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Results for “work hardening model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Work Hardening Model of Structure in Hall-Petch Strengthening

The microstructural length scale of metals changes by orders of magnitude under extreme processing conditions producing a concurrent wide range of mechanical strength and plasticity behaviors. A unified stress-strain σε σ(ε) model is formulated that’s based on superposing the components of asymptotic-curvilinear work hardening Θσ Θ(σ) to qualify and quantify these mechanical behaviors. This approach accounts for the rapid strengthening of metals beyond the initial yield point, through extended steady-state deformation, to the structural instability. The relationship between the softening coefficients cbi c bi of the work hardening formulation Θσ Θ(σ) and strength are found to reveal the microstructural scale in the material. Specifically, the rapid decrease in the slope of the Θσ Θ(σ) curve provides a measure for microstructural size consistent with a functional Hall-Petch relationship of strength. A successful application is shown for the tensile behavior of pure aluminum microstructures that result from extreme plastic deformation by equal-channel angle pressing.

Hall-Petch strengthening↗
DOE OSTI2025

Unified Stress-Strain Model for Plasticity to the Structural Instability

A unified model for the work hardening Θσ Θ(σ) and stress-strain σε σ(ε) behavior is presented that accounts for deformation under tensile loading, from the onset of yielding at the proportional limit up to the ultimate strength as defined at the structural instability. The origin of this approach is based on a negative exponential formulation for an asymptotic-curvilinear work-hardening model that accounts for the rapid strengthening of metals as well as the continuation of steady-state deformation to the instability.

36 MATERIALS SCIENCE↗
NASA NTRS1977

Development of a moderately sized finite element program for nonlinear structural analysis

AGGIE 1 is a computer program for predicting the linear and nonlinear, static and dynamic structural response of two- and three-dimensional continuum solids. The program is based on isoparametric finite elements and allows for 2-D plane stress, plane strain, and axisymmetric analyses and general 3-D analyses. Large strain kinematics is based on the total Lagrangian formulation. Materially nonlinear models include several elastic-plastic work-hardening models as well as an incompressible Mooney-Rivlin model. Included in this report is a brief description of the theoretical bases of the program, the material models used, the element library and the overall program organization. Instructions for data input preparation are given in detail. Several sample problems are given along with the required program input and program generated solutions.

Haisler, W. E.↗
DOE OSTI2023

Stress-strain and work hardening relationships of 304L AM alloy

A new approach to analytically derive constitutive stress-strain relationships from modeling the work hardening behavior of alloys was developed for assessing the strength and ductility of the Ti-6Al-4V alloy. This new approach is now successfully applied for assessing the quasi-static stress-strain behavior of an additively manufactured 304L sample. A predictive capability of this modelling approach may then be extended to model material stress-strain behavior at higher strain rates of loading.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The Effect of Antiphase Boundary Tubes on the Hardness of FeAl

The high work hardening rate unique to ordered intermetallic alloys has long been attributed to antiphase boundary (APB) tubes. In this work, APB tubes are introduced in Fe–40 at. pct Al and Fe–43 at. pct Al by cold-rolling and then removed by annealing. The presence and absence of APB tubes is verified with magnetic measurements. When APB tubes are annealed out the hardness does not change, thus indicating that APB tubes do not contribute to strengthening.

36 MATERIALS SCIENCE↗
DOE OSTI2022

The annihilation of antiphase boundary tubes and their effect on strengthening in Ni 3 Al

The temperature at which antiphase boundary (APB) tubes anneal out of lightly-strained Ni-rich Ni 3 Al thin foils has been measured via in-situ heating in a transmission electron microscope to be ~530 °C. Given this new information, the wealth of literature on the mechanical properties of Ni 3 Al across the entire temperature regime of the yield stress anomaly, ~25–800 °C, is re-evaluated to consider the impact of APB tubes. Contrary to previous theoretical predications, APB tubes do not appear to affect the strength of Ni 3 Al.

36 MATERIALS SCIENCE↗
NASA NTRS1983

Inelastic work and thermomechanical coupling in viscoplasticity

The inelastic deformation of engineering alloys was recently shown to be rate (time)-dependent at room temperature. Experiments reported herein demonstrate that inelastic strain path length is a suitable measure for the modeling of work hardening for these materials, whereas inelastic work is not appropriate. The measured deformation induced temperature change is well predicted by a previously proposed theory of thermomechanical coupling. It has been derived by neglecting the stored energy of cold work and by assuming tha the internal energy expression for thermoelasticity is valid even when the mechanical deformation is inelastic.

