Isotonic regression for metallic microstructure data: estimation and testing under order restrictions.

Investigating the main determinants of the mechanical performance of metals is not a simple task. Already known physically inspired qualitative relations between 2D microstructure characteristics and 3D mechanical properties can act as the starting point of the investigation. Isotonic regression allows to take into account ordering relations and leads to more efficient and accurate results when the underlying assumptions actually hold. The main goal in this paper is to test order relations in a model inspired by a materials science application. The statistical estimation procedure is described considering three different scenarios according to the knowledge of the variances: known variance ratio, completely unknown variances, and variances under order restrictions. New likelihood ratio tests are developed in the last two cases. Both parametric and non-parametric bootstrap approaches are developed for finding the distribution of the test statistics under the null hypothesis. Finally an application on the relation between geometrically necessary dislocations and number of observed microstructure precipitations is shown.

A Data-Driven Approach for Studying the Influence of Carbides on Work Hardening of Steel.

This study proposes a new approach to determine phenomenological or physical relations between microstructure features and the mechanical behavior of metals bridging advanced statistics and materials science in a study of the effect of hard precipitates on the hardening of metal alloys. Synthetic microstructures were created using multi-level Voronoi diagrams in order to control microstructure variability and then were used as samples for virtual tensile tests in a full-field crystal plasticity solver. A data-driven model based on Functional Principal Component Analysis (FPCA) was confronted with the classical Voce law for the description of uniaxial tensile curves of synthetic AISI 420 steel microstructures consisting of a ferritic matrix and increasing volume fractions of M23C6 carbides. The parameters of the two models were interpreted in terms of carbide volume fractions and texture using linear mixed-effects models.

Quantitative Study on Dissolution Behavior of Nd2O3 in Fluoride Melts.

The dissolution of rare earth oxides in molten fluorides is a critical step in the preparation of the corresponding rare earth metals by oxide-fluoride electrolysis. However, quantitatively understanding the nature of dissolution, especially in the case of molten salts, is usually difficult to be achieved by postmortem characterization. In this paper, the dissolution behavior of Nd2O3 particles in molten fluorides was studied via in situ observation with confocal scanning laser microscopy. Combining direct observation with thermodynamic analyses on the oxide dissolution, the rate-limiting step(s) and the effects of parameters like temperature, salt type, and composition on the dissolution rate are identified. This study provides a methodology to estimate the dissolution kinetics of rare earth oxides in molten fluorides during their primary and secondary processing.

Interface conditions during mixed-mode phase transformations in metals.

A fast three-dimensional phase transformation model is formulated for the transformation from ferrite to austenite in low-carbon steel. The model addresses the parent microstructure, the nucleation behaviour of the new phase and the growth of the new phase. During the growth, the interface velocity of the ferrite grains is calculated using a mixed-mode growth model. The simulated transformation kinetics is compared with experimental kinetics for an Fe-C-Mn steel for four different cooling rates. In general, the model predicts the kinetics quite well. In addition, the mixed-mode character of the transformation is shown for the different cooling rates.