Free and obstructed glide of dislocations: A theoretical framework

Celebi, Orcun Koray

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https://hdl.handle.net/2142/124237 Copy

Description

Title

Free and obstructed glide of dislocations: A theoretical framework

Author(s)

Celebi, Orcun Koray

Issue Date

2024-04-15

Director of Research (if dissertation) or Advisor (if thesis)

Sehitoglu, Huseyin

Doctoral Committee Chair(s)

Sehitoglu, Huseyin

Committee Member(s)

• Krogstad, Jessica A.
• Ertekin, Elif
• Stinville, Jean-Charles

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Dislocations
• Computational Mechanics

Abstract

Yield strength, which marks the transition from the elastic to plastic deformation regimes, represents the fundamental mechanical property of structural materials. Beyond the yield point, microstructural changes occur driven by the underlying deformation mechanisms such as slip, twinning, and phase transformation. In crystalline structural materials, the most common mechanism responsible for this plastic deformation is the slip of line defects, known as dislocations. These defects translate under external shear stress and produce plastic flow within the material. The Critical Resolved Shear Stress (CRSS) marks the stress required for slip activation and is related to the yield strength of the material through the Schmid factor. The magnitude of CRSS in different slip-systems and in grains of different orientations dictate the anisotropy of materials relevant to overall polycrystalline response and development of crystallographic texture. The magnitude of CRSS at crack tips dictates the fracture and fatigue response of materials and is an important quantity in understanding failure processes. The experimental CRSS levels are difficult to determine for all slip-systems because their activation requires precise sample orientation, precise measurement of strains, minimal interaction among different slip-systems to isolate a single slip case, and testing in tension and compression modes to reveal the asymmetry. On the other hand, its theoretical determination has been challenging because many of the idealized models give stress levels in GPas while the experimental values are of the order of MPas in metals. Existing approaches for CRSS determination are highly unsatisfactory because of empiricism associated with determination of dislocation “core-width” and nature of core-advance. This study proposes a predictive model addressing both shortcomings. The core-width is rigorously determined from an optimized balance between continuum strain-energy and atomistic misfit-energy of the dislocation’s core. The strain-energy is calculated using the fully-anisotropic Eshelby-Stroh formalism accommodating the inherent mixed characters of the partials constituting the extended dislocation. The misfit-energy is determined from critical fault-energies of the slip-plane input to a novel misfit-model capturing the lattice structure of the slip-plane and involving the discrete Wigner-Seitz cell area at each lattice site, advancing over an 80-year old misfit-energy model that has missed the role of both concepts. For the first time in literature, the nature of motion of the extended-dislocation’s core is rigorously derived from an optimized trajectory of its total-energy. It is shown that each partial’s core moves intermittently (“zig-zag” motion), and not together, allowing the stacking-fault width to fluctuate during advance of the extended-dislocation. The critical stress is shown to involve a trajectory-dependent combination of Schmid factors for each partial, also revealed for the first time. The proposed model is used to predict critical stress for multiple FCC and HCP materials including pure metals, solid-solution alloys, and High Entropy Alloys (HEAs), displaying excellent agreement with experiments. The work opens future avenues for rapid reliable assessment of a multitude of compositions across varying lattice structures, addressing a major void in structure-property prediction for structural materials, also instrumental for ab-initio materials design. Dislocations interact with other pre-existing defects in the crystal, such as twins, resulting in favorable improvements in mechanical properties. The superior mechanical response of twinnable materials fundamentally arises from an elevation of CRSS due to Dislocation-Twin Boundary (D-TB) reactions. These reactions exhibit rich variety with several possible outcomes and exhibit complex dependence on microstructural properties, causing state-of-the-art models to adopt a case-by-case simulation of each reaction relying on empirical potentials or twin-interaction parameters. We develop an analytical “Evolving Dislocation Core” (EDC) model devoid of empiricism, capable of predicting the CRSS-elevation for any reaction, given the microstructural properties (elastic constants, twin crystallography, etc.). The approach is fundamentally rooted in energy-minimization within a fully-anisotropic framework revealing the evolution of dislocation cores with progression of the reaction. The core-structure of complex dislocations (e.g. stair-rod) in the reaction is proposed, for the first time in literature, as a non-planar composite of disregistries distributed on slip and twin planes. The model is applied to multiple slip-incorporation reactions in several Face-Centered-Cubic (FCC) materials (Pb, Ag, Cu, Ni-Co alloys and Ni-Ti alloys and high-entropy alloy FeNiCoCrMn). The predicted CRSS-elevations show agreement with atomistic simulations (Ni) and experiment (FeNiCoCrMn). The model further establishes a strong correlation of the elevation with unstable stacking/twinning fault energy and the magnitude of the sessile dislocation’s Burgers vector, while revealing poor correlation with the stable intrinsic stacking fault energy which is a common benchmark. Thus, the analytical EDC model developed in this study advances understanding of slip-twin interactions on multiple fronts while serving as an effective predictive model for CRSS-elevation instrumental in materials design.

Graduation Semester

2024-05

Type of Resource

Thesis

Copyright and License Information

© 2024 Orcun Koray Celebi

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