Dear Zhe Sun ,

The RVE is just a representation of the microstructure of a (usually multiphase) material. There are several types of analyses that can be performed using such kind of microstructures most of them regarding the material characterisation. Are you referring as limitation to the RVE creation method or to the analyses that can be performed with an RVE?

Thanks a lot for your reply.

As my research object is high strength structural steel plate, please allow me to take it as an example. As a paper "Wudtke Idna et al. A hierarchical multi-scale approach to mechanical characterization of heat affected zone in welded connections [J]. Computational Materials Science, 2015, 96: 396-402." concludes under Fig.11: "Note that the yielding behavior of

the material measured in the experiment cannot be modeled with

the current numerical approach." I found it probably exists a limitation for RVE method when applied for structural steel which have obvious yield behavior as you said "the limitation to the analyses that can be performed with an RVE".

Besides, most papers I read about DP steel using RVE method show really good agreement in stress-strain behaviour, like "Zhou Jiming, et al. Realistic microstructural RVE-based simulations of stress–strain behavior of a dual-phase steel having high martensite volume fraction [J]. Materials Science and Engineering: A, 2015, 630: 107-115." In this case, I am so curious about why there is such a difference.

In this study, a novel approach for generating Representative Volume Elements (RVEs) is introduced. In contrast to common generators, the new RVE generator is based on discrete methods to reconstruct synthetic microstructures, using simple methods and a modular structure. The plain and uncomplicated structure of the generator makes the extension with new features quite simple. It is discussed why certain features are essential for microstructural simulations. The discrete methods are implemented into a python tool. A Random Sequential Addition (RSA)-Algorithm for discrete volumes is developed and the tessellation is realized with a discrete tessellation function. The results show that the generator can successfully reconstruct realistic microstructures with elongated grains and martensite bands from given input data sets.

Numerical simulation of dual-phase steel based on real and

virtual three-dimensional microstructures

The complexity of the geometry under consideration and the large size of the volume to be investigated are common problems in simulations based on real microstructures [3,35]. Tomographies in the size range of the representative volume element (RVE) of dual-phase steel often consist of several million to several hundred million voxels. In this context, the RVE describes the section of the microstructure that is just large enough to contain all relevant information about themicrostructure [36–38]. Although the size of the FE mesh can still be

reduced by sophisticated, unstructured geometry conforming meshing, the possible data reduction is limited due to the complexity of the structures. Many works therefore consider only 2D microstructures [38–41]. In addition to the reduced numerical effort of the 2D calculation, the experimental effort also decreases in 2D, since only a single SEM image or micrograph is sufficient to determine the microstructure. However, the real material behaviour is not fully mapped in simulations when 2D microstructures are used, see [19,41–43]. The

main reason for this is the lack of information about the mechanically relevant material areas in the direct vicinity above or below the selected 2D section and about the 3D connectivity. As another approach, simulations based on virtual microstructures were carried out already very early in order to avoid the experimental and numerical difficulties of real microstructures described above. The work of Karlsson et al. [44–46] is to be especially emphasized here.The aim is to generate smaller, more easily meshable microstructures and to dispense with the complex, experimental determination of the real microstructure. There

are many different ways to create virtual microstructures, e. g. tessellations [47–52] or physically motivated simulations of structural development [53–55]. In the presented work, geometric entities are used in the sense of a statistically similar RVE [3,56–58]. For a detailed overview of various other methods for generating

virtual microstructures, also for other material classes, a comprehensive review article by Bargmann et al. [59] is referred to. Despite all the advantages of virtual structures, simulations based on real microstructures are still an indispensable reference for the simulation based on virtual microstructures. In addition to the generation of smaller and less computationally intensive RVEs, a major advantage of virtual microstructures is that they can be used for the prospective investigation of the properties of new microstructures. For that reason, the virtual

microstructure is not fitted to the real microstructure’s geometry but to a set of new geometric parameters.

In this work, the entire process chain of the numerical investigation of dual-phase steel is presented, from the experimental determination of the microstructure properties to the implementation of the numerical models in the open source C++ program library deal.II [60,61] and the simulation of the mechanical properties on the basis of the 3D microstructure. As one of the most important experiments for the characterization of materials, the uniaxial tensile test serves as a reference in the simulation. As sample necking and damage are not taken into

account, only the deformation range below10%strain is observed. In addition to the simulation based on the real microstructure of the steel, a process for the generation of virtual microstructures is also developed, enabling

both the creation of virtual microstructures for known real structures and the evaluation of new microstructures before they are produced. The paper is organized as follows: in Sect. 2 the investigated material as well as

the experimental methods for the determination of the real microstructure and the single-phase properties are presented. Sect. 3 covers the numerical methods, i. e.the FE implementation of the mechanical simulation and the structure generation process. In Sects. 4 and 5 the results for the simulations on real and virtual microstructures are shown and discussed. Section 6 concludes the work.