An official website of the United States government
A physically-informed continuum crystal plasticity model is presented to elucidate deformation mechanisms, dislocation evolution and the non-Schmid effect in body-centered-cubic (bcc) tantalum widely used as a key structural material for mechanical and thermal extremes. We show the unified structural modeling framework informed by mesoscopic dislocation dynamics simulations is capable of capturing salient features of the large inelastic behavior of tantalum at quasi-static (10−3 s−1) to extreme strain rates (5000 s−1) and at low (77 K) to high temperatures (873 K) at both single- and polycrystal levels. We also present predictive capabilities of the model for microstructural evolution in the material. To this end, we investigate the effects of dislocation interactions on slip activities, instability and the non-Schmid behavior at the single crystal level. Furthermore, ex situ measurements on crystallographic texture evolution and dislocation density growth are carried out for polycrystal tantalum specimens at increasing strains. Numerical simulation results also support that the modeling framework is capable of capturing the main features of the polycrystal behavior over a wide range of strains, strain rates and temperatures. The theoretical, experimental and numerical results at both single- and polycrystal levels provide critical insight into the underlying physical pictures for micro- and macroscopic responses and their relations in this important class of refractory bcc materials undergoing large inelastic deformations.
more »
« less
Study of the Thermomechanical Behavior of Single-Crystal and Polycrystal Copper
This research paper presents an experimental, theoretical, and numerical study of the thermomechanical behavior of single-crystal and polycrystal copper under uniaxial stress compression loading at varying rates of deformation. The thermomechanical theory is based on a thermodynamically consistent framework for single-crystal face-centered cubic metals, and assumes that all plastic power is partitioned between stored energy due to dislocation structure evolution (configurational) and thermal (kinetic vibrational) energy. An expression for the Taylor–Quinney factor is proposed, which is a simple function of effective temperature and is allowed by second-law restrictions. This single-crystal model is used for the study of single- and polycrystal copper. New polycrystal thermomechanical experimental results are presented at varying strain rates. The temperature evolution on the surface of the polycrystal samples is measured using mounted thermocouples. Thermomechanical numerical single- and polycrystal simulations were performed for all experimental conditions ranging between 10−3 and 5 × 103 s−1. A Taylor homogenization model is used to represent polycrystal behavior. The numerical simulations of all conditions compare reasonable well with experimental results for both stress and temperature evolution. Given our lack of understanding of the mechanisms responsible for the coupling of dislocation glide and atomic vibration, this implies that the proposed theory is a reasonably accurate approximation of the single-crystal thermomechanics.
more »
« less
- Award ID(s):
- 2051355
- PAR ID:
- 10543395
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Metals
- Volume:
- 14
- Issue:
- 9
- ISSN:
- 2075-4701
- Page Range / eLocation ID:
- 1086
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Deshpande, Vikram (Ed.)The yield surface of a material is a criterion at which macroscopic plastic deformation begins. For crystalline solids, plastic deformation occurs through the motion of dislocations, which can be captured by discrete dislocation dynamics (DDD) simulations. In this paper, we predict the yield surfaces and strain-hardening behaviors using DDD simulations and a geometric manifold learning approach. The yield surfaces in the three-dimensional space of plane stress are constructed for single-crystal copper subjected to uniaxial loading along the [100] and [110] directions, respectively. With increasing plastic deformation under loading, the yield surface expands nearly uniformly in all directions, corresponding to isotropic hardening. In contrast, under [110] loading, latent hardening is observed, where the yield surface remains nearly unchanged in the orientations in the vicinity of the loading direction itself but expands in other directions, resulting in an asymmetric shape. This difference in hardening behaviors is attributed to the different dislocation multiplication behaviors on various slip systems under the two loading conditions.more » « less
-