Krempl, E.↗
DOE OSTI2024

On the Onset of Plasticity: Determination of Strength and Ductility

The analysis of the work hardening variation with stress reveals insight to operative stress-strain mechanisms in material systems. The onset of plasticity can be assessed and related to ensuing plastic deformation up to the structural instability using one constitutive relationship that incorporates both behaviors of rapid work hardening (Stage 3) and the asymptotic leveling of stress (Stage 4). Results are presented for the mechanical behavior analysis of Ti-6Al-4V wherein the work hardening variation of Stages 3 and 4 are found to: be dependent through a constitutive relationship; be useful in a Hall-Petch formulation of yield strength; and provide the basis for a two point-slope fit method to model the experimental work hardening and stress-strain behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Model for the Softening Factor within Stages of Work Hardening

A formulation for a dimensionless coefficient c b is derived that represents a scale of microstructural softening for alloys which follow Kocks-Mecking (K-M) work hardening behavior. The variation of the true plastic strain ε p between the proportional limit σ y and the strength σ u at the instability is determined using the Considère criterion. Parameterization of the model is limited to variables expressly measured within tensile experiments. Further development is now made for the softening factor c bi through the individual and sequential stages 3 and 4 of plastic deformation during K-M work hardening Q behavior. Application is shown for tensile test results of Ti-6Al-4V made by different additively manufactured (AM) processes. It is found that the variation in plastic strain as a function of c bi produces a continuous curve representative of the alloy system. The results of data analysis indicate that Θ o3 and c b3 increase, while Θ o4 and c b4 decrease, as the total plastic strain ε p increases. Furthermore, formulations derived for K-M stages 3 and 4 enable the evaluation of other material parameters such as the activation volume ν* for the onset of plastic deformation. This activation volume is found to be near constant, at a ν*-value of 0.353±0.036 nm 3 as computed using a strain-rate sensitivity of strength exponent m of 0.014, irrespective of the AM method used to produce the Ti-6Al-4V alloy.

36 MATERIALS SCIENCE↗
NASA NTRS2017

Grain Size-Dependent Crystal Plasticity Constitutive Model for Polycrystal Materials

A new method to introduce grain size-dependence in classical crystal plasticity constitutive model is developed by considering the resistance to dislocation motion in the grain boundary influence region as equivalent to that of a work hardening. A general framework for the size-dependent constitutive model is derived by implementing this method on a core and mantle model. The work hardening, equivalent to grain boundary effect, is realized by introducing a fictitious, pre-existing, plastic strain grain boundary influence region (mantle) following the principles of classical crystal plasticity. This fictitious plastic strain, in effect, increases the yield strength and decreases the initial hardening coefficient of the grain. With the thickness of grain boundary influence region and the distribution of introduced plastic strain remaining the same, the grain boundary effect increased as the grain size becomes smaller. A simplified model that considers the grain boundary effect on a grain average sense is also developed under this general framework. Implementation of this general framework to the specific cases of crystal plasticity constitutive models is demonstrated by considering the case of power law flow rule and hyperbolic-secant hardening rule. Finally, the grain size-dependent constitutive model is validated by comparing the predicted stress-strain behavior of polycrystal samples with different average grain sizes under uniaxial loading with the experimental results.

Grain Size↗
DOE OSTI2023

On the constitutive stress-strain relationships and evaluation of the softening coefficient in work hardening mechanisms

The constitutive stress-strain relationships for structural alloys, such as additively manufactured Ti- 6Al-4V, are reconstructed by assessing the form and mechanism of work hardening relationships. The stress-strain relationships are best fit using both the Hollomon and Voce expressions wherein the Voce expression well-reproduces the later stage(s) of work hardening whereas the Hollomon relationship provides a better fit just beyond the proportional limit.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Modification of the MTS model for high strain-rate behavior of TI-6AL-4V

