Modeling the deformation textures and microstructural evolutions of a Fe–Mn–C TWIP steel during tensile and shear testing

The high manganese austenitic steels with low stacking fault energy (SFE) present outstanding mechanical properties due to the occurrence of two strain mechanisms: dislocation glide and twinning. Both mechanisms are anisotropic. In this paper, we analyzed the effect of monotonous loading path on the texture, the deformation twinning and the stress–strain response of polycrystalline high Mn TWIP steel. Experimental data were compared to predicted results obtained by two polycrystalline models. These two models are based on the same single crystal constitutive equations but differ from the homogenization scheme. The good agreement between experiments and calculations suggest that the texture plays a key role in twinning activity and kinetics with regard to the intergranular stress heterogeneities. Rolling direction simple shear induces single twinning while rolling and transverse direction uniaxial tensions induce multi-twinning leading to lower twin volume fractions due to twin–twin interactions

How can large-scale twisted magnetic structures naturally emerge from buoyancy instabilities?

We consider the three-dimensional instability of a layer of horizontal magnetic field in a polytropic atmosphere where, contrary to previous studies, the field lines in the initial state are not unidirectional. We show that if the twist is initially concentrated inside the unstable layer, the modifications of the instability reported by several authors (see e.g. Cattaneo et al. (1990)) are only observed when the calculation is restricted to two dimensions. In three dimensions, the usual interchange instability occurs, in the direction fixed by the field lines at the interface between the layer and the field-free region. We therefore introduce a new configuration: the instability now develops in a weakly magnetised atmosphere where the direction of the field can vary with respect to the direction of the strong unstable field below, the twist being now concentrated at the upper interface. Both linear stability analysis and non-linear direct numerical simulations are used to study this configuration. We show that from the small-scale interchange instability, large-scale twisted coherent magnetic structures are spontaneously formed, with possible implications to the formation of active regions from a deep-seated solar magnetic field

Modeling the deformation textures and microstructural evolutions of a Fe–Mn–C TWIP steel during tensile and shear testing

The high manganese austenitic steels with low stacking fault energy (SFE) present outstanding mechanical properties due to the occurrence of two strain mechanisms: dislocation glide and twinning. Both mechanisms are anisotropic. In this paper, we analyzed the effect of monotonous loading path on the texture, the deformation twinning and the stress–strain response of polycrystalline high Mn TWIP steel. Experimental data were compared to predicted results obtained by two polycrystalline models. These two models are based on the same single crystal constitutive equations but differ from the homogenization scheme. The good agreement between experiments and calculations suggest that the texture plays a key role in twinning activity and kinetics with regard to the intergranular stress heterogeneities. Rolling direction simple shear induces single twinning while rolling and transverse direction uniaxial tensions induce multi-twinning leading to lower twin volume fractions due to twin–twin interactions

Evolution and characteristics of forced shear flows in polytropic atmospheres: Large and small Péclet number regimes

Complex mixing and magnetic field generation occurs within stellar interiors particularly where there is a strong shear flow. To obtain a comprehensive understanding of these processes, it is necessary to study the complex dynamics of shear regions. Due to current observational limitations, it is necessary to investigate the inevitable small-scale dynamics via numerical calculations. Here, we examine direct numerical calculations of a local model of unstable shear flows in a compressible polytropic fluid primarily in a two-dimensional domain, where we focus on determining how key parameters affect the global properties and characteristics of the resulting saturated turbulent phase. We consider the effect of varying both the viscosity and the thermal diffusivity on the non-linear evolution. Moreover, our main focus is to understand the global properties of the saturated phase, in particular estimating for the first time the spread of the shear region from an initially hyperbolic tangent velocity profile. We find that the vertical extent of the mixing region in the saturated regime is generally determined by the initial Richardson number of the system. Further, the characteristic quantities of the turbulence, i.e. typical length-scale and the root-mean-square velocity are found to depend on both the Richardson number, and the thermal diffusivity. Finally, we present our findings of our investigation into saturated flows of a ‘secular’ shear instability in the low Péclet number regime with large Richardson numbers

