AbstractTo capture and predict the chemo-thermo-mechanical behavior of ceramic foam filters, material models and simulation tools are required. The description of the thermo-mechanical inelastic behavior as well as the in-situ layer formation on reactive filters have been the aims of this subproject. Challenging aspects in the whole progress are the exact geometrical replication of the underlying foam structure of the filter and the lack of experimental data for many relevant loading cases. The software FoamGUI is developed to generate parametrized, periodic three-dimensional representative volume elements (RVE) of foam structures, which are used in continuum and fluid mechanical simulations as well as for 3D-printing. Calculation concepts are formulated to predict the inelastic deformation and failure behavior of ceramic open-cell foams under thermo-mechanical loading. First-order homogenization approaches are used to conclude from the mesoscopic behavior of the foam RVE to the macroscopic response of filter structures. A hybrid approach is developed in the established framework of rate-independent plasticity in combination with neural networks, which replace the plastic flow potential and the evolution equations of internal state variables. Another modeling aspect is motivated by the experimentally observed growth of an in situ layer during the so-called reactive phase of the filtration process. This phenomenon motivates the development of a model to describe diffusion, chemical reactions and phase transition processes of multi-phase/multi-component systems using the phase-field method. This allows the simulation of spatially and temporally resolved microstructure evolution leading to the layer formation.

Certain metals experience a substantial deterioration in mechanical properties when exposed to a hydrogen environment, an effect termed hydrogen embrittlement. To understand, predict, and counteract this hydrogen-assisted material degradation, sufficiently accurate material models are needed. According to the current hypothesis, hydrogen diffusion is driven by gradients of concentration and hydrostatic stress. To capture this, a phase-field model is formulated as a multi-field problem coupling deformation, crack propagation, and diffusion to analyze hydrogen-promoted fracture. Here, the displacements, a fracture-related phase-field, the hydrogen lattice occupancy, and the chemical potential are considered as primary field variables. Approaches proposed in the literature often use an extrapolation of the hydrostatic stress calculated at the material point level onto the nodes and later use the B-matrix to compute the gradient of hydrostatic stress. In order to circumvent this potentially inaccurate extrapolation, the model is recast into a mixed rate-type variational setting, where the chemical potential—whose gradient governs the hydrogen flux—is obtained from the numerical solution of a saddle point problem. A representative boundary value problem is presented to demonstrate the applicability of the developed numerical framework.

Hydrogen embrittlement in ductile metals, such as steel, is a significant concern, for instance, in the safety assessment of existing pipeline infrastructure intended for hydrogen transport. The ductile damage mechanism in steels is characterized by the nucleation, growth, and coalescence of microvoids, which is further enhanced by the presence of hydrogen. This leads to material damage and premature failure in components. Mechanisms contributing to hydrogen-induced reduction of strength in steels include hydrogen-enhanced decohesion (HEDE), hydrogen-enhanced local plasticity (HELP), and hydrogen-enhanced strain-induced vacancies (HESIV). The HEDE mechanism leads to a principal stress-controlled brittle failure mode. Conversely, the HELP and the HESIV mechanisms, which are dominated by plastic deformation, alter the ductile damage behavior as they lead to accelerated void growth and coalescence. Furthermore, interstitial diffusion of hydrogen leading to lattice expansion, commonly referred to as swelling, also contributes to hydrogen-induced embrittlement. Hydrogen embrittlement is therefore a stress-diffusion process that involves chemo-mechanical coupling, where hydrogen atoms primarily diffuse toward areas with high hydrostatic stress. In this regard, we propose a framework using the finite element method and combining coupled chemo-mechanics and the well-known Gurson-Tvergaard-Needleman (GTN) damage model. The framework is motivated by mixed rate-type potentials, that account for the influence of hydrogen concentration on the damage behavior. An additional dependence of the fracture strain and evolution of the void volume fraction on hydrogen is included. A comparison of the fully-coupled model to simplified versions is conducted to individually assess the role of hydrogen concentration on damage evolution and the stress state on diffusion.

