RVE and Homogenization Modeling

Experimental and numerical study on geometrically necessary dislocations and non-homogeneous mechanical properties of the ferrite phase in dual phase steels

The microstructure of dual phase steels can be compared with a composite composed of a matrix of ferrite reinforced by small islands of martensite. This assumption has been used in several attempts to model the mechanical properties of dual phase steels. However, recent measurements show that the properties of the ferrite phase change with distance from the martensite grains. These measurements showed that the grains of the ferrite phase are harder in the vicinity of martensite grains. As a consequence of this local hardening effect, the ferrite phase has to be considered as an inhomogeneous matrix in modeling dual phase steels. This experiment inspired the idea that local hardening is caused by geometrically necessary dislocations. The idea is investigated experimentally and numerically in the present analysis, which for the first time leads to good agreement with experimental observations of the mechanical stress–strain behavior.

dual phase steel, RVE, strain gradients, GND, micromechanics, representative volume element, mechanical properties Modeling of dual phase steel using (a) two layer and (b) 10 layer phase boundary models (Acta Materialia 59 (2011) 4387)
dual phase steel, RVE, strain gradients, GND, micromechanics, representative volume element, mechanical properties, FEM Results of the simulation for the layered model. (a–e) Initial model with different numbers of interface layers; (f–j) von Mises stress for tensile loading; (k–o) equivalent plastic strain for tensile loading.(Acta Materialia 59 (2011) 4387)
dual phase steel, RVE, strain gradients, GND, micromechanics, representative volume element, mechanical properties, FEM Simulation vs. experimental results for different grain sizes.
Experimental and numerical study on geometrically necessary dislocations and non-homogeneous mechanical properties of the ferrite phase in dual phase steels
Acta Materialia 59 (2011) 4387–4394
Acta Mater 2011 dual phase steel GND sim[...]
PDF-Dokument [1.7 MB]

Polycrystal model of the mechanical behavior of a Mo–TiC30 vol.% metal–ceramic composite using a three-dimensional microstructure map obtained by dual beam focused ion beam scanning electron microscopy

The mechanical behavior of a Mo–TiC30 vol.% ceramic–metal composite was investigated over a wide temperature range (25–700 °C). High-energy X-ray tomography was used to reveal percolation of the hard titanium carbide phase through the composite. Using a polycrystal approach for a two-phase material, finite-element simulations were performed on a real three-dimensional (3-D) aggregate of the material. The 3-D microstructure, used as the starting configuration for the predictions, was obtained by serial sectioning in a dual beam focused ion beam scanning electron microscope coupled to an electron backscattered diffraction system. The 3-D aggregate consists of a
molybdenum matrix and a percolating TiC skeleton. As for most body-centered cubic (bcc) metals, the molybdenum matrix phase is characterized by a change in plasticity mechanism with temperature. We used a polycrystal model for bcc materials which was extended to two phases (TiC and Mo). The model parameters of the matrix were determined from experiments on pure molydenum. For all temperatures investigated the TiC particles were considered to be brittle. Gradual damage to the TiC particles was treated, based on an accumulative failure law that is approximated by evolution of the apparent particle elastic stiffness. The model enabled us to determine the
evolution of the local mechanical fields with deformation and temperature. We showed that a 3-D aggregate representing the actual microstructure of the composite is required to understand the local and global mechanical properties of the composite studied.

Polycrystal model of the mechanical behavior of a Mo–TiC30 vol.% metal–ceramic composite using a three-dimensional microstructure map obtained by dual beam focused ion beam scanning electron microscop
Acta Materialia 60 (2012) 1623–1632
Acta Materialia 60 (2012) 1623-Mo-polycr[...]
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Computational modeling of dual-phase steels based on representative three-dimensional microstructures obtained from EBSD data

dual phase steel, RVE, strain gradients, GND, micromechanics, representative volume element, mechanical properties, FEM The grayscale image-quality map of a DP steel microstructure and b the corresponding binary image of the phase reconstruction (black=martensite, white=ferrite) using the threshold, which is determined from c the probability density function.
dual phase steel, RVE, strain gradients, GND, micromechanics, representative volume element, mechanical properties, FEM Reconstruction of microstructure obtained from Slicescan 1: a full phase representation (red ferrite, green martensite), b ferrite phase. The dimensions are 15.9 μm × 16.45 μm × 5 μm.
dual phase steel, RVE, strain gradients, GND, micromechanics, representative volume element, mechanical properties, FEM ominal stresses P11 in MPa versus strains l/l0 in uniaxial tension (loading direction: RD) for the experimental data.

