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## Über dieses Buch

This open access book presents a collection of the most up-to-date research results in the field of steel development with a focus on pioneering alloy concepts that result in previously unattainable materials properties. Specifically, it gives a detailed overview of the marriage of high-performance steels of the highest strength and form-ability with damage-tolerant zirconia ceramics by innovative manufacturing technologies, thereby yielding a new class of high-performance composite materials. This book describes how new high-alloy stainless TRIP/TWIP steels (TRIP: TRansformation-Induced Plasticity, TWIP: TWinning-induced Plasticity) are combined with zirconium dioxide ceramics in powder metallurgical routes and via melt infiltration to form novel TRIP-matrix composites. This work also provides a timely perspective on new compact and damage-tolerant composite materials, filigree light-weight structures as well as gradient materials, and a close understanding of the mechanisms of the phase transformations.

With a detailed application analysis of state-of-the-art methods in spatial and temporal high-resolution structural analysis, in combination with advanced simulation and modelling, this edited volume is ideal for researchers and engineers working in modern steel development, as well as for graduate students of metallurgy and materials science and engineering.

## Inhaltsverzeichnis

Open Access

### Chapter 1. Ceramic Casting Technologies for Fine and Coarse Grained TRIP-Matrix-Composites

Abstract
The present contribution focuses on the development of composite materials using innovative ceramic casting technologies. Within this work different processing routes, the relevance of their process parameters as well as the resulting mechanical and microstructural characteristics are discussed. The successfully developed TRIP-matrix foams as well as full beads reinforced with 5 and 10 vol.% zirconia achieve higher compressive strengths and energy absorption during deformation in comparison to the pure metal materials as references. The functionally graded beads allowed a compression of up to 20% with corresponding specific energy absorption of 10.7 kJ/kg. In a further approach, metal-matrix composites have been generated via paper-manufacturing technology. The partial replacement of cellulose fibers by commercially available zirconia fibers resulted in fiber reinforced TRIP-matrix composites with an increased tensile strength of approx. 33% as compared to the pure metal material as reference. Large-size ceramic matrix composites with high potential for applications requiring sufficient wear and thermal shock resistance have been successfully prepared via pressure slip casting. The last topic is concerned with the development of yttria-stabilized zirconia fibers with a tailored phase composition (monoclinic-tetragonal-cubic) via electrospinning.
Claudia Heuer, Marie Oppelt, Christos G. Aneziris

Open Access

### Chapter 2. Design of High Alloy Austenitic CrMnNi Steels Exhibiting TRIP/TWIP Properties

Abstract
This chapter is centered on the development of austenitic high strength cast CrMnNi steels with excellent strength-ductility combination by triggering TWIP and TRIP effects. Special attention is given to obtain a high yield strength and a good formability. For this purpose, three generations of steels were developed. The 1st generation is comprised of cast X3CrMnNi16-7-x steels. Their Ni concentration was varied in order to manipulate the stacking fault energy of austenite and change the operative deformation mechanisms. Based on the mechanical properties of the 1st generation steels, the 2nd generation steels were developed with a composition similar to the X3CrMnNi16-7-6 steel. Interstitial alloying elements were added to take advantage of solid solution strengthening and precipitation hardening effects. The substitutional alloy contents were carefully adjusted to ensure the occurrence of TRIP/TWIP effects during plastic deformation. For the 3rd generation, two steels from the 2nd generation, X16CrNiMnN15-3-3 and X16CrNiMnN19-4-3, were treated with tailored quenching and partitioning (Q&P) processing routines to further increase the strength, especially the yield strength. The developed Q&P cast steels exhibited an outstanding strength-ductility combination, e.g. a yield strength over 1000 MPa and a total elongation exceeding 20% for the steel X16CrNiMnN15-3-3 containing 0.12 wt% N.
Qiuliang Huang, Marco Wendler, Javad Mola, Andreas Weiß, Lutz Krüger, Olena Volkova