null (Ed.)Continuum dislocation dynamics models of mesoscale plasticity consist of dislocation transport-reaction equations coupled with crystal mechanics equations. The coupling between these two sets of equations is such that dislocation transport gives rise to the evolution of plastic distortion (strain), while the evolution of the latter fixes the stress from which the dislocation velocity field is found via a mobility law. Earlier solutions of these equations employed a staggered solution scheme for the two sets of equations in which the plastic distortion was updated via time integration of its rate, as found from Orowan’s law. In this work, we show that such a direct time integration scheme can suffer from accumulation of numerical errors. We introduce an alternative scheme based on field dislocation mechanics that ensures consistency between the plastic distortion and the dislocation content in the crystal. The new scheme is based on calculating the compatible and incompatible parts of the plastic distortion separately, and the incompatible part is calculated from the current dislocation density field. Stress field and dislocation transport calculations were implemented within a finite element based discretization of the governing equations, with the crystal mechanics part solved by a conventional Galerkin method and the dislocation transport equations by the least squares method. A simple test is first performed to show the accuracy of the two schemes for updating the plastic distortion, which shows that the solution method based on field dislocation mechanics is more accurate. This method then was used to simulate an austenitic steel crystal under uniaxial loading and multiple slip conditions. By considering dislocation interactions caused by junctions, a hardening rate similar to discrete dislocation dynamics simulation results was obtained. The simulations show that dislocations exhibit some self-organized structures as the strain is increased.more » « less
-
null (Ed.)Abstract We performed deformation experiments on dry natural single crystals of magnetite and ilmenite to determine the rheological behavior of these oxide minerals as a function of temperature, orientation, and oxygen fugacity. Samples were deformed at temperatures of 825–1150 $$\,^{\circ }$$ ∘ C to axial strains of up to 15–24% under approximately constant stress conditions up to 120 MPa in a dead-load-type creep rig at ambient pressure in a controlled gas atmosphere. Oxygen fugacity ranged from 10 $$^{-9.4}$$ - 9.4 to 10 $$^{-4}$$ - 4 atm. Ilmenite creep was insensitive to oxygen fugacity, while magnetite displayed a strong, non-monotonic oxygen fugacity dependence, with creep rates varying as $$f_{O_{2}}^{-0.7}$$ f O 2 - 0.7 and $$f_{O_{2}}^{0.4}$$ f O 2 0.4 at more reducing and more oxidizing conditions, respectively. Dislocation creep rates of magnetite single crystals were weakly dependent on crystallographic orientation with stress exponents that varied between 2.8 and 4.3 (mean 3.5 ± 0.4). Magnetite compressed parallel to <100>, <110>, and <111> axes exhibited apparent activation energies of 315±5, 345±30, and 290±5 kJ/mol, respectively. We estimated $${f_O}_2$$ f O 2 -independent magnetite activation energies of 715 ± 150, 725 ± 145, and 690 ± 150 kJ/mol for <100>, <110>, and <111> orientations, respectively, in the region of negative $${f_O}_2$$ f O 2 -dependence. Ilmenite single crystals were compressed parallel, normal, and inclined to the c-axis. Stress exponents of 3.4, 4.3, and 3.9 indicate dislocation creep with activation energies of 420 ± 35, 345 ± 30, and 360 ± 40 kJ/mol, respectively, for these orientations. Mechanical anisotropy in ilmenite is notably higher than in magnetite, as expected from its lower crystal symmetry. Constitutive equations were formulated for ilmenite and magnetite creep.more » « less
-
Mapping dislocation densities resulting from severe plastic deformation using large strain machiningThe multiplication of dislocations determines the trajectories of microstructure evolution during plastic deformation. It has been recognized that the dislocation storage and the deformation-driven subgrain formation are correlated—the principle of similitude, where the dislocation density (ρ i ) scales self-similarly with the subgrain size (δ): $$\delta \sqrt {{\rho _{\rm{i}}}}$$ ∼ constant. Here, the robustness of this concept in Cu is probed utilizing large strain machining across a swathe of severe shear deformation conditions—strains in the range 1–10 and strain-rates 10–10 3 /s. Deformation strain, strain-rate, and temperature characterizations are juxtaposed with electron microscopy, and dislocation densities are measured by quantification of broadening of X-ray diffraction peaks of crystallographic planes. We parameterize the variation of dislocation density as a function of strain and a rate parameter R , a function of strain-rate, temperature, and material constants. We confirm the preservation of similitude between dislocation density and the subgrain structure across orders-of-magnitude of thermomechanical conditions.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/met14091086
