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DOE OSTI2024

A macro-micro approach for identifying crystal plasticity parameters for necking and failure in nickel-based alloy haynes 282

Here, this work develops a two-scales macro-micro approach to address the challenge in calibrating crystal plasticity microstructural models when samples undergo necking prior to fracture. The crystal plasticity models are crucial for predicting the materials’ plastic deformation and failure at the microstructure level, identifying the materials’ intrinsic properties as well as investigating the microstructure-properties relationships. However, after necking occurs, the experimentally measured stress-strain curves fail to reflect the materials ‘true’ stress-strain behavior and cannot be directly fitted into crystal plasticity models. The proposed macro-micro approach employs a top-down strategy to address this challenge, which has been studied with experimental tests on precipitation-strengthened Ni-based superalloy Haynes® 282®. In this approach, a macro rate-dependent anisotropic plasticity model with Voce-type hardening and Rice-Tracey damage law is first utilized to model the deformation and failure of the tensile bar, and calibrated by matching the stress-strain curves, necking strain, and reduction of area. Especially, to match the testing results under different applied strain rates, the rate-sensitivity parameter m and saturation stress in the elasticity model are modified to incorporate dependence on the local strain rate. Then, the ‘true’ stress-strain behaviors are extracted from the necking zone of the macro-model, which are used to calibrate a micro-model with explicit microstructures and governed by an extended crystal plasticity law. The consistency between the micro-model and macro-model are enforced during calibration. The calibration outcomes from the crystal plasticity model elucidate the materials intrinsic properties for slip, hardening, and failure, which is vital for further investigations into the microstructure-properties relationship and for accurate prediction of the material behavior under various test and service conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Coupled phase field damage and crystal plasticity analysis of intragranular fracture: The role of crystallographic orientation and voids

Damage evolution in engineering metal alloys at the grain scale exhibits significant microstructural heterogeneity and anisotropy. These heterogeneities create local hotspots for stress and strain localization, leading to void nucleation. Crystal orientation influences the active slip systems around voids, affecting lattice rotation and potentially forming discontinuities. At low triaxiality, voids may change shape due to lower stress, rotation, elongation, and coalescence. At high triaxiality, the correlation between crystal orientation and void growth rate becomes stronger, resembling the behavior observed in isolated single crystals. Therefore, understanding the effects of crystal orientation, heterogeneous strain, and defect evolution is crucial for single crystal fracture characterization. Here, in this work, a coupled phase-field damage (PFD) and crystal plasticity (CP) model is implemented within a finite element framework to analyze crystal deformation and failure. The CP method employs a dislocation density-based constitutive model, while intragranular failure is modeled using an anisotropic PFD method. The PFD model considers both the stored energy due to elastic stretching and the energy release due to defect formation and crack formation. A single crystal Al2219 with an intracrystalline spherical void is chosen to analyze fracture. The study finds that fracture propagation is strongly correlated with crystal orientations. This coupled CP-PFD model provides accurate failure prediction in crystalline materials by incorporating the effects of crystal orientations and existing voids. This study demonstrates how the local microstructure and defects influence plastic deformation and failure mechanisms in metal alloys.

Aluminum alloy↗

DOE OSTI2020

Modeling of fluid injection-induced fault reactivation using coupled fluid flow and mechanical interface model

The present study is aimed at developing a numerical model to reproduce coupled hydro-mechanical processes associated with fault reactivation by fluid injection in low permeability rock, as part of the DECOVALEX-2019 project Task B. We proposed a modeling approach for simulating the processes using the TOUGH-FLAC simulator, and modeled a fault reactivation experiment conducted at Mont Terri Rock Laboratory in Switzerland. The first step of the study involved benchmark calculations considering a simplified fault plane and geometry. Fluid flow along a fault was modeled using elements of aperture-sized thickness on the basis of Darcy's law and the cubic law in TOUGH2, whereas the mechanical behavior of a single fault was represented by zero-thickness interface elements in FLAC3D upon which a slip and/or separation is allowed. A methodology to connect a TOUGH2 volume element to a FLAC3D interface element was developed for handling the hydro-mechanical interactions on the fault during fluid injection. Two different fault models for describing the evolutions of hydraulic aperture by elastic fracture opening and failure-induced aperture increase were considered in the benchmark calculations. In the coupling process, the changes in geometrical features and hydrological properties induced by mechanical deformation were continuously updated. The transient responses of the fault and host rock to stepwise pressurization were examined during the simulation. The hydro-mechanical behavior, including the injection flow rate, pressure distribution around the borehole, stress conditions, and displacements in normal and shear directions were monitored in the surrounding rock and along the fault. The results of benchmark calculations suggest that the developed model reasonably represents the hydro-mechanical behavior of a fault and the surrounding rock. This modeling approach was applied to the fault reactivation experiment of the Mont Terri Rock Laboratory. In this interpretive modeling, a parametric study was conducted to examine the effects of input parameters regarding in situ stress and fault properties on the hydro-mechanical responses of the fault to water injection. Then, an optimal parameter set to reproduce the field experiment results was chosen by trial-and-error. The injection flow rate and pressure response during fault reactivation closely matched those obtained at the site, which indicates the capability of the model to appropriately capture the progressive pathway evolution during fault reactivation tests at the site. Finally, the anchor displacements were overestimated by the model, but a fair agreement was obtained in terms of the order of magnitude and the variation tendency.

