. The internal stresses (higher-order effect) dominate at large length scales, while at small length scales, the GND density hardening (lower-order effect) dominates. As a result, GM predicts that strain heterogeneity and consequent GND internal stresses are important factors in anelasticity.
Radiation effects on stress evolution and dimensional stability of large fusion energy structures
Here we assess the effects of neutron irradiation on the deformation and stress evolution of large-scale fusion energy structures. This is accomplished through non-linear finite element structural analysis of the coupled thermal and mechanical fields at the Beginning-Of-Life (BOL), at 45 dpa, and at 90 dpa. Radiation effects include volumetric swelling and the influence of radiation on the mechanical properties. The system studied here is a large section of a full inboard module of an integrated structure comprising the First Wall and Blanket (FW/B) of a Dual Cooled Lithium-Lead (DCLL) energy conversion unit in the Fusion Nuclear Science Facility (FNSF). The structural material is the ferritic/martensitic steel F82H. We analyze several radiation effects phenomena that can lead to significant impact on the mechanical design and lifetime of the structure. These include volumetric swelling effects on the assembly and disassembly of modules and the impact of spatial gradients in neutron damage and helium generation on deformation, stress evolution, and plastic strain accumulation. We show that the stress state is strongly influenced by the accumulation of swelling strains, radiation hardening and softening, and by spatial gradients in displacement damage and helium gas generation. Several key regions in the FW/B structure are identified where severe plastic strains accumulate and may be potential sites for failure, especially during cyclic reactor operations. We finally show that minimum gaps between Inboard (IB) blanket sectors must be present during assembly so as to avoid excessive stress and strain in FW/B modules critical regions and raising chances of failure. A range of structural displacements are shown, from as low as 4 mm at BOL for free side walls to as high as 46 mm at 90 dpa for fully constrained side walls.
Intrinsic size dependent plasticity in BCC micro-pillars under uniaxial tension and pure torsion
The mechanical behavior of submicron body-centered cubic (BCC) micro-pillars is investigated by three-dimensional dislocation dynamics (DD) simulations to better understand the governing mechanisms for size dependent plasticity under uniaxial tension and pure torsion. A formula is developed to compute the incremental plastic twist due to dislocation motion in DD simulations. The DD simulations show that different dislocation microstructures are created depending on the loading conditions, which leads to different size dependent mechanical behavior. While in tension plasticity is mainly governed by the kinetics of dislocation motion controlled partly by the surface dislocation sources, plastic flow in torsion is controlled by dislocation pile-ups associated with strain gradients. The simulation results also reveal a Bauschinger effect and plastic recovery under cyclic twist, which have been observed in recent experiments.
Atomistic simulations of nanoindentation on nanoglasses: Effects of grain size and gradient microstructure on the mechanical properties
The use of nanoglass (NG) microstructures has been shown as an effective strategy to improve the ductility of rather brittle metallic glass alloys. To evaluate the effects of grain size and gradient design on the mechanical properties of NGs, we perform molecular dynamics simulations of nanoindentation on Cu 64 Zr 36 NGs. We consider samples with uniform 3 and 7 nm grain sizes as well as gradient microstructures with gradient grain sizes varying from 3 to 7 nm. Here, the results show that the deformation mechanism in NGs with small grain sizes is dominated by the activation and evolution of multiple shear transformation zones. Increasing grain sizes enhances the elastic modulus and hardness at the cost of reduced abrasion resistance. Though the average grain size at the indentation surface plays a crucial role in the deformation behavior of gradient NG models, their strain localization and plastic deformation states are affected by the grain sizes far from the indenter. Desired combinations of mechanical properties can be realized by different NG microstructure designs.
Dynamic phase transformations in additively manufactured Ti-6Al-4V during thermo-mechanical gyrations
A complex interaction of process parameters, geometry and scan strategies in Additive Manufacturing (AM), can bring about spatial and temporal transients, i.e., Σ T ( x, y, z, time ), within a part. Published literature focusses on fluctuating thermal cycles on the microstructure evolution. However, the microstructural variations have not been correlated to dynamic flow behavior due to the macro- and micro-scale phenomena, i.e., accumulated plastic strains brought about by large thermal gradients, transformational strains and crystallographic misfit strains. Therefore, here we studied the mechanical response of Ti6Al4V alloys produced by AM under externally imposed controlled thermo-mechanical reversals in a Gleeble® thermo-mechanical simulator. The stress-strain behaviors were correlated to phase fractions, lattice strains, and also limited information on crystallographic texture using neutron diffraction techniques at the VULCAN Beamline at SNS, ORNL and also metallographic studies. The results are discussed and rationalized based on theories of static and dynamic phase transformations.