Open Access

### Chapter 3. Tailoring of Thermophysical Properties of New TRIP/TWIP Steel Alloys to Optimize Gas Atomization

Abstract
This work is dedicated to the optimization of the inert gas atomization process applied for production of steel powders. One aim is the optimization of melt parameters with the target to reduce the particle size of atomized powder. A second aim is focused on the atomization equipment optimization. In order to study thermophysical properties of steel melts the development of a new research units was accomplished: Maximum Bubble Pressure device for measurement of the surface tension and density of liquid steels and alloys, patented vibrating finger viscometer, dedicated to the investigation of low-viscosity fluids under the conditions of high temperatures and high reactivity of the studied media; density measurement cell based on the Archimedean principle for the precise estimation of steel alloys density. Then, the effect of thermophysical properties on the inert gas atomization of high-alloy steels was studied. The effects of alloying with Mn and Ni were studied as well as microalloying with S, P, Se on the surface tension and viscosity of liquid steels. Surface tension and viscosity modification of the alloys led to considerable reduction of the size of inert gas atomized powders. Alloying with N allowed finding effect on the powder phase structure.
Iurii Korobeinikov, Humberto Chaves, Olena Volkova

Open Access

### Chapter 4. Production of Ceramic Steel Composite Castings Through Infiltration

Abstract
TRIP-matrix composites unite the outstanding properties of austenitic-martensitic cast steels with those of ceramics. To manufacture them via infiltration by steel melt, basic investigations are needed. Therefore, the following aspects were studied: the influence of sodium silicate bonded sand molds on solidification of high alloyed TRIP-steels, chemical reactions between steel and molding sand and the positive impact of sulfur and phosphorus on the infiltration quality. Composite materials made of steel and ceramics, in particular, melt-broken zircon corundum, have comparatively high wear resistance. The wear behavior of the composites is characterized by a ring-block test rig. In order to generate a stable bond between the steel and the ceramic phase, the ceramics were coated with titanium oxide prior to infiltration. During infiltration of the coated ceramics, spinel compounds are formed which reduce expansion-related cracks in the boundary layer.
Paul Rähmer, Claudia Dommaschk, Gotthard Wolf

Open Access

### Chapter 5. Ceramic Extrusion Technologies for Fine Grained TRIP Matrix Composite Materials

Abstract
Metal-Matrix-Composites (MMCs) based on steel with certain ceramic additions offer a wide range of applications in automotive, construction, and mechanical engineering. These MMCs combine the specific properties of steels such as their room temperature deformation behavior with the advantageous hard but brittle ceramic reinforcements which makes them favorable in crash-absorbing or strengthening components. However, common technologies such as casting or infiltration of ceramic preforms by metal melts suffer from the differences between metal and ceramic material characteristics involved during material processing and from geometrical restrictions. The adaption of the ceramics-derived extrusion technology at ambient temperature on materials established in the powder metallurgy (PM) enables an efficient manufacturing process of advanced fine-grained materials with particularly cellular (lightweight) structures as well as bulk specimens. Using powder raw materials enables a wide range of material combinations between TRIP/TWIP steels and various ceramic components considering the pronounced material characteristics of the composite. Knowing the influence of the raw materials, the processing parameters for shaping and the indispensable thermal processing transforming the formed powders into a solid material is crucial for proper manufacturing of MMCs with tailored characteristics. The joining process for these components extends the applicability of the investigated PM-MMCs.
Christian Weigelt, Marie Oppelt, Christos G. Aneziris

Open Access

### Chapter 6. Understanding of Processing, Microstructure and Property Correlations During Different Sintering Treatments of TRIP-Matrix-Composites

Abstract
This chapter presents scientifically robust results on the sintering behavior of transformation-induced plasticity (TRIP)-matrix composites based on different consolidation processes, such as conventional sintering, resistance sintering and hot pressing. The correlation of the processing parameters to the adjusted properties, such as the density, porosity, grain size, phase composition and mechanical properties is discussed. The theoretical modeling, including validation with experiments, enabled us to describe, understand and quantitatively optimize the sintering process.
Sergey Guk, Rudolf Kawalla, Ulrich Prahl

Open Access

### Chapter 7. Understanding of Processing, Microstructure and Property Correlations for Flat Rolling of Presintered TRIP-Matrix Composites

