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DOE OSTI2025

Response tailoring of elasto-plastic trusses

Abstract In this work we tailor the response of trusses loaded beyond their yield limit. The truss structures are modeled using finite strain theory and rate-independent elasto-plasticity. We design trusses with a tailored mechanical response that is between “elastic” and “elastic-ideal-plastic” subject to the volume constraint. The design updates are generated by the gradient-based Method of Moving Asymptotes (MMA) solver and the sensitivities of the response functions are computed using a path-dependent adjoint sensitivity analysis. The computations are performed in Matlab.

42 ENGINEERING↗

DOE OSTI2024

A B-spline based gradient-enhanced micropolar implicit material point method for large localized inelastic deformations

The quasi-brittle response of cohesive-frictional materials in numerical simulations is commonly represented by softening plasticity or continuum damage models, either individually or in combination. However, classical models, particularly when coupled with non-associated plasticity, often suffer from ill-posedness and a lack of objectivity in numerical simulations. Moreover, the performance of the finite element method significantly degrades in simulations involving finite strains when mesh distortion reaches excessive levels. This represents a challenge for modeling cohesive-frictional materials, given their tendency to experience strongly localized deformations, such as those occurring during shear band dominated failure. Hence, accurate modeling of the response of cohesive-frictional solids is a demanding task. To address these challenges, we present an extension of the material point method (MPM) for the unified gradient-enhanced micropolar continuum, aiming at the analysis of finite localized inelastic deformations in cohesive-frictional materials. The generalized gradient-enhanced micropolar continuum formulation is employed to tackle challenges related to localization and softening material behavior, while the MPM addresses issues arising from excessive deformations. The method utilizes a B-spline formulation for the rigid background mesh to mitigate the well-known cell crossing errors of the MPM. To demonstrate the performance of the method, 2D and 3D numerical studies on localized failure in sandstone in plane strain compression and triaxial extension tests are presented. A comparison with finite element results confirms the suitability of the formulation. Moreover, an efficient numerical implementation of the formulation is presented, and it is demonstrated that the additional MPM specific overhead is negligible.

B-spline↗

DOE OSTI2020

Thermomechanical conversion in metals: dislocation plasticity model evaluation of the Taylor-Quinney coefficient

Using a partitioned-energy thermodynamic framework which assigns energy to that of atomic configurational stored energy of cold work and kinetic-vibrational, in this study we derive an important constraint on the Taylor-Quinney coefficient, which quantifies the fraction of plastic work that is converted into heat during plastic deformation. Associated with the two energy contributions are two separate temperatures – the ordinary temperature for the thermal energy and the effective temperature for the configurational energy. We show that the Taylor-Quinney coefficient is a function of the thermodynamically defined effective temperature that measures the atomic configurational disorder in the material. Finite-element analysis of recently published experiments on the aluminum alloy 6016-T4 [1], using the thermodynamic dislocation theory (TDT), shows good agreement between theory and experiment for both stress-strain behavior and temporal evolution of the temperature. The simulations include both conductive and convective thermal energy loss during the experiments, and significant thermal gradients exist within the simulation results. Computed values of the differential Taylor-Quinney coefficient are also presented and suggest a value which differs between materials and increases with increasing strain.

36 MATERIALS SCIENCE↗

NASA NTRS1996

[?]Nonlinear Issues in the Aerothermochemistry of Gases and Materials and the Associated Physics and Dynamics of Interfaces