58 GEOSCIENCES↗

DOE OSTI2021

In situ neutron diffraction study of fatigue behavior of CrFeCoNiMo 0.2 high entropy alloy

In situ neutron diffraction measurement was applied to study the low-cycle fatigue behavior of CrFeCoNiMo 0.2 high entropy alloy. A two-step stress-controlled fatigue test with a stress range of 100–460 and 20–500 MPa was employed. The as-cast sample was cycled 129,000 and 61,000 times, respectively, before fracture. The evolution of the lattice strain and peak intensity demonstrates that the main deformation mechanism is dislocation slip, while no evidence of stacking fault was found. A three-stage ratcheting was clearly observed. Under the stress-controlled mode, the experimentally determined dislocation density increases linearly with the ratcheting strain. Here, the increase of the dislocation density results in a decay of the ratcheting strain rate, which stabilizes the structure and is beneficial for fatigue resistance.

36 MATERIALS SCIENCE↗

DOE OSTI2020

DFT and microkinetic comparison of Pt, Pd and Rh-catalyzed ammonia oxidation

Ammonia oxidation is the heart of the Ostwald process and is important in emissions control. Catalytic behaviors are a function of conditions and are observed to vary across the platinum group metals (PGMs) Pt, Pd, Rh. Here, we combine density functional theory computations and microkinetic modeling to rationalize these dependencies. We compute reactions over model (2 1 1) and (1 1 1) surfaces of PGMs. Binding energies are similar on Pd and Pt and generally greater on Rh, while activation energies vary across all metals. Rates on (2 1 1) surfaces are greater than (1 1 1) surfaces. Additionally, the stepped Pt is most active and stepped Rh most selective to N 2 at ammonia slip conditions, while at Ostwald process conditions, stepped Pd is most active and stepped Pt most selective to NO. Degree of rate and selectivity control analysis provides insights into the reactions limiting performance of PGMs. Both activation barriers and surface coverages influence rates and selectivities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Multiscale formulation of frictional contact mechanics at the pore scale

Direct numerical simulation (DNS) yields the highest fidelity predictions of mechanical deformation at the pore scale, but is prohibitively expensive for analyzing large or many samples. Discrete element methods (DEM) are an efficient alternative, but are limited to granular media and incapable of estimating or controlling prediction errors. We present a pore-level multiscale method (PLMM) that approximates DNS efficiently and with controllable accuracy. We focus on the linear elastic response of a consolidated geologic porous medium with arbitrary microstructure, heterogeneous mineralogy, containing cracks or defects. PLMM decomposes the solid phase into non-overlapping subdomains, on which local basis functions are constructed. The bases are then coupled with a global interface problem that accounts for slip or stick contact conditions between the subdomains. PLMM produces an initial, but accurate, approximation to DNS that can be iteratively improved. It is amenable to parallelism and allows for different mesh, models, and physics in each subdomain. An algebraic interpretation of PLMM as a preconditioner is also presented to allow non-intrusive implementation into existing solvers. Lastly, this work extends previous developments of PLMM in fluid dynamics to solid mechanics and enables future extensions towards modeling coupled flow and mechanics problems.

42 ENGINEERING↗

DOE OSTI2022

FSISPH: An SPH formulation for impacts between dissimilar materials

Here, we present an SPH formulation with several new features designed to better model the fully-compressible interaction of dissimilar materials. We developed the new method to simulate the atmospheric entry and break-up of small celestial bodies in planetary atmospheres. The formulation uses a unity-based, density-energy discretization of the hydrodynamic conservation laws with linear-corrected kernel gradients. To account for variations in compressibility, we use an HLLC approximate Riemann solver to adjust the velocity gradient at material interfaces. To handle large transverse velocity discontinuities, we introduce a simple slip interface model that limits the artificial viscosity at material interfaces. Diffusion is optionally applied through the velocity gradient and this allows the density and specific thermal energy to evolve in a manner more consistent with the first law of thermodynamics in comparison to other more direct diffusion schemes. We also introduce a material-local second-order artificial conduction scheme used to smooth the specific thermal energy field. Material damage fits neatly under this framework by treating the damage front as a material interface. The method has been implemented as a solver, FSISPH, within the code, Spheral++, and is publicly available on github. We test our new solver on a number of classic shock, mixing, and multi-material problem. The components we outline can significantly improve accuracy of SPH for problems with sharp contact discontinuities.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Weak boundary conditions for Lagrangian shock hydrodynamics: A high-order finite element implementation on curved boundaries

