Effect of the silicon-carbide micro- and nanoparticle size on the thermo-elastic and time-dependent creep response of a rotating Al–SiC composite cylinder

The history of stresses and creep strains of a rotating composite cylinder made of an aluminum matrix reinforced by silicon carbide particles is investigated. The effect of uniformly distributed SiC micro- and nanoparticles on the initial thermo-elastic and time-dependent creep deformation is studied. The material creep behavior is described by Sherby’s constitutive model where the creep parameters are functions of temperature and the particle sizes vary from 50 nm to 45.9 μm. Loading is composed of a temperature field due to outward steady-state heat conduction and an inertia body force due to cylinder rotation. Based on the equilibrium equation and also stress-strain and strain-displacement relations, a constitutive second-order differential equation for displacements with variable and time-dependent coefficients is obtained. By solving this differential equation together with the Prandtl–Reuss relation and the material creep constitutive model, the history of stresses and creep strains is obtained. It is found that the minimum effective stresses are reached in a material reinforced by uniformly distributed SiC particles with the volume fraction of 20% and particle size of 50 nm. It is also found that the effective and tangential stresses increase with time at the inner surface of the composite cylinder; however, their variation at the outer surface is insignificant.     

One parameter model for creep in a whisker reinforced anisotropic rotating disc of Al–SiCw composite

Steady state creep in a rotating disc of anisotropic aluminum silicon carbide whisker composite has been studied in the present study. The creep behavior is described by Norton's power law. Stress and strain rate distributions for anisotropic discs have been calculated and compared with those obtained for isotropic disc. It is concluded that the radial strain rate which always remained compressive for the isotropic composite ($\alpha =1.0$) and anisotropic disc ($\alpha =1.3$), becomes tensile in the middle region of the disc when the anisotropy parameter $\alpha =0.7$. Also if α is reduced from 1.3 to 0.7 the variation of tensile strain rate in the tangential direction remains similar but the magnitude reduces by five orders of magnitude. The study revealed that anisotropy introduces significant change in the strain rates although its effect on the resulting stress distribution may be relatively small.     

Thermal–mechanical coupled analysis of a brake disk rotor

The main purpose of this study is to analyze the thermomechanical behavior of the dry contact between the brake disk and pads during the braking phase. The simulation strategy is based on computer code ANSYS11. The modeling of transient temperature in the disk is actually used to identify the factor of geometric design of the disk to install the ventilation system in vehicles The thermal–structural analysis is then used with coupling to determine the deformation and the Von Mises stress established in the disk, the contact pressure distribution in pads. The results are satisfactory when compared to those of the specialized literature.     

Steady-state coupling vibration analysis of shaft–disk–blade system with blade crack

Nonlinear Dynamics - Rotating shaft–disk–blade (RSDB) system is one of the most important parts of turbomachinery, such as aero-engine, gas turbine and power plant. The coupling...     

Fluid–structure interaction analysis of flexible composite marine propellers

There is an increasing interest in the marine industry to use composites to improve the hydrodynamic and structural performance of naval structures. Composite materials have high strength-to-weight and stiffness-to-weight ratios, and the fiber orientations can be exploited to tailor the structural deformation to reduce the load and stress variations by automatically adjusting the shape of the structure. For marine propellers, the bending–twisting coupling characteristics of anisotropic composites can be exploited to passively tailor the blade rake, skew, and pitch distributions to improve propeller performance. To fully explore the advantages of composite marine propellers, a coupled boundary element (BEM) and finite element (FEM) approach is presented to study the fluid–structure interaction of flexible composite propellers in subcavitating and cavitating flows. An overview of the formulation for both the fluid and structural models is presented. Experimental validation studies are shown for two composite propellers tested at the Naval Surface Warfare Center (NSWCCD). The feasibility of passive hydroelastic tailoring of composite marine propellers is discussed.     

