Conference Agenda

Nanoporous metals, built out of complex ligament networks, can be produced with an additional level of hierarchy [S. Shi et al., Science 371, 1026-1033, 2021]. The resulting complexity of the structure makes modeling of the mechanical behaviour computationally highly expensive and time consuming. In addition, multiaxial stresses occur in the higher hierarchy ligaments. Therefore, knowledge of the multiaxial material behaviour, including the 6D yield surface, is required. For finite element (FE) modeling, we separate the hierarchical nanoporous structure into the upper and lower level of hierarchy. This allows independent adjustment of structural parameters on both hierarchy levels and therefore an efficient analysis of structure-property-relationships. Furthermore, a promising approach to significantly reduce computational cost is to use surrogate models and FE-beam models to predict the mechanical behaviour of the lower level of hierarchy.

As a first step towards such a model, we studied the elastic behaviour and yield surfaces of idealized diamond and Kelvin beam models, representation of the lower level of hierarchy, using FE simulations. The yield surfaces exhibit pronounced anisotropy, which could not be described properly by models like the Deshpande-Fleck model for isotropic solid foams. For this reason, we used data-driven and hybrid artificial neural networks, as well as data-driven support vector machines and compared them regarding their potential for the prediction of these yield surfaces. All considered methods turned out to be well suited and resulted in relative errors < 4.5. Of the considered methods, support vector machines exhibit the highest generalization and accuracy in 6D stress space and outside the range of the used training data.

Implementation of the trained SVC into Abaqus [A. Hartmaier, Materials 13, 1060, 2022] results in a promising agreement with the mechanical material response of the original FE beam model, provided that a non-associated flow rule is used. Furthermore, the evolution of the yield surface for higher plastic strains during radial loading were included and as such allow an implementation of the hardening behaviour into the UMAT.

In recent years, the application of lattice structures in additive manufacturing (AM) has gained a lot of attention due to their unique properties, such as high surface-to-volume ratio and self-supporting capabilities. They enable the production of complex parts that are difficult or even impossible to manufacture using conventional methods such as casting or machining. However, despite the advantages of 3D printing over conventional manufacturing technologies, its potential is limited by various phenomena such as warpage due to residual stresses and strains or porosity, leading to a lack of knowledge about the mechanical properties of lattice structures and hindering their commercial application.

To address this shortcoming, this study employs Finite Element Analysis (FEA) to examine the influence of residual stress and porosity defects on the mechanical properties of lattice structures, including Young's modulus, yield strength, and Specific Energy Absorption (SEA). The simulation results are validated through experimental data on the compressive behavior of lattice structures produced through Laser Powder Bed Fusion (L-PBF) with varying parameters. The sequentially coupled thermomechanical finite element model utilized in the simulation evaluates the thermal histories and residual stress evolution throughout the entire AM process. The findings of this study provide valuable insights into the mechanical properties of lattice structures, paving the way for their practical applications in diverse fields.

Apart from experimentation, computational models are helpful to aid understanding and subsequently predict the damage processes of concrete under fire, considering physical effects such as chemical dehydration or aggregate-matrix mismatch. These temperature-driven multi-physical deterioration processes are mainly influenced by the macroscopic effective thermal conduction because it predominantly governs the macroscopic temperature distribution. To quantify all degradation factors according to the macroscopic effective thermal conductivity separately, a multiscale model for concrete is proposed.

Four scales of observation characterize the concrete, namely hydrates, cement paste, mortar, and concrete. Based on Eshelby-type homogenization techniques, such as Mori-Tanka and Self-Consistent schemes, the effective thermal conductivity of different blended concretes is calculated at elevated temperatures, considering thermally induced chemical porosity increase of hydrates, initial microcrack density, aggregate degradation, and aggregate-matrix bonding via interfacial transition zones (ITZ).

A stoichiometric model based on an Arrhenius equation is used to predict the volume fraction of chemical dehydration products and porosity at the level of hydrates. The porosity increase and initial crack density lowers the thermal conductivity on the cement paste level, which is calculated using the Mori-Tanaka homogenization framework by considering randomly distributed spherical pores and three orthogonal oriented penny-shaped inclusions, respectively embedded in the matrix material. The effective thermal conductivity of mortar and concrete is determined within the same framework using an analytical expression based on the Kapitza resistance, which characterizes the ITZ morphology.

