Instability Domain Research Articles

Hot Compression Deformation Behavior and Microstructural Evolution of Al-7.5Zn-1.5Mg-0.2Cu-0.2Zr Alloy

Hot compression tests of as-homogenized Al-7.5Zn-1.5Mg-0.2Cu-0.2Zr alloy were carried out on Gleeble-3500 thermal simulation machine at the temperature ranging from 350°C to 550°C and strain rate ranging from 0.001s-1 to 10s-1. Processing maps were established on the basis of dynamic material model, and the microstructure was studied using electron back scattered diffraction (EBSD) technique. The results showed that the peak stress and steady flow stress decrease with decreasing strain rate or increasing deformation temperature. There are one peak efficiency domain and one flow instability domain in the processing maps. The flow instability domain which exists in high-strain-rate region becomes larger with increasing strain. Shear bands occur at 45° toward the compression axis at grain interiors and meanwhile flow localization occurs. The optimum deformation temperature and strain rate ranges from 450°C to 500°C and 0.003s-1 to 0.1s-1, respectively, with high power dissipation efficiency of 34-39%.

To Calculation of Rectangular Plates on Periodic Oscillations

Geometrically nonlinear mathematical model of the problem of parametric oscillations of a viscoelastic orthotropic plate of variable thickness is developed using the classical Kirchhoff-Love hypothesis. The technique of the nonlinear problem solution by applying the Bubnov-Galerkin method at polynomial approximation of displacements (and deflection) and a numerical method that uses quadrature formula are proposed. The Koltunov-Rzhanitsyn kernel with three different rheological parameters is chosen as a weakly singular kernel. Parametric oscillations of viscoelastic orthotropic plates of variable thickness under the effect of an external load are investigated. The effect on the domain of dynamic instability of geometric nonlinearity, viscoelastic properties of material, as well as other physical-mechanical and geometric parameters and factors are taken into account. The results obtained are in good agreement with the results and data of other authors.

Hot Compression Test of AA 2014 aluminum Alloy with Microstructure Analysis and Processing Maps

In the present work an attempt has been made to study the flow behavior of AA 2014 Al alloy containing 10% wt silicon carbide particle of size 20-40 microns. The flow behavior is investigated from room temperature up to 5000C and the strain rate 0.01 to 100 per second. Also, the microstructure and processing map of 2014 Al alloy 10% wt SiC composite are evaluated and presented. The efficiency curve represents the formation of entropy during hot deformation and characterized the dissipative microstructure under different temperature and strain rate. The presence of various instabilities in the microstructure of the component is generally termed as flow instabilities. The instability map is obtained by plotting a dimensionless parameter as a function of temperature and strain rate. In order to have the safe zone in efficiency map one has to superimpose the instability map into it. The region outside the instability zone will be the safe zone for material processing. The instability domains occur at high strain rate deformation in all the temperatures. From the results it is concluded that, at low strains composite material shows an abnormal grain growth due to which dynamic recrystallization is not favored and no super plasticity behavior observed. However, at high strain the dynamic recrystallization process refines the grain size and superplastic domain exists. Also, results show that the peak efficiency of power dissipation in the domain of super plasticity increases at high temperature & low strain rate indicating that high temp and low strain rate enhance the dynamic recrystallization process.

The Study of Hot Deformation Behavior of Mechanically Milled and Hot Extruded Al–BN Nanocomposite

Hot deformation behavior of mechanically milled and hot extruded Al–BN nanocomposite is investigated by hot compression test in the temperature range of 350–500 °C and strain rate of 0.001–1 s−1. The plastic flow of the nanocomposite as a function of temperature and strain rate is described using a constitutive equation. Based on dynamic materials model, the processing map is developed at the strain of 0.7 representing stable and instable domains. The stable and instable domains in the processing map are verified by microstructural evaluation using transmission and scanning electron microscopes. The results show that the flow instability domains including micro voids and surface cracks have occurred in the range of: (1) T = 350–380 °C, \(\dot{\varepsilon }\) = 0.001–0.015 s−1, (2) T = 370–430 °C, \(\dot{\varepsilon }\) = 0.1–1 s−1, and (3) T = 460–500 °C, \(\dot{\varepsilon }\) = 0.001–0.03 s−1. The safe and stable domains for hot deformation of nanocomposite have occurred in the range of: (1) T = 350–370 °C, \(\dot{\varepsilon }\) = 0.1–1 s−1, (2) T = 390–450 °C, \(\dot{\varepsilon }\) = 0.003–0.05 s−1, and (3) T = 440–500 °C, \(\dot{\varepsilon }\) = 0.1–1 s−1. Finally, the investigation shows that the best processing parameters for this new nanocomposite are within the temperature range of 390–450 °C and strain rate range of 0.003–0.05 s−1.