Here, we propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries. Specifically, the variational formulation is appropriately modified to enforce free-slip wall boundary conditions, without perturbing the structure of the function spaces used to represent the solution, with a considerable simplification with respect to traditional approaches. Total energy is conserved and the resulting mass matrices are constant in time. The robustness and accuracy of the proposed method are validated with an extensive set of tests involving nontrivial curved boundaries.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

A robust framework for frictional fault contact in geological formations using a stabilized augmented Lagrangian approach

Numerical simulations are essential to evaluate the performance and safety of engineered subsurface systems such as geological carbon storage sites, enhanced geothermal fields, and oil and gas reservoirs. A key challenge lies in accurately modeling the frictional contact behavior along fault surfaces. This problem involves inequality constraints that arise from the physics of frictional slip, requiring specialized numerical methods to handle the resulting highly nonlinear and path-dependent behavior. Here, in this work, we address this challenge using an Augmented Lagrangian Method (ALM) implemented via the Uzawa algorithm. The formulation employs mixed finite element spaces, combining low-order piecewise linear displacements within the 3D domain cells with piecewise constant tractions defined on the fault surfaces. Furthermore, to ensure stability and satisfy the inf-sup condition, the discrete displacement space is enriched with face bubble functions on both sides of the contact interfaces. This approach offers several advantages over other stabilization techniques that rely on additional terms, and it integrates naturally in the Uzawa framework.

58 GEOSCIENCES↗

DOE OSTI2023

Scalable simulation of coupled adsorption and transport of methane in confined complex porous media with density preconditioning

The growing significance of shales and tight formations in the transition to less carbon-intensive and clean energy drives the research endeavor to understand the physics of gas flow within these systems. However, shales are composed of massively heterogeneous physical and chemical features. Most nano-sized pores connect to millimeter-scale fractures, leading to multiscale transport. These nano-scale pore throats demonstrate non-classical flow behavior, such as non-negligible slip velocities and adsorbed gas layers at the boundary. As a result, classical computational fluid dynamics models do not capture the physics. In this work, we develop a coupling scheme for the multiple-relaxation-time (MRT) lattice Boltzmann (LB) method that integrates the Peng-Robinson equation of state into a pseudo-potential interaction model to capture the physics of methane flow in irregular networks of channels that represent nano-scale porous media. We use atomistic simulations to calibrate and validate our model in slit nano-channels. We propose a preconditioning scheme to initialize the coupled transport and adsorption simulation of methane in complex porous media. The results of this implementation of LB agree with Direct Simulation Monte Carlo (DSMC) and Molecular Dynamics (MD) simulations. We then scale up the LB implementation through vectorization and indirect addressing. We parallelize it using Message Passing Interface (MPI) and OpenMP frameworks to simulate transport and adsorption in complex media with a million lattices. Additionally, we analyze the differences between coupled and transport-only simulations in two case studies and show that considering phase behavior, i.e., adsorption, can significantly change the flow behavior. This work constitutes an important step towards bridging the gap between molecular flow and system-scale behavior of complex disordered porous media.

42 ENGINEERING↗

DOE OSTI2024

Quantification of grain boundary effects on the geometrically necessary dislocation density evolution and strain hardening of polycrystalline Mg 4Al using in situ tensile testing in scanning electron microscope and HR-EBSD

In situ tensile testing in a scanning electron microscope (SEM) in conjunction with high-resolution electron backscatter diffraction (HR-EBSD) under load was used to characterize the evolution of geometrically necessary dislocation (GND) densities at individual grain boundaries as a function of applied strain in a polycrystalline Mg—4Al alloy. The increase in GND density was investigated at plastic strains of 0 %, 0.6 %, 2.2 %, 3.3 % from the area including 76 grains and correlated with (i) geometric compatibility between slip systems across grain boundaries, and (ii) plastic incompatibility. We develop expressions for the grain boundary GND density evolution as a function of plastic strain and plastic incompatibility, from which uniaxial tensile stress-strain response of polycrystalline Mg—4Al are computed and compared with experimental measurement. The findings in this study contribute to understanding the mechanisms governing the strain hardening response of single-phase polycrystalline alloys and more reliable prediction of mechanical behaviors in diverse microstructures.

