Simulation of brittle crack growth in functionally graded materials

We consider a thermodynamic consistent framework for crack propagation by applying a dissipation inequality to a time dependent migrating control volume. The direction of crack growth is obtained in terms of material forces as a result of the principle of maximum dissipation. In the numerical implementation a staggered algorithm – deformation update for fixed geometry followed by geometry update for fixed deformation – is employed within each time increment. The corresponding mesh is generated by combining Delaunay triangulation with local mesh refinement. A numerical example with inhomogeneous material properties illustrates the capability of the resulting algorithm. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A thermodynamics framework and numerical aspects for transformation-induced plasticity at large strains

In this work, we present a macroscopic material model for simulation transformation-induced plasticity, which is an important phenomenon in metal forming processes. The model is formulated within a thermodynamic framework at large strains. In order to account for both, phase transformation and plasticity, yield functions are related to these effects. Then, applying the concept of maximum dissipation evolution equations are obtained for the inelastic strains, the transformation strains, a hardening variable and the volume fraction of martensite. Furthermore the numerical implementation of the constitutive equations into a finite element program is described. In a numerical example we investigate the austenite-to-martensite phase transformation in a shaft subjected to thermo-mechanical loading in a hybrid-forming process.     

Delocalization-localization transition due to anharmonicity

Analytical and numerical calculations for a reduced Fermi-Pasta-Ulam chain demonstrate that energy localization does not require more than one conserved quantity. Clear evidence for the existence of a sharp delocalization-localization transition at a critical amplitude A_c is given. Approaching A_c from above and below, diverging time scales occur. Above A_c, the energy packet converges towards a discrete breather. Nevertheless, ballistic energy transportation is present, demonstrating that its existence does not necessarily imply delocalization.     

A thermodynamic framework for coupled multiphase field and diffusion models for lower bainite transformation

The lower bainite transformation is characterized by a displacive transformation from austenite to bainitic ferrite and a subsequent separation of carbon within the new supersaturated phase. At accumulations of carbon carbides precipitate. To model this complex process a framework considering phase changes and carbon diffusion is required. In this work we present a thermodynamic framework based on the theory of microforce balances considering multiphase Ginzburg-Landau equations coupled with Cahn-Hilliard diffusion. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two accuracy improvements on nonuniform transformation field analysis for plasticity coupled to softening

A reduced order homogenization scheme for the case of plasticity coupled with softening effects is proposed. This is based on a straightforward extension of the so-called nonuniform transformation field analysis (NTFA, [2]). Two related new methods, denoted as uneven NTFA and adaptive NTFA accounting for accuracy improvements, are also presented, which are based on the ideas of parameter identification and adaptive modeling, respectively. A complementary numerical study is given. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A macroscopic consitutive model on induced anisotropy for polymers with weighting functions

The alignment of polymer chains is a well known microstructural evolution effect due to straining of polymers. This has a drastic influence on the macroscopic properties of the initially isotropic material, such as a pronounced strength in the loading direction of stretched films. Experiments on strain induced anisotropy at room temperature are analyzed by optical measurements. For modeling the effect of strain induced anisotropy a macroscopic constitutive model is presented. As a key idea, weighting functions are introduced to represent a strain-softening/hardening-effect to account for induced anisotropy. These functions represent the ratio between the total strain rate and a structural tensor. In this way, material parameters are used as a sum of weighted direction related quantities. In the finite element examples we simulate the cold-forming of amorphous thermoplastic films below the glass transition temperature subjected to different re-loading directions. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Macroscopic and mesoscopic modeling based on the concept of generalized stresses for cutting simulation

Based on the concept of generalized stresses proposed by GURTIN [2] and FOREST et al. [1] macro- and meso-scopic modelling are presented. For the macroscopic modelling we develop a multi-mechanism model for strain rate and temperature dependent asymmetric plastic material behavior accompanied by phase transformation with consideration of the trip-strain. Furthermore, we extend the multi-mechanism model with the gradient of phase fraction, which is considered as an extra degree of freedom. For mesoscopic modelling a phase field model is implemented for describing phase transformations. For the scenario of a cutting process we have a martensite-austenite-martensite transformation. A generalized principle of virtual power is postulated involving generalized stresses and used to derive the constitutive equations for both approaches. Furthermore, parameters of the multi-mechanism model related to visco-plasticity with SD-effect and the trip-strain are identified for the material DIN 100Cr6. In the examples a cutting simulation for testing the multi-mechanism model and a phase-transformation simulation are shown. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermo-mechanical homogenisation – application to HVOF thermal-sprayed WC-Co coatings

Hard material coatings are widely employed as wear protection for highly engrossed surfaces. For example, coatings consisting of tungsten carbide (WC) and cobalt (Co) are used for sheet metal forming tools. A relatively cost-efficient coating technique is the high velocity oxygen fuel (HVOF) thermal spraying process which, as a trade-off, induces a large amount of energy into the heterogeneous coating and the substrate. Hence, this leads to a complex transient, thermomechanically coupled problem. In order to predict the residual stresses during the quenching procedure, a two scale finite element framework is established wherein the scale bridging is performed by application of two different homogenisation approaches. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Local Tensor Valuations

The local Minkowski tensors are valuations on the space of convex bodies in Euclidean space with values in a space of tensor measures. They generalize at the same time the intrinsic volumes, the curvature measures and the isometry covariant Minkowski tensors that were introduced by McMullen and characterized by Alesker. In analogy to the characterization theorems of Hadwiger and Alesker, we give here a complete classification of all locally defined tensor measures on convex bodies that share with the local Minkowski tensors the basic geometric properties of isometry covariance and weak continuity.     

Artefacts in XAD-8 NOM fractionation

The XAD-8 resin has been widely used during the last decades to characterize and isolate natural organic matter (NOM) in water. The present work focuses on the performance and limitations of the XAD-8 method. A number of different NOM samples (mostly RO-isolates) have been XAD-8 fractionated with the purpose to study (1) the impact of DOC concentration of the samples on the quality of the resulting fractions and (2) the stability of NOM in the different fractions during the XAD-8 fractionation procedure and storage. Focus is placed on the method's independence of NOM concentration, the stability (quantity and quality) of the hydrophilic fraction during the fractionation, the relationship between hydrophilic and hydrophobic fractions, and the stability of the obtained fractions after the fractionation is completed.

The main conclusions are that the division into hydrophobic and hydrophilic fractions are not independent of the NOM concentration and not constant during the procedure, furthermore that the XAD-8 fractions may undergo irreversible alteration of structure due to the procedure or storage that will influence on the interpretation of the data. The possible consequences for the interpretation of results and further analysis or use of the XAD-8 based fractions are discussed.