Austenitic TRIP/TWIP Steels and Steel-Zirconia Composites

Collected experimental data are used to adjust optimized parameters for Gibbs energy functions. The purpose of the CALPHAD method is to obtain a uniform description of all phases in the system that reproduces the thermodynamic properties.

Optimization

The Gibbs solvation energy described by the sublattice model with three sublattices is given by Higher order interaction parameters could also be included, giving more complicated excess Gibbs energy terms.

The Latest Results Concerning

The consideration of temperature dependence of endmember parameters and the introduction of mixing parameters for the Gibbs energy description of phase. The optimization of the thermodynamic parameters using all available experimental as well as theoretical data.

Conclusions

In addition, thermodynamic modeling methods provided the basis for the further development of the TRIP-Matrix-Composite. In addition, the inclusion of oxygen in the steel database dataset requires the implementation of system descriptions such as Fe–O, Mn–O, Cr–O, Ni–O and the associated ternary systems Fe–Ni–O, Fe–Mn–O, Fe–Cr–O, Ni–Cr–O, etc.

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Thermodynamic-Mechanical Modeling of Metastable High Alloy Austenitic

Introduction

The accuracy of such calculations will then depend on the reliability of the thermodynamic data. The focus of this work is the thermodynamic-mechanical modeling of metastable high-alloy austenitic CrMnNi steels.

Experimental Methods

This led to a magnetic field strength of 15 kA/m in the profile part of the tensile samples. The conversion of the stress induced in the second coil to the martensite fraction was carried out by a correlation procedure.

Fig. 20.1 Experimental setup showing tensile specimen and in situ magnetic measurement system with a tensile specimen, b first coil and c second coil

Theoretical Background

According to (20.3), the mechanical work consists of two terms: the first term is the shear stress (τr) responsible for the shear stress (γ0) parallel to the habit plane and the second term is the normal stress (σN) responsible for the volume expansion perpendicular to the habit plane (ε0) [23]. To calculate the angle θ associated with the maximum value of Wmech, the difference of (20.4) from θ must be set to zero. 20.5) The values ε0, γ0 and θmax are influenced by the lattice parameters of austenite and martensite, which in turn depend on the chemical composition.

Fig. 20.2 Schematic representation of the temperature dependence of the chemical driving force for α -martensite formation ( G γ chem →α ), minimum external mechanical work required to trigger the transformation (W min ), maximum applicable mechanical w

Model Development Based on an Austenitic X5CrNi18-10 Steel

According to Weiß et al., the second inflection point, marked Rmγ, corresponds to the tensile strength of the austenite [18,28]. This means that the trigger stressσAγ→αand the tensile strength Rmγ of the austenite are equal, which defines the Mdγ→α temperature.

Figure 20.6 shows the measured fractions of ε- and α -martensite in tensile speci- speci-mens tested at various temperatures until the onset of necking

Effect of Nickel on the Deformation Mechanisms of Metastable CrMnNi Cast Steels

The elongation temperature anomaly (broad maximum in Figure 20.11) in X3CrMnNi16-7-3 steel is mainly caused by strain-induced ε-TRIP [20]. In the temperature range between 0 and 50 °C, the triggering stress for the formation of α-martensite is very low.

Fig. 20.9 True stress-strain curves for tensile specimens of a X3CrMnNi16-7-3, b X3CrMnNi16- X3CrMnNi16-7-6 and c X3CrMnNi16-7-9 steel in the temperature range of − 196 to 250 °C [19, 34]

Conclusions

The critical driving force for the formation of α (−2496 J/mol) was obtained by determining the mechanical energy required to initiate the deformation-induced formation of α-martensite at 0 °C. The results made it possible to calculate the modified driving forces for the occurrence of the phase transformation γ →α.

Multi-scale Modeling of Partially Stabilized Zirconia with Applications

Introduction

Aims and Scopes of the Present Work
Introduction to Partially Stabilized Zirconia

To complement the fabrication and characterization of this MMC, thorough theoretical-numerical modeling of the composite material was required to understand and simulate the phase transformation and deformation behavior of both components. This work was devoted to the simulation of the phase transformation processes in the PSZ ceramic and the MMC, while another work investigated the behavior of the TRIP steel.

Fig. 21.1 Different scales of modeling partially stabilized zirconia

Micromechanical Phase-Field Approach

Phase-Field Method
Model Setup
Selected Results and Discussion

Phase Stability and Energy Barriers
Variant Selection by Energy Barriers
Origin and Effect of Residual Stresses

The Gibbs enthalpy landscapes based on pure thermodynamic contribution for both temperatures are compared in Fig.21.5b. As the operating temperature decreases, the residual voltage required to introduce a barrier for transformation increases (see Fig.21.10).

