Mesoscale theory of grains and cells: crystal plasticity and coarsening

Solids with spatial variations in the crystalline axes naturally evolve into cells or grains separated by sharp walls. Such variations are mathematically described using the Nye dislocation density tensor. At high temperatures, polycrystalline grains form from the melt and coarsen with time: the dislocations can both climb and glide. At low temperatures under shear the dislocations (which allow only glide) form into cell structures. While both the microscopic laws of dislocation motion and the macroscopic laws of coarsening and plastic deformation are well studied, we hitherto have had no simple, continuum explanation for the evolution of dislocations into sharp walls. We present here a mesoscale theory of dislocation motion. It provides a quantitative description of deformation and rotation, grounded in a microscopic order parameter field exhibiting the topologically conserved quantities. The topological current of the Nye dislocation density tensor is derived from a microscopic theory of glide driven by Peach-Koehler forces between dislocations using a simple closure approximation. The resulting theory is shown to form sharp dislocation walls in finite time, both with and without dislocation climb.Comment: 5 pages, 3 figure

Stress-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density tensor

We derive general relations between grain boundaries, rotational deformations, and stress-free states for the mesoscale continuum Nye dislocation density tensor. Dislocations generally are associated with long-range stress fields. We provide the general form for dislocation density fields whose stress fields vanish. We explain that a grain boundary (a dislocation wall satisfying Frank's formula) has vanishing stress in the continuum limit. We show that the general stress-free state can be written explicitly as a (perhaps continuous) superposition of flat Frank walls. We show that the stress-free states are also naturally interpreted as configurations generated by a general spatially-dependent rotational deformation. Finally, we propose a least-squares definition for the spatially-dependent rotation field of a general (stressful) dislocation density field.Comment: 9 pages, 3 figure

Micro-plasticity and intermittent dislocation activity in a simplified micro structural model

Here we present a model to study the micro-plastic regime of a stress-strain curve. In this model an explicit dislocation population represents the mobile dislocation content and an internal shear-stress field represents a mean-field description of the immobile dislocation content. The mobile dislocations are constrained to a simple dipolar mat geometry and modelled via a dislocation dynamics algorithm, whilst the shear-stress field is chosen to be a sinusoidal function of distance along the mat direction. The latter, defined by a periodic length and a shear-stress amplitude, represents a pre-existing micro-structure. These model parameters, along with the mobile dislocation density, are found to admit a diversity of micro-plastic behaviour involving intermittent plasticity in the form of a scale-free avalanche phenomenon, with an exponent for the strain burst magnitude distribution similar to those seen in experiment and more complex dislocation dynamics simulations.Comment: 30 pages, 12 figures, to appear in "Modelling and Simulation in Materials Science and Engineering

Cyclic plasticity and fatigue damage of CrMnFeCoNi high entropy alloy fabricated by laser powder-bed fusion

The CrMnFeCoNi high-entropy alloy is highly printable and holds great potential for structural applications. However, no significant discussions on cyclic plasticity and fatigue damage in previous studies. This study provides significant insights into the link between print processes, solidification microstructure, cyclic plasticity and fatigue damage evolution in the alloy fabricated by laser powder bed fusion. Thermodynamics-based predictions (validated by scanning transmission electron microscopy (STEM) energy dispersive X-ray spectroscopy (EDX)) showed that Cr, Co and Fe partition to the core of the solidification cells, whilst Mn and Ni to the cell boundaries in all considered print parameters. Both dislocation slip and deformation twinning were found to be responsible for plastic deformation under monotonic loading. However, the former was found to be the single dominant mechanism for cyclic plasticity. The surface finish helped to substantially delay the crack initiation and cause lack-of-fusion porosity to be the main source of crack initiation. Most significantly, the scan strategies significantly affect grain arrangements and grain dimensions, leading to noticeable effects on fatigue crack propagation; in particular, the highest resistance crack propagation was seen in the meander scan strategy with 0° rotation thanks to the most columnar grains and the smallest spacing of grain boundaries along the crack propagation path

