Microstructure simulation using self‐consistent clustering analysis

Proc Appl Math and Mech

Reese

2021

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In forming processes of metals, different physical phenomena are observable which may alter the material properties and behavior severely. These observations can be attributed to changes in the surface layer of the material. This research is a part of the transregional collaborative research center SFB/TRR 136 which deals with surface layer modifications in 42CrMo4 steels and aims to determine process independent correlations between material loads and material modifications. These correlations are called process signatures. The present work is concerned with investigating thermally induced solid-solid phase transformations in steels. An example of a predominantly thermal process is the induction hardening process. In this process, an initially ferritic-pearlitic structure is at first heated until reaching a temperature that lies above the temperature at which homogeneous austenite is formed. During this heating process, the steel undergoes diffusion-driven phase transformations which are heating-rate-and time-dependent. After sufficiently long incubation, a homogeneous austenitic microstructure is obtained. Then, the specimen temperature is lowered at a very high cooling rate. This invokes high-temperature rates on the microstructure and results in an austenitic-martensitic phase transformation, see e.g. [1]. Based on the Principle of the Minimum of the Dissipation Potential (PDMP) as presented in [2], the austenitic-martensitic transformation has been widely discussed in the context of shape memory alloys. We present a material model which is also able to show the ferritic-austenitic transformation. The individual phase transitions are modeled using a rate-and transformation-process-dependent formulation of the dissipation potential. The presented material model is finally tested with numerical simulations.

“…This first numerical example shows that the material model is able to show both transformations. Further investigations as well as an experimental calibration can be found in [5].…”

Section: Numerical Resultsmentioning

confidence: 99%

A variational concept and its experimental calibration for temperature‐induced rate‐dependent phase transformations in steel

Jaworek

Proc Appl Math and Mech

Reese

2021

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“…To further reduce the computational costs which are necessary to calculate the stress state and the evolution of internal variables within the microstructure, the proposed model order reduction technique for the calculations using the fast Fourier transformations is coupled with a clustered microstructure [4,6,7]. The clusters consist of grid points which show a similar material behavior and are calculated in a preprocessing step, in which the reduced set of frequencies is also used, see also [6]. Thus, the n GP grid points are allocated to the clusters.…”

mentioning

confidence: 99%

FFT‐based homogenization using a reduced set of frequencies and a clustered microstructure

Gierden

Schmidt

et al. 2021

Proc Appl Math & Mech

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To capture the material behavior of composite microstructures, Moulinec and Suquet [5] proposed a homogenization scheme making use of fast Fourier transforms (FFT) and fixed-point iterations. To reduce the computational effort of this spectral method, Kochmann et al.[3] introduced a model order reduction technique, which is based on using a fixed reduced set of frequencies for the computations in Fourier space. Within the current work, we improved the accuracy of the approach by use of a geometrically adapted set of frequencies, see [1]. Since the constitutive relations are still evaluated in real space, the technique is most beneficial for a linear material behavior. Considering nonlinear material behavior, most of the computing time is related to solving the constitutive relations. Therefore, the total speed-up is lower. To achieve a further reduction of the computational effort for a nonlinear material behavior, the earlier proposed model order reduction technique is coupled with a clustering analysis [4]. The whole microstructure is thus divided into clusters, which show a similar material behavior. Within these clusters, the micromechanical fields are assumed to be constant which leads to a significant reduction of computational costs compared to the highly resolved solution.

A Review of FE-FFT-Based Two-Scale Methods for Computational Modeling of Microstructure Evolution and Macroscopic Material Behavior

Gierden

Kochmann

Arch Computat Methods Eng

et al. 2022

The overall, macroscopic constitutive behavior of most materials of technological importance such as fiber-reinforced composites or polycrystals is very much influenced by the underlying microstructure. The latter is usually complex and heterogeneous in nature, where each phase constituent is governed by non-linear constitutive relations. In order to capture such micro-structural characteristics, numerical two-scale methods are often used. The purpose of the current work is to provide an overview of state-of-the-art finite element (FE) and FFT-based two-scale computational modeling of microstructure evolution and macroscopic material behavior. Spahn et al. (Comput Methods Appl Mech Eng 268:871–883, 2014) were the first to introduce this kind of FE-FFT-based methodology, which has emerged as an efficient and accurate tool to model complex materials across the scales in the recent years.