Sonderforschungsbereich 799 Teilprojekt C5: Particle Reinforced TRIP-Matrix-Composites
Prof. Dr.rer.nat.habil. Meinhard Kuna, i.R.
Responsible Research Assistant
In the DFG Collaborative Research Centre 799 "TRIP-Matrix-Composites" steels and ceramics are developed which exhibit outstanding properties due to martensitic phase transformation and mechanical twin formation (TRIP or TWIP effect). The combination of these two materials in order to form new innovative materials is the main focus of our research activities. Various production routes are being investigated for this purpose. One possible manufacturing process is the hot pressing of metallic and ceramic powders into particle-reinforced TRIP matrix composites. Under mechanical loading, these composites show different damage mechanisms: separation of interfaces, brittle failure of the ceramic and ductile damage of the matrix. A continuum mechanical description and optimization of the material can be improved by precise knowledge of the effects of the damage mechanisms, whereby micromechanical simulations make a valuable contribution. With the help of continuum mechanical material models for the TRIP steel and the TRIP matrix composites, structural mechanical optimizations can be carried out which, for example, lead to an improved behavior of crash structures made of TRIP matrix composites.
The aim of subproject C5 is the micro- and macroscopic description of the deformation and failure behavior of a particle-reinforced TRIP matrix composite using continuum mechanical and numerical methods. Within the third funding period (2016-2020), the development and numerical implementation of regularized damage models and thermomechanically coupled models for TRIP steels are in focus.
Currently developed methods
The modelling of softening material behavior with continuum mechanical means leads to the loss of the ellipticity of the mechanical boundary value problem and thus to the discretization dependence of the numerical solution within the framework of the finite element method, see Figure 1. To avoid this unphysical behavior, various regularization methods have been developed (non-local averaging methods, gradient extended approaches, etc.). The starting point of our own work is the implicit gradient extension following Peerlings, which leads to an additional field equation of Helmholtz type and contains an additional parameter: the internal length. For the implementation of this class of damage models in commercial FE codes (e.g. ABAQUS) an efficient method is used which exploits the similarity of the boundary value problem to thermomechanically coupled problems [10a]. In Figure 1, the implementation is verified by means of an example, i.e., the structure response converges during mesh refinement (ratio of element edge length to internal length L).
Figure 1: Simulation of a damage-induced shear band with a regularized approach (nonlocal, non-local) and a local damage model (local, local): Left: Contour plot of the damage development. Right: Force-displacement response with refinement of discretization be/L
The FE implementation of regularized models for ductile damage allows the simulation of crack propagation. This is illustrated using a 2D example (double notched tensile specimen, plane strain state) in Figure 2.
Figure 2: Crack propagation simulation using a gradient extended damage model in a double notched tensile specimen, calculated with the commercial software ABAQUS.
For the transfer of the developed damage models into practical application appropriate calibration strategies must be available. It is proposed to use fracture mechanical tests for calibration, which complement the classical tensile and notched tensile tests [12a]. This seems to make it possible to identify the individual model parameters. Using the example of a pressure vessel steel, the calibration of a modelling approach for ductile damage was carried out, see [12a]. The macroscopic force-displacement response of smooth and notched tensile specimens (Figure 3) as well as the crack growth resistance curve of a 4-point SENB-specimen (Figure 4) can be matched very well with the calibrated model.
Figure 3: Experimental data (dashed lines) and simulation result using the calibrated damage model (full lines) for various notched tensile tests (notch radius R1-R10 and smooth tension rod RS): a) force over diameter reduction and b) force over longitudinal strain, c) geometries of the specimens
Figure 4: Simulated and experimentally determined crack resistance curves of a 4-point SENB test. a) FE mesh of the crack tip, b) geometry of the specimen (symmetrical) and c) crack resistance curve (J integral over crack propagation). The initial rounding of the crack tip to avoid strong element distortions is designated by rt.
Simulations of a miniaturized small punch test can be predicted with the calibrated model, validating the modeling approach. Figure 5 compares the experimental and simulation predicted force-displacement curves of the Small Punch Test. The predicted structural response falls into the experimentally determined range when damage is considered. Figure 6 shows the deformation states during damage initiation and sample failure.
Figure 5: Force-displacement curve of the Small Punch Test. Shown are the upper and lower limits of the experiments as well as the damage model and a typical plasticity law without damage (w/o damage).