Geometrically necessary dislocations↗

DOE OSTI2022

Crystal plasticity including a phase-field deformation twinning model for the high-rate deformation of cyclotetramethylene tetranitramine

A new finite strain thermomechanical model for the high-rate deformation of the β-polymorph of cyclotetramethylene tetranitramine (β-HMX) has been developed and applied to simulations of plate impact experiments. The crystal plasticity model is based on a model developed previously for RDX (Luscher et al. 2017), which is extended to incorporate deformation twinning. Twinning during normal plate impacts is simulated with a phase-field twin model. First, material parameters governing the kinetics of dislocation slip are calibrated on the subset of simulations which had negative Schmid factors for the twin system. Second, a parametric study of the twin material parameters was performed to find suitable values. Overall, the results of the simulations with the phase-field twinning model are reported for impacts on several crystal orientations. We find that the twin growth decreases with increasing distance from the impact surface because of dissipation of the shock front via dislocation-mediated plasticity, and that the simulated interface velocity with and without phase-field twinning do not show appreciable differences. These modeling results suggest that the significance of twinning in β-HMX cannot be determined with traditional loading configurations and diagnostics.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Non-local large-strain FFT-based formulation and its application to interface-dominated plasticity of nano-metallic laminates

Here, this paper presents a novel formulation and its robust numerical implementation of strain-gradient (SG) crystal plasticity within a large-strain (LS) elasto-viscoplastic (EVP) fast Fourier transform (FFT)-based micromechanical model. The resulting non-local SG-LS-EVPFFT formulation is used to model and understand the process of kink band formation during layer-parallel compression of nano-metallic laminates (NMLs). NMLs are layered composites with nanoscale thicknesses, thus requiring consideration of the interaction between dislocations and interfaces within the micromechanical model. The length-scale parameter of the SG model is calibrated by simulating a double pile-up and comparing predictions to analytical solution. This required new expressions for the defect energy, resulting in more accurate double pile-up predictions. The calibrated SG-LS-EVPFFT model is then used to simulate layer-parallel compression of copper-niobium NML. Formation of kink bands is predicted, and the model is used to rationalize the microscopic mechanisms enabling the formation process. It is found that accumulation of dislocations at interfaces leads to activation of layer-parallel slip, which in turn leads to kink band formation.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Phase-field modeling of dislocation–interstitial interactions

The mechanical behavior of body-centered cubic (BCC) materials can be dramatically affected by the presence of interstitial solute atoms. Here we present a new phase-field dislocation dynamics formulation to include the diffusion of interstitials. Short-range interactions are accounted for by a concentration-dependent lattice energy, and long-range interactions are accounted for by modifications to the elastic energy. The interstitial diffusion law introduces gradients that require methods for minimizing Gibbs oscillations, which is done via a modified Green’s function. The formulation is general to any solute-solvent system and is applied here to Nb-O as a model system, whose interstitial parameters are obtained from ab initio calculations. The effect of O on the core structures of Nb edge and screw dislocations is calculated. The diffusion of O to form interstitial atmospheres around dislocation cores is simulated, as well as the critical stresses required for dislocations to break away or cross slip from these atmospheres. Future applications of the method to simulate complex interstitial embrittlement mechanisms are discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Effects of Zn and Ca on the deformation texture evolution of Mg–Zn–Ca alloys at elevated temperatures

This work utilized crystal plasticity simulations and experimental thermo-mechanical processing to examine how Zn and Ca content affects texture evolution in Mg–Zn–Ca alloys during simulated hot rolling. Four different compositions were studied: unalloyed Mg and three Mg alloys of ZX0p50 (Mg- 0.5 wt% Zn- 0.1 wt% Ca), ZX30 (Mg-3 wt% Zn- 0.1 wt% Ca), and ZX31 (Mg-3 wt% Zn- 0.3 wt% Ca). Multi-pass Gleeble experiments simulated hot rolling using plane strain conditions. Unalloyed Mg developed a strong basal texture, while the addition of Zn and Ca significantly weakened the texture in ZX30 and ZX31; this reduction was not seen in ZX0p50. Notably, ZX31 exhibited a split basal texture aligned with the rolling direction. Crystal plasticity simulations revealed that the weaker basal texture in ZX30 and ZX31 resulted from reduced activation of basal and twinning modes compared to unalloyed Mg and Zx0p50. Increased Zn and Ca content raised the ratios of basal to pyramidal critical resolved sheer stress (CRSS) and twin to pyramidal CRSS, enhancing pyramidal slip activity and weakening the basal texture. Extension twinning played a critical role in texture development during the first deformation pass. In unalloyed Mg and ZX0p50, twinning led to a strong basal texture, while ZX30 and ZX31 had weak basal textures that increased only slightly with further deformation. The split basal poles simulated in ZX31 were consistent with the experimental findings, highlighting the interplay between alloy composition and texture evolution.

