High-temperature creep of single-crystal nickel-based superalloy : microstructural changes and effects of thermal cycling

Creep tests were performed on MC2 single crystal superalloy at 950°C/200 MPa and 1150°C/80 MPa under isothermal and thermal cycling conditions with a tensile axis along the [0 0 1] direction. It was found that the thermal cycles strongly affect the creep behavior at 1150°C but not at 950°C. This was related to the repetitive precipitation and dissolution of small γ′ rafts at the higher temperature, as revealed by quantitative characterization of the γ/γ′ microstructure. The dislocation microstructure exhibits similar trends in all the tested conditions, with a very high activity of a[1 0 0]-type dislocations climbing through the rafts. Such climbing dislocations constitute a recovery process for the deformation active system. It appears that the density of a[1 0 0] dislocations, and not their climb velocity or diffusion rate, is the key parameter for the control of creep rate. The thermal cycles, which imply the creation and subsequent dissolution of rafts, provided new dislocations, which explains the acceleration of creep observed under such conditions

Diffusion-controlled phase growth on dislocations

We treat the problem of diffusion of solute atoms around screw dislocations. In particular, we express and solve the diffusion equation, in radial symmetry, in an elastic field of a screw dislocation subject to the flux conservation boundary condition at the interface of a new phase. We consider an incoherent second-phase precipitate growing under the action of the stress field of a screw dislocation. The second-phase growth rate as a function of the supersaturation and a strain energy parameter is evaluated in spatial dimensions d=2 and d=3. Our calculations show that an increase in the amplitude of dislocation force, e.g. the magnitude of the Burgers vector, enhances the second-phase growth in an alloy. Moreover, a relationship linking the supersaturation to the precipitate size in the presence of the elastic field of dislocation is calculated.Comment: 10 pages, 4 figures, a revised version of the paper presented in MS&T'08, October 5-9, 2008, Pittsburg

Sheared Solid Materials

We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure. With this new ingredient, solving the equations yields formation of dislocation dipoles or slips. In plastic flow high-density dislocations emerge at large strains to accumulate and grow into shear bands where the strains are localized. In addition to the elastic displacement, we also introduce the local free volume {\it m}. For very small $m$ the defect structures are metastable and long-lived where the dislocations are pinned by the Peierls potential barrier. However, if the shear modulus decreases with increasing {\it m}, accumulation of {\it m} around dislocation cores eventually breaks the Peierls potential leading to slow relaxations in the stress and the free energy (aging). As another application of our scheme, we also study dislocation formation in two-phase alloys (coherency loss) under shear strains, where dislocations glide preferentially in the softer regions and are trapped at the interfaces.Comment: 16pages, 11figure

Phase field modeling of nonlinear material behavior

Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use instead phase-field-type theories where conventional linear elastic strain is quadratically coupled to an additional field that describes the evolution of the reference state and solely accounts for nonlinearity. In this paper we propose a systematic method allowing one to split the non-convex energy into harmonic and nonharmonic parts and to convert a nonconvex mechanical problem into a partially linearized phase-field problem. The main ideas are illustrated using the simplest framework of the Peierls-Nabarro dislocation model.Comment: 12 pages, 4 figures. v1: as submitted. v2: as published (conclusion added, unessential part of appendix removed, minor typesetting revisions). To appear in: K. Hackl (ed.), Proceedings of the IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, September 22-26, 2008, Bochum. (Springer-Verlag, 2010 presumably

Subatomic movements of a domain wall in the Peierls potential

Movements of individual domain walls in a ferromagnetic garnet were studied with angstrom resolution. The measurements reveal that domain walls can be locked between adjacent crystallographic planes and propagate by distinct steps matching the lattice periodicity. Domain walls are found to be weakly mobile within valleys of the atomic washboard but become unexpectedly flexible on Peierls ridges, where they can be kept in a bi-stable state by ac magnetic field. We describe the latter observation in terms of a single magnetic kink propagating along a domain wall

Mechanical properties of β-HMX

Background: For a full understanding of the mechanical properties of a material, it is essential to understand the defect structures and associated properties and microhardness indentation is a technique that can aid this understanding. Results: The Vickers hardness on (010), {011} and {110} faces lay in the range of 304-363 MPa. The Knoop Hardnesses on the same faces lay in the range 314-482 MPa. From etching of three indented surfaces, the preferred slip planes have been identified as (001) and (101). For a dislocation glide, the most likely configuration for dislocation movement on the (001) planes is (001) [100] (|b| = 0.65 nm) and for the (101) plane as (101) 101~(|b| = 1.084 nm) although (101) [010] (|b| = 1.105 nm) is possible. Tensile testing showed that at a stress value of 2.3 MPa primary twinning occurred and grew with increasing stress. When the stress was relaxed, the twins decreased in size, but did not disappear. The twinning shear strain was calculated to be 0.353 for the (101) twin plane. Conclusions: HMX is considered to be brittle, compared to other secondary explosives. Comparing HMX with a range of organic solids, the values for hardness numbers are similar to those of other brittle systems. Under the conditions developed beneath a pyramidal indenter, dislocation slip plays a major part in accommodating the local deformation stresses. © 2015 Gallagher et al.; licensee Springer

Dislocation multi-junctions and strain hardening

At the microscopic scale, the strength of a crystal derives from the motion, multiplication and interaction of distinctive line defects--dislocations. First theorized in 1934 to explain low magnitudes of crystal strength observed experimentally, the existence of dislocations was confirmed only two decades later. Much of the research in dislocation physics has since focused on dislocation interactions and their role in strain hardening: a common phenomenon in which continued deformation increases a crystal's strength. The existing theory relates strain hardening to pair-wise dislocation reactions in which two intersecting dislocations form junctions tying dislocations together. Here we report that interactions among three dislocations result in the formation of unusual elements of dislocation network topology, termed hereafter multi-junctions. The existence of multi-junctions is first predicted by Dislocation Dynamics (DD) and atomistic simulations and then confirmed by the transmission electron microscopy (TEM) experiments in single crystal molybdenum. In large-scale Dislocation Dynamics simulations, multi-junctions present very strong, nearly indestructible, obstacles to dislocation motion and furnish new sources for dislocation multiplication thereby playing an essential role in the evolution of dislocation microstructure and strength of deforming crystals. Simulation analyses conclude that multi-junctions are responsible for the strong orientation dependence of strain hardening in BCC crystals