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In this contribution, selected results from [1–3] are presented in a compact and simplified way. In addition, the variety of fiber orientation tensors is used to determine a maximum deviation of the direction-dependent Young's modulus, which can arise if only second-order directional information is included in a specific meanfield homogenization. Focusing on the special case of planar fiber distributions, the variety of fiber orientation tensors identified in [1] is considered as a design space. This design space is completely explored for the orientation-averaging homogenization following [4], fixed material parameters and fixed fiber volume content. The possible directional dependence of the resulting effective stiffnesses is graphically presented using polar plots of the direction-dependent Young's modulus. These polar plots are arranged on two-dimensional slices within the parameter space of planar fourth-order fiber orientation tensors. This gives a complete representation of the influence of the orientation tensor on the anisotropic stiffness tensor. Consequences of closure approximations, i.e., restriction to second-order directional information, are demonstrated and motivate measurement of fourth-order fiber orientation tensors.

Thermoplastic polyamides are used in many industrial areas due to their potential in lightweight applications. Polyamides serve as matrix material in fiber reinforced thermoplastics, for instance. The mechanical behavior of polyamides is characterized by pronounced viscoelastic effects that are strongly affected by environmental conditions like temperature or humidity. In this work, linear thermoviscoelastic behavior of polyamide 6 is considered. Viscoelastic behavior is modeled by the generalized Maxwell model while extended time-temperature superposition is used to model temperature dependency. A temperature-frequency sweep conducted by dynamic mechanical analysis serves as input for the model. By horizontal and vertical shifting, master curves of the loss factor, storage modulus, and loss modulus are obtained. Based on this, limitations of time-temperature superposition and linear thermoviscoelastic modeling are discussed. Furthermore, it is shown that the horizontal shifts can be well approximated by the Williams-Landel-Ferry equation for temperatures above and below the glass transition temperature.

The prediction of local field statistics from effective properties is an open problem in the field of micromechanics. Partial information on the local field statistics is accessible from homogenization assumptions. In particular, exact phase-wise second moments of stresses can be calculated analytically from the effective strain energy density. In recent years, full-field calculations have become efficient enough to sample large ensembles of microstructures in the plastic regime (e.g. Gehrig et. al [4]). In the present work, the maximum entropy method known from statistical thermodynamics is used to estimate first and second moments of local stresses from known eigenstrain distributions. The simple and refined formulations of the maximum entropy method proposed by Kreher and Pompe [9] are considered. While the simple method yields satisfactory results for a large amount of material classes (cf. Krause and Böhlke [7]), we prove that it does not respect the linearity of the eigenstrain problem. We further show that neither method corresponds to the exact second moments of stresses known from the effective strain energy density. By incorporating additional information, we find an improved maximum entropy method. As an example, we analyze stress fluctuations in polycristalline titanium.For the exact analytical solution and the maximum entropy methods, we use the singular approximation and the Hashin-Shtrikman bounds. For comparison, we numerically approximate full-field statistics using an FFT approach. In all methods, the stress fluctuations caused by the anisotropy of the single crystal strongly influence the elastic-plastic transition.

This document includes the complete list and descriptions of the Participant Projects (PPs) and related Infrastructure-Use-Cases (IUCs) the consortium NFDI-MatWerk referred to within its proposal. For the NFDI-MatWerk proposal, refer to https://doi.org/10.5281/zenodo.5082837. Methodically, the consortium proceeded by identifying so-called Participant Projects within its research community. PPs represent the heterogeneity of this research domain in all its facets. They usually face diverse but recurring challenges in the context of research data management from a user or scientist's perspective. Such challenges, resulting from the PPs, were accumulated to shape the so-called Infrastructure-Use-Cases (IUCs). For this end, the consortium identified recurring technological user needs from the PPs and isolated them into individually necessary functionalities of the aimed research data management infrastructure for NFDI-MatWerk. The consortium plans to reiterate this process as the project starts, to manage a continuous integration and feedback-loop from a strict user-centered perspective and thus ensure relevance of the developed solutions. For more information on the consortium NFDI-MatWerk refer to www.nfdi-matwerk.de. For questions about this method, refer to the contacts listed under www.nfdi-matwerk.de/kontakt/.

Multi-phase materials often times consist of constituents with high contrasts in phase-specific mechanical properties. Here, even after homogeneous plastic deformation phase-specific residual stresses develop that may affect the components behaviour in service. For numerical simulation of phase-specific residual stresses, knowledge of the particular phase-specific strain hardening behaviour is essential. In this study, the strain hardening of ferrite and austenite in cold rolled duplex stainless steel of type X2CrNiN23-4 is investigated. By means of X-ray diffraction, the phase-specific load partitioning and residual stress evolution are analysed for uniaxial load application in three directions within the sheets plane, taking into account the sheet metals phase specific anisotropy. In order to assess the necessity for experimental determination of anisotropic phase specific behaviour, the strain hardening parameters, derived from only one loading direction, are implemented in a mean-field approach for prediction of phase-specific stresses. A simplified simulation approach is applied that only considers macroscopic plastic anisotropy and results are compared to experimental findings. For all investigated loading directions, it was observed that austenite is the high-strength phase. This load partitioning behaviour was confirmed by the evolution of phase-specific residual stresses as a result of uniaxial elasto-plastic loading. With the simplified and fast numerical approach, satisfying results for prediction of anisotropic phase-specific (residual) stresses are obtained.