Parametric instability analysis of truncated conical shells using the Haar wavelet method

Abstract In this paper, the Haar wavelet method is employed to analyze the parametric instability of truncated conical shells under static and time dependent periodic axial loads. The present work is based on the Love first-approximation theory for classical thin shells. The displacement field is expressed as the Haar wavelet series in the axial direction and trigonometric functions in the circumferential direction. Then the partial differential equations are reduced into a system of coupled Mathieu-type ordinary differential equations describing dynamic instability behavior of the shell. Using Bolotin’s method, the first-order and second-order approximations of principal instability regions are determined. The correctness of present method is examined by comparing the results with those in the literature and very good agreement is observed. The difference between the first-order and second-order approximations of principal instability regions for tensile and compressive loads is also investigated. Finally, numerical results are presented to bring out the influences of various parameters like static load factors, boundary conditions and shell geometrical characteristics on the domains of parametric instability of conical shells.

LAMOST views δ Scuti pulsating stars

About 766 $\delta$ Scuti stars were observed by LAMOST by June 16, 2017. Stellar atmospheric parameters of 525 variables were determined, while spectral types were obtained for all samples. In the paper, those spectroscopic data are catalogued. We detect a group of 131 unusual and cool variable stars (UCVs) that are distinguished from the normal $\delta$ Scuti stars (NDSTs). On the H-R diagram and the $\log g-T$ diagram, the UCVs are far beyond the red edge of pulsational instability trip. Their effective temperatures are lower than 6700\,K with periods in the range from 0.09 to 0.22\,days. NDSTs have metallicity close to that of the Sun as expected, while UCVs are slightly metal poor than NDSTs. The two peaks on the distributions of the period and stellar atmospheric parameters are all caused by the existence of UCVs. When those UCVs are excluded, it is discovered that the effective temperature, the gravitational acceleration and the metallicity all are correlated with the pulsating period for NDSTs and their physical properties and evolutionary states are discussed. The detecting of those UCVs indicates that about 25\% of the known $\delta$ Scuti stars may be misclassified. However, if some of them are confirmed to be pulsating stars, they will be a new-type pulsator and their investigations will shed light on theoretical instability domains and on the theories of interacting between the pulsation and the convection of solar-type stars. Meanwhile, 88 $\delta$ Scuti stars are detected to be the candidates of binary or multiple systems.

Necessary conditions for exponential stability of linear neutral type systems with multiple time delays

In this paper, we will give necessary conditions for the exponential stability of linear neutral type systems with multiple time delays by employing the Lyapunov–Krasovskii functional approach. These conditions not only extend the existing results of the neutral-delay-free systems, but also provide a new tool for stability analysis of linear neutral type systems with multiple time delays by characterizing instability domains. As a medium step, we will investigate several crucial properties which are involved with both the fundamental matrix and Lyapunov matrix. Numerical examples illustrate the validity of the theoretical results.

Hot deformation behavior of AZ40 magnesium alloy at elevated temperatures

Hot compression tests on AZ40 magnesium alloy were conducted on a Gleeble 1500d hot simulation testing machine in a deformation temperature range of 330 °C-420 °C and a strain rate range of 0.002-2 s-1. Hot deformation behaviors were investigated on the basis of the analysis of the flow stressstrain curves, constitutive equation, and processing map. The stress exponent and apparent activation energy were calculated to be 5.821 and 173.96 kJ/mol, respectively. Deformation twins and cracks located in grain boundaries were generated at 330 °C and 0.02 s-1, which are associated with a high strain rate and a limited number of available slip systems. With increasing temperature and decreasing strain rate, the twins disappeared and the degree of dynamic recrystallization increased. The alloy was completely dynamically recrystallized at 420 °C and 0.002 s-1, with a homogenous grain size of approximately 13.7 μm. The instability domains of the deformation behavior can be recognized by processing maps. By considering the processing maps and characterizing the microstructure, the optimum hot deformation parameters in this experiment were determined to be 420 °C and 0.002 s-1.

