15. 6. 2017, 10:00

Quasibrittle Failure Probability and Scaling

 
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.
 

3. 5. 2017, 10:00

Non-standard damped oscillators

Damped oscillators of the form x'' + a(x)x' + b(x) = f(t) are classical models in mechanics and for regular enough a(.), b(.), say C1 or Lipschitz, the mathematical theory is very well understood. Non-standard analysis (NSA), on the other hand, is a rather strong and abstract logical framework. Using NSA, various mathematical theories can be embedded into larger universes with non-standard ("ideal") elements. The simplest and most famous examples are infinitely large and small numbers (which are thought by some advocates of NSA to be fatally missing from Calculus for nearly 200 years by now.)

Curiously enough, some nonstandard choices of the functions a(.) and b(.), taking infinitely large values, or with infinitely steep growth, are natural models of some "non-standard" mechanical elements: damper with Coulomb's friction, inextensible string, or more generally, collision of a moving mass with a wall.
In our talk, we will see how these situations can be modelled within the framework of NSA. We show that interesting dynamics can occur and even more, new interesting questions can be asked.
 

5. 4. 2017, 10:00

Implosive magnetocumulative generator for effective energy conversion

History of magnetohydrodynamic generators goes back to 1832 when Michael Faraday tried first experiments. Magnetocumulative generators were developed by Andrei Sakharov at the start of the 1950s, but up to these days such devices are not used for public energetics and remain in experimental, often military development. Therefore we have developed new thermal plasma source for magnetohydrodynamic or magnetocumulative generator suitable for general energetics. The thermal plasma is created from combustible mixture by implosion - spherical compression driven by convergent detonation wave. The detonation wave is initiated by a weak spark and by means of deflagration to detonation transition in detonation tube. Convergent polyhedral shape of the detonation wave is formed by large number of vents opened to hemispherical combustion chamber. Propagation of the detonation wave and its multiple branches is tracked by an array of ionization probes. Resulting high velocity plasma is ejected from a nozzle near the geometrical center of the device. The plasma is observed by capturing emitted light by hi-speed camera to determine plasma velocity. Construction of the implosion plasma source and possible variants of extraction of electrical energy from kinetic energy of the plasma by interaction of high velocity plasma with seed magnetic field will be also discussed in this presentation.
 

1. 3. 2017, 10:00

Atmospheric Boundary Layer: main characteristics and methods of the research in context of continuum mechanics

 
The bulk of the fluid on the Earth's surface can be found in the atmosphere and the oceans. Geophysical Fluid mechanics investigate it. The flow inside the area near the Earth's surface is called Atmospheric Boundary Layer in a certain analogy with the classical theory of fluid mechanics. Its properties, methods of research, taking into account their shortcomings; will be discussed in the following paragraphs.
1) Introduction: the introduction of the concept of and the reasons for its monitoring;
2) The basic characteristics (Equations of motion in continuum mechanics approximation, Flow in a rotating coordinate system, The temperature stratification, Turbulence and determinism)
3) Modelling (experimental methods, numerical methods)
4) Tasks solved in the Laboratory of Environmental Aerodynamics;
5) New problems to solve:
Verification and validation of mathematical models,
Many scales problem;
6) Conclusion: applications
 

14. 2. 2017, 10:00

Modelling of complex processes in nanopowder fabrication using thermal plasma flows

Thermal plasmas have been expected as a promising tool for mass-production of nanopowders [1] because thermal plasmas offer a distinctive thermal-fluid field involving high temperature, high chemical reactivity and variable properties. Furthermore, thermal plasmas have steep temperature gradients at their fringes where many small nanoparticles are produced rapidly from the material vapour as a result of the highly supersaturated state. However, it is still difficult to investigate the formation mechanism of nanoparticles generated in/around a thermal plasma because the process involves remarkably intricate mass transfer of phase conversions in micro-second scales. Moreover, the plasma fringe is fluid-dynamically unstable and consequently it forms a turbulent mixing field composed of multiscale eddies [2]. The growing nanoparticles are transported by the complicated convection as well as diffusion and thermophoresis. In this lecture, several modelling works to simulate those complex processes are explained.

1. 2. 2017, 10:00

Highlights of plasma spraying in the life of one researcher

Thermal spraying techniques are coating processes in which melted or heated materials are sprayed onto a surface. There is a great variety of feedstock materials that can be thermally sprayed including solid powders and suspension liquids. There is also a great variety of thermally sprayed coatings used for many different applications including for example the thermal barrier coatings in jet engines. Plasma spraying process is a member of the thermal spraying family of techniques. It uses plasma gun to generate a plasma jet that melts feedstock materials. This talk is not going to present a complete overview of plasma sprayed coatings and their applications. It will rather present a set of interesting and sometimes intriguing examples of what can achieved by plasma spraying. The examples will include nanopowders, epitaxial growth of crystals in plasma sprayed coatings, amorphous and nanocomposite coatings, spraying of suspension and more.
 

4.1. 2017, 10:00

Usage of time reversal signal processing in nondestructive diagnostics of materials and structures

Time reversal processing of acoustic and ultrasonic signals (TRA) is very effective tool for complicated problems solution in many fields like nondestructive testing and evaluation (NDT/NDE) of materials and structures. TRA enables waves focusing in time and space and therefore precise localization and reconstruction of wave sources in strongly inhomogeneous, anisotropic, and dispersive media. Properties of TRA may be used to signal processing in acoustic emission (AE), nonlinear elastic wave spectroscopy (NEWS), and also e.g. in seismology, medicine, telecommunications, etc.

TRA principles will be mentioned in the talk, and its potentials in AE source location and identification will be discussed. Outlined will be also some questions of a new approach to that inverse problems solution by using the ultrasonic signal transfer from a real body onto its laboratory and/or numerical model where they can be analyzed more easily.