Effects of Unidirection/Bidirection Torsional Thermomechanical Processes on Grain Boundary Characteristics and Plasticity of Pure Nickel

The “torsion and annealing” grain boundary modification of pure nickel wires with different diameters was carried out in this paper. The effects of torsional cycles as well as unidirectional/bidirectional torsion methods on grain boundary characteristic distribution and plasticity were investigated. The fraction of special boundaries, grain boundary characteristic distributions and grain orientations of samples with different torsion parameters were detected by electron backscatter diffraction. Hardness measurement was conducted to characterize the plasticity. Then, the relationship between micro grain boundary characteristics and macro plasticity was explored. It was found that the special boundaries, especially Σ3 boundaries, are increased after torsion and annealing and effectively broke the random boundary network. The bidirectional torsion with small torsional circulation unit was the most conducive way to improve the fraction of special boundaries. The experiments also showed that there was a good linear correlation between the fraction of special boundaries and hardness. The plasticization mechanism was that plenty of grains with Σ3 boundaries, [001] orientations and small Taylor factor were generated in the thermomechanical processes. Meanwhile, the special boundaries broke the random boundary network. Therefore, the material was able to achieve greater plastic deformation. Moreover, the mechanism of torsion and annealing on the plasticity of pure nickel was illustrated, which provides theoretical guidance for the pre-plasticization of nickel workpieces.

Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM

Elliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loading. While this domain mapping method is quite efficient for theory and practice, since only a single domain discretisation is needed, it also requires the knowledge of the domain mapping. However, in certain applications, the random domain is only described by its random boundary, while the quantity of interest is defined on a fixed, deterministic subdomain. In this setting, it thus becomes necessary to compute a random domain mapping on the whole domain, such that the domain mapping is the identity on the fixed subdomain and maps the boundary of the chosen fixed, nominal domain on to the random boundary. To overcome the necessity of computing such a mapping, we therefore couple the finite element method on the fixed subdomain with the boundary element method on the random boundary. We verify on one hand the regularity of the solution with respect to the random domain mapping required for many multilevel quadrature methods, such as the multilevel quasi-Monte Carlo quadrature using Halton points, the multilevel sparse anisotropic Gauss–Legendre and Clenshaw–Curtis quadratures and multilevel interlaced polynomial lattice rules. On the other hand, we derive the coupling formulation and show by numerical results that the approach is feasible.

Probabilistic constrained optimization on flow networks

Uncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and a dynamic flow model with uncertain boundary data on networks. We introduce two different ways how to compute the probability for random boundary data to be feasible, discussing their advantages and disadvantages. In this context, feasible means, that the flow corresponding to the random boundary data meets some box constraints at the network junctions. The first method is the spheric radial decomposition and the second method is a kernel density estimation. In both settings, we consider certain optimization problems and we compute derivatives of the probabilistic constraint using the kernel density estimator. Moreover, we derive necessary optimality conditions for an approximated problem for the stationary and the dynamic case. Throughout the paper, we use numerical examples to illustrate our results by comparing them with a classical Monte Carlo approach to compute the desired probability.

Thermal characterization of building walls under random boundary conditions

This work aims to improve the knowledge on dynamic thermophysical characterization of building envelopes by comparing three numerical methods applied on an experimental wall made of masonry brick. The thermal conductivity λ and the thermal capacity ρcp are determined by performing a data fitting optimization between the experimental measurements of the heat flux and the heat flux resulting from these numerical models. The experimental device consists of a thermal box with a controlled ambiance through a radiator linked to a thermostatic bath and placed inside the thermal box, on the opposite side facing the wall. Three different methods were examined: The Heat Transfer Matrix analytical method (HTM) using the heat transfer matrix, the Finite Element Method (FEM) using COMSOL Multiphysics® software, and the Building Simulation Model method (BSM) using TRNSYS® Type 56 coupled with Genopt® optimization tool. The reproducibility of the methods was also validated through two other datasets (one random and one harmonic). The obtained results were satisfactory for both λ and for ρcp and for the three studied methods with deviations less than 5% between the results of the different methods. The data logging duration for random boundary conditions was found to be around five days while in harmonic boundary conditions two days were sufficient for the solution to converge.