Within the scope of this study, the macroscopic temperature distribution in the steady-state temperature condition during Field Assisted Sintering Technique/Spark Plasma Sintering (FAST/SPS) in functionally graded materials (FGM) was investigated. The sample material exhibited a diameter of 50 mm and a thickness of 9 mm. The FGM samples were composed of steel X2CrMnNi 16-7-6 and Mg-PSZ ceramic (MgO partly stabilized ZrO2). By varying the sintering tool setup, a specific modification of the macroscopic temperature distribution within the sample material and the sintering tool was achieved. The aim of the modifications was to optimize the temperature gradients in order to allow for the simultaneous compaction of all FGM layers under ideal circumstances. This involves achieving enhanced ceramic densification without inducing steel melting. Finite element method (FEM) simulations were carried out to get information about the temperature distribution within the sample material and the sintering tool. Furthermore, for this propose, thermocouple temperature measurements were conducted at various measurement points on pre-sintered FGM within the specific sintering tool setup. Additionally, all findings regarding the temperature distribution within the sample material and the sintering tool were compared with results concerning the temperature distribution from the microstructural and mechanical characterization of the center and edge regions of the FGM samples. The FGM samples exhibited a significant increase in temperature from the center to the edge in the radial direction depending on the used sintering tool setup. While the FGM samples showed only minor vertical temperature gradients in the center, the highest vertical temperature gradients were determined at the edge of the FGM sample using an asymmetric sintering tool setup.

The present phase‐field approach is based on a mixture theory for multiple components and phases within the framework of non‐equilibrium thermodynamics of internal state variables. More specifically, diffuse interfaces are included in the state potential by terms depending on spatial gradients of the component mass fractions as well as order parameters representing different phases. Coupled field equations of generalized Cahn‐Hilliard and Allen‐Cahn type are derived directly from a local entropy balance, under the assumption of a localized Gibbs fundamental equation. Additionally, thermodynamically consistent kinetics for equilibrium reactions are formulated. The field equations are recast into a mixed variational formulation, which allows a discretization by finite elements with low‐order ansatz functions. The numerical implementation is discussed by means of a benchmark problem for reactive binary systems, of which the thermodynamic equilibrium solution is known.

Ductile materials are used in many applications such as hydrogen storage and transport, energy plants and additively manufactured components. High safety standards are vital for such applications, which underline the necessity of thoroughly investigating ductile failure to ensure safety and increase components efficiency. Ductile failure is mainly prompted by the evolution of the so‐called ductile damage, characterized by the nucleation, growth and coalescence of microvoids due to plastic deformation. Moreover, the plastic zones formed at the crack tip of ductile materials exhibit high sensitivity to the stress triaxiality level, which in turn distinctly depends on the geometry of the considered component. The quantification of the stress triaxiality at the crack tip is therefore essential to better understand and predict ductile crack propagation and failure. For that reason, a non‐local ductile damage model is employed in this work to simulate the ductile crack propagation under different stress triaxiality conditions. Different geometries are considered, such as constrained geometries of notched bending specimens and unconstrained geometries of center cracked tension specimens, which characterize the different triaxiality levels. To address the effects of thickness and initial crack length, three‐dimensional geometries are simulated, which account for the out‐of‐plane crack‐tip constraints. Finally, to evaluate the prediction quality of the simulations, corresponding experiments have been carried out and direct comparisons are conducted, with respect to the crack length, ductile crack propagation and resistance curves.

Damage mechanics models exhibit favorable properties such as the intrinsic influence of stress triaxiality on damage evolution and the prediction of crack initiation as well as propagation leading to structural failure. However, their application requires advanced expertise hindering the transfer of these models into industrial practice, especially since the parameter calibration is a key obstacle. In this paper, a simplified procedure is proposed for a non-local extension of the Gurson–Tvergaard–Needleman model (GTN), which is a highly accepted model for ductile failure of metals. The procedure is iteration free and requires experimental input data from only two standardized tests. The parameters are determined using look-up diagrams created on the basis of systematic simulations and made available for different material behavior covering the majority of ductile metals. Benchmark tests for three different steels are conducted to evaluate the robustness of the proposed procedure. The reliability of the GTN model is validated for all investigated materials.

The considered highly alloyed TRIP-steel (TRansformation Induced Plasticity-TRIP) exhibits a phase transition from austenite to martensite during large deformation which leads to a remarkable strain hardening capability. However, the martensite evolution highly depends on temperature and stress state. Therefore, especially self heating during deformation has a great influence on the behavior of the material. A thermomechanically coupled viscoplasticity model is applied accounting for strain induced martensite formation and Lode-angle dependent strain hardening. Using fully thermomechanically coupled simulations of tensile and compression tests the model is able to capture the observed asymmetric hardening behavior of the considered CrMnNi-steel as well as the recorded crossing effect of yield curves at elevated strain rates.