Abstract
Descriptions of material behavior during forming operations have become increasingly important in recent years due to the increasing use of simulation systems for understanding processing-microstructure-property correlations and regulating forming facilities. This information has become particularly important for composite materials, including metal matrix composites. This necessity poses new challenges in particular for testing technology, which significantly contributes to the analysis of material characteristics. The characteristic values of materials are prerequisites for the numerical design of manufacturing processes. This chapter presents an overview of the strategies currently available for describing material behavior during flat rolling; the materials investigated herein are presintered TRIP-matrix composites. In addition, the test procedures and methods necessary for determining material parameters are briefly listed and explained. Furthermore, this chapter presents both the classical test methods and equipment and their areas of application, which have been further developed in recent years.
Sergey Guk, Rudolf Kawalla, Ulrich Prahl

Open Access

### Chapter 8. Powder Forging of Presintered TRIP-Matrix Composites

Abstract
This chapter addresses bulk forming processes-especially powder forging-used to produce complex shaped components from presintered TRIP-matrix composites. Based on experimentally determined material and process parameters (e.g., shrinkage, Poisson’s ratio, elastic modulus, oxidation behavior), extended process maps for compressible materials were presented. Subsequently, a characterization of the material flow as a function of the material conditions was reproduced via the visioplastic method and metallographic analysis, and then connections were drawn between the results and the extended process maps. The knowledge gained was used to develop a powder forging tool for a Gleeble HDS-V40, which was used to conduct model tests aiming to improve the component properties. The tool was equipped with compensating gaps to provide better compaction to the components. To find the optimal compaction for the solid material, different variants of compensating gaps were investigated. The components obtained through this approach were examined on the basis of their mechanical properties and microstructures. Furthermore, the deformation of graded components was analyzed in this study. In addition to the formation of a damage-tolerant interface and the shear strength of the different layers, special attention was paid to process-relevant parameters, such as the maximum deformation degree, the tool and specimen temperature and the pressure holding time.
Markus Kirschner, Sergey Guk, Rudolf Kawalla, Ulrich Prahl

Open Access

### Chapter 9. Synthesis of TRIP Matrix Composites by Field Assisted Sintering Technology—Challenges and Results

Abstract
This chapter analyses options to synthesis TRIP matrix composites (reinforced with Mg-PSZ), which stand out due to a high strength and the possibility to undergo a stress- and strain-induced phase transformation. These composites are processed using Field Assisted Sintering Technology (FAST). Both, the influence of the powder treatment before sintering and the impact of parameter setting during sintering by FAST are discussed. Due to a careful alignment of these factors, a TRIP matrix composite (reinforced with 5 vol% Mg-PSZ) with an 1% compressive yield strength of 700 MPa was generated. Furthermore, both composite components exhibited a phase transformation during compressive deformation. The fundamental investigations are the basis for the development of Functionally Graded Materials (FGM) with a varying Mg-PSZ content along the sample height. To synthesize these FGMs by FAST, a temperature gradient has to be generated during sintering, which allows to sinter the pure ceramic layer without melting the steel phase. Several possibilities to generate a temperature gradient are discussed.
Sabine Decker, Markus Radajewski, Lutz Krüger

Open Access

### Chapter 10. Electron Beam Technologies for the Joining of High Alloy TRIP/TWIP Steels and Steel-Matrix Composites

Abstract
The use of new, high-alloy TRIP/TWIP steels and the corresponding composite materials requires innovative joining processes. Due to the high power density, the inert working atmosphere and the software-based control, the electron beam is predestined to study different joining strategies. This paper shows how the electron beam can be used as a tool to join high-alloy TRIP/TWIP materials with and without particle reinforcement. Microstructure-property relationships based on the microstructure and tensile tests are established and correlated to the material used. From this, a corresponding joining strategy is derived for each material, which is presented on the basis of various evaluation criteria.
Lars Halbauer, Anja Buchwalder, Horst Biermann