Constitutive behavior of as-cast A356

The constitutive behavior of aluminum alloy A356 in the as-cast condition has been characterized using compression tests performed over a wide range of deformation temperatures (30-500{\deg}C) and strain rates (\approx0.1-10 /s). This work is intended to support the development of process models for a wide range of conditions including those relevant to casting, forging and machining. The flow stress behavior as a function of temperature and strain rate has been fit to a modified Johnson-Cook and extended Ludwik-Hollomon expression. The data has also been assessed with both the strain-independent Kocks-Mecking and Zener-Hollomon frameworks. The predicted plastic flow stress for each expression are compared. The results indicate that the extended Ludwik-Hollomon is best suited to describe small strain conditions (stage III hardening), while the Kocks-Mecking is best employed for large strain (stage IV). At elevated temperatures, it was found that the Zener-Hollomon model provides the best prediction of flow stress.Comment: 34 pages, 12 figure

Domain wall pinning and dislocations: Investigating magnetite deformed under conditions analogous to nature using transmission electron microscopy

In this study, we deformed samples cut from a single magnetite octahedron and used transmission electron microscopy (TEM) and magnetic measurements to experimentally verify earlier computational models of magnetic domain wall pinning by dislocations and to better understand the nature of dislocations in magnetite. Dislocations in magnetite have been of interest for many decades because they are often cited as a likely source of stable thermoremanent magnetizations in larger multidomain (MD) magnetite grains, so a better understanding of dislocation effects on coercivity in MD magnetite is crucial. TEM imaging shows, for the first time, domain walls sweeping through the magnetite sample and being pinned at dislocations. In agreement with theory, these findings demonstrate that domain walls are more strongly pinned at networks of dislocations than at single dislocations and that domain walls pinned at longer dislocations have higher microcoercivities than those pinned at shorter dislocations. This experimentally illustrates the ability of dislocations to increase the coercivity of larger multidomain magnetite grains. The observed values for microcoercivity and bulk coercivity are in reasonable agreement with theoretical calculations. Burgers vectors were determined for some dislocations to verify that they were in keeping with expected dislocation orientations. The dislocations were found to be primarily located on close-packed {111} planes within the magnetite. Deformation caused only a minor change in bulk coercivity, but first-order reversal curve diagrams show populations with increased coercivity not visible in hysteresis loops.The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC grant agreement 320750. The Institute for Rock Magnetism and LacCore are supported by the NSF EAR Instrumentation and Facilities Program and by the University of Minnesota, Earth Sciences Division, National Science Foundation. To obtain the data used for this paper, please contact A.K.L. This work was funded by EAR-0810085 to J.M.F., by EAR-0810252 to A.J.N., and by a Geological Society of America grant to A.K.L. This is IRM publication 1406.This is the final published version. It first appeared at http://onlinelibrary.wiley.com/doi/10.1002/2014JB011335/abstract?rememberMePresent=false

"Cold Melting" of Invar Alloys

An anomalously strong volume magnetostriction in Invars may lead to a situation when at low temperatures the dislocation free energy becomes negative and a multiple generation of dislocations becomes possible. This generation induces a first order phase transition from the FCC crystalline to an amorphous state, and may be called "cold melting". The possibility of the cold melting in Invars is connected with the fact that the exchange energy contribution into the dislocation self energy in Invars is strongly enhanced, as compared to conventional ferromagnetics, due to anomalously strong volume magnetostriction. The possible candidate, where this effect can be observed, is a FePt disordered Invar alloy in which the volume magnetostriction is especially large

The Hall-Petch effect as a manifestation of the general size effect

The experimental evidence for the Hall-Petch dependence of strength on the inverse square-root of grain size is reviewed critically. Both the classic data and more recent results are considered. While the data can be fitted to the inverse square-root dependence excellently (but using two free fitting parameters for each dataset), it is also consistent with a dependence on the simple inverse of grain size (with one free fitting parameter for each dataset). There have been difficulties, recognised for half-a-century, in explaining the inverse square-root expression. A Bayesian analysis shows that the data strongly supports the simple inverse expression proposed. Since this expression derives from underlying theory, it is also more readily explicable. It is concluded that the Hall-Petch effect is not to be explained by the variety of theories found in the literature, but is a manifestation of, or underlain by, the general size effect observed throughout micromechanics, due to the inverse relationship between the stress required and the space available for dislocation sources to operate.Comment: Paper presented at Plasticity 2014, The Bahama