The present study proposes a parameter identification and calibration strategy for a specific non-local GTN-model, which has been developed to circumvent spurious mesh dependency during simulation of ductile failure. The parameter calibration strategy is applied to an experimental database of a pressure vessel steel tested at moderate to high stress triaxialities. Relevant parameters of the non-local GTN-model can be identified using simulated/experimental crack growth resistance curves determined by a fracture mechanics test (Mode I loading). In addition, only results of a smooth tensile test are utilized in order to identify an appropriate strain hardening law. Based on this input information, the failure behavior of smooth and notched tensile specimens as well as miniaturized deep drawing tests is predicted by finite element simulations. A fairly good agreement with experiments is obtained, which validates the feasibility of the suggested approach.

The mechanical behavior of TRIP-steels (TRansformation Induced Plasticity) under monotonic loading conditions has been extensively studied both experimentally and by continuum mechanical modeling. The cyclic response received far less attention so far, although the mechanically induced martensitic phase transformation highly affects the cyclic deformation behavior. Especially in high alloy austenitic TRIP-steels a pronounced cyclic hardening is observed in cyclic deformation curves, which evolves proportionally to the volume fraction of deformation-induced martensite. In the present contribution a phenomenological material model is proposed, which is able to capture this effect. A rate independent two-surface plasticity approach is employed. The first surface is of J(2)-type and describes plastic yielding, whereas the second surface is of Drucker-Prager type and represents the mechanically induced phase transformation. The formulation of the plastic behavior incorporates nonlinear kinematic hardening. The model is calibrated based on a consistent set of uniaxial cyclic deformation experiments with constant strain amplitude under tension-compression. Results of the simulations match the cyclic deformation curves for a large range of strain amplitudes including the transformation induced cyclic hardening well. The qualitative and quantitative agreement between numerical and experimental data as well as the capabilities and limitations of the model are discussed in detail.

The aim of this chapter is to give insight into the continuum mechanics based modeling of high alloy TRIP-steels. A powerful thermomechanical framework is presented, which incorporates finite viscoplasticity, the TRIP-effect, complete thermomechanical coupling, and non-local damage. Based on this, different variants of material models are developed. Thereby, selected topics concerning the material behavior of TRIP-steels are examined: Firstly, the mechanical behavior at different temperatures and strain rates is modeled including tension-compression-asymmetry and curve crossing effects. Secondly, the influence of phase transformation on fracture is investigated. Because of the TRIP-effect, higher stresses occur during crack tip blunting. Furthermore, a transformation induced shielding effect is revealed by the evaluation of material forces. Thirdly, damage evolution and crack extension are simulated with a cohesive zone model and with the non-local damage model, respectively. The damage related parameters of these models are determined using available experimental data. The developed numerical models enable quantitative assessments of failure in components made of TRIP-steels.

We present recent enhancements of an engineering concept, which was introduced by Lian et al. [1], to model ductile failure. The concept consists of using an appropriate plasticity model, an uncoupled indicator of damage initiation, and a simple model of damage evolution which is fully coupled to the constitutive equations leading to material softening. We focus on the following improvements which have been recently published [2]: 1) In order to account for the impact of hydrostatic stress on macroscopic plasticity due to the evolution of damage (nucleation and growth of voids), an elliptic yield function in terms of hydrostatic and equivalent stress is proposed. The plastic yielding deviates from J2-plasticity in case of damage onset only. Damage is driven by the additive combination of equivalent and volumetric plastic strain leading to a triaxiality dependent damage evolution law similar to the one suggested by Mediavilla et al., [3]. 2) The important issue of spurious mesh dependency is handled by incorporating an implicit gradient-enhancement, see [4]. The non-local counterpart of the previously mentioned damage driving strain is used to formulate the damage law. The model is efficiently implemented into the FE-code ABAQUS, utilizing the similarities between the field equations of the implicit gradientenhancement and the equation of heat conduction, see [5]. A convergence study is performed to show the mesh-independence and other features of the enhanced damage model. Finally, the proposed model is exemplarily applied to experimental data of a pressure vessel steel (18Ch2MFA) at moderate to high stress triaxialities. It is shown that groups of model parameters can be calibrated independently. The calibration has been performed using a crack growth resistance curve of a SENB-test and results from notched tensile tests. The numerical prediction of a small punch test shows good agreement compared to experiments. Additional numerical examples are performed to discuss further applications, restrictions, and open issues of the model.