Necessary conditions of exponential stability for a class of linear neutral-type time-delay systems

ABSTRACTFor a class of linear neutral-type time-delay systems (NTTDSs), this paper will present necessary exponential stability conditions by employing the Lyapunov--Krasovskii functional approach. Since these conditions are represented by the Lyapunov matrix and the neutral coefficient matrix, they not only offer a novel tool for analysing stability of linear NTTDSs by characterising instability domains, but also extend the existing results of the neutral-delay-free systems. As a medium step, the relations between the Lyapunov matrix and the fundamental matrix are characterised. The validation of the obtained results is explained by numerical examples and comparison with some existing results.

Stability of new exact solutions of the nonlinear Schrödinger equation in a Pöschl–Teller external potential

We discuss the stability properties of the solutions of the general nonlinear Schrödinger equation in 1 + 1 dimensions in an external potential derivable from a parity-time () symmetric superpotential that we considered earlier in Kevrekidis et al (2015 Phys. Rev. E 92 042901). In particular we consider the nonlinear partial differential equation for arbitrary nonlinearity parameter κ, where and V is the well known Pöschl–Teller potential which we allow to be repulsive as well as attractive. Using energy landscape methods, linear stability analysis as well as a time dependent variational approximation, we derive consistent analytic results for the domains of instability of these new exact solutions as a function of the strength of the external potential and κ. For the repulsive potential we show that there is a translational instability which can be understood in terms of the energy landscape as a function of a stretching parameter and a translation parameter being a saddle near the exact solution. In this case, numerical simulations show that if we start with the exact solution, the initial wave function breaks into two pieces traveling in opposite directions. If we explore the slightly perturbed solution situations, a 1% change in initial conditions can change significantly the details of how the wave function breaks into two separate pieces. For the attractive potential, changing the initial conditions by 1% modifies the domain of stability only slightly. For the case of the attractive potential and negative g perturbed solutions merely oscillate with the oscillation frequencies predicted by the variational approximation.

Prominence Eruption Initiated by Helical Kink Instability of an Embedded Flux Rope

Abstract We study the triggering mechanism of a limb-prominence eruption and the associated coronal mass ejection (CME) near AR 12342 using Solar Dynamics Observatory and Large Angle and Spectrometric Coronagraph/Solar Heliospheric Observatory observations. The prominence is seen with an embedded flux thread (FT) at one end and bifurcates from the middle to a different footpoint location. The morphological evolution of the FT is similar to that of an unstable flux rope (FR), which we regard as a prominence-embedded FR. The FR twist exceeds the critical value. In addition, the morphology of the prominence plasma in 304 Å images marks the helical nature of the magnetic skeleton, with a total of 2.96 turns along arc length. The potential field extrapolation model indicates that the critical height of the background magnetic field gradient falls within the inner corona (105 Mm), which is consistent with the extent of coronal plasma loops. These results suggest that the helical kink instability in the embedded FR caused the slow rise of the prominence to the height of the torus instability domain. Moreover, the differential emission measure analysis unveils heating of the prominence plasma to coronal temperatures during an eruption, suggesting reconnection-related heating underneath the upward rising embedded FR. The prominence starts with a slow rise motion of 10 km s−1, which is followed by fast and slow acceleration phases that have an average acceleration of 28.9 m s−2 and 2.4 m s−2 in C2 and C3 field of view, respectively. As predicted by previous numerical simulations, the observed synchronous kinematic profiles of the CME leading edge and the core support the involved FR instability in the prominence initiation.

Investigation of the Deformation Mechanism of a near β Titanium Alloy through Isothermal Compression

This study investigated the hot deformation behavior of Ti-4Al-1Sn-2Zr-5Mo-8V-2.5Cr alloy through isothermal compression tests at temperatures from 780 to 930 °C with strain rates ranging from 0.001 to 1 s−1. The flow stress decreases with a decreased strain rate and an increased temperature. A constitutive equation was established for this alloy and the dependence of activation energy on temperature and strain rate is discussed. We further proposed a processing map using the dynamic materials model. On the processing map various domains of flow stability and flow instability can be identified. The deformation mechanisms associated with flow stability regions are mainly dynamic recrystallization (DRX) and dynamic recovery (DRV). The flow instability is manifested in the form of the band of flow localizations. The optimum processing conditions are suggested such that the temperature range is from 780 to 880 °C and the strain rate ranges from 0.001 to 0.01 s−1.

