Swantje Bargmann

Modeling of polycrystals with gradient crystal plasticity: A comparison of strategies

This paper treats the computational modeling of size dependence in microstructure models of metals. Different gradient crystal plasticity strategies are analyzed and compared. For the numerical implementation, a dual-mixed finite element formulation which is suitable for parallelization is suggested. The paper ends with a representative numerical example for polycrystals.

Models of Solvent Penetration in Glassy Polymers With an Emphasis on Case II Diffusion. A Comparative Review

The objective of this review is to provide an overview and a classification of the key literature on models of non-Fickian case II type diffusion. Several extensive review articles concerning non-Fickian diffusion exist in the literature; our objective is not to reproduce these worthy contributions. Rather, we focus on a limited number of, seemingly disparate, notable models and attempt to unify them using the language of thermodynamics and continuum mechanics. This attempted unification of selected models arising from various modeling communities serves to elucidate the key strengths and potential weaknesses of the models.

Damage modeling of small-scale experiments on dental enamel with hierarchical microstructure

Dental enamel is a highly anisotropic and heterogeneous material, which exhibits an optimal reliability with respect to the various loads occurring over years. In this work, enamels microstructure of parallel aligned rods of mineral fibers is modeled and mechanical properties are evaluated in terms of strength and toughness with the help of a multiscale modeling method. The established model is validated by comparing it with the stress-strain curves identified by microcantilever beam experiments extracted from these rods. Moreover, in order to gain further insight in the damage-tolerant behavior of enamel, the size of crystallites below which the structure becomes insensitive to flaws is studied by a microstructural finite element model. The assumption regarding the fiber strength is verified by a numerical study leading to accordance of fiber size and flaw tolerance size, and the debonding strength is estimated by optimizing the failure behavior of the microstructure on the hierarchical level above the individual fibers. Based on these well-grounded properties, the material behavior is predicted well by homogenization of a representative unit cell including damage, taking imperfections (like microcracks in the present case) into account.

Computational modelling of submicron-sized metallic glasses

The present contribution is concerned with the modelling and computation of stable shear localization process in submicron-sized metallic glasses. To this end, a non-local thermodynamically consistent, continuum mechanical, constitutive model is developed. In our previous work, we formulated the model in the small strain framework. In current work, this model is extended to finite strains. The numerical implementation is carried out with the help of the finite element method. Numerical examples are presented – illustrating the general model behaviour which is correlated to experimental observations. It is shown that the proposed finite deformation model is well suitable to predict the stable shear localization process in submicron-sized metallic glasses and its size effect. The model confirms that with decreasing sample size the shear localization process starts at a later deformation state. Additionally, the finite deformation model is able to predict the failure process in submicron-sized metallic glasses as well as the delay of it with decreasing sample size qualitatively correct.

On energy and entropy influxes in the Green–Naghdi Type III theory of heat conduction

The energy-influx/entropy-influx relation in the Green–Naghdi Type III theory of heat conduction is examined within a thermodynamical framework à la Müller–Liu, where that relation is not specified a priori irrespectively of the constitutive class under attention. It is shown that the classical assumption, i.e. that the entropy influx and the energy influx are proportional via the absolute temperature, holds true if heat conduction is, in a sense that is made precise, isotropic. In addition, it is proved that influx proportionality cannot be postulated in general, because a counterexample can be given in the case of transversely isotropic conduction.

Experimental characterization of microstructure development during loading path changes in bcc sheet steels

Interstitial free sheet steels show transient work hardening behavior, i.e., the Bauschinger effect and cross hardening, after changes in the loading path. This behavior affects sheet forming processes and the properties of the final part. The transient work hardening behavior is attributed to changes in the dislocation structure. In this work, the morphology of the dislocation microstructure is investigated for uniaxial and plane strain tension, monotonic and forward to reverse shear, and plane strain tension to shear. Characteristic features such as the thickness of cell walls and the shape of cells are used to distinguish microstructural patterns corresponding to different loading paths. The influence of the crystallographic texture on the dislocation structure is analyzed. Digital image processing is used to create a “library” of schematic representations of the dislocation microstructure. The dislocation microstructures corresponding to uniaxial tension, plane strain tension, monotonic shear, forward to reverse shear, and plane strain tension to shear can be distinguished from each other based on the thickness of cell walls and the shape of cells. A statistical analysis of the wall thickness distribution shows that the wall thickness decreases with increasing deformation and that there are differences between simple shear and uniaxial tension. A change in loading path leads to changes in the dislocation structure. The knowledge of the specific features of the dislocation structure corresponding to a loading path may be used for two purposes: (i) the analysis of the homogeneity of deformation in a test sample and (ii) the analysis of a formed part.