Material models for ductile damage, crack initiation, and crack growth are of high interest, e.g. for metal forming simulations. Empirical engineering approaches are often applied, but the numerical results are sensitive to the discretization if no method is utilized to prevent ill-posedness of the underlying boundary value problem due to strain softening. In order to face this issue, an empirical damage model is equipped with a gradient-enhancement which introduces an additional length scale parameter. Until the initiation of damage, the material is modeled with standard von Mises plasticity. Damage initiation is taken into account by an uncoupled failure indicator. After damage initiation, material degradation is assumed to be driven by a non-local quantity, which depends on plastic deformation and stress triaxiality. During damage evolution, the macroscopic material behavior becomes dependent on hydrostatic stress, which is motivated by well known void growth and coalescence mechanisms. A calibration strategy is developed to determine the parameters of strain hardening, damage initiation, and damage evolution as well as the internal length step-by-step. The proposed model is calibrated to experimental data of a pressure vessel steel. Reasonable predictions of smooth and notched tensile tests as well as a small punch test show the validity of the model for loadings from moderate to high stress triaxialities.

We present a strategy which allows to implement a fully coupled, gradient-enhanced damage law into commercial FEM-codes with little effort. This enables a robust simulation of practical engineering problems avoiding spurious mesh dependency due to damage influence. The method is applied to a model for shear dominated, ductile damage of metals, which is used by engineers and often available in its local formulation within FEM-programs; e.g., ABAQUS. The model consists of a damage initiation criterion, followed by a damage evolution law which is coupled to the elastic-plastic constitutive equations. Convergence studies show the applicability of the implementation for 2D and 3D boundary value problems. Crack growth simulations of a benchmark problem show reasonable results compared to similar approaches from literature.

In this study, the constitutive modeling of loading state dependent strain hardening and martensite evolution of high alloyed TRIP-steels are addressed, which are experimentally observed comparing uni-axial tension and compression test results. Furthermore, a damage mechanics extension of the model is proposed, which is based on the continuum damage mechanics framework. An implicit gradient based enrichment method is applied to realize a non-local damage formulation. For the implementation into the commercial FEM-software ABAQUS, the analogy between the additional Helmholtz type equation of implicit gradient enrichment and the already built-in heat conduction equation is used. Finally, the developed model is fitted to experimental data and cell model calculations. A convergence study using the non-local extension is discussed.

A phenomenological damage model is proposed to describe the mechanical behavior of a particle reinforced TWIP-steel matrix composite. Starting point of the study is Rousselier's model for ductile damage of metals, which is extended by a damage nucleation criterion. This criterion involves an overall progress of particle based damage events like particle cracking or debonding from matrix. The dependency of the material behavior on triaxiality and Lode-parameter is taken into account. Micromechanical simulations and experiments are used to test and calibrate the model. Deformation behavior, damage evolution and final failure predicted by the calibrated damage model are in good agreement with numerically generated and experimentally determined material data.

The present paper investigates a metastable austenitic stainless steel under different biaxial-planar load paths by using a cruciform specimen geometry. The material behavior was described by stress–strain curves and initial yield surface. Furthermore, the hardening behavior was determined by load sequence tests. To investigate the influence of the stress state on the martensite formation a ferrite sensor as well as electron backscatter diffraction measurements were used. Two cruciform specimen geometries were utilized and compared for the considered load cases. The stress state within the cruciform specimens was evaluated by an elastic unloading procedure with subsequent calculation of the stress components. Isotropic initial yielding and non-isotropic hardening were found. A recommendation for the use of the cruciform specimen geometry with respect to the load case is given.

Aim of this study is to describe the ductile damage of metastable austenitic steels which show TRansformation Induced Plasticity (TRIP). Therefore, a criterion for the austenite to martensite transformation, the caused additional hardening and evolution equations for the TRIP-strain are incorporated into the damage model of Rousselier. As a first approach, the model is calibrated against unit cell simulations of the porous material for different stress triaxialities.