Fig. 21.3 Order parameter and lattice transformation representation of parent and product phases during martensitic phase transformation in zirconia ceramics

Mesomechanical Model

Transformation Criterion for a Single Precipitate Embedded in an Infinite Matrix

Working Hypotheses
Energetic Contributions
The Transformation Criterion

Uniaxial Loading

Orientation Dependence of the Transformation Stress
Sensitivity with Respect to the Inclusion Size, Aspect Ratio and Interfacial Energy

As expected, the stress required to initiate the phase transformation strongly depends on the orientation of the inclusion with respect to the applied load and is minimal if the tetragonal c axis is aligned along the direction of maximum shear (see Fig. 21.13). 21.14, 21.15 and 21.16 and agree with expectations: The transformation stress decreases with increasing size B and aspect ratio α of the inclusions and increases with increasing surface energy βI/I.

Fig. 21.11 Illustration of homogenization techniques used to model the effective material behavior of a polycrystal, influenced by the microstructure of each grain

Homogenization Within an Infinite Grain

Consequently we can write the elastic (tangential) stiffness of the inclusion in Voigt notation with reference to the usual crystallographic coordinate system as

Continuum Mechanics Approach

Constitutive Model for Phase Transformation in PSZ

Homogenization of PSZ Material
Thermodynamic State Potentials

Numerical Results

Particle Size Dependent Surface Energy Change
Temperature-Induced Phase Transformation

According to the thermodynamic framework of material modeling (see e.g. [39]), the constitutive equations of an elastic-plastic material can be derived from potential energy functions. This energy term per volume of RVE is calculated from the specific surface free energy change φsur(t→m) of zircon and the monoclinic volume fraction fmas follows. 21.58) In the original work [29] all transformable inclusions are assumed to be spheres of equal size with radius r(fm)=const.

Fig. 21.17 Representative volume element of PSZ:

Simulations of ZrO 2 -Particle Reinforced TRIP-Steel Composite

Unit Cell Model of the Composite
Results and Discussion

The phase transformation propensity in TRIP fα steel increases at higher zirconium oxide content, but is limited by ceramic failure. Due to the non-cohesive interface, tensile stresses are not transferred from the TRIP steel matrix to the zirconia inclusion.

Fig. 21.21 Sketch of unit cell (one-eighth volume) for the TRIP-ZrO 2 composite. Symmetry bound- bound-ary conditions are set on the coordinate planes x = 0, y = 0 and z = 0

Conclusions

The influence of the tetragonal particle size distribution on the phase transformation can be qualitatively predicted quite well. The influence of the volume content and boundary properties of ZrO2 particles on the overall response of the composite is investigated.

Modeling of the Thermomechanical Behavior, Damage, and Fracture of High

Introduction

In addition, the model is used in fundamental research on the fracture mechanics aspects of high-alloy TRIP-steel, revealing the role of martensitic phase transformation on ductility and fracture toughness [19–21]. In addition, substantial improvements to the micromechanical model have been proposed elsewhere, particularly to include thermomechanical coupling and stress-state-dependent hardening behavior of high-alloy TRIP steels [9,22] .

Thermomechanical Framework

Balance Equations
Constitutive Assumptions and Equations

State Potential
Consistent Rate Formulation
Generalized Stresses
Thermodynamic Forces

Dissipation and Heat Equation

The spatial area currently occupied by the material body is given by B. The boundary of the material body and the infinitesimal volume element are respectively denoted as∂Banddv. The conjugate thermodynamic forcesKα= {R,Fsb,Z,Y} associated with the set of internal variables are specified by (22.20) as. 22.40) The driving force for the martensitic phase transition consists of the energy difference gachem→m(ϑ), which is negative when the temperature is below the thermodynamic equilibrium temperature [36], i.e., in the region of interest.

Material Models

Preliminaries for both Models

Multiplicative Viscoplasticity
Strain Induced Martensite
TRIP Kinematics

Micromechanically Motivated Model

Homogenization Method
Martensite Kinetics and

Phenomenological Model

Viscoplastic Flow Rules
Isotropic Strain Hardening
Martensite Kinetics and TRIP-Kinematics: Empirical Model Motivated by the sound investigations on stress state dependency of strain induced
Ductile Damage
Thermodynamic Consistency

Numerical Implementation

Exceeding a critical value ω≥ωc determines the initiation of damage, i.e. the beginning of the development of the local damage driving force. For experimentally calibrated models, z˙ should vanish in this temperature range, i.e. the chemical part is typically thermodynamically consistent.

Results

Material
Deformation and Phase Transition Behavior

Martensite Kinetics
Asymmetric Strain Hardening
Strain Rate Dependency
Inhomogeneous Loading States

Stress Analysis and Material Forces for Cracks in TRIP-steels

Crack Tip Fields in Front of a Blunting Crack Tip
Material Forces in Consideration of Phase Transformation

Damage and Fracture of High Alloy TRIP-steel

Simulation of Crack Growth Using a Cohesive Zone Model
Simulations Using the Micromorphic Model of Ductile Damage

Towards the crack tip (from right to left) an increase in the stress components is seen. For the first calibration step, the parameters of the strain hardening model for cast X3CrMnNi 16-6-6 (section.22.4.2) have been slightly changed.

