5.5 Materialmodellierung
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Aero-engine turbine disks are safety-relevant components which are operated under high thermal and mechanical stress conditions. The actual part qualification and certification procedures make use of spin-tests conducted on production-similar disks. While these tests provide, on the one hand, a reliable definition of the critical conditions for real components, on the other hand they represent a relevant cost item for engine manufacturers. The aim of this work is to present two alternative burst speed assessment methods under development based on the Failure Assessment Diagram (FAD) and a global stability criterion, respectively. In the scope of the fracture mechanics assessment, the failure modes hoop-burst and rim-peeling are investigated with semicircular surface cracks modelled at the critical regions on the turbine disk. The comparison of the predicted critical rotational speed shows good agreement between the assessment methods.
Grain boundaries (GBs) are planar lattice defects that govern the properties of many types of polycrystalline materials. Hence, their structures have been investigated in great detail. However, much less is known about their chemical features, owing to the experimental difficulties to probe these features at the atomic length scale inside bulk material specimens. Atom probe tomography (APT) is a tool capable of accomplishing this task, with an ability to quantify chemical characteristics at near-atomic scale. Using APT data sets, we present here a machine-learning-based approach for the automated quantification of chemical features of GBs. We trained a convolutional neural network (CNN) using twenty thousand synthesized images of grain interiors, GBs, or triple junctions. Such a trained CNN automatically detects the locations of GBs from APT data. Those GBs are then subjected to compositional mapping and analysis, including revealing their in-plane chemical decoration patterns. We applied this approach to experimentally obtained APT data sets pertaining to three case studies, namely, Ni-P, Pt-Au, and Al-Zn-Mg-Cu alloys. In the first case, we extracted GB specific segregation features as a function of misorientation and coincidence site lattice character. Secondly, we revealed interfacial excesses and in-plane chemical features that could not have been found by standard compositional analyses. Lastly, we tracked the temporal evolution of chemical decoration from early-stage solute GB segregation in the dilute limit to interfacial phase separation, characterized by the evolution of complex composition patterns. This machine-learning-based approach provides quantitative, unbiased, and automated access to GB chemical analyses, serving as an enabling tool for new discoveries related to interface thermodynamics, kinetics, and the associated chemistry-structure-property relations.
For more than half a century, spinodal decomposition has been a key phenomenon in considering the formation of secondary phases in alloys. The most prominent aspect of the spinodal phenomenon is the lack of an energy barrier on its transformation pathway, offering an alternative to the nucleation and growth mechanism. The classical description of spinodal decomposition often neglects the influence of defects, such as grain boundaries, on the transformation because the innate ability for like-atoms to cluster is assumed to lead the process. Nevertheless, in nanocrystalline alloys, with a high population of grain boundaries with diverse characters, the structurally heterogeneous landscape can greatly influence the chemical decomposition behavior. Combining atom-probe tomography, precession electron diffraction and density-based phase-field simulations, we address how grain boundaries contribute to the temporal evolution of chemical decomposition within the miscibility gap of a Pt-Au nanocrystalline system. We found that grain boundaries can actually have their own miscibility gaps profoundly altering the spinodal decomposition in nanocrystalline alloys. A complex realm of multiple interfacial states, ranging from competitive grain boundary segregation to barrier-free low-dimensional interfacial decomposition, occurs with a dependency upon the grain boundary character.
Phase diagrams are the roadmaps for designing bulk phases. Similar to bulk, grain boundaries can possess various phases, but their phase diagrams remain largely unknown. Using a recently introduced density-based model, here we devise a strategy for computing multi-component grain boundary phase diagrams based on available bulk (CALPHAD) thermodynamic data. Fe-Mn-Cr, Fe-Mn-Ni, Fe-Mn-Co, Fe-Cr-Ni and Fe-Cr-Co alloy systems, as important ternary bases for several trending steels and high-entropy alloys, are studied. We found that despite its solute segregation enrichment, a grain boundary can have lower solubility limit than its corresponding bulk, promoting an interfacial chemical decomposition upon solute segregation. This is revealed here for the Fe-Mn-base alloy systems. The origins of this counter-intuitive feature are traced back to two effects, i.e., the magnetic ordering effect and the low cohesive energy of Mn solute element. Different aspects of interfacial phase stability and GB co-segregation in ternary alloys are investigated as well. We show that the concentration gradient energy contributions reduce segregation level but increase grain boundary solubility limit, stabilizing the GB against a chemical decomposition. Density-based grain boundary phase diagrams offer guidelines for systematic investigation of interfacial phase changes with applications to microstructure defects engineering.
