Discrete dislocation and crystal plasticity analyses of load shedding in polycrystalline titanium alloys

The focus of this paper is the mechanistic basis of the load shedding phenomenon that occurs under the dwell fatigue loading scenario. A systematic study was carried out using a discrete dislocation plasticity (DDP) model to investigate the effect of crystallographic orientations, localised dislocation behaviour and grain combinations on the phenomenon. Rate sensitivity in the model arises from a thermal activation process at low strain rates, which is accounted for by associating a stress- and temperature-dependent release time with obstacles; the activation energy was determined by calibrating an equivalent crystal plasticity model to experimental data. First, the application of Stroh's dislocation pile-up model of crack nucleation to facet fracture was quantitatively assessed using the DDP model. Then a polycrystalline model with grains generated using a controlled Poisson Voronoi tessellation was used to investigate the soft-hard-soft rogue grain combination commonly associated with load shedding. Dislocation density and peak stress at the soft/hard grain boundary increased significantly during the stress dwell period, effects that were enhanced by dislocations escaping from pile-ups at obstacles. The residual stress after dwell fatigue loading was also found to be much higher compared to standard fatigue loading. Taylor (uniform strain) and Sachs (uniform stress) type assumptions in a soft-hard grain combination have been assessed with a simple bicrystal DDP model. Basal slip nucleation in the hard grain was found to be initiated by high stresses generated by strong pile ups in the soft grain, and both basal and pyramidal slip nucleation was observed in the hard grain when the grain boundary orientation aligned with that of an active slip system in the soft grain. The findings of this study give new insight into the mechanisms of load shedding and faceting associated with cold dwell fatigue in Ti alloys used in aircraft engines

Investigation of slip transfer across HCP grain boundaries with application to cold dwell facet fatigue

This paper addresses the role of grain boundary slip transfer and thermally-activated discrete dislocation plasticity in the redistribution of grain boundary stresses during cold dwell fatigue in titanium alloys. Atomistic simulations have been utilised to calculate the grain boundary energies for titanium with respect to the misorientation angles. The grain boundary energies are utilised within a thermally-activated discrete dislocation plasticity model incorporating slip transfer controlled by energetic and grain boundary geometrical criteria. The model predicts the grain size effect on the flow strength in Ti alloys. Cold dwell fatigue behaviour in Ti-6242 alloy is investigated and it is shown that significant stress redistribution from soft to hard grains occurs during the stress dwell, which is observed both for grain boundaries for which slip transfer is permitted and inhibited. However, the grain boundary slip penetration is shown to lead to significantly higher hard-grain basal stresses near the grain boundary after dwell, thus exacerbating the load shedding stress compared to an impenetrable grain boundary. The key property controlling the dwell fatigue response is argued to remain the time constant associated with the thermal activation process for dislocation escape, but the slip penetrability is also important and exacerbates the load shedding. The inclusion of a macrozone does not significantly change the conclusions but does potentially lead to the possibility of a larger initial facet

Practically linear analogs of the Born-Infeld and other nonlinear theories

I discuss theories that describe fully nonlinear physics, while being practically linear (PL), in that they require solving only linear differential equations. These theories may be interesting in themselves as manageable nonlinear theories. But, they can also be chosen to emulate genuinely nonlinear theories of special interest, for which they can serve as approximations. The idea can be applied to a large class of nonlinear theories, exemplified here with a PL analogs of scalar theories, and of Born-Infeld (BI) electrodynamics. The general class of such PL theories of electromagnetism are governed by a Lagrangian L=-(1/2)F_mnQ^mn+ S(Q_mn), where the electromagnetic field couples to currents in the standard way, while Qmn is an auxiliary field, derived from a vector potential that does not couple directly to currents. By picking a special form of S(Q_mn), we can make such a theory similar in some regards to a given fully nonlinear theory, governed by the Lagrangian -U(F_mn). A particularly felicitous choice is to take S as the Legendre transform of U. For the BI theory, this Legendre transform has the same form as the BI Lagrangian itself. Various matter-of-principle questions remain to be answered regarding such theories. As a specific example, I discuss BI electrostatics in more detail. As an aside, for BI, I derive an exact expression for the short-distance force between two arbitrary point charges of the same sign, in any dimension.Comment: 20 pages, Version published in Phys. Rev.

"Background Field Integration-by-Parts" and the Connection Between One-Loop and Two-Loop Heisenberg-Euler Effective Actions

We develop integration-by-parts rules for Feynman diagrams involving massive scalar propagators in a constant background electromagnetic field, and use these to show that there is a simple diagrammatic interpretation of mass renormalization in the two-loop scalar QED Heisenberg-Euler effective action for a general constant background field. This explains why the square of a one-loop term appears in the renormalized two-loop Heisenberg-Euler effective action. No integrals need be evaluated, and the explicit form of the background field propagators is not needed. This dramatically simplifies the computation of the renormalized two-loop effective action for scalar QED, and generalizes a previous result obtained for self-dual background fields.Comment: 13 pages; uses axodraw.st

The Synthesis and Characterization of New, Robust Titanium (IV) Scorpionate Complexes

