Program semináře Ústavu termomechaniky – 2019 – 2014 – Ústav termomechaniky AV ČR, v. v. i.

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The presented concept deals with production of entropy generated by the nonequilibrium processes in consequence of the mass and energy transfer. Often used concept of endoreversible thermodynamics is based on non-realistic conjecture that the entire entropy production is realized at the system boundary. In this contribution, the open system in the thermodynamically non-equilibrium state is assumed. Production of entropy is generated due to the non-equilibrium processes accompanied by the energy conversion. The non-equilibrium steady state is maintained by a negative entropy flux. The stability conditions of the state with the minimum of entropy production are used to replace the endoreversibility concept.

This theory is applied to three different open non-equilibrium systems.

i) Efficiency of thermal machines and chemical reactors.
Hydrogen fuel cell with polymer electrolyte membrane are studied in details. The transport coefficients for reactants inlet, i.e. hydrogen and air, and for the products outlet, i.e. water, are connected with the actual electric efficiency. The calculated efficiency qualitatively and quantitatively corresponds to the experimentally obtained values. The further research shall focus on the relation of the parameters characterizing the membrane and transport of reactants and products to the power output.

ii) Energetic limitations of population growth.
Entropy production is characterized by general form of chemical reaction based on the mass action law. This law is usable for description of dynamics of population biology, e.g. cells, species. Moreover, this law can be even used to study dynamics of ecological systems. The reproduction process is spontaneous process with increase of entropy. The entropy increase is compensated by the negative entropy flux from the Sun. From the thermodynamic point of view, the sex reproduction is more advantageous as the cellular division because of it is reached by the lower Gibbs free enthalpy. This is probably the reason why sex reproduction is evolutionarily more advantageous.

iii) Dynamics of ecological system with migration.
Influence of reproduction and migration dynamics is evident on example of two competitive ecological systems (in general two auto catalytic reactions) of type predator and prey. The migration decreases the frequency of dynamical state of system. Due the migration this dynamical state can change to the stationary state, when time period is high enough. In principle, it is a diffusion reaction system in which a stationary spatial change of concentrations can occur. An example may be the presence of colored stripes on the body of some animals, such as cats, some fish, hornets, and the like.

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The traditional view for the martensitic transformation in In-xat%Tl alloys, for 15.5 ≤ x ≤ 30.5 was via a double shear such as: (101)[10-1]; (011)[01-1], on the basis of optical microscopy observations and measurements of the (c11 - c12)/2 elastic constant. These early results, together with a calculation of the phonon dispersion relations based on a model pseudopotential and the measured elastic constants as input parameters, suggested that the transformation was driven by the softening of low-ζ [ζζ0][ζ-ζ0] phonons, which provided the motivation for a measurement of the phonon dispersion relations using neutron, inelastic scattering. This now historical background for the transformation in In-Tl alloys will be reviewed.
However, the suggested low-ζ [ζζ0][ζ-ζ0] phonon softening has never been observed experimentally, despite phonon measurements to as low as ζ = 0.02 rlu on the [ζζ0][ζ-ζ0] branch. An alternative model for the formation of coherent nuclei and growth along conjugate {111} planes was once proposed by Geisler. This model is consistent with some electron diffuse scattering data as well as yielding identical x-ray pole figure results as those for the double-shear mechanism. Appropriate nuclei could be generated by <111><11-2> atomic displacements.
To test such an idea, we have measured the [ζζζ]T phonon branch for a good quality In-Tl crystal in a recent experiment using the cold triple-axis instrument, SIKA, at the Australian OPAL Research Reactor. The initial results have shown that the zone-boundary, [ζζζ]T phonon softens with decreasing temperature, which may provide the dynamical behaviour consistent with the Geisler model for the transformation. Further experiments are planned to investigate this softening and the consequential microstructural behaviour.

Associate Professor Trevor Finlayson has been an Honorary Principal Fellow at the University of Melbourne since February, 2007, following an academic career at Monash University where he had been engaged to introduce and teach Materials Science as an undergraduate discipline during the early 1970s. His research has covered a range of projects in the field of condensed matter physics/materials science, including aspects of superconductivity, magnetism, ferro- and piezo-electricity, phase transformations and the direct measurement of stresses in materials using diffraction techniques. His current projects involve studies on martensitic alloys and magnesia-partially-stabilized zirconia, using neutron scattering.

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The present talk will focus on rotating disk dynamics by introducing a novel signal-processing method geared towards capturing the dynamics of such systems. The method exploits multiple sensors and is thus capable of handling spatially complex transient dynamics. Rotating disks identification methods rely on special features of rotating elements, e.g. cyclic-symmetry, gyroscopic effects, directional whirling and circumferentially traveling deformations, all have a physical meaning and are exploited in the proposed approach.
The ‘eyes’ of ‘Smart Rotating Machines’ are the sensors and the accompanied, real-time signal processing methods play the role of a ‘brain’ in the assessment of measured data. Indeed ‘smart’ also means combining advanced sensing capabilities with an electronic brain which is aware of the underlying physics laws to which the model obeys. At the moment, it seems that the pendulum leans heavily towards numerical modeling. Finite Element models are the basis for analysis and design, while testing and measurements provide only limited verification means for some of the model parameters due to poor deployment and simplistic signal processing procedures. The new method narrows the gap between models and experiment and it illustrates what can be gained when they are added.
The presentation will highlight the advantages of model-based signal processing over past and presently used methods and will try to point to a path leading from older methods and techniques towards present, state-of-the-art methods and further into the future where smart machines will have ‘eyes’ and ‘brains’.
Specifically, the presentation will describe spatial, temporal and directional decomposition of rotating machine vibrations during rapid rotational accelerations. Real time signal processing methods that exploit Hilbert transform based decompositions; directional order-tracking and time-frequency maps will be demonstrated via simulations and experiments. The spatial and temporal decomposition method enables a Smart-Machine to assess true stress and strain on parts rotating relative to an array of sensors and thus help to enhance safety.
One additional topic will be briefly shown if time allows: active detection of imbalance for high-speed modes, using slow rotation data.

