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Metal alloys frequently contain distributions of second-phase particles that deleteriously affect the material behavior by acting as sites for void nucleation. These distributions are often extremely complex and processing can induce high levels of anisotropy. The particle length-scale precludes high-fidelity microstructure modeling in macroscale simulations, so computational homogenization methods are often employed. These, however, involve simplifying assumptions to make the problem tractable and many rely on periodic microstructures. Here we propose a methodology to bridge the gap between realistic microstructures composed of anisotropic, spatially varying second-phase void morphologies and idealized periodic microstructures with roughly equivalent mechanical responses. We create a high-throughput, parametric study to investigate 96 unique bridging methods. We apply our proposed solution to a rolled AZ31B magnesium alloy, for which we have a rich dataset of microstructure morphology and mechanical behavior. Our methodology converts aµ-CT scan of the realistic microstructure to idealized periodic unit cell microstructures that are specific to the loading orientation. We recreate the unit cells for each parameter set in a commercial finite element software, subject them to macroscopic uniaxial loading conditions, and compare our results to the datasets for the various loading orientations. We find that certain combinations of our parameters capture the overall stress–strain response, including anisotropy effects, with some degree of success. The effect of different parameter options are explored in detail and we find that excluding certain particle populations from the analysis can give improved results. 

We present details on a new measurement of the muon magnetic anomaly, $a_{\mu }=(g_{\mu }-2)/2$. The result is based on positive muon data taken at Fermilab’s Muon Campus during the 2019 and 2020 accelerator runs. The measurement uses $3.1\mathrm{GeV}/c$polarized muons stored in a 7.1-m-radius storage ring with a 1.45 T uniform magnetic field. The value of $a_{\mu }$is determined from the measured difference between the muon spin precession frequency and its cyclotron frequency. This difference is normalized to the strength of the magnetic field, measured using nuclear magnetic resonance. The ratio is then corrected for small contributions from beam motion, beam dispersion, and transient magnetic fields. We measure $a_{\mu }=116592057\left(25\right)\times {10}^{-11}$(0.21 ppm). This is the world’s most precise measurement of this quantity and represents a factor of 2.2 improvement over our previous result based on the 2018 dataset. In combination, the two datasets yield $a_{\mu }\left(\mathrm{FNAL}\right)=116592055\left(24\right)\times {10}^{-11}$(0.20 ppm). Combining this with the measurements from Brookhaven National Laboratory for both positive and negative muons, the new world average is $a_{\mu }\left(\exp \right)=116592059\left(22\right)\times {10}^{-11}$(0.19 ppm). Published by the American Physical Society2024 

We present a new measurement of the positive muon magnetic anomaly, 𝑎𝜇≡(𝑔𝜇−2)/2, from the Fermilab Muon 𝑔−2 Experiment using data collected in 2019 and 2020. We have analyzed more than 4 times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, 𝜔𝑝, and of the anomalous precession frequency corrected for beam dynamics effects, 𝜔𝑎. From the ratio 𝜔𝑎/𝜔𝑝, together with precisely determined external parameters, we determine 𝑎𝜇=116 592 057⁢(25)×10−11 (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain 𝑎𝜇⁡(FNAL)=116 592 055⁢(24)×10−11 (0.20 ppm). The new experimental world average is 𝑎𝜇⁡(exp)=116 592 059⁢(22)×10−11 (0.19 ppm), which represents a factor of 2 improvement in precision.