Determinants of the assembly and function of antibody variable domains

The antibody Fv module which binds antigen consists of the variable domains VL and VH. These exhibit a conserved ß-sheet structure and comprise highly variable loops (CDRs). Little is known about the contributions of the framework residues and CDRs to their association. We exchanged conserved interface residues as well as CDR loops and tested the effects on two Fvs interacting with moderate affinities (KDs of ~2.5 µM and ~6 µM). While for the rather instable domains, almost all mutations had a negative effect, the more stable domains tolerated a number of mutations of conserved interface residues. Of particular importance for Fv association are VLP44 and VHL45. In general, the exchange of conserved residues in the VL/VH interface did not have uniform effects on domain stability. Furthermore, the effects on association and antigen binding do not strictly correlate. In addition to the interface, the CDRs modulate the variable domain framework to a significant extent as shown by swap experiments. Our study reveals a complex interplay of domain stability, association and antigen binding including an unexpected strong mutual influence of the domain framework and the CDRs on stability/association on the one side and antigen binding on the other side.

Optical turbulence and transverse rogue waves in a cavity with triple-quantum-dot molecules

We show that optical turbulence extreme events can exist in the transverse dynamics of a cavity containing molecules of triple quantum dots under conditions close to tunneling-induced transparency. These nanostructures, when coupled via tunneling, form a four-level configuration with tunable energy-level separations. We show that such a system exhibits multistability and bistability of Turing structures in instability domains with different critical wave vectors. By numerical simulation of the mean-field equation that describes the transverse dynamics of the system, we show that the simultaneous presence of two transverse solutions with opposite nonlinearities gives rise to a series of turbulent structures with the capability of generating two-dimensional rogue waves.

Effect of SiC particles and the particulate size on the hot deformation and processing map of AZ91 magnesium matrix composites

Isothermal hot compression at the temperature range of 573–698K and strain rates of 0.005–1.0s−1 was used to investigate the flow behavior and processing characteristics of the nano-SiCp/AZ91 composites. Effects of the incorporated particles and their particulate size on the workability of the base alloy were then compared and discussed. Results show that compared with the monolithic AZ91 alloy, the incorporated nano-SiC particles effectively increase the flow stress of the composites by blocking the strain-induced dislocations, while effect of the micro-SiC particles varies due to the competition between pinning effect and particle stimulating nucleation (PSN) mechanism. Three domains of peak energy dissipation efficiency are identified in the processing map and the corresponding microstructures examined by EBSD indicate that continuous dynamic recrystallization (DRX) occurs during the compression. The instability characteristics at low temperature are severe mechanical twinning and micro-cracks, while that at high temperature is intergranular cracking. The incorporation of SiC particles enhances the high temperature (>655K) workability of AZ91 by increasing the upper limit of the processing strain rate and enables low temperature processing by decreasing the lower limit of the temperature. However, the added particles impose a side effect by enlarging the instability domain of the base alloy to a lower strain rate and even higher temperature.

Hot Workability of the as-Cast 21Cr Economical Duplex Stainless Steel Through Processing Map and Microstructural Studies Using Different Instability Criteria

To develop a fundamental understanding of the flow behavior and optimal hot workability parameters of this material, the hot workability and deformation mechanisms of the as-cast 21Cr EDSS were studied using processing map technology combined with microstructure analysis and isothermal hot compression over the temperature range of 1000–1150 °C and strain rate range of 0.01–10 s−1. The processing maps and constitutive equation of peak stress were developed based on Prasad’s and Murty’s criteria. The results show that the processing maps exhibit a stable domain at 1000–1150 °C and 0.01–1 s−1. The instability domain is exhibited at high strain rates (≥1 s−1). This implies that Murty’s criterion can predict the unstable domain with high reliability. The detailed deformation mechanisms are also studied by microstructure observation, showing that the flow localization and microcracking are responsible for the flow instability.

Characterization of hot deformation behavior of Ti–3Al–5Mo–4.5V alloy with a martensitic starting microstructure

The hot deformation behavior of Ti–3Al–5Mo–4.5V alloy with an [Formula: see text] martensitic microstructure was studied in the temperature range of 700–1000[Formula: see text]C and strain rates range of 0.001–[Formula: see text] up to a height reduction of 50%. The results show that an ultrafine equiaxed microstructure with an average grain size of [Formula: see text] were successfully produced through thermomechanical processing of a martensitic starting microstructure. A processing map was successfully constructed and provides appropriate processing parameters for hot deformation which are located in the temperature range of 700–800[Formula: see text]C and the low strain rate range of 0.001–[Formula: see text]. The instability domain mainly occurs at the strain rate higher than [Formula: see text] for the whole deformation temperature, which should be avoided during practice. The flow softening mechanism of the alloy is determined to be continuous dynamic recrystallization and the unstable flow is caused by the macro-fracture and flow localization.