Fig. 22.1 Martensite volume fraction z versus true strain curves for uni-axial tension-compression loadings at different temperatures and constant strain rate

Conclusions

Acknowledgments The authors gratefully acknowledge the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) for funding the research in the framework of the Collaborative Research Center "TRIP-Matrix-Composite", (project number 54473466—SFB 799, subproject C5). Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution, and reproduction in any medium or format, as long as you credit the original author(s) and the source appropriately, provide a link to the Creative, and provide a link to the Creative.

Properties of Phase Microstructures and Their Interaction with Dislocations

Introduction

Computer simulations and numerical modeling of TRIP steels can be very useful for understanding the interaction of various microstructural phenomena, such as plane defects (e.g. phase transformations) and linear defects (dislocations), all of which can have a significant impact on the mechanical properties of the bulk material. The combination of martensitic phase transformations and dislocation activity results in lattice deformations and may eventually lead to more work hardening.

Interaction Between Martensitic Phase Transformations and Dislocations

Dislocations and Mechanical Equilibrium Conditions
Simulation Setup and Boundary Conditions
Simulation Results

Martensitic Seed and Edge Dislocation
Penny Shaped Crack in Austenitic Matrix

Any solid body in static equilibrium obeys the mechanical equilibrium equation, i.e. the divergence of the stress tensor, S, must be zero. However, the introduction of the dislocation breaks the symmetry (compare the right red region of the stress in Fig.23.4att=ts) and thus determines the growth direction of the band.

Fig. 23.1 Potential of phase transition. The two wells signify martensite variants 1 and 2

On the Interaction of Planar Defects with Dislocations Within the Phase-Field Approach

Introduction
Balance Equations and Boundary Conditions
Constitutive Equations

Laws of State
Free Energy and Dissipation Potential

Special Cases

Homogeneous Bulk Material
Grain Boundaries as Planar Defects
Twin Boundaries as Planar Defects
Phase Boundaries Between Cubic Phases

Examples

Regularization in the Dislocation Core
Effect of the Regularization on the Interaction of Dislocations with a Phase Boundary

Furthermore, without loss of generality, Etr(φ)=0. 23.44c) The isotropy of the gradient length voltage scale for cubic crystals implies that Q(φ)∗==l2I, which simplifies (23.44) to the following form. As shown in Section 23.3.4.1, the present model reduces to the set of equations proposed by Po et al.

Fig. 23.6 Shear stress component S 12 in the glide plane of a single edge dislocation

Conclusions

The result in this case is grid-sensitive, since the calculated voltage magnitude depends on the choice of discretization and is therefore unsuitable for quantitative investigation of the interaction of planar defects with dislocations. Gross, Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, vol.

Towards the Crystal Plasticity Based Modeling of TRIP-Steels—From

Material Point to Structural Simulations

Introduction

Here, the influence of the sequence of thermal and mechanical loading on the mechanical response and transformation behavior is investigated. Here again the influence of the initial crystal orientation on the mechanical behavior under homogeneous deformations is considered.

Fig. 24.1 Deformation mechanisms observed in the TRIP-steel X3CrMnNi16-6-6 as functions of temperature T or equivalently stacking-fault energy γ SF

Material Model

First, a purely phenomenological hardening formulation of the Taylor type in the form Yα=Y. 24.11) is introduced, incorporating the cumulative inelastic slip A=. To study the influence of the type of viscosity law on the deformation behavior of single crystals - in particular in the velocity-independent limit - this contribution considers two specific cases:.

Table 24.1 Primary slip systems of a face-centered cubic single crystal Miller indices Schmid/Boas

Material Response Under Homogeneous Deformation

Simple Shear Loading
Non-proportional Tension/compression-Shear Loading

The influence of the chosen increment size γ on the stress-strain curve is depicted in Fig.24.2. Fig. 24.8b along with the uniaxial stress path of the perfectly oriented single crystal simulated using the rate-dependent OM viscosity function.

Table 24.2 Material parameters for finite strain, simple shear loading

Constrained Tension Test

Symbols indicate the deformation at which field distributions of the logarithmic strain LE22 are shown in Fig.24.12. Motivated by similar studies presented in [81], the influence of the boundary conditions indicated in Fig.24.9 will now be analysed.

Conclusions

Gupta, Micromechanical modeling of martensitic phase transformation in steel based on nonlocal crystal plasticity. Rotary Advanced Material Models for the Crystal Plasticity Finite Element Method- Development of a General CPFEM Framework.