Systematic microstructure design requires reliable thermodynamic descriptions and phase diagrams of each and all microstructure elements. While such descriptions are well established for most bulk phases, thermodynamic assessment of crystal defects is greatly challenged by their individualistic aspects. In this talk, we present a density-based thermodynamic concept to describe defects based on available bulk thermodynamic data. Here dealing with grain boundaries (GBs), we apply this concept to compute GB (phase) diagram. Applications to segregation engineering of GBs in bulk and nanocrystalline alloys will be presented. We further develop this model to include the effect of elastic interactions due to atom size mismatch and obtain the corresponding GB (phase) diagram for the ternary Al-Cu-Li system.
The phase-like behavior of grain boundaries (GBs), recently evidenced in several materials, is opening up new possibilities in the design of alloy microstructures. In this context, GB phase diagrams are contributing to a predictive description of GB segregation and (interfacial) phase changes. The influence of chemo-mechanical solute-GB interactions on the GB phase diagram remains elusive so far. This is particularly important for multi-component alloys where the elastic interactions among solute atoms, of various sizes and bonding energies, can prevail, governing a complex co-segregation phenomenon. Recently, we developed a density-based model for GB thermodynamics that intrinsically accounts for GB elasticity in pure elements. In this work, we incorporate the homogeneous and heterogeneous elastic energies associated with the solutes into the density-based framework. We derive the multi-component homogeneous elastic energy by generalizing the continuum misfitting sphere model and extend it for GBs. The density-based free energy functional directly uses bulk CALPHAD thermodynamic data. The model is applied to binary and ternary Al alloys. We reveal that the elastic energy can profoundly affect the GB solubility and segregation behavior, leading to Cu segregation in otherwise Cu-depleted Al GBs. Consequently, GB segregation transition, i.e., a jump in the GB segregation as a function of alloy composition, is revealed in Al-Cu and Al-Cu-Mg alloy systems with implications for subsequent GB precipitation in these alloys. CALPHAD-informed elasticity-incorporated GB phase diagrams enable addressing a broader range of GB phenomena in engineering multi-component alloys.
Along with the desire for developing novel multi-principal element alloys, also known as high-entropy alloys, the concern about their safe application is also increasingly growing. This relates to the alloys’ phase stability, in particular, the control required over unexpected phase decompositions resulting from solute segregation at grain boundaries. Yet, the mechanisms of co-segregation and grain boundary phase decomposition in multi-component alloys are rather challenging to explore. In fact, quantitative investigation of grain boundary behaviors is mostly conducted for binary and a few ternary alloys. In this work, we apply the recently introduced CALPHAD-integrated density-based formalism [RSC Advances 10 (2020) 26728-26741] for considering co-segregation phenomena in alloys with an arbitrary number of components —the term ‘co-segregation’ here refers to co-evolution and any mutual interplay among the solute atoms during their interaction with a grain boundary. Quaternary Fe-Co-Mn-Cr alloy system is studied. We present two major advances beyond previous results: First, a co-segregation-induced multi-component grain boundary spinodal decomposition is quantitatively simulated for the first time. We found that in addition to its low cohesive energy and asymmetrical mixing enthalpy due to magnetic ordering, Mn plays a leading role in triggering interfacial phase decomposition by having a relatively large, concentration-dependent atomic mobility. Second, as an alternative to grain boundary phase diagrams proposed for binary and ternary alloys, we introduce the concept of co-segregation maps for grain boundary segregation screening and design in multi-component alloys. Applying the co-segregation maps, the nonlinear Mn and Cr co-segregation are discussed. Depicted on the alloying composition and phase space, the co-segregation maps enable the required insights to guide a safer, more controlled design of high-entropy alloys.