Titanium complexes possessing sterically encumbered ligands have allowed for the preparation of reactive moieties (imido, alkylidene and alkylidyne species) relevant to reactions such as olefin polymerization and alkyne hydroamination. For this reason, we have targeted robust scorpionate ancillary ligands to support reactive titanium centers. Thus, a series of titanium complexes were synthesized using an achiral oxazoline-based scorpionate ligand, tris(4,4-dimethyl-2-oxazolinyl)phenyl borate [To^M^]^-^ as well as the related chiral ligand, tris(4-isopropyl-2-oxazolinyl)phenyl borate [To^P^]^-^. The complex [Ti(κ^3^- To^M^)Cl~3~] was prepared in moderate yield (43%) by the rapid (<1 min at room temperature) reaction of Li[To^M^] and TiCl~4~ in methylene chloride; this new compound was characterized by ^1^H NMR spectroscopy as the expected C~3v~-symmetric species. One route to Ti (IV) alkyls involves salt metathesis; accordingly, syntheses of [To^M^]Ti alkyl complexes by interaction of [Ti(κ^3^-To^M^)Cl~3~] and one or three equivalents of alkylating agents, such as benzyl potassium (KCH~2~C~6~H~5~), trimethylsilylmethyl
lithium (LiCH~2~Si(CH~3~) ~3~), or neopentyl lithium (LiCH~2~C(CH~3~)~3~) are currently under investigation. The complexes [Ti(=NBut) (κ~3~-To^M^)(Cl)(Bu^t^py)] (Bu^t^py=4 tert-butylpyridine) and [Ti(=NBu^t^) (κ~3~-To^P^)(Cl)(Bu^t^py)] were synthesized by reaction of the known Ti imido [Ti(=NBu^t^)(Cl)~2~(Bu^t^py)~2~] with Li[To^M^] or Li[To^P^], respectively, by stirring overnight in methylene chloride at ambient temperature. The complexes were identified using ^1^H NMR spectroscopy, ^1^H-^13^C HMQC and ^1^H-^15^N HMBC correlation experiments

Symmetry protected fractional Chern insulators and fractional topological insulators

In this paper we construct fully symmetric wavefunctions for the spin-polarized fractional Chern insulators (FCI) and time-reversal-invariant fractional topological insulators (FTI) in two dimensions using the parton approach. We show that the lattice symmetry gives rise to many different FCI and FTI phases even with the same filling fraction $\nu$ (and the same quantized Hall conductance $\sigma_{xy}$ in FCI case). They have different symmetry-protected topological orders, which are characterized by different projective symmetry groups. We mainly focus on FCI phases which are realized in a partially filled band with Chern number one. The low-energy gauge groups of a generic $\sigma_{xy}=1/m\cdot e^2/h$ FCI wavefunctions can be either $SU(m)$ or the discrete group $Z_m$, and in the latter case the associated low-energy physics are described by Chern-Simons-Higgs theories. We use our construction to compute the ground state degeneracy. Examples of FCI/FTI wavefunctions on honeycomb lattice and checkerboard lattice are explicitly given. Possible non-Abelian FCI phases which may be realized in a partially filled band with Chern number two are discussed. Generic FTI wavefunctions in the absence of spin conservation are also presented whose low-energy gauge groups can be either $SU(m)\times SU(m)$ or $Z_m\times Z_m$. The constructed wavefunctions also set up the framework for future variational Monte Carlo simulations.Comment: 24 pages, 13 figures, published versio

Entrant Experience and Plant Exit

Producers entering a market can differ widely in their prior production experience, ranging from none to extensive experience in related geographic or product markets. In this paper, we quantify the nature of prior plant and firm experience for entrants into a market and measure its effect on the plant's decision to exit the market. Using plant-level data for seven regional manufacturing industries in the U.S., we find that a producer's experience at the time it enters a market plays an important role in the subsequent exit decision, affecting both the overall probability of exit and the method of exit. After controlling for observable plant and market profit determinants, there remain systematic differences in failure patterns across three groups of plants distinguished by their prior experience: de novo entrants, experienced plants that enter by diversifying their product mix, and new plants owned by experienced firms. The results indicate that the exit decision cannot be treated as determined solely by current and future plant, firm, and market conditions, but that the plant's history plays an important independent role in conditioning the likelihood of survival.

On the QED Effective Action in Time Dependent Electric Backgrounds

We apply the resolvent technique to the computation of the QED effective action in time dependent electric field backgrounds. The effective action has both real and imaginary parts, and the imaginary part is related to the pair production probability in such a background. The resolvent technique has been applied previously to spatially inhomogeneous magnetic backgrounds, for which the effective action is real. We explain how dispersion relations connect these two cases, the magnetic case which is essentially perturbative in nature, and the electric case where the imaginary part is nonperturbative. Finally, we use a uniform semiclassical approximation to find an expression for very general time dependence for the background field. This expression is remarkably similar in form to Schwinger's classic result for the constant electric background.Comment: 27 pages, no figures; reference adde

The Buddha\u27s Mandate: Buddhism and Japanese Kingship

An argument for the central role of Buddhism in the formation of kingship in Asuka-era Japan

Fermion Determinants

The current status of bounds on and limits of fermion determinants in two, three and four dimensions in QED and QCD is reviewed. A new lower bound on the two-dimensional QED determinant is derived. An outline of the demonstration of the continuity of this determinant at zero mass when the background magnetic field flux is zero is also given.Comment: 10 page