Crystal plasticity finite element↗

DOE OSTI2022

Stress-controlled fatigue of HfNbTaTiZr high-entropy alloy and associated deformation and fracture mechanisms

The stress-controlled fatigue tests are carried out at a stress ratio of 0.1 and a frequency of 10 Hz, and span both low-cycle and high-cycle regimes by varying the applied stress amplitudes. The high-cycle fatigue regime gives a fatigue strength of 497 MPa and a fatigue ratio of 0.44. At equivalent conditions, the alloy's fatigue strength is greater than all other high-entropy alloys (HEAs) with reported high-cycle fatigue data, dilute body-centered cubic alloys, and many structural alloys such as steels, titanium alloys, and aluminum alloys. Through in-depth analyses of crack-propagation trajectories, fracture-surface morphologies and deformation plasticity by means of various microstructural analysis techniques and theoretical frameworks, the alloy's remarkable fatigue resistance is attributed to delayed crack initiation in the high-cycle regime, which is achieved by retarding the formation of localized persistent slip bands, and its good resistance to crack propagation in the low-cycle regime, which is accomplished by intrinsic toughening backed up by extrinsic toughening. Additionally, the stochastic nature of the fatigue data is neatly captured with a 2-parameter Weibull model.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Shear band velocity and activation volume during shear deformation by acoustic emission in a Zr-based bulk metallic glass

Here, an analysis is presented for the shear band velocity of plastic deformation and activation volume of the shear transformation zone (STZ) in a Zr 60 Cu 30 Al 10 bulk metallic glass (BMG). Compared to the values calculated by the stick-slip model, the values of shear band velocity calculated after optimization by the acoustic emission technique are much larger than those reported previously. Plastic flow in BMGs is found to be described by a power-law correlation between the maximum velocity of the shear band and the strain rates. Combining the free volume theory and the STZ theory, the relationship between the volume change in the STZ and the shear band velocity is derived as $Ω=A$(27–ln$v/l$). The value of A, which is a material dependent constant, is 5.43 × 10 –3 for the current BMG at room temperature.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Global and local texture development during initial plastic deformation of cold-pilgered Zircaloy-4 tubing

In this work we present a thorough characterization of the texture development during the initial step of a cold pilgering process of a Zircaloy-4 TREX tube, on which the axial cross section is reduced by 80% over a 40cm length with an overall Q-ratio of 2.34, followed by a recrystallization thermal treatment. Texture across a tapered specimen representing this working zone was characterized by neutron diffraction and high energy synchrotron x-ray diffraction at 28 positions (4 locations along its length and 7 locations across its thickness with 0.3 mm spatial resolution), and on the deformed end after the thermal treatment. Results show that the starting material (TREX tube) presents a texture gradient through its wall thickness, with the c poles aligned to the hoop direction at the outer surface (with radial and hoop Kearns factors: f R =0.36, f H = 0.50), and gradually rotating around the axial direction to become a quasi-radial orientation (~35 o out of the radial direction) at the inner surface ( f R =0.43, f H =0.35). The overall texture becomes more radial due to the cold pilgering, but the texture gradient remains during the whole deformation process, being always more radial at the inner surface, ( f R =0.53, f H =0.37 at 80%) than at the outer surface ( f R =0.41, f H =0.50at 80%). The most remarkable changes in texture produced by the rolling process is a 30 o rotation of the grains around their c-axis, producing a marked increase of the <11 2 ¯ 0> // axial fiber texture at expenses of the original <10 1 ¯ 0> // axial fiber texture observed in the TREX tube. The observed changes in texture during deformation were correctly explained by visco-plastic self-consistent (VPSC) modelling. This was achieved after the inclusion of the basal <a> slip system, which plays a central role to explain the 30 o rotation around the c-axis during deformation. The texture evolution was correctly described after the inclusion of a drag effect to grain rotation due to the interaction with neighbouring grains. The through thickness texture differences are greatly reduced by the recrystallization thermal treatment, with similar Kearns factors at the inner surface ( f R =0.50, f H =0.28) and the outer surface ( f R =0.48, f H =0.39). The predominance of the <10 1 ¯ 0> // axial fiber texture is recovered after recrystallization.

36 MATERIALS SCIENCE↗