The Mechanical Threshold Stress (MTS) model provides excellent predictive capabilities for the material constitutive response for a wide range of temperatures and strain rates. However, the MTS model fails to capture the rapidly increasing yield stress at high strain rate behavior as the deformation controlling mechanism transitions from thermal activation to drag mechanisms, only capturing the linear behavior. Further, the model typically over predicts the flow stress behavior at yield and post yield due to its use of a constant work hardening rate parameter derived from the stress–strain response at constant saturation stress. An alternative approach to fitting portions of the MTS model is investigated and mathematical models are developed to address these issues. The results show that with appropriate experimental data, the mechanical threshold stress and work hardening rate parameters within the MTS model can quite easily and accurately be modified to extend applicability to high strain rate behavior and more accurately model the initial flow stress behavior at early work hardening rates without modification of the functions core to the MTS model itself.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Utilizing integrated neutron diffraction and elastoplastic self-consistent crystal plasticity model to quantitatively assess the strengthening mechanism in Al–12.5Ce and Al–12.5Ce–0.4Mg alloys

An integrated in-situ neutron diffraction and elastic plastic self-consistent crystal plasticity (EPSC-CP) modeling scheme is performed on a binary Al–12Ce alloy and a ternary Al–12Ce–0.4Mg alloys. Using this scheme, the constitutive parameters, i.e. elastic constants and slip system parameters of individual phases can be calibrated which can be used in microstructure-based CP models to predict materials performance. From this study, it is shown that the elastic constants of Al 11 Ce 3 intermetallics calculated from density function theory calculation in the literature are rather accurate. When applied to the EPSC-CP model, the lattice strains of both the binary and ternary alloys are correctly predicted as compared with experiments, and large lattice strain differences between Al (100) plane and Al 11 Ce 3 (010) plane are demonstrated. The slip system parameters calibrated by the scheme shows that the addition of 0.4 wt% Mg in the alloy has little influence on the critical resolved shear stress of initial dislocation glide in the Al matrix which caused plastic yield in the material. This can be explained by the very dilute Mg solute content in the Al solid solution, causing large spacing of Al–Mg lattice misfit sites and little impact on resistance of dislocation glide at initial yield. The 0.4 wt% Mg addition, on the other hand, has a large influence on the hardening term in the slip system parameters, indicating those Al–Mg misfit sites do help dislocation accumulation during the deformation. The impact of dilute Mg addition on the Al slip system parameters is also reflected in the flow behavior of the ternary alloy: little impact on the yield stress, but a large impact on working hardening and tensile strength of the materials which is consistent with the literature.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A constitutive structural parameter c b for the work hardening behavior of additively manufactured Ti-6Al-4V

The mechanical behavior of Ti-6Al-4V produced by additive manufacturing processes is assessed as based on a model derived from the Kocks–Mecking relationship. A constitutive parameter c b is derived from a linear Kocks–Mecking relationship for the microstructure that is characteristic of the work hardening behavior. The formulation for c b is determined by considering the plastic strain between the strengths at the proportional limit and the plastic instability. In this way, the model accommodates the variation in work hardening behavior observed when evaluating material as produced and tested along different orientations. The modeling approach is presented and evaluated for the case of Ti-6Al-4V additively manufactured materials as tested under quasi-static uniaxial tension. It is found that different test specimen orientations, along with postbuild heat treatments, produce a change in the microstructure and plasticity behavior which can be accounted for in the corresponding change of the c b values.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Dislocation density-based plasticity model from massive discrete dislocation dynamics database

In this work, we present a dislocation density-based strain hardening model for single crystal copper through a systematic coarse-graining analysis of more than 200 discrete dislocation dynamics (DDD) simulations of plastic deformation under uniaxial tension. The proposed constitutive model has two components: a generalized Taylor relation connecting resolved shear stresses to dislocation densities on individual slip systems, and a generalized Kocks-Mecking model for dislocation multiplication. The DDD data strongly suggests a logarithmic dependence of flow stress on the plastic shear strain rate on each slip system, and, equivalently, an exponential dependence of the plastic shear strain rate on the resolved shear stress. Hence the proposed generalized Taylor relation subsumes the Orowan relation for plastic flow. The DDD data also calls for a correction to the Kocks-Mecking model of dislocation multiplication to account for the increase of dislocation density on slip systems with negligible plastic shear strain rate. This is accomplished by allowing the multiplication rate on each slip system to include contributions from the plastic strain rates of the two coplanar slip systems. The resulting constitutive model successfully captures the strain hardening rate dependence on the loading orientation as predicted by the DDD simulations, which is also consistent with existing experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A phase-field fracture formulation for generalized standard materials: The interplay between thermomechanics and damage

Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.

36 MATERIALS SCIENCE↗