Mikael Nygårds

Three-dimensional periodic Voronoi grain models and micromechanical FE-simulations of a two-phase steel

Abstract A three-dimensional model is proposed for modeling of microstructures. The model is based on the finite element method with periodic boundary conditions. The Voronoi algorithm is used to generate the geometrical model, which has a periodic grain structure that follows the original boundaries of the Voronoi cells. As an application, the model is used to model a two-phase ferrite/pearlite steel. It is shown that periodic cells with only five grains generate representative stress–strain curves.

Number of grains necessary to homogenize elastic materials with cubic symmetry

A numerical model based on the finite element method is presented for modeling of microstructures. The model uses a discrete version of the Voronoi algorithm to partition the mesh into grains. The model is utilized to study representativity of grain structures. The number of grains needed in a representative volume element is evaluated for materials with cubic symmetry and random texture. It is shown that the number of grains needed depend on the anisotropy, and a simple expression that relates anisotropy and the number of grains is suggested.

A study of the surface deformation behaviour at grain boundaries in an ultra-low-carbon steel

Tensile specimens of ultra-low-carbon ferritic steel with two different grain sizes were studied by atomic force microscopy (AFM) and electron backscatter diffraction (EBSD) after different plastic strains up to 10%. Different parameters, such as the change in surface roughness and the change in misorientation with strain, were evaluated. There was good agreement between the AFM and EBSD results. Both the surface roughness and the misorientation measurements on the surface showed a linear increase with the overall strain, an obvious consequence being that both AFM and EBSD are suitable for characterising the surface deformation behaviour. The results are discussed with respect to the difference in grain size in the samples and the implication on the strain hardening behaviour.

Micromechanical modeling of ferritic/pearlitic steels

A two-dimensional micromechanical model based on the Voronoi algorithm is presented to model two-phase ferritic/pearlitic steels. Special care is taken to generate periodic grain structures as well as periodic finite element meshes. The model is evaluated by generalized plane strain finite element calculations, periodic representative cells are generated with the desired volume fraction pearlite. Loading by an arbitrary combination of average stresses or strains is possible by application of periodic boundary conditions. Uniaxial tension tests are performed on pure ferrite and pearlite specimens, as well as on materials containing 25 and 58% pearlite. Modeling of the two-phase materials was performed by using the stress-strain curves of the pure phases, in the description of the plastic properties. Comparisons between generated data and experiments at a loading strain of 2% show good agreement. Moreover, local stresses and strains are studied within the different unit cells. In addition, the model is used to investigate the plastic behavior under biaxial loading. It is shown that Hills yield criterion gives a good fit to the numerical data.

Anisotropy and texture in thin copper films—an elasto-plastic analysis

The role of elastic anisotropy on the stress inhomogeneity and effective behavior of columnar grained textured Cu thin films have been analyzed within a continuum framework. The analysis is based on a three-dimensional model of a film/substrate system. The film exhibits a fiber texture with (111), (001) and randomly oriented grains. Mainly two load cases have been considered. Biaxial loading of a film deposited on a silicon substrate and tensile loading of a film deposited on a polyimide substrate. The stress distributions in the (111) and (001) grains were generally found to be very different when subjected to biaxial loading and quite similar when subjected to tensile loading. When plastic behavior is invoked, a structural hardening effect is observed. The plastic behavior differs significantly between biaxial and tensile cyclic loading respectively. A new orientation dependent hardening law is proposed. This hardening law causes the plastic hardening behavior to be orientation dependent and scale with elastic anisotropy. The newly proposed hardening law is demonstrated on a film with small grain aspect ratio.

Incorporating Strain Gradients in Micromechanical Modeling of Polycrystalline Aluminum

It is a well known fact that polycrystals exhibit grain size dependence. Traditional continuum models can however not catch this effect. Lately, there has however been an increased interest in the development of non-local theories that can account for the size effect. In this work a non-local crystal plasticity theory is implemented, where slip gradients enter in the hardening modulus. A new proposal for the incorporation of strain gradients in the hardening modulus is presented. The non-local theory is used in a three-dimensional finite element model to model Aluminum (Al). A representative volume element (RVE) containing a random grain structure is used to model the material by the finite element method (FEM). Thus, the mesh is partitioned into a periodic grain structure by a discrete version of the Voronoi algorithm. The model is used to simulate uniaxial tension, by using periodic boundary conditions to constrain the model. The non-local theory contains an internal length scale l that needs to be defined in the model. The internal length scale is determined from comparisons to reported experimental data on Al. The coupling between the microstructure and the numerical model is discussed, and the proposed hardening relation is justified. It is shown that a model containing 30 grains predicts the grain size effect well. But cells containing 15, 45 and 60 grains are also investigated. It is shown that the size effect can be predicted by changing the size of the periodic cell, and also by changing the number of grains in the cell. E-mail: nygards@kth.se, Phone: +46 8 790 9490, Fax: +46 8 411 2418

Stiffness heterogeneity of multiply paperboard examined with VFM

Mechanical heterogeneity of a multiply paperboard was characterized in uniaxial tension using DIC and VFM. The specimen was divided into three subregions based on axial strain magnitude. VFM analysis showed that the subregions had stiffnesses and Poisson’s ratio’s that varied in a monotonically decreasing fashion, but with the stiffness differences between subregions increasing with applied tensile stress. An Equilibrium Gap analysis showed improved local equilibrium when comparing a homogeneous analysis with the subregion analysis. Although only a single specimen was examined, results suggest that high stiffness regions provide only marginal improvement of mechanical behavior. The analysis also showed that even though the subregions themselves were non-contiguous, their mechanical behavior was similar.

Role of colonies of large elliptical grains in high-strength steel

In this communication, we report an investigation of the mechanical properties of a two-phase steel under the assumption of a periodic microstructure consisting of ellipsoidal grains in a matrix of small grains. It is believed that the mixed microstructure creates stress concentrations that could be the source of delamination, when loaded in the rolling direction. Of particular interest were local stress concentrations in the thickness direction originating from axial loading.

Micromechanical Modeling of Two-Phase Steels

A two-dimensional micromechanical model based on the finite element method is presented to model two-phase ferritic/pearlitic steels, by aid of generalised plane strain elements. A periodic represe ...