New Mechanism for Yield Point Phenomena
Yield point phenomena (YPP) are widely attributed to discrete dislocation locking by solute atmospheres. An alternate YPP mechanism was recently suggested by simulations of Ta single crystals without any influence of solutes or discrete dislocations. The general meso-scale (GM) simulations consist of crystal plasticity (CP) plus accounting for internal stresses of geometrically necessary dislocation content. GM predicted the YPP while CP did not, suggesting a novel internal stress mechanism. The predicted YPP varied with crystal orientation and boundary conditions, contrary to expectations for a solute mechanism. The internal stress mechanism was probed by experimentally deforming oligocrystal Ta samples and comparing the results with independent GM simulations. Strain distributions of the experiments were observed with high-resolution digital image correlation. A YPP stress–strain response occurred in the 0–2% strain range in agreement with GM predictions. Shear bands appeared concurrent with the YPP stress–strain perturbation in agreement with GM predictions. At higher strains, the shear bands grew at progressively slower rates in agreement with GM predictions. It was concluded that the internal stress mechanism can account for the existence of YPP in a wide variety of materials including ones where interstitial-dislocation interactions and dislocation transient avalanches are improbable. Furthermore, the internal stress mechanism is a CP analog of various micro-scale mechanisms of discrete dislocations such as pile-up or bow-out. It may operate concurrently with strain aging, or either mechanism may operate alone. A suggestion was made for a future experiment to answer this question.
The effect of microstructure on the relationship between grain boundary sliding and slip transmission in high purity aluminum
The relationship between grain boundary sliding (GBS) and slip transmission is investigated experimentally at grain boundaries in 99.99% aluminum with a through-thickness, coarse grained microstructure deformed in tension at 190 °C. Using scanning electron microscope enabled digital image correlation (SEM-DIC) and electron backscatter diffraction (EBSD), high resolution strain fields and microstructural information were measured to examine the influence of microstructural neighborhoods on interactions between GBS and slip transmission and strain localization. Several distinct cases are presented that highlight important microstructural factors that govern deformation near grain boundaries. The findings include (1) direct transmission and GBS were anti-compatible and facilitated by opposing boundary types (low misorientation and high energy grain boundaries respectively); (2) increased GBS activity was correlated with decreased indirect transmission behavior; (3) GBS accommodation at triple junctions was enabled by intragranular plasticity; and (4) the local intragranular plastic strain discontinuity between grains determined the magnitude of GBS gradients. Finally, this work provides insight into the nature of these mechanisms and can be used to identify strain transfer criteria that can lead to improved GBS-sensitive crystal plasticity models.
Eulerian finite element implementations of a dislocation density-based continuum model
In Eulerian finite element simulations, the mesh moves relative to the material. After every change of position between the mesh and the material, the state variables are interpolated to the new mesh position, which is referred to as advection. Large strain crystal plasticity models are based on the multiplicative decomposition of the total deformation gradient. Further, the stress is evaluated as a function of the thermoelastic strain, temperature, and other state variables. Advection of tensor quantities, such as the strain, is coupled with possibly significant advection errors. In an effort to reduce the advection errors, we develop two rate forms of an established dislocation density-based continuum model. To that end, we replace the multiplicative decomposition of the deformation gradient with the additive decomposition of the velocity gradient, and define the stress rate instead of the total stress. The Eulerian implementation is compared with Lagrangian calculations, and two numerical examples with severe deformation levels are presented.
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.
Gradient nanostructured steel with superior tensile plasticity
Nanostructured metallic materials with abundant high-angle grain boundaries exhibit high strength and good radiation resistance. While the nanoscale grains induce high strength, they also degrade tensile ductility. We show that a gradient nanostructured ferritic steel exhibits simultaneous improvement in yield strength by 36% and uniform elongation by 50% compared to the homogenously structured counterpart. In situ tension studies coupled with electron backscattered diffraction analyses reveal intricate coordinated deformation mechanisms in the gradient structures. The outermost nanolaminate grains sustain a substantial plastic strain via a profound deformation mechanism involving prominent grain reorientation. This synergistic plastic co-deformation process alters the rupture mode in the post-necking regime, thus delaying the onset of fracture. The present discovery highlights the intrinsic plasticity of nanolaminate grains and their significance in simultaneous improvement of strength and tensile ductility of structural metallic materials.