Figure 6: Small Punch Test: a) FE model, b) contour plot to illustrate damage initiation and c) damage distribution in case of sample failure
Deutsche Forschungsgemeinschaft (DFG) 2008 - 2020, (project number 54473466 –SFB 799, subproject C5)
a) Peer-reviewed papers:
- [12a] Seupel, A., Kuna, M.: A gradient-enhanced damage model motivated by engineering approaches to ductile failure of steels, International Journal of Damage Mechanics, 28 (2019) Nr. 8, S. 1261-1296
- [11a] Giang, N. A., Seupel, A., Kuna, M., Hütter, G.: Dislocation pile-up and cleavage: effects of strain gradient plasticity on micro-crack initiation in ferritic steel, International Journal of Fracture, 214 (2018) Nr. 1, S. 1-15
- [10a] Seupel, A., Hütter, G., Kuna, M.: An efficient FE-implementation of implicit gradient-enhanced damage models to simulate ductile failure, Engineering Fracture Mechanics, 199 (2018), S. 41-60
- [9a] Seupel, A., Eckner, R., Burgold, A., Kuna, M., Krüger, L.: Experimental characterization and damage modeling of a particle reinforced TWIP-steel matrix composite, Materials Science & Engineering A, 662 (2016), S. 342-355
- [8a] Seupel, A., Kuna, M.: Application of a Local Continuum Damage Model to Porous TRIP-Steel, Applied Mechanics and Materials, 784 (2015), S. 484-491
- [7a] Kulawinski, D., Ackermann, S., Seupel, A., Lippmann, T., Henkel, S., Kuna, M., Weidner, A., Biermann, H.: Deformation and strain hardening behavior of powder metallurgical TRIP steel under quasi-static biaxial-planar loading, Materials Science and Engineering A, 642 (2015), S. 317-329
- [6a] Prüger, S., Seupel, A., Kuna, M.: A thermomechanically coupled material model for TRIP-steel, International Journal of Plasticity, 55 (2014), S. 182-197
- [5a] Prüger, S., Mehlhorn, L., Mühlich, U., Kuna, M.: Study of Reinforcing Mechanisms in TRIP-Matrix-Composites under Compressive Loading by Means of Micromechanical Simulations, Advanced Engineering Materials, 15 (2013) 7, S. 542-549
- [4a] Prüger, S., Mehlhorn, L., Soltysiak, S., Kuna, M.: Influence of material and interface properties on the transformation behaviour of particle reinforced TRIP-matrix composites, Computational Materials Science, 64 (2012), S. 273-277
- [3a] Kulawinski, D., Nagel, K., Henkel, S., Hübner, P., Fischer, H., Kuna, M., Biermann, H.: Characterization of stress-strain behavior of a cast TRIP steel under different planar load ratios, Engineering Fracture Mechanics, 78 (2011), S. 1684-1695
- [2a] Mehlhorn, L., Prüger, S., Soltysiak, S., Mühlich, U., Kuna, M.: Influence of material and interface properties on the overall behaviour of particle reinforced steel with focus on the phase transformation capabilities of the individual components, Steel Research International, 82 (2011) 9, S. 1022-1031
- [1a] Prüger, S., Kuna, M., Wolf, S., Krüger, L.: A material model for TRIP-steels and its application to a CrMnNi cast alloy, Steel Research International, 82 (2011) 9, S. 1070-1079
b) Conference proceedings:
- [6b] Seupel, A., Kuna, M.: Phenomenological Modeling of Strain Hardening Phase Transformation and Damage Effects of TRIP-Steels, XIV International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS XIV (04.-10.09.2017), S. 576–587
- [5b] Seupel, A., Kuna, M.: Damage model of a particle reinforced TRIP-steel matrix composite, XXIV ICTAM (2016)
- [4b] Seupel, A., Kuna, M.: Erweiterung eines duktilen Schädigungsmodells zur Beschreibung von TRIP-Stählen, DVM Bericht, 247 (2015), S. 83-92
- [3b] Mehlhorn, L., Prüger, S.: Modellierung des Werkstoffverhaltens von TRIP-Stahlguss und ZrO2 -Keramik, in: Schriftenreihe Werkstoffe und werkstofftechnische Anwendungen, Band 37, Hrsg.: B. Wielage, Chemnitz, 2010, S. 292-300, ISBN 978-3-00-032471-0
- [2b] Prüger, S., Kuna, M.: Implementation of a material model for cast CrMnNi TRIP-steel, XI. International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2011, Barcelona
- [1b] Prüger, S., Kuna, M.: A constitutive model for a high alloyed cast CrMnNi TRIP-steel, Proceedings in Applied Mathematics and Mechanics 11 (2011), S. 425-426
c) Selected talks:
- [10c] Seupel, A., Kuna, M.: A gradient-enhanced model for ductile damage and failure of steels based on an engineering approach, Sixth International Conference on Computational Modeling of Fracture and Failure of Materials and Structures (2019)
- [9c] Seupel, A., Kuna, M.: Ein gradientenerweitertes Modell für duktile Schädigung motiviert durch
ingenieurmäßige Ansätze–Anwendung und Grenzen, DVM Arbeitskreis Bruchvorgänge (2019)
- [8c] Seupel, A., Kuna, M.: A gradient-enhanced damage model motivated by engineering approaches to ductile failure of steels, 10th European Solid Mechanics Conference ESMC (2018)
- [7c] Seupel, A., Hütter, G., Kuna, M.: An efficient FE-implementation of implicit gradient-enhanced damage models,
Joint DMV and GAMM Annual Meeting (2018)
- [6c] Seupel, A., Kuna, M.: Phenomenological Modeling of Strain Hardening Phase Transformation and Damage Effects of TRIP-Steels, XIV International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS XIV (2017)
- [5c] Seupel, A., Burgold, A., Kuna, M.: Damage modeling of a particle reinforced TWIP-steel matrix composite, Joint DMV and GAMM Annual Meeting (2016)
- [4c] Seupel, A., Kuna, M.: Application of a Local Continuum Damage Model to Porous TRIP-Steel, Second International Conference on Damage Mechanics (2015)
- [3c] Kuna, M., Seupel, A.: A Phenomenological Damage Model for Elastoplastic Behavior of Particle Reinforced TRIP-Steel Matrix Composites based on Micromechanical Simulations , Fourth International Conference on Computational Modeling of Fracture and Failure of Materials and Structures (2015)
- [2c] Seupel, A., Kuna, M.: Erweiterung eines duktilen Schädigungsmodells zur Beschreibung von TRIP-Stählen , DVM Arbeitskreis Bruchvorgänge (2015)
- [1c] Seupel, A., Kuna, M.: Simulation of Damage Mechanisms in TRIP-Steel Matrix Composites, Materials Science Engineering (2014)
- [20d] S. Prüger: Thermomechanische Modellierung der dehnungsinduzierten Phasenumwandlung und der asymmetrischen Verfestigung in einem TRIP-Stahlguss, TU Bergakademie Freiberg (2016), Berichte des Instituts für Mechanik und Fluiddynamik Heft 23 (2016)