Longitudinal Combustion Instability in a Rocket Engine with a Single Coaxial Injector

Longitudinal combustion instability in liquid-propellant rocket engines is investigated using an in-house axisymmetric, multispecies compressible flow solver. Turbulence is treated using a hybrid Reynolds-averaged Navier–Stokes/large-eddy simulation approach. The combustion–turbulence interactions are modeled using the flamelet/progress-variable approach. The computational time is at least an order of magnitude smaller than existing axisymmetric simulations with a more detailed chemistry mechanism. Three flow configurations with a choked nozzle are studied: unstable cases with 12 and 14 cm oxidizer post lengths, and a semiunstable case with a 9 cm oxidizer port length. Numerical results for oscillation frequencies and amplitudes agree with the continuously variable resonance combustor experiments conducted at Purdue University. Good agreements with existing computational results are also found. An additional open-end constant-pressure simulation with (otherwise) the same configuration as the continuously variable resonance combustor experiment with the 14 cm oxidizer post is performed, yielding minor acoustic oscillation. The open-end vortex-shedding frequency is found to be roughly one-half of the frequency of vortex shedding calculated in the continuously variable resonance combustor configuration. The flame region compacts as the combustion chamber becomes more unstable. The choked nozzle allows large-amplitude oscillation, thereby enhancing mixing and leading to more complete combustion near the pressure antinode (combustion chamber entrance) as compared to the open-end chamber. Pulse timing in the unstable case is identified as a major factor for the instability mechanism. Oscillatory behaviors for all three instability domains are described.

Intrinsic flame instabilities in combustors: Analytic description of a 1-D resonator model

The study is concerned with theoretical examination of thermo-acoustic instabilities in combustors and focuses on recently discovered ‘flame intrinsic modes’. These modes differ qualitatively from the acoustic modes in a combustor. Although these flame intrinsic modes were intensely studied, primarily numerically and experimentally, the instability properties and dependence on the characteristics of the combustor remain poorly understood. Here we investigate analytically the properties of intrinsic modes within the framework of a linearized model of a quarter wave resonator with temperature and cross-section jump across the flame, and a linear n−τ model of heat release. The analysis of dispersion relation for the eigen-modes of the resonator shows that there are always infinite numbers of intrinsic modes present. In the limit of small interaction index n the frequencies of these modes depend neither on the properties of the resonator, nor on the position of the flame. For small n these modes are strongly damped. The intrinsic modes can become unstable only if n exceeds a certain threshold. Remarkably, on the neutral curve the intrinsic modes become completely decoupled from the environment. Their exact dispersion relation links the intrinsic mode eigen-frequency ωi with the mode number mi and the time lag τ: ωi=(2mi+1)(π/τ)+mπ/τ, where m=0, +/−1. The main results of the study follow from the mode decoupling on the neutral curve and include explicit analytic expressions for the exact neutral curve on the n−τ plane, and the growth/decay rate dependence on the parameters of the combustor in the vicinity the neutral curve. The instability domain in the parameter space was found to have a very complicated shape, with many small islands of instability, which makes it difficult, if not impossible, to map it thoroughly numerically. The analytical results have been verified by numerical examination.

Characterization of hot deformation behavior of AA2014 forging aluminum alloy using processing map

The hot deformation behavior of AA2014 forging aluminum alloy was investigated by isothermal compression tests at temperatures of 350–480 °C and strain rates of 0.001–1 s−1 on a Gleeble–3180 simulator. The corresponding microstructures of the alloys under different deformation conditions were studied using optical microscopy (OM), electron back scattered diffraction (EBSD) and transmission electron microscopy (TEM). The processing maps were constructed with strains of 0.1, 0.3, 0.5 and 0.7. The results showed that the instability domain was more inclined to occur at strain rates higher than 0.1 s−1 and manifested in the form of local non-uniform deformation. At the strain of 0.7, the processing map showed two stability domains: domain I (350–430°C, 0.005–0.1 s−1) and domain II (450–480 °C, 0.001–0.05 s−1). The predominant softening mechanisms in both of the two domains were dynamic recovery. Uniform microstructures were obtained in domain I, and an extended recovery occurred in domain II, which would lead to the potential sub-grain boundaries progressively transforming into new high-angle grain boundaries. The optimum hot working parameters for the AA2014 forging aluminum alloy were determined to be 370–420 °C and 0.008–0.08 s−1.