Open Access

### Chapter 11. Microstructure Aspects of the Deformation Mechanisms in Metastable Austenitic Steels

Abstract
This chapter presents microstructure features, which are responsible for transformation-induced and twinning-induced plasticity in austenitic steels, gives an overview of relevant microstructure defects and shows how the microstructure defects and their interactions affect the deformation behaviour of these steels. Numerous examples illustrate the capability of scanning and transmission electron microscopy and X-ray and electron diffraction to detect, to identify and to quantify dislocations, stacking faults, twins and their clusters. In this context, the benefits of the in situ techniques of microstructure analysis are emphasized. As the presence and arrangement of stacking faults in austenite play a central role in the plasticity of the austenitic steels, a large part of this chapter is devoted to the characterization and description of their formation, widening and ordering. A novel method for determination of the stacking fault energy is presented that utilizes in situ X-ray or synchrotron diffraction under deformation. Finally, the dependence of the stacking fault energy on the chemical composition of the steel and on the deformation temperature is addressed, and considered as an effective tool for design of steels with desirable mechanical properties.
David Rafaja, Christiane Ullrich, Mykhaylo Motylenko, Stefan Martin

Open Access

### Chapter 12. Investigations on the Influence of Strain Rate, Temperature and Reinforcement on Strength and Deformation Behavior of CrMnNi-Steels

Abstract
This section presents the results of comprehensive investigations into the strength and deformation behavior of CrMnNi-TRIP/TWIP steels and particle-reinforced TRIP-Matrix-Composites. These investigations combined quasi-static and dynamic tensile, compressive, and plate impact tests with ex situ microstructure analysis using electron microscopy and diffraction techniques on representative samples. The aim was the investigation and microstructurally-based description and modeling of the temperature and strain rate dependent strength, deformation and failure behavior of these advanced materials. It could be shown that the behavior of austenitic CrMnNi steels is controlled by different deformation mechanisms. These include mechanical twinning and martensitic phase transformations, whose occurrences or interactions are influenced by the chemical composition or the austenite stability, the stacking fault energy, the deformation temperature and rate as well as by the loading direction. Furthermore, the mechanical properties of honeycomb structures made of CrMnNi steel or TRIP-Matrix-Composites have been investigated. These are intended as lightweight and high strength components to improve the crash performance of constructions in the field of mobility. Since their mechanical properties are influenced by several parameters such as the chemical composition of the material, the structure type or the reinforcement content, detailed analyses are necessary before their application in vehicle components.
Ralf Eckner, Christine Baumgart, Lutz Krüger

Open Access

### Chapter 13. Cyclic Deformation and Fatigue Behavior of Metastable Austenitic Steels and Steel-Matrix-Composites

Abstract
The present contribution highlights the cyclic deformation behavior of metastable austenitic steels focusing on the effects of different (i) chemical compositions, (ii) manufacturing methods and (iii) strengthening methods in terms of a particle reinforcement and a quenching and partitioning treatment. The investigations are based on total strain controlled fatigue tests and the observed mechanical properties are discussed in context with the microstructural processes in the material, in particular the fatigue-induced α′-martensite formation. Overall, a major relevance is ascribed to the stacking fault energy and the grain size of the material. The fatigue behavior of the steels with different chemical compositions and the steels processed via casting, additive manufacturing, reversion annealing and hot pressing, respectively, is dominated by these two factors. In contrast, the most important factor in case of the reinforced steel-matrix-composites are the Mg-PSZ particles. The advantage of increasing stress amplitudes with increasing particle fraction is purchased with particle-related damage mechanisms like debonding and particle rupture causing a shorter fatigue life. The quenching and partitioning steel on the other hand benefits from higher α′-martensite fractions after partitioning increasing both, the strength and the fatigue life of the material.
Horst Biermann, Matthias Droste