For material modeling of microstructured media, an accurate characterization of the underlying microstructure is indispensable. Mathematically speaking, the overall goal of microstructure characterization is to find simple functionals which describe the geometric shape as well as the composition of the microstructures under consideration, and enable distinguishing microstructures with distinct effective material behavior. For this purpose, we propose using Minkowski tensors, in general, and the quadratic normal tensor, in particular, and introduce a computational algorithm applicable to voxel-based microstructure representations. Rooted in the mathematical field of integral geometry, Minkowski tensors associate a tensor to rather general geometric shapes, which make them suitable for a wide range of microstructured material classes. Furthermore, they satisfy additivity and continuity properties, which makes them suitable and robust for large-scale applications. We present a modular algorithm for computing the quadratic normal tensor of digital microstructures. We demonstrate multigrid convergence for selected numerical examples and apply our approach to a variety of microstructures. Strikingly, the presented algorithm remains unaffected by inaccurate computation of the interface area. The quadratic normal tensor may be used for engineering purposes, such as mean-field homogenization or as target value for generating synthetic microstructures.

A micro‐mechanically motivated phenomenological yield function, for polycrystalline cubic metals is presented. In the suggested yield function microstructure is taken into account by the crystallographic orientation distribution function in terms of tensorial Fourier coefficients. The yield function is presented in a polynomial form in powers of the stress state. Known group‐theoretic results are used to identify isotropic and anisotropic parts in the yield function, whereby anisotropic parts are characterized by tensorial Fourier coefficients. The form of the presented yield function is inspired by the classic, phenomenological von Mises ‐ Hill yield function first published in 1913. For a specific choice of material parameters, both functions coincide, thus a micro‐mechanically motivated generalization of the von Mises ‐ Hill yield function is presented. For the given yield function, two dimensional experimental results are sufficient, to identify a three dimensional anisotropic yield behavior. The work concludes with a treatment of the isotropic special case, i.e. a tension‐compression split in yield behavior as well as parameter ranges for convexity and shapes of the yield surface.

Effective mechanical properties of fiber-reinforced composites strongly depend on the microstructure, including the fibers' orientation. Studying this dependency, we identify the variety of fiber orientation tensors up to fourth-order using irreducible tensors and material symmetry. The case of planar fiber orientation tensors, relevant for sheet molding compound, is presented completely. Consequences for the reconstruction of fiber distributions and mean field homogenization are presented.

The aim of this work is to model and experimentally characterize the anisotropic material behavior of SMC composites on the macroscale with consideration of the microstructure. Temperature-dependent thermoelastic behavior and failure behavior are modeled and the corresponding material properties are determined experimentally. Additionally, experimental biaxial damage investigations are performed. A parameter identification merges modeling and experiments and validates the models.

A physically-based dislocation theory of plasticity is derived within an extended continuum mechanical context. Thermodynamically consistent flow rules at the grain boundaries are derived. With an analytical solution of a three-phase periodic laminate, dislocation pile-up at grain boundaries and dislocation transmission through the grain boundaries are investigated. For the finite element implementations, numerically efficient approaches are introduced based on accumulated field variables.

Wir präsentieren einen Algorithmus zur schnellen Erzeugung von SMC Mikrostrukturen hoher Güte, durch Verwendung einer exakten Schließung und eines quasi-zufälligen Samplings. Darüber hinaus stellen wir ein modulares Framework zur Modellierung anisotroper Schädigung vor. Unser Konzept der Extraktionstensoren und Schädigungsfunktionen ermöglicht die Beschreibung komplexer Vorgänge. Darüber hinaus schlagen wir einen ganzheitlichen Multiskalenansatz zur Bestimmung anisotroper Versagenskriterien vor.

Martensite forms under rapid cooling of austenitic grains accompanied by a change of the crystal lattice. Large deformations are induced which lead to plastic dislocations. In this work a transformation model based on the sharp interface theory, set in a finite strain context is developed. Crystal plasticity effects, the kinetic of the singular surface as well as a simple model of the inheritance from austenite dislocations into martensite are accounted for.

An overview of different methods for the derivation of extended continuum models is given. A gradient plasticity theory is established in the context of small deformations and single slip by considering the invariance of an extended energy balance with respect to Euclidean transformations, where the plastic slip is considered as an additional degree of freedom. Thermodynamically consistent flow rules at the grain boundary are derived. The theory is applied to a two- and a three-phase laminate.