Automatic three-dimensional geometry and mesh generation of periodic representative volume elements for matrix-inclusion composites

Generation of randomized periodic representative volume elements (RVE) is presented.We introduce a novel method of discretizing the geometry with a periodic mesh topology.The meshing approach is efficient, robust and results in a high quality mesh.RVEs with high number of anisotropic inclusions are achievable.Our new meshing method results in low number of elements still maintaining a high quality mesh. This paper introduces an efficient method to automatically generate and mesh a periodic three-dimensional microstructure for matrix-inclusion composites. Such models are of major importance in the field of computational micromechanics for homogenization purposes utilizing unit cell models. The main focus of this contribution is on the creation of cubic representative volume elements (RVEs) featuring a periodic geometry and a periodic mesh topology suitable for the application of periodic boundary conditions in the framework of finite element simulations. Our method systematically combines various meshing tools in an extremely efficient and robust algorithm. The RVE generation itself follows a straightforward random sequential absorption approach resulting in a randomized periodic microstructure. Special emphasis is placed on the discretization procedure to maintain a high quality mesh with as few elements as possible, thus, manageable for computer simulations applicable to high volume concentrations, high number of inclusions and complex inclusion geometries. Examples elucidate the ability of the proposed approach to efficiently generate large RVEs with a high number of anisotropic inclusions incorporating extreme aspect ratios but still maintaining a high quality mesh and a low number of elements.

Continuum damage modeling and simulation of hierarchical dental enamel

Dental enamel exhibits high fracture toughness and stiffness due to a complex hierarchical and graded microstructure, optimally organized from nano- to macro-scale. In this study, a 3D representative volume element (RVE) model is adopted to study the deformation and damage behavior of the fibrous microstructure. A continuum damage mechanics model coupled to hyperelasticity is developed for modeling the initiation and evolution of damage in the mineral fibers as well as protein matrix. Moreover, debonding of the interface between mineral fiber and protein is captured by employing a cohesive zone model. The dependence of the failure mechanism on the aspect ratio of the mineral fibers is investigated. In addition, the effect of the interface strength on the damage behavior is studied with respect to geometric features of enamel. Further, the effect of an initial flaw on the overall mechanical properties is analyzed to understand the superior damage tolerance of dental enamel. The simulation results are validated by comparison to experimental data from micro-cantilever beam testing at two hierarchical levels. The transition of the failure mechanism at different hierarchical levels is also well reproduced in the simulations.

A Thermomechanically Consistent Constitutive Theory for Modeling Micro-Void and/or Micro-Crack Driven Failure in Metals at Finite Strains

Within a continuum approximation, we present a thermomechanical finite strain plasticity model which incorporates the blended effects of micro-heterogeneities in the form of micro-cracks and micro-voids. The former accounts for cleavage-type of damage without any volume change whereas the latter is a consequence of plastic void growth. Limiting ourselves to isotropy, for cleavage damage a scalar damage variable d ∈ [0, 1] is incorporated. Its conjugate variable, the elastic energy release rate, and evolution law follow the formal steps of thermodynamics of internal variables requiring postulation of an appropriate damage dissipation potential. The growth of void volume fraction f is incorporated using a Gurson-type porous plastic potential postulated at the effective stress space following continuum damage mechanics principles. Since the growth of micro-voids is driven by dislocation motion around voids the dissipative effects corresponding to the void growth are encapsulated in the plastic flow. Thus, the void volume fraction is used as a dependent variable using the conservation of mass. The predictive capability of the model is tested through uniaxial tensile tests at various temperatures Θ ∈ [−125∘C, 125∘C]. It is shown, via fracture energy plots, that temperature driven ductile-brittle transition in fracture mode is well captured. With an observed ductile-brittle transition temperature around − 50∘C, at lower temperatures fracture is brittle dominated by d whereas at higher temperatures it is ductile dominated by f.

Geometrically Nonlinear Continuum Thermomechanics Coupled to Diffusion: A Framework for Case II Diffusion

This chapter introduces a geometrically nonlinear, continuum thermomechanical framework for case II diffusion: a type of non-Fickian diffusion characterized by the wave-like propagation of a low-molecular weight solvent in a polymeric solid. The key objective of this contribution is to derive the coupled system of governing equations describing case II diffusion from fundamental balance principles. A general form for the Helmholtz energy is proposed and the resulting constitutive laws are derived from logical, thermodynamically consistent argumentation. The chapter concludes by comparing the model developed here to various others in the literature. The approach adopted to derive the governing equations is not specific to case II diffusion, rather it encompasses a wide range of applications wherein heat conduction, species diffusion and finite inelastic effects are coupled. The presentation is thus applicable to the generality of models for non-Fickian diffusion: an area of increasing research interest.