Open Access

### Chapter 14. Behaviour of Metastable and Stable Austenitic Stainless Steels Under Planar-Biaxial Load

Abstract
The aim of the present study was to investigate the behaviour of a powder metallurgically produced high alloy X5CrMnNi16-7-6 metastable austenitic stainless steel under planar-biaxial loading. For this purpose, cruciform specimens made of this material were subjected both to quasi-static loading and to cyclic loading for low cycle fatigue and crack growth investigations. In addition to quasi-static shear loading with load axes force ratio $$\uplambda =-1$$ and quasi-static equibiaxial loading with $$\uplambda =1$$, further specimens were subjected to a load ratio of $$\uplambda ={0.5}$$ to determine the yield surface. Quasi-static sequence tests with permanently changing $$\uplambda$$ were carried out to determine load sequence effects. The characterization of the low cycle fatigue behavior was carried out under equibiaxial tensile loading with load axes strain ratio $$\Phi =1$$ and shear loading with $$\Phi =-1$$. Furthermore, investigations were carried out at different strain ratios. The description of the low cycle fatigue lives was performed using the Basquin-Manson-Coffin relationship. For both quasi-static and LCF experiments, the martensite content was measured in situ, so that the influence of the phase transformation on the material behaviour could be described. The fatigue crack growth investigations were performed on cruciform specimens under uniaxial, equibiaxial and initially equibiaxial and subsequently phase-shifted loading on a stable austenitic steel variant. In order to describe the fatigue crack growth, a finite element (FE) analysis of the specimen geometry was carried out first, so that a correlation between force and resulting stress in the uncracked specimen could be established. A geometry function for straight growing cracks was established by correlation between force and resulting stress in the specimen and K-solution at different crack lengths. A comparison of the crack growth between uniaxial or equibiaxial and phase-shifted loading with kinking crack paths was made by means of Paris law.
Carl H. Wolf, Sebastian Henkel, Horst Biermann

Open Access

### Chapter 15. Scanning Electron Microscopy and Complementary In Situ Characterization Techniques for Characterization of Deformation and Damage Processes

Abstract
This chapter presents results on in situ deformation experiments performed either inside the scanning electron microscope or in combination with other complementary in situ characterization techniques such as digital image correlation, acoustic emission or infrared thermography. The range of materials investigated extends from austenitic CrMnNi steels enabling TRIP (TRansformation Induced Plasticity) and/or TWIP (TWinning Induced Plasticity) effect and austenitic-martensitic-carbidic CrMnNi steels after quenching and partitioning to MgO-partially stabilized zirconia and TRIP matrix composites. The performed mechanical tests include both tensile and compressive loading as well as cyclic loading in a temperature range from room temperature up to 200 °C. The great potential of the applied in situ characterization techniques is their complementarity, which is shown, in particular, by the seven case studies presented. The combination of different techniques—such as the in situ deformation within the SEM combined with the digital image correlation—has a high potential to gain a deeper understanding on strain localizations by different microstructural features such as deformation bands, twin bundles or martensitic nuclei. In addition, these complementary in situ techniques can contribute to the modelling of the deformation behavior of TRIP/TWIP steels, in particular, or for any other kind of materials with complex deformation processes. Here, the acoustic emission measurements offer, in particular, a great potential, since this is the only real time in situ characterization technique delivering bulk information with a time-resolution in the range of microseconds.
Anja Weidner, Robert Lehnert, Horst Biermann

Open Access

### Chapter 16. X-Ray Computer Tomography for Three-Dimensional Characterization of Deformation and Damage Processes

Abstract
The investigation of phase transformations in metastable ceramic systems such as zirconia often requires local phase analysis within the areas of interest. Electron backscatter diffraction is a suitable method. The effect of the combination with focused ion beam sample preparation was determined in this work. In addition metal matrix compositemetal matrix composite honeycombs and foams as well as beads were investigated. The foams and honeycombs were composed of austenitic steel exhibiting TRansformation Induced Plasticity (TRIP) and magnesia partially stabilized zirconia. Both components exhibit martensitic phase transformation during deformation, thus generating the potential for improved mechanical properties such as strength, ductility, and energy absorption capability. The aim of these investigations was to show that stress-assisted phase transformations within the ceramic reinforcement correspond to strong local deformation, and to determine whether they can trigger martensitic phase transformations in the steel matrix. To this end, in situ interrupted compression experiments were performed in an X-ray Computed Tomography Device (XCT). By using a recently developed reconstruction algorithm, local deformation was calculated and regions of interest were defined. Corresponding cross sections were prepared and used to analyze the local phase composition by electron backscatter diffraction. The results show a strong correlation between local deformation and phase transformation.
Harry Berek, Marie Oppelt, Christos G. Aneziris

Open Access

### Chapter 17. The Corrosion Behavior of High-Alloy CrMnNi Steels—A Research Work on Electrochemical Degradation in Salt- and Acid-Containing Environments