Shear instabilities in a fully compressible polytropic atmosphere

Shear flows have an important impact on the dynamics in an assortment of different astrophysical objects including accreditation discs and stellar interiors. Investigating shear flow instabilities in a polytropic atmosphere provides a fundamental understanding of the motion in stellar interiors where turbulent motions, mixing processes, as well as magnetic field generation takes place. Here, a linear stability analysis for a fully compressible fluid in a two-dimensional Cartesian geometry is carried out. Our study focuses on determining the critical Richardson number for different Mach numbers and the destabilising effects of high thermal diffusion. We find that there is a deviation of the predicted stability threshold for moderate Mach number flows along with a significant effect on the growth rate of the linear instability for small Peclet numbers. We show that in addition to a Kelvin-Helmholtz instability a Holmboe instability can appear and we discuss the implication of this in stellar interiors

Inverse cascade and symmetry breaking in rapidly-rotating Boussinesq convection

In this paper we present numerical simulations of rapidly-rotating Rayleigh-B\'enard convection in the Boussinesq approximation with stress-free boundary conditions. At moderately low Rossby number and large Rayleigh number, we show that a large-scale depth-invariant flow is formed, reminiscent of the condensate state observed in two-dimensional flows. We show that the large-scale circulation shares many similarities with the so-called vortex, or slow-mode, of forced rotating turbulence. Our investigations show that at a fixed rotation rate the large-scale vortex is only observed for a finite range of Rayleigh numbers, as the quasi-two-dimensional nature of the flow disappears at very high Rayleigh numbers. We observe slow vortex merging events and find a non-local inverse cascade of energy in addition to the regular direct cascade associated with fast small-scale turbulent motions. Finally, we show that cyclonic structures are dominant in the small-scale turbulent flow and this symmetry breaking persists in the large-scale vortex motion

From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence

We study structure formation in two-dimensional turbulence driven by an external force, interpolating between linear instability forcing and random stirring, subject to nonlinear damping. Using extensive direct numerical simulations, we uncover a rich parameter space featuring four distinct branches of stationary solutions: large-scale vortices, hybrid states with embedded shielded vortices (SVs) of either sign, and two states composed of many similar SVs. Of the latter, the first is a dense vortex gas where all SVs have the same sign and diffuse across the domain. The second is a hexagonal vortex crystal forming from this gas when the instability is sufficiently weak. These solutions coexist stably over a wide parameter range. The late-time evolution of the system from small-amplitude initial conditions is nearly self-similar, involving three phases: initial inverse cascade, random nucleation of SVs from turbulence and, once a critical number of vortices is reached, a phase of explosive nucleation of SVs, leading to a statistically stationary state. The vortex gas is continued in the forcing parameter, revealing a sharp transition towards the crystal state as the forcing strength decreases. This transition is analysed in terms of the diffusion of individual vortices and tools from statistical physics. The crystal can also decay via an inverse cascade resulting from the breakdown of shielding or insufficient nonlinear damping acting on SVs. Our study highlights the importance of the forcing details in two-dimensional turbulence and reveals the presence of nontrivial SV states in this system, specifically the emergence and melting of a vortex crystal

Growth rate degeneracies in kinematic dynamos

We consider the classical problem of kinematic dynamo action in simple steady flows. Due to the adjointness of the induction operator, we show that the growth rate of the dynamo will be exactly the same for two types of magnetic boundary conditions: the magnetic field can be normal (infinite magnetic permeability, also called pseudovacuum) or tangent (perfect electrical conductor) to the boundaries of the domain. These boundary conditions correspond to well-defined physical limits often used in numerical models and relevant to laboratory experiments. The only constraint is for the velocity field u to be reversible, meaning there exists a transformation changing u into −u. We illustrate this surprising property using S2T2 type of flows in spherical geometry inspired by [Dudley and James, Proc. R. Soc. London A 425, 407 (1989)]. Using both types of boundary conditions, it is shown that the growth rates of the dynamos are identical, although the corresponding magnetic eigenmodes are drastically different

Rheology of granular flows across the transition from soft to rigid particles

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Topography generation by melting and freezing in a turbulent shear flow

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