Concretes with different water-to-cement ratios, aggregate types, and cement paste conductivities are analyzed after the validation process in a sensitivity study comparing the influence on the effective thermal conductivities of concrete at elevated temperatures. Furthermore, the influence of the ITZ morphology and initial crack density is studied in detail. Based on the discussed analyses, it is demonstrated that the model predicts the thermal conductivity deterioration of different concretes or cement compositions from 20°C to 850°C with adequate accuracy.

Current research aims at the targeted introduction of residual stresses into components during their manufacturing process instead of minimizing them, for example, by subsequent heat treatments. Hot bulk forming processes offer a good opportunity to modify residual stresses in a specific way, since the interactions of thermal, mechanical and metallurgical kind can be exploited. In general, such a hot bulk forming process of a steel component can be divided into three steps: First, the component is heated to over 1000°C, which leads to a full austenitization of the material and an assumed to be stress-free initial configuration. Subsequently, forming takes place at this high temperature before the component is cooled down to room temperature. This third step results in a diffusion controlled or diffusionless phase transformation on the microscale based on the cooling rate, see [1].

In this contribution, the focus is on the last process step, i.e., cooling. Different cooling media lead to different phase transformations, which in turn lead to different residual stress distributions in the component. Motivated by the definition of residual stresses, which are characterized by the scale they act on, multi-scale finite element simulations of this cooling process are performed. The comparison of two- and three-dimensional boundary value problems shows the importance of the third dimension to represent the temperature development in the component and to predict residual stress distributions well. For this reason, a three-dimensional FE^2 calculation is presented, see [2], in which the microscale is determined by a three-dimensional representative volume element. The resulting residual stresses on macro- and microscale are evaluated and discussed.

[1] B.-A. Behrens, J. Schröder, D. Brands, K. Brunotte, H. Wester, L. Scheunemann, S. Uebing, C. Kock. Numerische Prozessauslegung zur gezielten Eigenspannungseinstellung in warmmassivumgeformten Bauteilen unter Berücksichtigung von Makro- und Mikroskala, Forschung im Ingenieurwesen (Engineering Research), 10.1007/s10010-021-00482-x, 2021.

[2] J. Schröder. A numerical two-scale homogenization scheme: the FE2-method. In J. Schröder and K. Hackl (Eds.), Plasticity and Beyond - Microstructures, Crystal-Plasticity and Phase Transitions, Volume 550 of CISM Courses and Lectures, 1–64. Springer, (2014).

A recent thrust in structural alloys research is the development of advanced Austenitic steels strengthened by nano-scale precipitates. Of the candidate precipitate phases, nanoscale dispersions of the ordered BCC (B2) NiAl phase have been demonstrated to provide significant increases in yield strength, while allowing reasonable ductility despite the intermetallic nature of this phase. The chemical complexity of the alloy involving small sizes of the particles on the order of few nm severely complicates the physically based prediction of macroscale mechanical properties induced by the characteristics of the particles and their ensembles.

Therefore, we use an integrated computational materials engineering (ICME) approach towards materials design with the aim of predicting mechanical properties such as yield strength based on an input material microstructure. Given the small size and high density of precipitates in the current alloy, we develop a coarse-grained approach for predicting a representative critical resolved shear stress (CRSS) inside local volume elements following the percolation idea for flow-stress from Kocks and Mecking [1]. Using this approach, we model realistic nano-precipitate size distributions in large scale Discrete Dislocation Dynamics (DDD) simulations with the aim of predicting macroscale mechanical properties.

This work seeks to fill the gap in modeling plastic deformation phenomena in stainless steels incorporating chemical heterogeneities on the nanoscale and resulting mechanical properties. Informed by atomistic simulations (DFT/MD), discrete microstructural data extracted from atom probe tomography, and meso-scale modeling (DDD) we present a unique coarse-graining approach in predicting material yield strength for materials with nanoprecipitates.

[1] U.F. Kocks, H. Mecking, Progress in Materials Science 48 (2003) 171–273