Abstract
The electrochemical corrosion behavior of high-alloy cast steels as well as of steel/ceramic composites was analyzed by conventional polarization, electrochemical impedance and long term-outdoor exposure tests in sulfuric acid and chloride containing solutions. Additionally, for the determination of corrosion initiation processes and its subsequent implications, potentiodynamic polarization and electrochemical noise were combined with the acoustic emission technique. The results of these studies show that several corrosion mechanisms occur simultaneously when the surface is potentiodynamically stressed, and that pitting corrosion starts with a specific time-shift to its initiation at the surface.
Marcel Mandel, Volodymyr Kietov, Lutz Krüger

Open Access

### Chapter 18. CFD Analysis of the Particle and Melt Flow Behavior During Fabrication and Processing of TRIP-Matrix-Composites

Abstract
Computational fluid dynamics simulations are conducted to supplement experimental investigations in order to gain a deeper understanding of physical effects during fluid flow and heat transfer in steel making and processing. This offers the possibility to examine physical effects of the liquid steel in greater detail and isolated of entire processes. Liquid steel is present in the fabrication processes of TRIP-Matrix-Composites, namely gas atomization of the steel melt to produce powder, and liquid steel infiltration into ceramic structures. It also occurs during further processing, e.g. in welding or coating. Numerical simulations of these processes are performed with the finite volume method using the free open-source software package OpenFOAM. The libraries are extended where needed. This includes formulations for phase change, heat sources, latent heat, additional forces, calculations for material properties in multiphase flows, and particle tracking. The models are used to simulate electron beam welding, infiltration, gas atomization, and flame spraying and to reveal significant effects for each particular process.
Sebastian Borrmann, Sebastian Neumann, Rüdiger Schwarze

Open Access

### Chapter 19. Thermodynamic Modelling in the Frames of the TRIP-Matrix-Composite Development

Abstract
The present chapter is focused on thermodynamic modelling as a part of a complex development of metal-ceramic composite materials. Within this chapter the main examples of successful application of thermodynamic calculation for a solving of technological problems are highlighted, basic theory and methods of thermodynamic investigations and modelling are described in details and the most important results are briefly given. The purpose of this chapter is to give a deep understanding of thermodynamic modelling from basic experiments to modern methods of simulation. There is a set of recommendations for performing thermodynamic assessment and creation of multicomponent thermodynamic databases.
Ivan Saenko, Olga Fabrichnaya

Open Access

### Chapter 20. Thermodynamic-Mechanical Modeling of Metastable High Alloy Austenitic CrMnNi Steels

Abstract
The deformation-induced formation of α′-martensite was investigated by tensile testing of a X5CrNi18-10 wrought austenitic steel and X3CrMnNi16-7-3/6/9 (Ni contents of 3, 6, and 9 mass%) as well as X15CrNiMnN19-4-3 cast austenitic steels at temperatures between −80 and 400 °C. The results were presented in the form of Stress-Temperature-Transformation (STT) and Deformation-Temperature-Transformation (DTT) diagrams. The diagrams laid foundations for the development of a method for the quantitative determination of strength and elongation contributions by means of induced and often overlapping deformation processes in the austenite. The summation of such contributions yielded the tensile strength and the uniform elongation of the steel. In order to determine the critical Gibbs free energy for the formation of martensite at temperatures between $$M_{\text{s}}$$ and $$M_{\text{d}}$$, the chemical and mechanical contributions to deformation-induced martensite formation were determined by CALPHAD method using Thermo-Calc software. The mechanical contribution was estimated by determining the triggering stress for the formation of martensite using an in situ magnetic measurement device. This was done using the model proposed by Patel and Cohen. The magnitudes of shear strain ($$\gamma_{0}$$) and dilatational strain ($$\varepsilon_{0}$$), required for the calculations, were obtained based on the martensite crystallography theory of Wechsler-Lieberman-Read. The sum of the chemical and mechanical contributions yielded the critical driving force for the martensitic transformation.
Michael Hauser, Marco Wendler, Javad Mola, Olga Fabrichnaya, Olena Volkova, Andreas Weiß