Our research and technology are focused on nonlinear issues in the aerothermochemistry of gases and materials and the associated physics and dynamics of interfaces. Our program is now organized to aggressively support the NASA Aeronautics Enterprise so as to: (a) develop a new generation of environmentally compatible, economic subsonic aircraft; (b) develop the technology base for an economically viable and environmentally compatible high-speed civil transport; (c) develop the technology options for new capabilities in high-performance aircraft; (d) develop hypersonic technologies for air-breathing flight; and (e) develop advanced concepts, understanding of physical phenomena, and theoretical, experimental, and computational tools for advanced aerospace systems. The implications from our research for aeronautical and aerospace technology have been both broad and deep. For example, using advanced computational techniques, we have determined exact solutions for the Schrodinger equation in electron-molecule scattering allowing us to evaluate atmospheric models important to reentry physics. We have also found a new class of exact solutions for the Navier Stokes equations. In experimental fluid dynamics, we have found explicit evidence of turbulence modification of droplet sizes in shock tube flow with condensation. We have developed a new diagnostic tool for the direct estimation of flow velocities at MHz sampling rates in quasi-one dimensional turbulent flow. This procedure suggests an unexpected confirmation of the possibility of 'natural' closure in Reynolds stresses with deep implications for the development of turbulent models. A transient increase is observed in both the spectral energy decay rate and the degree of chaotic complexity at the interface of a shock wave and a turbulent ionized gas. Even though the gas is apparently brought to rest by the shock wave, no evidence is found either of the expected relaminarization. A unique diamond-shaped nozzle has been designed for a detailed investigation of the effect of significant streamwise vorticity on the acoustic and IR characteristics of supersonic jets. Our results provide convincing evidence of the significant effect of vorticity on the far-field noise for the diamond jet as compared to the conventional round jets. We have found that the countercurrent shear layer mixes much more efficiently than conventional coflowing shear layers. We also developed the fluid thrust vectoring procedures which use counter flow to vector a jet. Our materials research has shown that the steep stress gradients at the fiber-matrix interface could be the primary cause of interface cracks after the processing of metallic and intermetallic matrix composites. New techniques have been evolved for: the microcharacterization of materials including microplastic strain and, point by point, the misorientation and plasticity for matrix composites; thermally induced stress measurements and load relaxation; the growth and characterization of metallic matrix composite interfaces; and for the growth of ferrite materials by pulsed laser deposition. The FAMU commitment to the HBCU Research Center also continues to be broad and deep.

Johnson, Joseph A., III↗

DOE OSTI2020

Experimental verification of a crystal plasticity-based simulation framework for predicting microstructure and geometric shape changes: Application to bending and Taylor impact testing of Zr

This paper is concerned with experimental verification of a recently developed multi-scale simulation framework for plastic deformation of metallic materials from quasi-static to impact deformation conditions. The framework is a visco-plastic self-consistent (VPSC) polycrystalline model embedded in an implicit finite element method (FE-VPSC) to provide a microstructure-sensitive constitutive response at each material point. Each material point of the FEM model is a polycrystalline aggregate with crystallographic deformation mechanisms operating at the single crystal scale with their evolving activity based on a dislocation density-based hardening law and texture. Four beams and three cylinders machined in different orientations from a textured plate of high-purity zirconium are tested quasi-statically in 4-point bending and at speeds of 100 m/s, 170 m/s and 243 m/s during Taylor impact tests, respectively. The variation in dimensional changes resulting from different sample orientations in the plate with respect to loading directions is measured for each sample. Moreover, texture and twinning characterization is performed using electron backscattered diffraction (EBSD). The deformation processes and underlying evolution of microstructure are successfully simulated using the FE-VPSC framework. In doing so, the model parameters are optimized and validated across a broad range of strain rates and temperatures. Simulation results in terms of geometrical changes and microstructural evolution are compared with the experimental measurements. The model predicts anisotropic material flow resulting from the hard-to-deform crystallographic directions, the development of gradients in texture and twinning through the geometries, tension–compression asymmetry, as well as the extent of plasticity under impact.

42 ENGINEERING↗

DOE OSTI2021

In-situ synchrotron X-ray micro-diffraction investigation of ultra-low-strain deformation microstructure in laminated Ti-Al composites

An ultra-low-strain deformation microstructure was revealed for the first time non-destructively in the bulk interior of an annealed laminated Ti-Al composite-in the "fully recrystallized" Al layer-by a synchrotron-based micro-diffraction technique, namely differential aperture X-ray microscopy (DAXM), through real space mapping with a very high angular resolution (0.01 degrees). This ultra-low-strain deformation microstructure was found to result from the thermal stress, induced during cooling after annealing, due to the different coefficients of thermal expansion for the Ti and Al layers. The annealed sample was further tensile deformed to a strain of 1.66% and followed by in situ DAXM and analyzed by various misorientation mapping methods. The results pointed to the important effects of the initial microstructure and the interface constraint, as well as the grain size and crystal orientation, on the plastic deformation. A gradient in dislocation density from the layer interface to the center was found in the Al layer of the annealed sample, and this gradient increased slightly during tensile deformation. The variation of the dislocation density was further discussed based on the activation and interaction of dislocations in grains of different sizes and orientations during plastic deformation. The findings of this study provided valuable insights in understanding the constraint effect of the laminated metal composite and the design of novel composite materials. (c) 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Crystallographic orientation↗

