Al-Li Alloys – The Analysis of Material Behaviour during Industrial Hot Forging

Al-Li alloys are a promising class of aerospace materials that combine light weight with high strength, comparable to those of steels. In the case of critical components, it is well known that providing the required reliability is impossible without tailoring the output microstructure of the material. This, in turn, requires a clear understanding of the logic behind microstructure formation depending on the total processing history (especially temperature and strain-rate history). However, uniaxial isothermal laboratory tests provide very limited information about the material behaviour. Real forging processes, especially involving complex geometries, sometimes develop quite complicated temperature-strain-rate paths that vary across the deformed part. A proper analysis of the microstructural transformations taking place in the material under these conditions is therefore very important. In this paper, the correlation between the loading history and microstructural transformations was analysed for AA2099 alloy using the hot forging of a disk-shaped component at selected forging temperatures and strain rates. The obtained results were compared to industrial processing maps based on uniaxial tests

Refining Finite-Time Lyapunov Exponent Ridges and the Challenges of Classifying Them

While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of a FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by a FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model. (C) 2015 AIP Publishing LLC.ONR N000141210665Center for Nonlinear Dynamic

Nonlinear stabilization via system immersion and manifold invariance: Survey and new results

Published versio

Mathematical Model of Power Supply System for Remotely Operated Underwater Vehicle with DC Power Transmission Line and Load Voltage Feedback

The paper deals with a mathematical model of the closed loop power supply system for a remotely operated underwater vehicle with a DC transmission line via a rope-cable and the load voltage feedback. The state-space method is used to develop the mathematical model. Using differential equations in the form of Cauchy alleviates significantly the mathematical description. The results for both simulation and mathematical models of the closed loop system are compared, thus, confirming the adequacy of mathematical description and prospects for further application in the design of a versatile tool for calculating and adjusting the parameters of the control system for the power supply system under study

Asymptotic of 'rigid-body' motions for nonlinear dynamics: physical insight and methodologies

The purpose of the present work is to show that an adequate basis for understanding the essentially nonlinear phenomena must also be essentially nonlinear however still simple enough to play the role of a basis. It is shown that such types of 'elementary' nonlinear models can be revealed by tracking the hidden links between analytical tools of analyses and subgroups of the rigid-body motions or, in other terms, rigid Euclidean transformation. While the subgroup of rotations is linked with linear and weakly nonlinear vibrations, the translations with reflections can be viewed as a geometrical core of the strongly nonlinear dynamics associated with the so-called vibro-impact behaviors. It is shown that the corresponding analytical approach develops through non-smooth temporal substitutions generated by the impact models.Comment: Presented at 12th DSTA Conference, December 2-5, 2013 {\L}\'od\'z, Polan

q-Breathers and the Fermi-Pasta-Ulam Problem

The Fermi-Pasta-Ulam (FPU) paradox consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number $q$. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed here $q$-Breathers (QB). They are characterized by time periodicity, exponential localization in the $q$-space of normal modes and linear stability up to a size-dependent threshold amplitude. Trajectories computed in the original FPU setting are perturbations around these exact QB solutions. The QB concept is applicable to other nonlinear lattices as well.Comment: 4 pages, 4 figure

Thermodynamic modeling of the LiF-YF3 phase diagram

A thermodynamic optimization of the LiF-YF3 binary phase diagram was performed by fitting the Gibbs energy functions to experimental data that were taken from the literature, as well as from own thermoanalytic measurements (DTA and DSC) on HF-treated samples. The Gibbs energy functions for the end member compounds were taken from the literature. Excess energy terms, which describe the effect of interaction between the two fluoride compounds in the liquid phase, were expressed by the Redlich-Kister polynomial function. The calculated phase diagram and thermodynamic properties for the unique formed compound, LiYF4, are in reasonable agreement with the experimental data.Comment: 4 pages, 3 figure