Open Access

### Chapter 21. Multi-scale Modeling of Partially Stabilized Zirconia with Applications to TRIP-Matrix Composites

Abstract
The understanding of how the microstructure influences the mechanical response is an essential pre-requisite for materials tailored to match specific requirements. The aim of this chapter is to further this understanding in the context of Mg-PSZ-TRIP-steel composites on three different scales using a set of methods ranging from phase-field simulations over micromechanics to continuum constitutive modeling. On the microscale, using a Ginzburg-Landau type phase-field model the effects of cooling- and stress-induced martensitic phase transformation in MgO-PSZ is clearly distinguished. Additionally with this method the role of energy barrier in variant selection and the effect of residual stress contributing to the stability of the tetragonal phase are also investigated. On the mesomechanical scale, an analytical 2D model for the martensitic phase transformation and self-accommodation of inclusions within linear elastic materials has been successfully developed. The influences of particle size and geometry, chemical driving force, temperature and surface energy on the $$t \rightarrow m$$ transformation are investigated in a thermostatic approach. On the continuum scale, a continuum material model for transformation plasticity in partially stabilized zirconia ceramics has been developed. Nonlinear hardening behavior, hysteresis and monoclinic phase fraction during a temperature cycle are analyzed. Finally, The mechanical properties of a TRIP steel matrix reinforced by ZrO$$_2$$ particles are analyzed on representative volume elements. Here the mechanical properties of the composite as function of volume fraction of both constituents and the strength of the interface are studied.
Mohan Kumar Rajendran, Michael Budnitzki, Meinhard Kuna

Open Access

### Chapter 22. Modeling of the Thermomechanical Behavior, Damage, and Fracture of High Alloy TRIP-Steel

Abstract
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.
Andreas Seupel, Andreas Burgold, Stefan Prüger, Michael Budnitzki, Meinhard Kuna

Open Access

### Chapter 23. Properties of Phase Microstructures and Their Interaction with Dislocations in the Context of TRIP Steel Systems

Abstract
Transformation Induced Plasticity (TRIP) steels undergo a diffusionless phase transformation from austenite to martensite, resulting in a material exhibiting desireable material properties such as exceptional balance of strength and ductility as well as good fatigue behavior. Computational modeling at the mesoscale is potentially a suitable tool for studying how plastic deformation interacts with phase transformations and ultimately affects the bulk properties of these steels. We introduce models that represent the phase microstructure in a continuum approach and couple a time-dependent Ginzburg-Landau equation with discrete dislocation via their elastic strain energy densities. With this, the influence of several dislocation configurations are examined, namely a single dislocation, a “penny-shaped crack”, and a “dislocation cascade”. It is shown that the strain due to the presence of dislocations has a significant influence on the resultant martensitic microstructure. Furthermore, the importance of using a non-local elasticity approach for the dislocation stress fields is demonstrated.
Rachel Strobl, Michael Budnitzki, Stefan Sandfeld

Open Access

### Chapter 24. Towards the Crystal Plasticity Based Modeling of TRIP-Steels—From Material Point to Structural Simulations

Abstract
With the complex multi-scale behavior of high-alloyed TRIP steels in mind, this contribution aims to complement recently established continuum mechanical modeling approaches for such materials, by considering their anisotropic inelastic response at the single crystal level. This approach generally enables the consideration of initial textures and their deformation-induced evolutions. It also represents the key theoretical and algorithmic foundation for future extensions to include phase transformation and twinning effects. Several rate-independent and rate-dependent formulations are investigated. The former are naturally associated with Karush-Kuhn-Tucker type inequality constraints in the sense of a multi-surface plasticity problem, whereas in the latter, these constraints are handled by penalty-type approaches. More specifically, the primary octahedral slip systems of face-centered cubic crystal symmetry are explicitly taken into account in our model application of the general framework and hardening models of increasing complexity are incorporated. To test the efficiency and robustness of the different formulations, material point simulations are carried out under proportional and non-proportional deformation histories. A rate-independent augmented Lagrangian formulation is identified as most suitable in the considered context and its finite element implementation as a User-defined MATerial subroutine (UMAT) is consequently studied in depth. To this end, the loading orientation dependence of the deformation and localization behaviors are analyzed through simulation of a mildly notched tensile specimen as a representative inhomogeneous boundary value problem.
Stefan Prüger, Björn Kiefer

### Backmatter

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