DOE OSTI2021

A finite element formulation for deformation twinning induced strain localization in polycrystal magnesium alloys

Deformation twinning induces shear strain localization in hexagonal close-packed crystals and is critical for the material’s ductility and failure. Cracks often occur at twin-twin or twin-grain boundary intersections and propagate along twin bands. However, most crystal plasticity models for deformation twinning are based on a “pseudo-slip” approach and do not capture the localized deformation associated with the formation of each discrete twin band. The few exceptions are discrete twin models that involve very complex numerical algorithms and are often compromised in accuracy due to the numerical convergence. These factors make the discrete twin models hard to adopt. This paper proposes a modification to the conventional finite element weak form, to fully incorporate a twin-induced heterogeneous deformation that does not depend on the “pseudo-slip” assumption. The model starts by splitting the deformation gradient into elastic-slip-twinning components. The twin-induced deformation gradient component is computed separately by solving a microstructural evolution problem and then implemented into finite element weak form by constructing a global “twin-force” vector. The constitutive update (e.g., in the user-defined material subroutine, or UMAT, for ABAQUS) therefore avoids dealing with the twinning and recovers to the form of a regular slip-based crystal plasticity model. The results presented here indicate that the twin-induced strain localization and the associated stress-reversal phenomena near the twin band were naturally captured in the model, which was validated against an in-situ synchrotron X-ray micro-diffraction experiment.

36 MATERIALS SCIENCE↗

NASA NTRS1990

Finite element elastic-plastic-creep and cyclic life analysis of a cowl lip

Results are presented of elastic, elastic-plastic, and elastic-plastic-creep analyses of a test-rig component of an actively cooled cowl lip. A cowl lip is part of the leading edge of an engine inlet of proposed hypersonic aircraft and is subject to severe thermal loadings and gradients during flight. Values of stresses calculated by elastic analysis are well above the yield strength of the cowl lip material. Such values are highly unrealistic, and thus elastic stress analyses are inappropriate. The inelastic (elastic-plastic and elastic-plastic-creep) analyses produce more reasonable and acceptable stress and strain distributions in the component. Finally, using the results from these analyses, predictions are made for the cyclic crack initiation life of a cowl lip. A comparison of predicted cyclic lives shows the cyclic life prediction from the elastic-plastic-creep analysis to be the lowest and, hence, most realistic.

Arya, Vinod K.↗

NASA NTRS1991

Finite element elastic-plastic-creep and cyclic life analysis of a cowl lip

Results are presented of elastic, elastic-plastic and elastic-plastic-creep analyses of a test-rig component of an actively cooled cowl lip. A cowl lip is part of the leading edge of an engine inlet of proposed hypersonic aircraft and is subject to severe thermal loadings and gradients during flight. Values of stresses calculated by elastic analysis are well above the yield strength of the cowl lip material. Such values are highly unrealistic, and thus elastic stress analyses are inappropriate. The inelastic (elastic-plastic and elastic-plastic-creep) analyses produce more reasonable and acceptable stress and strain distributions in the component. Finally, using the results from these analyses, predictions are made for the cyclic crack initiation life of a cowl lip. A comparison of predicted cyclic lives shows the cyclic life prediction from the elastic-plastic-creep analysis to be the lowest and, hence, most realistic.

Arya, V. K.↗

DOE OSTI2023

Resolving intragranular stress fields in plastically deformed titanium using point-focused high-energy diffraction microscopy

Abstract The response of a polycrystalline material to a mechanical load depends not only on the response of each individual grain, but also on the interaction with its neighbors. These interactions lead to local, intragranular stress concentrations that often dictate the initiation of plastic deformation and consequently the macroscopic stress–strain behavior. However, very few experimental studies have quantified intragranular stresses across bulk, three-dimensional volumes. In this work, a synchrotron X-ray diffraction technique called point-focused high-energy diffraction microscopy (pf-HEDM) is used to characterize intragranular deformation across a bulk, plastically deformed, polycrystalline titanium specimen. The results reveal the heterogenous stress distributions within individual grains and across grain boundaries, a stress concentration between a low and high Schmid factor grain pair, and a stress gradient near an extension twinning boundary. This work demonstrates the potential for the future use of pf-HEDM for understanding the local deformation associated with networks of grains and informing mesoscale models. Graphical abstract

