Papers by Keyword: Representative Volume Element

Abstract: Macroscopic damage models can describe the toughness behavior and formability of metals in terms of limit strains. However, it requires time-, cost-, and material-intensive calibration. In this work, a simulation framework is proposed to derive macroscopic damage model parameters and related properties directly from the microstructure. For this purpose, statistically Representative Volume Elements of the investigated DP1000 steel were generated utilizing the Python framework DRAGen. This was based on quantitative characterization of EBSD measurements of the present microstructure. Mechanical properties were assigned to the geometrical microstructure model by calibrating a phenomenological Crystal Plasticity model for distinct phases. Martensite cracking was identified as the predominant damage mechanism. This behavior on the microscale was represented by an isotropic brittle damage model in DAMASK, using a fracture mechanical literature value as the critical energy release rate parameter. The presented modeling approach enables stress state-dependent prediction of macroscopic damage properties out of the present microstructure.

Abstract: Understanding the relationships between microstructure and (mechanical) properties is inevitable for the design of modern structural metallic materials. A crucial property for most high-strength steels is ductile damage tolerance, since ductile damage can accumulate during cold forming, which either leads to failure in the forming process or subsequently affects the performance. Structure-property relations are often investigated using numerical methods, e.g. crystal plasticity (CP) modeling with representative volume elements (RVE). In a previous study, CP-simulations on 3D-RVE were coupled with surrogate modeling techniques performing a variance-based sensitivity analysis. This analysis enables quantitative descriptions of the relationships between microstructure features with the damage tolerance, quantified by individual indicators for individual damage mechanisms. To investigate the effect of the material model and the corresponding phase properties, 500 sRVE simulations were carried out with different CPparameter sets and the damage tolerance is investigated. All sets stem from the same DP800 but were calibrated with different approaches. Surrogate models were trained on the simulative database to calculate Sobol Indices (SI), which are a measure of how strong damage tolerance is affected by a particular microstructure feature. The SI are compared for the individual material models and damage indicators. The structure-property quantification is heavily influenced by the different material models, resulting in different values for the SI and a different order for the individual microstructure features. The main factor for the pronounced differences is the differently evolving mechanical phase contrast between ferrite and martensite.

Abstract: Lotus-type porous materials (LTPMs) are considered as a new category of engineering materials. They are porous materials characterized by long, straight, unidirectional cylindrical pores, and are obtained via unidirectional solidification from a melt under hydrogen and argon atmospheres. The anisotropic pore morphology of lotus-type materials results in the anisotropy of their mechanical and physical properties. This study aims at investigating the effect of cross-sectional pore shapes on the effective Young's modulus (EYM) of LTPMs. The representative volume element-based finite element homogenization method was used to compute the effective bulk and shear moduli. Subsequently, the EYM was deduced from the effective bulk and shear moduli. The numerical results of the circular pores were validated by comparing them with experimental results. Because the results indicated that the EYM is extremely sensitive to the variation in the pore shapes, a formula for estimating the EYM of LTPMs by considering the pore shapes was developed and validated.

Abstract: The aim of this work is the computation of effective elastic properties of 3D 3-phase random heterogeneous coated materials. For that, a new expression of the integral range for 3-phase random coated heterogeneous materials is used. The computation is achieved using a representative microstructure with non-overlapping inclusions. Numerical simulations is used under periodic boundary conditions (PBC) and kinematic uniform boundary conditions (KUBC) prescribed over Representative Volume Element (RVE). The obtained effective elastic properties are compared with different analytical models as Hashin and Shtrikman bounds and the n+1 phase model. Using the statistical methods, a new extension of the integral range for 3-phase coated materials is proposed.

Abstract: Asymmetric rolling with different work roll circumferential speeds is a process that can be used for improvement of mechanical properties of the processed metals and alloys. Development of the model, which allow to calculate the stress-strain state occurring in the microstructure of the ferritic-pearlitic steels during asymmetric rolling, was the main objective of this paper. Macro level models do not take into account the complicated behavior of the ferritic-pearlitic microstructure in the micro scale. Therefore, development of modelling methods, which allow predicting the properties distribution in the metal volume with the behavioral features of the microstructure under the influence of the deformation, was needed. Representative Volume Element (RVE), representing ferritic-pearlitic steel microstructure, was developed. Simulations of the asymmetric rolling process were performed and local deformation of each structural component was predicted. Selected results, as well as discussion of the effect of microstructure on obtained stress and strain distributions, are presented in the paper. Results of multiscale simulation analysis of the deformation characteristics, presented in this study, can be used for optimization of the asymmetric rolling process.

Abstract: The article presents the results of numerical and experimental studies of stress-strain curves of 1D-reinforced polymer composite materials based on hollow porous fibers and epoxy matrix. The two-scale nature of the composite under research was taken into account. A surrogate easily parameterized model based on Bezier curves was developed and used to approximate the stress-strain curve of ductile material. The calculations were performed using reversible homogenization and finite element methods, which were implemented in computational subsystem of DCS GCD. Representative volume elements of the investigated materials were created using the geometry generating subsystem of DCS GCD. Test samples were made using three-axis milling machine and compression tests were carried out. Computational results of effective stress-strain curves determination were obtained and compared with experiments.

Abstract: The paper presents a mathematical model of a finite element for modeling imperfect interface conditions for two contacting surfaces. The element is used in the numerical implementation of the Asymptotic Averaging Method (AAM) for the determination of effective elastic properties of composite materials under investigation. Numerical experiments are carried out to calculate the elastic properties taking into account the adhesion layer using a displacements field jump condition at the phase boundary. Results are compared with adhesion modeling using an additional bulk phase.

Abstract: One of the most important features of a material to know before using it is the maximum limit of the load at which it fails. This paper presents a micromechanical strength theory to estimate the tensile strength of the unidirectional fiber reinforced composite. The fibers used can be considered transversely isotropic and elastic till failure, but the matrix material is considered to be Elastic-plastic. The mathematical formulation used is the Variational-Asymptotic Method (VAM), which is used to construct the asymptotically-correct a reduced-dimensional model that is free of a priori assumption regarding the kinematics. The 3-D strain generated in each constituent material is explicitly expressed in 1-D strains and initial curvatures. The advantage of using VAM is that the stress state correlation of constituent materials is taken care of while applying warping constraints. Prandtl-Reuss plasticity theory has been implemented for the plastic region constitutive relationship. The other advantage of this work is that the load-bearing capacity of the composite beyond the elastic region has been considered. Good agreement has been found between experimental data and VAM analysis.

Abstract: The mechanical properties of KD-II type silicon carbide fiber braided three-dimensional four-directional (3D4d) SiC_f/SiC woven composites fabricated by PIP method were studied in this paper. The computed tomography (CT) technology was used to observe the cross section shape and orientation of the fiber bundles inside woven composite materials, and digital image correlation (DIC) method was used to measure deformation, during the tensile tests of the composites. Theoretical and numerical methods were adopted to predict mechanical properties of the 3D4d SiC_f/SiC woven composites, and effectiveness of different methods was discussed based on the comparison of results obtained from the experiments and prediction model.

Abstract: Transverse compaction and in-plane shear deformartion are the dominative deformation mode for woven preform during forming process. A full finite element model of the 2.5D woven composites has been established by the computed tomography (CT) in this paper. Based on the energy method, the effective orthotropic/anisotropic stiffness coefficients C_ij are calculated by performing a finite element analysis (FEA) of this full cell model. Using this model, the effects of the compaction and shear deformation of the 2.5D woven preform on the composites stiffness are investigated in detail. Compared the results of the static tensile tests, the rationality of the model and the method is verified.