A better understanding of the mechanics of borehole breakout utilizing a finite strain gradient-enhanced micropolar continuum model
Borehole breakout denotes the failure in rock mass subjected to drilling, caused by stress concentrations exceeding the material strength. Depending on the material properties, the preexisting in situ stress state, and the borehole dimensions, different types of borehole breakout, such as spiral-shaped breakout or v-shaped breakout, are distinguished in the literature. In the present work, we address the influence of the material properties on the predicted borehole breakout mode in a comprehensive finite element study. To this end, herein we employ a gradient-enhanced micropolar damage-plasticity model based on the Mohr–Coulomb strength criterion, formulated in the finite strain regime, which is calibrated based on experimental results from plane strain compression tests on Red Wildmoor sandstone. In the numerical study, the influence of the in situ stress state, the material friction angle, plastic dilation, post peak residual strength, and the inherent material length scale parameters are investigated. Thereby, we demonstrate that depending on the material parameters, substantially different failure modes, characterized by strongly localized shear bands or diffuse failure zones, are predicted. It is shown that in particular the brittleness of the material in the post peak regime has a major influence on the predicted breakout type. Moreover, a statistical validation of the results is obtained by considering different random field distributions of the initial material strength.
Primal interface debonding formulation for finite strain isotropic plasticity
In this work, a framework is developed for modeling ductile damage of nonlinear materials whose plastic deformation is characterized using rate independent classical plasticity. This method relies on the assumption that the free energy can be decomposed into elastic, plastic and damage parts. A thermodynamically consistent method is derived which satisfies the second law of thermodynamics in the Clausius–Duhem inequality form. The dissipation associated with plasticity takes place in the domain only, while damage dissipation is localized to the interface. The method is developed using Variational Multiscale ideas to obtain definitions of the interface fluxes within a primal formulation analogous to the Discontinuous Galerkin method, which ensures weakly vanishing interface gap prior to reaching a damage initiation criterion. The local nonlinear problem to calculate both plastic deformation gradient and damage variable follows an incremental approach similar to classical plasticity return mapping algorithm. This elastoplastic damage formulation is developed for material undergoing finite strain, and it naturally accommodates a trapezoidal traction separation law (TSL) whose shape can be varied to model either ductile interface behavior or brittle interface behavior. The formulation's performance is assessed through modeling a patch test and a compact tension specimen.
Heterogeneous microstructural evolution during hydrodynamic penetration of a high-velocity copper microparticle impacting copper
Microparticle hydrodynamic penetration (HDP) may be associated with the erosion regime in cold spray processing and other high-velocity impact events. Here, in an experimental approach where we can individually launch particles and study the impact sites, we explore copper microparticles impacted on copper substrates at velocities above 900 m/s where HDP begins. We lift cross-sectional lamellae from the impact sites with a focused-ion beam for further microstructural characterization using electron backscatter diffraction and scanning transmission electron microscopy. Due to the gradients of strain, strain rate, and temperature associated with HDP, heterogeneous microstructures result. The structural evolution processes observed include deformation twinning and multiple dislocation-mediated grain recrystallization mechanisms—geometric dynamic recrystallization (gDRX), discontinuous DRX (dDRX), and meta DRX (mDRX). The higher strains at the interface lead to the most significant structural changes and complex mechanisms. In contrast, there is a gradient to more conventional dislocation plasticity away from the interface (on either the particle or substrate side). Here, these microstructural observations are consistent with the deformation map for copper and extend the observations of impact-induced recrystallization across new regimes of behavior.
Modelling dislocation-graphene interactions in a BCC Fe matrix by molecular dynamics simulations and gradient plasticity theory
We report graphene nanosheets (GNS) can enhance the strength and ductility of metal-based composites as they can obstruct the propagation of dislocations. The present article employs Molecular Dynamics (MD) simulations to investigate dislocation-GNS interaction mechanisms and possible influencing factors, including the number of GNS layers, the thickness of the metallic amorphous layer and the C - C bond strength. The results indicated that the shear strength of the metal/GNS interface and the bending stiffness of GNS determined the ability of GNS to block dislocation transmission. A physically based phenomenological parameter that can capture such dislocation-GNS interactions is the mechanical interface energy that has been put forth within gradient plasticity. By fitting the theoretical expressions to the simulation data, it was possible to obtain estimates for the mechanical interface energy for the GNS. It was found that increasing the GNS layers and adding an amorphous layer resulted in a strengthening in the stress–strain response and increased the value of this interfacial parameter. This indicates that the mechanical interfacial energy can be a unified measure for capturing and tuning the strength of various interfaces such as grain boundaries, GNS, amorphous-crystalline interface and bimetal interfaces.