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The yield surface of a material is the boundary of the elastic region where every stress point inside the region result from the elastic response of the material. The experimental evidence shows that the yield surface changes position, size, shape, and orientation during the material undergoing the plastic loading which results in the permanent deformation. Based on the experimental observation, the modelling of the yield surface evolution is a key point to completely simulate the plastic behavior of the material. Most experiments of yield surface detection were conducted in the two-dimensional space (axial-torsional or bi-axial). Due to the complete stress space is six dimensional, detecting the yield surface in the space whose dimension is more than two can collect more detail of the yield surface evolution. For the experiment of yield surface detection, the determination of yield point underpins the accuracy of the geometry of the yield surface. Nowadays, test machines used for the experiments of yield surface detection are usually servo-controlled hydraulic system, hence the scatter of data should be taking into account in the determination of yield point. To this end, an automated yield stress determination based on the Weibull distribution is introduced. After conducting the experiment in the axial-torsional-hoop stress space, yield points are obtained according to the yield-stress determination and designed probing paths. To further capture the global information from these yield points and observe the evolution of yield surface during different pre-loading paths, a convex-closed-cubic polynomial, which is capable of description of the yield surface evolution, including translation, expansion/ contraction, rotation, affine deformation, and distortion in the three dimensional space, is proposed and the corresponding three-stage estimation for parameters of the polynomial is developed. This polynomial enable us to observe the yield surface evolution from the three dimensional point of view and it can also be a candidate of potential yield functions. Furthermore, the computation of elastoplastic models needs more attention to the special mathematical structure of the model containing ordinary differential equations, algebraic equations, and inequalities. Exploring the underlying structure of elastoplastic models shows part of them possesses internal symmetry that is the pseudo-sphere of real pseudo-Euclidean space Rp,q on which the proper orthochronous pseudo-orthogonal group SOo(p,q), a sub group of the Lie group, leaves acts. Based on the internal symmetry, a return-free integration is developed and it keeps the computed stress point on the yield surface automatically and exactly without any extra enforcement during the plastic deformation.

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The size effect on structural strength and its probability distribution function (pdf) is a complex problem for quasibrittle materials because their failure behavior transits from quasi-plastic at small sizes to brittle at large sizes. These are heterogeneous materials with brittle constituents in which the size of inhomogeneity, or representative volume element (RVE), is not negligible compared to the structure size. Aside from concrete, the archetypical example, they include fiber composites, coarse-grained ceramics, rocks, sea ice, snow slabs, wood, bone, foam, stiff soil, dry snow,ccarton, etc., and on the micro- or nano-scale, all brittle materials become quasibritle. Since the break probability is known exactly only for interatomic bonds (being equal to frequency), Kramer’s rule of transition rate theory is applied to nano-crack jumps. Based on proving the rules of multiscale transition of tail probabilities of break to material scale, the probability distribution function (pdf) of strength of one macro-scale representative volume element (RVE) is shown to have a Weibullian tail, calibrated to reach to probability circa 0.001, the rest being Gaussian. On the structure scale, only Type 1 failure is considered, i.e., the structure fails as soon as the first RVE fails. Hence the weakest-link model applies on the structure scale. But, crucially, the number of links is finite, because of non-negligible RVE. For increasing structure size, the Weibullian portion gradually spreads into the Gaussian core. Only in the infinite size limit the distribution becomes purely Weibull, but, importantly, with a zero threshold. Based on an atomistic derivation of the power law for subcritical macro-crack growth, a similar Gauss-Weibull transition is shown to apply to structure lifetime. The theory is then extended to the size dependence of Paris law and Basquin law for fatigue fracture, to statistics of fatigue lifetime, and to residual strength after a period of preload. The theory is shown to match the existing experimental results on the monotonic strength, residual strength after preload, static and fatigue crack growth rates, and static and fatigue lifetimes, including their distributions and size effects on the distributions. There are three essential consequences: 1) The safety factors must depend on structure size and shape; 2) To predict the pdf of strength, the size effect tests of mean strength suffice; 3) To predict the static and fatigue lifetimes, it suffices to add tests of initial subcritical crack growth rate. An interesting mathematical analogy predicting the lifetime of nano-scale high-k dielectrics is also pointed out. Finally, a new “fishnet” statistics for strength of biomimetic nacre-like lamellar structures, modelled as a square fishnet pulled diagonally, is presented. This simple model differs from the weakest-link model as well as the fiber bundle model. The pdf is found again to transit from Gaussian to Weibullian, but in a different way.

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