36 MATERIALS SCIENCE↗

DOE OSTI2022

Investigation of deformation mechanisms in an advanced FeCrAl alloy using in-situ SEM-EBSD testing

The deformation mechanisms associated with uniaxial tensile testing are observed by conducting tensile experiments of an FeCrAl alloy using scanning electron microscopy (SEM) coupled with electron backscattered diffraction (EBSD). Prior to the deformation, investigated alloy was consisting grain and precipitate size of ~63.0 μm and ~6.7 μm, respectively. The recorded SEM micrographs and EBSD data at increasing levels of strains revealed the complex phenomena of slip bands’ formation in the presence of surface grain morphology evolution and their (001), (110) and (111) crystallographic planes distortions. The grains with orientation (110)||tensile direction (TD) shows higher shape change; however, (001)||TD and (111)||TD oriented grains show higher lattice gradient formation. Extracted information from the EBSD indicates that the crystallographic rotations drive towards specific, fiber-like texture in relation to the loading direction. Postmortem analysis of the recorded microstructure during the tensile deformation explains the phenomena of crack formation in the hard-intermetallic particles before the ultimate tensile strength (UTS). However, after the UTS, pores were identified in the neck that resulted from extensive plastic deformation. In-depth analysis was carried out to identify the cause of cracks and pores formation phenomena during the tensile test.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

Higher-Order Approximations for Stabilizing Zero-Energy Modes in Peridynamics Crystal Plasticity Models with Large Horizon Interactions

The non-ordinary state-based peridynamics theory combines non-local dynamic techniques with a desirable correspondence material principle, allowing for the use of continuum mechanics constitutive models. Such an approach presents a unique capability for solving problems involving discontinuities (e.g., strain localization, fracture, and fragmentation). However, the correspondence-based peridynamics models often suffer from zero-energy mode instabilities in numerical implementation, primarily due to the approximations of the non-local deformation gradient tensor. This paper focuses on a computational scheme for eliminating the zero-energy mode oscillations using a choice of influence functions that improve the truncation error in a higher-order Taylor series expansion of the deformation gradient. The novelty here is a tensor-based derivation of the linear constraint equations, which can be used to systematically identify the particle interaction weight functions for various user-specified horizon radii. In this paper, the proposed higher-order stabilization scheme is demonstrated for multi-dimensional examples involving polycrystalline and composite microstructures, along with comparisons against conventional finite element methods. The proposed stabilization scheme is shown to be highly effective in suppressing the spurious zero-energy mode oscillations in all numerical examples while enabling efficient simulations of strain localizations across material interfaces.

Non-Ordinary State-Based Peridynamics↗

DOE OSTI2020

Computational thermomechanics for crystalline rock. Part II: Chemo-damage-plasticity and healing in strongly anisotropic polycrystals

We present a thermal–mechanical–chemical-phase field model that captures the multi-physical coupling effects of precipitation creeping, crystal plasticity, anisotropic fracture, and crack healing in polycrystalline rock at various temperature and strain-rate regimes. This model is solved via a fast Fourier transfer solver with an operator-split algorithm to update displacement, temperature and phase field, and chemical concentration incrementally. In nuclear waste disposal in salt formation, brine inside the crystal salt may migrate along the grain boundary and cracks due to the gradient of interfacial energy and pressure. This migration has a significant implication on the permeability evolution, creep deformation, and crack healing within rock salt but is difficult to incorporate implicitly via effective medium theories compared with computational homogenization. As such, we introduce a thermodynamic framework and a corresponding computational implementation that explicitly captures the brine diffusion along the grain boundary and crack at the grain scale. Meanwhile, the anisotropic fracture and healing are captured via a high-order phase field that represents the regularized crack region in which a newly derived non-monotonic driving force is used to capture the fracture and healing due to the solution–precipitation. Numerical examples are presented to demonstrate the capacity of the thermodynamic framework to capture the multiphysics material behaviors of rock salt.

42 ENGINEERING↗

NASA NTRS1988

MHOST: An efficient finite element program for inelastic analysis of solids and structures

An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.