The microstructure of dual-phase steels consisting of a ferrite matrix with embedded martensite inclusions is the main contributor to the mechanical properties such as high ultimate tensile strength, high work hardening rate, and good ductility. Due to the composite structure and the wide field of applications
of this steel type, a wide interest exists in corresponding virtual computational experiments. For a reliable modeling, the microstructure should be included. For that reason, in this paper we follow a computational strategy based on the definition of a representative volume element (RVE). These RVEs will be constructed by a set of tomographic measurements and mechanical tests. In order to arrive at more efficient numerical schemes, we also construct statistically similar RVEs, which are characterized by a lower complexity compared with the real microstructure but which represent the overall material behavior accurately. In addition to the morphology of the microstructure, the austenite–martensite transformation during the steel production has a
relevant influence on the mechanical properties and is considered in this contribution. This transformation induces a volume expansion of the martensite phase. A further effect is determined in nanoindentation test, where it turns out that the hardness in the ferrite phase increases exponentially when approaching the martensitic inclusion. To capture these gradient properties in the computational model, the volumetric expansion is applied to the martensite phase, and the arising equivalent plastic strain distribution in the ferrite phase serves as basis for a locally graded modification of the ferritic yield curve. Good accordance of the model considering the gradient yield behavior in the ferrite phase is observed in the numerical simulations with experimental data.

Computational modeling of dual-phase steels based on representative three-dimensional microstructures obtained from EBSD data
Arch Appl Mech
DOI 10.1007/s00419-015-1044-1
DP steel AAM_2015.pdf
PDF-Dokument [2.4 MB]

The mechanical response of multiphase alloys is governed by the microscopic strain and stress partitioning behavior among microstructural constituents. However, due to limitations in the characterization of the partitioning that takes place at the submicron scale, microstructure optimization of such alloys is typically based on evaluating the averaged response, referring to, for example, macroscopic stress–strain curves. Here, a novel experimental–numerical methodology is introduced to strengthen the integrated understanding of the
microstructure and mechanical properties of these alloys, enabling joint analyses of deformation-induced evolution of the microstructure, and the strain and stress distribution therein, down to submicron resolution. From the experiments, deformation-induced evolution of (i) the microstructure, and (ii) the local strain distribution are concurrently captured, employing in situ secondary electron imaging and electron backscatter diffraction (EBSD) (for the former), and microscopic-digital image correlation (for the latter). From the simulations, local strain as well as stress distributions are revealed, through 2-D full-field crystal plasticity (CP) simulations conducted with an advanced spectral solver suitable for heterogeneous materials. The simulated model is designed directly from the initial EBSD measurements, and the phase properties are obtained by additional inverse CP simulations of nanoindentation experiments carried out on the original microstructure. The experiments and simulations demonstrate good correlation in the proof-of-principle study conducted here on a martensite–ferrite dual-phase steel, and deviations are discussed in terms of limitations of the techniques involved. Overall, the presented integrated computational materials engineering approach provides a vast amount of well-correlated structural and mechanical
data that enhance our understanding as well as the design capabilities of multiphase alloys.

Experimental–simulation analysis of stress and strain partitioning in multiphase alloys
Acta Materialia 81 (2014) 386–400
Acta Mater 81 (2014) 386 stress strain p[...]
PDF-Dokument [1.6 MB]

In this project we present a virtual laboratory to investigate the anisotropic yield behavior of polycrystalline materials by using high resolution crystal plasticity simulations. Employing a fast spectral method solver enables us to conduct a large number of full-field virtual experiments with different stress states to accurately identify the yield surface of the probed materials. Based on the simulated yield stress points, the parameters for many commonly used yield functions are acquired simultaneously with a nonlinear least square fitting procedure. Exemplarily, the parameters of four yield functions frequently used in sheet metal forming, namely Yld91, Yld2000-2D, Yld2004-18p, and Yld2004-27p are adjusted to accurately describe the yield behavior of an AA3014 aluminum alloy at two material states,
namely with a recrystallization texture and a cold rolling texture. The comparison to experimental results proves that the methodology presented, combining accuracy with efficiency, is a promising micromechanics-based tool for probing the mechanical anisotropy of polycrystalline metals and for identifying the parameters of advanced yield functions.

 

A virtual laboratory using high resolution crystal plasticity simulations to determine the initial yield surface for sheet metal forming operations
International Journal of Plasticity 80 (2016) 111-138
Here we present a virtual laboratory to investigate the anisotropic yield behavior of polycrystalline materials by using high resolution crystal plasticity simulations.
Intern J Plasticity 80 (2016) 111 Zhang [...]
PDF-Dokument [5.3 MB]
Yield surface fitting by DAMASK, a multiscale and multiphysics CP modeling framework. The figure shows the various conceptual ingredients with different deformation mechanisms, phases, orientations an Yield surface fitting by DAMASK, a multiscale and multiphysics CP modeling framework. The figure shows the various conceptual ingredients with different deformation mechanisms, phases, orientations and homogenization schemes that can be mapped.

 

Acta Mat. 2011, 59, p. 364