Application of statistically similar representative volume element in numerical simulations of crash box stamping

Ambroziński, M.; Bzowski, Krzysztof; Rauch, Ł.; Pietrzyk, M.

doi:10.1016/j.acme.2012.04.011

Cited by 19 publications

(8 citation statements)

References 5 publications

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“…Consequently, in the numerical simulation periodic boundary conditions can be applied. Further studies and information regarding the construction of SSRVE can be also found for the two-dimensional case in, e.g., [4,7,8]. On the construction of three-dimensional SSRVEs using Minkowski Functionals as statistical descriptors we refer to [73].…”

Section: Construction Of Ssvesmentioning

confidence: 98%

“…These SSRVEs are characterized by a lower complexity compared to the real microstructure, but they represent the overall material behavior accurately enough. The reliability of this method especially for DP steel microstructures was shown in, e.g., [4,7,8,78]. For an extension of this method to 3D see [9] and for the construction using Minkowski Functionals as statistical descriptors we refer to [73].…”

Section: Introductionmentioning

confidence: 98%

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Computational modeling of dual-phase steels based on representative three-dimensional microstructures obtained from EBSD data

et al. 2015

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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.Keywords Reconstruction of microstructure · Dual-phase steel · RVE · Microheterogeneous materials · EBSD-FIB · SSRVE · Volume expansion of martensite · Multiscale simulations

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Section: Construction Of Ssvesmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

Computational modeling of dual-phase steels based on representative three-dimensional microstructures obtained from EBSD data

et al. 2015

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“…From the computational point of view, the application of statistically similar representative volume elements, which have less complexity than the original random microstructure, could lead to a significant reduction in computation time. Basic considerations for the definition and optimization procedures based on suitable statistical measure are discussed in Povirk (1995), Ostoja-Starzewski (2006), Balzani et al (2009, , Ambrozinski et al (2012), in this context see also Swaminathan et al (2006) and Zohdi and Wriggers (2005). Details on the construction of statistically similar representative volume elements are presented in the contribution by Balzani et al in this book.…”

Section: Introductionmentioning

confidence: 99%

A numerical two-scale homogenization scheme: the FE2-method

Schröder

2014

CISM International Centre for Mechanical Sciences

109

123

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A wide class of micro-heterogeneous materials is designed to satisfy the advanced challenges of modern materials occurring in a variety of technical applications. The effective macroscopic properties of such materials are governed by the complex interaction of the individual constituents of the associated microstructure. A sufficient macroscopic phenomenological description of these materials up to a certain order of accuracy can be very complicated or even impossible. On the contrary, a whole resolution of the fine scale for the macroscopic boundary value problem by means of a classical discretization technique seems to be too elaborate. Instead of developing a macroscopic phenomenological constitutive law, it is possible to attach a representative volume element (RVE ) of the microstructure at each point of the macrostructure; this results in a two-scale modeling scheme. A discrete version of this scheme performing finite element (FE) discretizations of the boundary value problems on both scales, the macro-and the micro-scale, is denoted as the FE 2 -method or as the multilevel finite element method. The main advantage of this procedure is based on the fact that we do not have to define a macroscopic phenomenological constitutive law; this is replaced by suitable averages of stress measures and deformation tensors over the microstructure. Details concerning the definition of the macroscopic quantities in terms of their microscopic counterparts, the definition/construction of boundary conditions on the RVE as well as the consistent linearization of the macroscopic constitutive equations are discussed in this contribution. Furthermore, remarks concerning stability problems on both scales as well as their interactions are given and representative numerical examples for elasto-plastic microstructures are discussed.

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“…[6] Accounting for the two-phase structure in simulations using so called statistically similar representative volume element is presented in Refs. [7,8] Lack of validation of these models is the factor, which prevents their wider applications in the industrial practice. It is particularly important for the continuous annealing in the intercritical range of temperatures.…”

Section: Introductionmentioning

confidence: 99%

Physical and Numerical Simulation of the Continuous Annealing of DP Steel Strips

Pietrzyk

Kuziak

Radwański

et al. 2013

steel research int.

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Manufacturing of dual phase (DP) steels products is a complex process. Application of special thermal cycles during continuous annealing is one of the methods of obtaining DP microstructures. Development and validation of the numerical model for the continuous annealing of DP steels was the objective of the paper. Experimental part include dilatometric tests and physical simulations of various thermal cycles characteristic for the continuous annealing. The former were combined with the inverse analysis and were used for identification of the model. The latter supplied data regarding microstructure and properties after various annealing cycles. Numerical tests of the model confirmed its good predictive capabilities.

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Application of statistically similar representative volume element in numerical simulations of crash box stamping

Cited by 19 publications

References 5 publications

Computational modeling of dual-phase steels based on representative three-dimensional microstructures obtained from EBSD data

Computational modeling of dual-phase steels based on representative three-dimensional microstructures obtained from EBSD data

A numerical two-scale homogenization scheme: the FE2-method

Physical and Numerical Simulation of the Continuous Annealing of DP Steel Strips

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