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- ItemPrecipitate number density determination in microalloyed steels by complementary atom probe tomography and matrix dissolution(Dordrecht [u.a.] : Springer Science + Business Media B.V, 2022) Weber, Louis; Webel, Johannes; Mücklich, Frank; Kraus, TobiasParticle number densities are a crucial parameter in the microstructure engineering of microalloyed steels. We introduce a new method to determine nanoscale precipitate number densities of macroscopic samples that is based on the matrix dissolution technique (MDT) and combine it with atom probe tomography (APT). APT counts precipitates in microscopic samples of niobium and niobium-titanium microalloyed steels. The new method uses MDT combined with analytical ultracentrifugation (AUC) of extracted precipitates, inductively coupled plasma–optical emission spectrometry, and APT. We compare the precipitate number density ranges from APT of 137.81 to 193.56 × 1021 m−3 for the niobium steel and 104.90 to 129.62 × 1021 m−3 for the niobium-titanium steel to the values from MDT of 2.08 × 1021 m−3 and 2.48 × 1021 m−3. We find that systematic errors due to undesired particle loss during extraction and statistical uncertainties due to the small APT volumes explain the differences. The size ranges of precipitates that can be detected via APT and AUC are investigated by comparison of the obtained precipitate size distributions with transmission electron microscopy analyses of carbon extraction replicas. The methods provide overlapping resulting ranges. MDT probes very large numbers of small particles but is limited by errors due to particle etching, while APT can detect particles with diameters below 10 nm but is limited by small-number statistics. The combination of APT and MDT provides comprehensive data which allows for an improved understanding of the interrelation between thermo-mechanical controlled processing parameters, precipitate number densities, and resulting mechanical-technological material properties. Graphical abstract: [Figure not available: see fulltext.]
- ItemAnalysis of the compressible, isotropic, neo-Hookean hyperelastic model(Dordrecht [u.a.] : Springer Science + Business Media B.V, 2023) Kossa, Attila; Valentine, Megan T.; McMeeking, Robert M.The most widely-used representation of the compressible, isotropic, neo-Hookean hyperelastic model is considered in this paper. The version under investigation is that which is implemented in the commercial finite element software ABAQUS, ANSYS and COMSOL. Transverse stretch solutions are obtained for the following homogeneous deformations: uniaxial loading, equibiaxial loading in plane stress, and uniaxial loading in plane strain. The ground-state Poisson’s ratio is used to parameterize the constitutive model, and stress solutions are computed numerically for the physically permitted range of its values. Despite its broad application to a number of engineering problems, the physical limitations of the model, particularly in the small to moderate stretch regimes, are not explored. In this work, we describe and analyze results and make some critical observations, underlining the model’s advantages and limitations. For example, a snap-back feature of the transverse stretch is identified in uniaxial compression, a physically undesirable behavior unless validated by experimental data. The domain of this non-unique solution is determined in terms of the ground-state Poisson’s ratio and the state of stretch and stress. The analyses we perform are essential to enable the understanding of the characteristics of the standard, compressible, isotropic, neo-Hookean model used in ABAQUS, ANSYS and COMSOL. In addition, our results provide a framework for the parameter-fitting procedure needed to characterize this standard, compressible, isotropic neo-Hookean model in terms of experimental data.