Influence of nanoprecipitates on the creep strength and ductility of a Fe–Ni–Al alloy

Creep studies of a duplex Fe–Ni–Al intermetallic alloy, in two microstructural states, have been carried out at temperatures between 725 and 800 °C (about 0.6 T_m). In the as-cast state, the alloy contains a large volume fraction of nanoprecipitates (50–100 nm) which confer a very high creep strength with a stress exponent of 3 and an activation energy of 280 kJ/mol. The different microstructure obtained in the second state of the alloy, obtained after annealing at 1000 °C for 24 h, leads to a much lower creep strength with a higher stress exponent as well as a large value of the apparent activation energy. While volume diffusion appears to control creep in the as-cast state, both thermal and athermal processes seem to contribute to the different creep rate of material in the annealed state. The latter also exhibits a much larger ductility (12%) relative to that observed in the as-cast material (3%), due to the presence of large numbers of interfaces between the two phases present where strain incompatibilities can be accommodated.     

Stroh-like formalism for the coupled stretching–bending analysis of composite laminates

Due to the two-dimensional nature of thin plates, the lamination theory considering the composite laminates with in-plane and plate bending problems coupling each other is treated in this paper by using complex variable formulation. By following the steps of Stroh formalism for two-dimensional linear anisotropic elasticity, a displacement complex variable formalism developed by the other researchers was introduced and re-derived in a different but more Stroh-like way. In addition, a brand-new mixed formalism (mixed use of displacements and stresses as basic functions) is established to compensate the displacement formalism. In order to transfer all the related formulae and mathematical techniques of the Stroh formalism to these two formalisms, the general solutions for the basic equations of lamination theory and their associated eigenrelations have been purposely arranged in the form of Stroh formalism. Moreover, by using the presently developed mixed formalism, the explicit expressions for the fundamental matrix and eigenvectors are obtained first time for the most general composite laminates. Furthermore, letting the coupling stiffness vanish, the formalism has been reduced to the case of symmetric laminates and checked by a recently developed Stroh-like formalism for the plate bending problems. The comparison between Stroh formalism for two-dimensional problem, Stroh-like formalism for plate bending problem, displacement formalism and mixed formalism is then made at the end of this paper, and through their connection some useful relations are obtained.     

Overspeed burst of elastoviscoplastic rotating disks: Part II – Burst of a superalloy turbine disk

Burst of a turbo-engine disk in case of overspeed is investigated both from experimental and computational point of view. Two twin disks made of the same nickel based superalloy are tested. For the first one (B-disk), rotation rate in increased till burst. The second one (S-disk) is kept safe by stopping rotation just before burst, and unloading it to measure residual deformations. The material model parameters are deduced either from simple tension tests, or using an inverse method on the S-disk test. Two corresponding finite element simulations of the B-disk are then performed, using either an arc-length control method to overcome the limit point, or dynamic simulations. In both cases, the numerical burst rotation rate, associated with the loss of stability of the structure, is found to be in good agreement with the experimental result.     

Time-dependent plane Poiseuille flow of a Johnson–Segalman fluid

We numerically solve the time-dependent planar Poiseuille flow of a Johnson–Segalman fluid with added Newtonian viscosity. We consider the case where the shear stress/shear rate curve exhibits a maximum and a minimum at steady state. Beyond a critical volumetric flow rate, there exist infinite piecewise smooth solutions, in addition to the standard smooth one for the velocity. The corresponding stress components are characterized by jump discontinuities, the number of which may be more than one. Beyond a second critical volumetric flow rate, no smooth solutions exist. In agreement with linear stability analysis, the numerical calculations show that the steady-state solutions are unstable only if a part of the velocity profile corresponds to the negative-slope regime of the standard steady-state shear stress/shear rate curve. The time-dependent solutions are always bounded and converge to different stable steady states, depending on the initial perturbation. The asymptotic steady-state velocity solution obtained in start-up flow is smooth for volumetric flow rates less than the second critical value and piecewise smooth with only one kink otherwise. No selection mechanism was observed either for the final shear stress at the wall or for the location of the kink. No periodic solutions have been found for values of the dimensionless solvent viscosity as low as 0.01.     