Nakazawa, S.↗

NASA NTRS1972

Elasto-plastic bending of cracked plates, including the effects of crack closure

A capability for solving elasto-plastic plate bending problems is developed using assumptions consistent with Kirchhoff plate theory. Both bending and extensional modes of deformation are admitted with the two modes becoming coupled as yielding proceeds. Equilibrium solutions are obtained numerically by determination of the stationary point of a functional which is analogous to the potential strain energy. The stationary value of the functional for each load increment is efficiently obtained through use of the conjugate gradient. This technique is applied to the problem of a large centrally through cracked plate subject to remote circular bending. Comparison is drawn between two cases of the bending problem. The first neglects the possibility of crack face interference with bending, and the second includes a kinematic prohibition against the crack face from passing through the symmetry plane. Results are reported which isolate the effects of elastoplastic flow and crack closure.

Jones, D. P.↗

DOE OSTI2022

A parallel discrete dislocation dynamics/kinetic Monte Carlo method to study non-conservative plastic processes

Non-conservative processes play a fundamental role in plasticity and are behind important macroscopic phenomena such as creep, dynamic strain aging, loop raft formation, etc. In the most general case, vacancy-induced dislocation climb is the operating unit mechanism. While dislocation/vacancy interactions have been modeled in the literature using a variety of methods, the approaches developed rely on continuum descriptions of both the vacancy population and its fluxes. However, there are numerous situations in physics where point defect populations display heterogeneous concentrations and/or non-smooth kinetics. Here, a kinetic Monte Carlo (kMC) approach for modeling vacancy transport in response to arbitrary stress fields is used. Vacancies are treated as point particles and are coupled to the dislocation substructure representing a deformed material via an advection term defined by the local stress gradients. The stress fields and the dislocation substructure are evolved using a discrete dislocation dynamics (DDD) module. To extend the coupled model to the treatment of large systems, we have implemented it in the massively-parallel DDD code ParaDiS. To avoid numerical incompatibilities associated with merging deterministic (DDD) and stochastic (kMC) integration algorithms, we cast the entire elasto-plastic-diffusive problem within a single stochastic framework, taking advantage of a parallel kMC algorithm to evolve the system as a single event-driven process. The large-scale implementation enables the study of the evolution of a variety of dislocation-defect scenarios governed by non-conservative transport kinetics. After carrying out an exhaustive numerical and computational analysis of our parallel algorithm, we show results that emphasize situations where inhomogeneous vacancy dynamics are of relevance, and compare discrete kinetics to continuum solutions for several cases.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Residual Stress in Cold Spray SS304L Measured Via Neutron Diffraction and Comparison of Analytical Models to Predict the Residual Stress

Here, this study employs neutron diffraction to investigate the relationship between residual stress and coating thickness in cold sprayed 304L austenitic stainless steel. Results show that shot peening predominantly impacts the residual stress profile, leading to substantial in-plane compressive force. The impact of laser heating, a widely used method to alter cold spray's microstructural properties, on the coating's residual stress is also analyzed. The findings indicate that the maximum compressive residual stress in the in-plane component is mainly independent of coating thickness, which suggests that the material properties determine the maximum residual stress. The cold sprayed deposits possessed compressive, nearly biaxial strain and stresses. After laser heating, these stresses were replaced by tensile residual stresses. Two analytical models, the Tsui and Clyne and the Boruah models, for predicting residual stresses are also evaluated, and both models provide reasonable fits to the experimental data. At this point, the deviations between the experimental results and the models are principally caused by the inability of the current models to address plastic deformation and relaxation, and the residual stresses generated by thermal gradients.

36 MATERIALS SCIENCE↗

NASA NTRS1980

Cyclic plasticity and failure of structural components

An analytical approach for low-cycle fatigue prediction is presented. The approach combines a cyclic plasticity model with the finite element method and a damage accumulation criterion for ductile metals. The cyclic plasticity model is based on the concept of the combination of several yield surfaces. The surfaces are related to the material uniaxial stress-strain curve idealized by piecewise linear segments. The damage criterion is based on the Coffin-Manson formulae modified for the mean stress variation effect. It is extended to the multiaxial varying stress-strain field and applied for both the crack initiation and the crack growth processes. The stable slow crack growth rate is approximated by the damage accumulation gradient computed from the cracked finite element models. This procedure requires fatigue testing data of only smooth specimens under constant strain amplitudes. The present approach is illustrated by numerical examples of an aircraft wing stiffened panel subjected to compression, which causes material yielding and residual tension.

Kalev, I.↗