To model and quantify the variability in plasticity and failure of additively manufactured metals due to imperfections in their microstructure, we have developed uncertainty quantification methodology based on pseudo marginal likelihood and embedded variability techniques. We account for both the porosity resolvable in computed tomography scans of the initial material and the sub-threshold distribution of voids through a physically motivated model. Calibration of the model indicates that the sub-threshold population of defects dominates the yield and failure response. Finally, the technique also allows us to quantify the distribution of material parameters connected to microstructural variability created by the manufacturing process, and, thereby, make assessments of material quality and process control.
In this work we employ data-driven homogenization approaches to predict the particular mechanical evolution of polycrystalline aggregates with tens of individual crystals. In these oligocrystals the differences in stress response due to microstructural variation is pronounced. Shell-like structures produced by metal-based additive manufacturing and the like make the prediction of the behavior of oligocrystals technologically relevant. The predictions of traditional homogenization theories based on grain volumes are not sensitive to variations in local grain neighborhoods. Direct simulation of the local response with crystal plasticity finite element methods is more detailed, but the computations are expensive. To represent the stress-strain response of a polycrystalline sample given its initial grain texture and morphology we have designed a novel neural network that incorporates a convolution component to observe and reduce the information in the crystal texture field and a recursive component to represent the causal nature of the history information. This model exhibits accuracy on par with crystal plasticity simulations at minimal computational cost per prediction.
The third Sandia Fracture Challenge highlighted the geometric and material uncertainties introduced by modern additive manufacturing techniques. Tasked with the challenge of predicting failure of a complex additively-manufactured geometry made of 316L stainless steel, we combined a rigorous material calibration scheme with a number of statistical assessments of problem uncertainties. Specifically, we used optimization techniques to calibrate a rate-dependent and anisotropic Hill plasticity model to represent material deformation coupled with a damage model driven by void growth and nucleation. Through targeted simulation studies we assessed the influence of internal voids and surface flaws on the specimens of interest in the challenge which guided our material modeling choices. Employing the Kolmogorov–Smirnov test statistic, we developed a representative suite of simulations to account for the geometric variability of test specimens and the variability introduced by material parameter uncertainty. This approach allowed the team to successfully predict the failure mode of the experimental test population as well as the global response with a high degree of accuracy.
This corrigendum clarifies the conditions under which the proof of convergence of Theorem 1 from the original article is valid. We erroneously stated as one of the conditions for the Schwarz alternating method to converge that the energy functional be strictly convex for the solid mechanics problem. We have relaxed that assumption and changed the corresponding parts of the text. None of the results or other parts of the original article are affected.
We seek to develop a fundamental understanding of dynamic strain aging through discovery experiments to inform the development of a dislocation based micromechanical constitutive model that can tie to existing continuum level plasticity and failure analysis tools. Dynamic strain aging (DSA) occurs when dislocation motion is hindered by the repetitive interaction of solute atoms, most frequently interstitials, with dislocation cores. At temperatures where the interstitials are mobile enough, the atmospheres can repeatedly reform, lock, and release dislocations producing a characteristic serrated flow curve. This phenomenon can produce reversals in the expected mechanical behavior of materials with varying strain rate or temperature. Loss of ductility can also occur. Experiments were conducted on various forms of 304L stainless steel over a range of temperatures and strain rates, along with temporally extreme measurements to capture information from the data signals during serrated flow. The experimental approach and observations for some of the test conditions are described herein.