Setting and Analysis of the Multi-configuration Time-dependent Hartree–Fock Equations

In this paper, we formulate and analyze the multi-configuration time-dependent Hartree–Fock (MCTDHF) equations for molecular systems with pairwise interaction. This set of coupled nonlinear PDEs and ODEs is an approximation of the N-particle time-dependent Schrödinger equation based on (time-dependent) linear combinations of (time-dependent) Slater determinants. The “one-electron” wave-functions satisfy nonlinear Schrödinger-type equations coupled to a linear system of ordinary differential equations for the expansion coefficients. The invertibility of the one-body density matrix (full-rank hypothesis) plays a crucial rôle in the analysis. Under the full-rank assumption a fiber bundle structure emerges and produces unitary equivalence between different useful representations of the MCTDHF approximation. For a large class of interactions (including Coulomb potential), we establish existence and uniqueness of maximal solutions to the Cauchy problem in the energy space as long as the density matrix is not singular. A sufficient condition in terms of the energy of the initial data ensuring the global-in-time invertibility is provided (first result in this direction). Regularizing the density matrix violates energy conservation. However, global well-posedness for this system in L ² is obtained with Strichartz estimates. Eventually, solutions to this regularized system are shown to converge to the original one on the time interval when the density matrix is invertible.     

Global bifurcation analysis of Rayleigh–Duffing oscillator through the composite cell coordinate system method

In this paper, a new conception of composite cell coordinate system is presented by dividing the continuous state space into the cell state space with different scales. For a dynamical system, attractors, basins of attraction, basin boundaries, saddles, and invariant manifolds can be easily obtained, and any region of the state space can be refined by this method. The global bifurcations, such as crisis and metamorphosis, of the Rayleigh?CDuffing oscillator are studied by the composite cell coordinate system method. According to the sudden changes in shapes of the chaotic attractor and the chaotic saddle, we find that three types of crises can all occur, including boundary crisis, interior crisis, and attractor emerging crisis. In addition, the basin boundary metamorphoses, such as fractal-Wada, Wada-Wada, and Wada-fractal, are analyzed through observing the shapes of basin boundaries. These results demonstrate the efficiency and validity of this method in analyzing dynamical systems.     

Hadamard instability analysis of “negative creep” in coupled chemo-thermo-mechanical systems

The coupled system of nonlinear partial differential equations for momentum, diffusion and energy is examined in terms of Hadamard instability, which in a unified way provides the conditions of both “negative creep” and “spinodal decomposition” (loss of convexity of thermodynamic functions) (Markenscoff in Quart Appl Math 59:147–151, 2001; Quart Appl Math 59:471–477, 2001) by balancing terms of different orders in the eigenvalue equation. It is shown here that instabilities of “negative creep” occur in both infinite and finite domains.     

On the viscoelastic characterization of the Jeffreys–Lomnitz law of creep

In 1958, Jeffreys (Geophys J?R Astron Soc 1:92–95) proposed a power law of creep, generalizing the logarithmic law earlier introduced by Lomnitz, to broaden the geophysical applications to fluid-like materials including igneous rocks. This generalized law, however, can be applied also to solid-like viscoelastic materials. We revisit the Jeffreys–Lomnitz law of creep by allowing its power law exponent α, usually limited to the range 0?≤?α?≤?1 to all negative values. This is consistent with the linear theory of viscoelasticity because the creep function still remains a Bernstein function, that is positive with a completely monotone derivative, with a related spectrum of retardation times. The complete range α?≤?1 yields a continuous transition from a Hooke elastic solid with no creep $\left(\alpha \,\to\, -\infty\right)$ to a Maxwell fluid with linear creep $\left(\alpha \,=\,1\right)$ passing through the Lomnitz viscoelastic body with logarithmic creep $\left(\alpha\, =0\right)$ , which separates solid-like from fluid-like behaviors. Furthermore, we numerically compute the relaxation modulus and provide the analytical expression of the spectrum of retardation times corresponding to the Jeffreys–Lomnitz creep law extended to all α?≤?1.     