Determination of Distribution Function used in MCS on Safety Analysis of Hydrogen Pressure Vessel
(2019)
The test data of static burst strength and load cycle strength of composite pressure vessels are often described by GAUSSian normal or WEIBULL distribution function to perform safety analyses. The goodness of assumed distribution function plays a significant role in the inferential statistics to predict the population properties by using limited test data. Often, GAUSSian and WEIBULL probability nets are empirical methods used to validate the distribution function; Anderson-Darling and Kolmogorov-Smirnov tests are the mostly favorable approaches for Goodness of Fit. However, the different approaches used to determine the parameters of distribution function lead mostly to different conclusions for safety assessments. In this study, six different methods are investigated to show the variations on the rates for accepting the composite pressure vessels according to GTR No. 13 life test procedure. The six methods are: a) Norm-Log based method, b) Least squares regression, c) Weighted least squares regression, d) A linear approach based on good linear unbiased estimators, e) Maximum likelihood estimation and f) The method of moments estimation. In addition, various approaches of ranking function are considered. In the study, Monte Carlo simulations are conducted to generate basic populations based on the distribution functions which are determined using different methods. Then the samples are extracted randomly from a population and evaluated to obtain acceptance rate. Here, the “populations” and “samples” are corresponding to the burst strength or load cycle strength of the pressure vessels made from composite material and a plastic liner (type 4) for the storage of hydrogen. To the end, the results are discussed, and the best reliable methods are proposed.
Determination of Distribution Function used in MCS on Safety Analysis of Hydrogen Pressure Vessel
(2019)
The test data of static burst strength and load cycle strength of composite pressure vessels are often described by GAUSSian normal or WEIBULL distribution function to perform safety analyses. The goodness of assumed distribution function plays a significant role in the inferential statistics to predict the population properties by using limited test data. Often, GAUSSian and WEIBULL probability nets are empirical methods used to validate the distribution function; Anderson-Darling and KolmogorovSmirnov tests are the mostly favorable approaches for Goodness of Fit. However, the different approaches used to determine the parameters of distribution function lead mostly to different conclusions for safety assessments. In this study, six different methods are investigated to show the variations on the rates for accepting the composite pressure vessels according to GTR No. 13 life test procedure. The six methods are: a) NormLog based method, b) Least squares regression, c) Weighted least squares regression, d) A linear approach based on good linear unbiased estimators, e) Maximum likelihood estimation and f) The method of moments estimation. In addition, various approaches of ranking function are considered. In the study, Monte Carlo simulations are conducted to generate basic populations based on the distribution functions which are determined using different methods. Then the samples are extracted randomly from a population and evaluated to obtain acceptance rate. Here, the “populations” and “samples” are corresponding to the burst strength or load cycle strength of the pressure vessels made from composite material and a plastic liner (type 4) for the storage of hydrogen. To the end, the results are discussed, and the best reliable methods are proposed.
Grain boundaries (GBs)’s role in determining the functional and mechanical properties of polycrystalline materials is inscribed in both their structure and chemistry. Upon solute segregation, the structure and composition of a GB can change concurrently. We study the co-evolution of GB’s structure and segregation by enhancing the density-based phase-field model to account for the in-plane structural variations in the GB. Significant mutual coupling is revealed between the GB’s chemical and structural states during Mn segregation in Fe-Mn alloys. We found that the structural degrees of freedom in a GB (the ability of the GB structure to respond to the chemical variation) amplifies Mn segregation transition, even when the GB structure stays unchanged. When the GB structure is not uniform, that is the usual case, the coupling between GB structure and segregation evolution also enables the spinodally formed low- and high-Mn phases (upon segregation transition) to co-exist within the GB region. These findings explain the stabilizing mechanism of pronounced interfacial segregation fluctuations, experimentally evidenced in Fe-Mn GBs, and give new insights on the structural sensitivity of GBs’ segregation phenomena and the mutual chemo-structural interplay.