A.F. Plankensteiner

A thermo-elasto-plastic constitutive law for inhomogeneous materials based on an incremental Mori–Tanaka approach

Abstract The behavior of a composite consisting of aligned thermo-elastic reinforcements embedded in a thermo-elasto-plastic matrix is described by an incremental Mori–Tanaka mean field approach. The matrix phase behavior is described by incremental J2 plasticity and the breakdown of isotropy of the matrix phase upon yielding is accounted for. The proposed method is implemented as a constitutive material model for a finite element code incorporating temperature dependent material data. An implicit solution strategy is introduced and special emphasis is put on the appropriate handling of the thermal expansion behavior. The applicability of the method is shown by both material characterization and a structural analysis of a hybrid component.

Micromechanical studies of the densification of porous molybdenum

Abstract The densification by compressive loading of molybdenum containing initially spherical pores at volume fractions between 2 and 10% is studied by a unit cell approach. Model geometries containing pores of two sizes in a body centered cubic arrangement are developed and uniaxial compressive loading is simulated by the Finite Element method. The relative sizes of the pores have a noticeable influence on the overall density versus strain behavior and the smaller voids in a population collapse more rapidly than the larger ones. Contact and bonding between void surfaces are predicted to influence markedly the evolution of the shape of the pores, which is in agreement with experimental results.

Modeling of layer-structured high speed steel

Abstract High Speed Steels (HSSs) produced by electro slag remelting can be viewed as metal matrix composites containing alternating layers of high and low inclusion volume fraction. To account for such specific phase arrangements a hierarchical micro-meso-macro approach for elastoplastic analyses of HSSs is presented. It combines an extended lamination theory for modeling the layered structure at the mesoscale with the Multi-particle Effective Field Method for describing the matrix-inclusion topology at the microscale. The overall elastoplastic behavior and the microfields relevant for microscale damage initiation are studied with respect to their dependence on meso- and microtopology parameters. The results are compared with predictions from a two-dimensional finite element micromechanics model, which treats the HSS as a matrix-inclusion composite with a graded microstructure.

Hierarchical models for simulating the mechanical behavior of heterogeneous materials: an approach to high speed tool steel

A hierarchical modeling strategy is presented which allows the computational simulation of the thermo-mechanical behavior of materials exhibiting different morphological characteristics at different length scales. As a typical example of such materials high speed tool steel is considered as some sort of in-situ metal matrix composite containing, at the micro level, carbidic inclusions in a martensitic steel matrix, and, at the meso level, clusters or stringers of inclusion rich areas. The macroscopic stiffness and strength behavior depends on the morphology at both levels which can be taken into account simultaneously by the proposed hierarchical concepts.

A Local Theory of Elastoplastic Deformation of Two-Phase Metal Matrix Random Structure Composites

two-phase material is considered, which consists of a homogeneous elastoplastic matrix containing a homogeneous statistically uniform random set of ellipsoidal inclusions with the same form, orientation, and mechanical properties. The multiparticle effective field method (used in this paper) in the original form assumes constant plastic strains in the matrix. This assumption is replaced by the following micromechanical model: Each inclusion consists of an elastic core and a thin coating. The mechanical properties of both the matrix and the coating are the same but with different plastic strains. Homogeneous plastic strains are assumed inside the matrix and in each of separate subdomains of the coating. A general theory of plasticity is developed for arbitrary loading based on incremental elastoplastic analysis. The consideration of inhomogeneity of plastic strains in the coating enables to obtain some principally new effects of elastoplastic deformation. ©2002 ASME

Multiscale Treatment of Inhomogeneous Materials by Finite Elements

Some aspects of the Finite Element modeling of the thermo-mechanical behavior of structures and components made of inhomogeneous materials are discussed. Special attention is focused on micromechanically based material models, which may be used both at the mesoscale (e.g. to study clusters of reinforcing particles) and at the component level, i.e. the macroscale.

Modeling of the Densification of Porous Molybdenum by a Unit Cell Approach

Unit cell models are used to study the densification by coinpressive mechanical loading of molybdenum containing initially spherical pores at volume fractions between 2% and 10%. The model geometries correspond to body centered cubic arrangements of voids in a matrix. The stress and strain fields in the cells are solved for by the Finite Element Method. The molybdenum matrix is described by an elastoplastic material model and contact between the pore surfaces is provided for. Densification up to very small residual porosities is modeled by the above continuum micromechanical approach for two levels of the overall stress triaxiality. The evolution of the shapes of the pores is found to be markedly influenced by the loading conditions and the pore geometries are predicted to differ markedly from ellipsoids at elevated degrees of densification.