Quasi-steady prediction of coupled bending–torsion flutter under rotating stall

A method is presented in this paper to predict cascade flutter under subsonic stalled flow condition in a quasi-steady manner. The ability to predict the occurrence of aeroelastic flutter is highly important from the compressor design point of view. In the present work, the well known Moore–Greitzer compression system model is used to evaluate the flow under rotating stall and the linearized aerodynamic theory of Whitehead is used to estimate the blade loading. The cascade stability is then predicted by solving the structural model, which is posed as a complex eigenvalue problem. The possibility of occurrence of flutter in both bending and torsional modes is considered and the latter is found to be the dominant one, under subsonic stalled flow, for a large range of frequency ratios examined. It is also shown that the design of compressor blades at frequency ratios close to unity may result in rapid initiation of torsional flutter in the presence of stalled flow. A frequency ratio of 0.9 is primarily emphasized for most part of the study as many interesting features are revealed and the results are physically interpreted. Roughly a pitchfork pattern of energy distribution appears to occur between bending mode and torsional mode which ensures that only one flutter mode is possible at any instant in time. A bifurcation from bending flutter to torsional flutter is shown to occur during which the frequency of the two vibrating modes appear to coalesce for a very short period of time.     

Bending vibration analysis of rotating machineries using multibody dynamics technology — development of computer program RotB

This paper examines a computer program developed to analyze the vibration of rotating machineries based on theories of vibration and multibody dynamics (MBD). Bending vibration problems of rotating machineries have generally been categorized as either linear or nonlinear. Linear problems can be formulated by standard methods and nonlinear problems can be formulated by MBD methods. In our study, nonlinear problems are treated by the use of a general-purpose computer program, RecurDyn (RD). In the program we developed, rotor bending vibration analysis (RotB) structural properties such as shafts, rotating rotary disks, unbalanced masses and foundation structures are modeled as multibody elements. Also, nonlinearities such as contact, non-symmetrical shaft effects, bearing characteristics, nonlinear restoring and damping characteristics in the bearings are taken into account. The computational results demonstrate the validity of RotB.     

Dynamic analysis of a spinning composite “deep” hyperbolic coupling

A dynamic analysis of a “deep” hyperbolic composite coupling is presented. A model is developed based on “shell/beam” assumptions, the energy approach, and the application of the extended Lagrange’s Equations. The mathematical model is solved, using the finite element method, to study the effect of the minimum diameter of a specific “deep” coupling on its dynamic characteristics. The results of the developed finite element program are compared with the corresponding 3D-ANSYS ones. The effect of the spinning speed is also investigated. Results indicate that the developed model is very accurate in predicting the axial and meridional/tangential natural frequencies. The model, however, over predicts the flexural natural frequency. The model also successfully captures the branching phenomenon of the flexural natural frequency exhibited with spinning.     

Low-energy impact of adaptive cylindrical piezoelectric–composite shells

A theoretical framework for analyzing low-energy impacts of laminated shells with active and sensory piezoelectric layers is presented, including impactor dynamics and contact law. The formulation encompasses a coupled piezoelectric shell theory mixing first order shear displacement assumptions and layerwise variation of electric potential. An exact in-plane Ritz solution for the impact of open cylindrical piezoelectric–composite shells is developed and solved numerically using an explicit time integration scheme. The active impact control problem of adaptive cylindrical shells with distributed curved piezoelectric actuators is addressed. The cases of optimized state feedback controllers and output feedback controllers using piezoelectric sensors are analyzed. Numerical results quantify the impact response of cylindrical shells of various curvatures including the signal of curved piezoelectric sensors. Additional numerical studies quantify the impact response of adaptive cylindrical panels and investigate the feasibility of actively reducing the impact force.     

A finite element analysis of the morphology of the twinned-to-detwinned interface observed in microstructure of the Cu–Al–Ni shape memory alloy

A detailed morphology of the twinned-to-detwinned interface in microstructure of 2H-martensite phase of the Cu–Al–Ni shape memory alloy is observed by optical methods (optical microscopy, white-light interferometry). Based on these observations, a finite element model of the transition layer is constructed and applied to calculate the elastic stress distribution inside the observed microstructure. The results show that the real micromorphology does not correspond to the minimum of the sum of the elastic and surface energy, and that the maxima of the stress field necessary for the existence of this morphology are comparable to the elasticity limits of the 2H-martensite.