Computational multiscale modeling of steels assisted by transformation-induced plasticity

The contribution of the martensitic transformation to the overall stress-strain response of a multiphase steel assisted by a transformation- induced plasticity effect is analyzed in detail. A recently-developed multiscale transformation model is combined with a plasticity model to simulate the response of a three-dimensional grain of retained austenite embedded in a ferrite-based matrix. Results show that the effective hardening behavior of the material depends strongly on the grain orientation and, to a lesser extent, on the grain size

Crystalline damage growth during martensitic phase transformations

A thermomechanical model is developed within a large deformation setting in order to simulate the interactions between martensitic phase transformations and crystalline damage growth at the austenitic grain level. Subgrain information is included in the model via the crystallographic theory of martensitic transformations. The damage and transformation characteristics are dependent of the specific martensitic transformation systems activated during a loading process, which makes the model strongly anisotropic. The state of transformation for the individual transformation systems is represented by the corresponding volume fractions. The state of damage in the austenite and in the martensitic transformation systems is reflected by the corresponding damaged volume fractions. The thermodynamical forces energetically conjugated to the rate of volume fraction and the rate of damaged volume fraction are the driving forces for transformation and crystalline damage, respectively. The expressions for these driving forces follow after constructing the specific form of the Helmholtz energy for a phase-changing, damaging material. The model is used to analyze several three-dimensional boundary value problems that are representative of microstructures appearing in multiphase carbon steels containing retained austenite. The analyses show that the incorporation of damage in the model effectively limits the elastic stresses developing in the martensitic product phase, where the maximum value of the stress strongly depends on the toughness of the martensite. Furthermore, in an aggregate of randomly oriented grains of retained austenite embedded in a ferritic matrix the generation of crystalline damage delays the phase transformation process, and may arrest it if the martensitic product phase is sufficiently brittle. The response characteristics computed with the phase-changing damage model are confirmed by experimental results

Computational modelling of plasticity induced by martensitic phase transformations

A time integration scheme is presented for the martensitic phase transformation model developed in recent theoretical work of Turteltaub and Suiker (A multi-scale thermomechanical model for cubic to tetragonal martensitic phase transformations 2005; Transformation-induced plasticity in ferrous alloys 2005). The phase transformation model can be used for analysing transformation-induced plasticity (TRIP) phenomena in ferrous alloys. The microstructural information for the phase transformation model is provided by the crystallographic theory of martensitic transformations. The transformation characteristics depend on the specific transformation systems activated during a loading process. The time integration scheme is formulated within a framework of finite deformations, where the stress-update algorithm is based on a fully implicit Euler backward discretization. A robust search algorithm is used for detecting the transformation systems activated during loading. The completion of the transformation process is prescribed by a constraint on the total martensitic volume fraction, which is accurately satisfied in the converged state using a sub-stepping algorithm. The computation of the consistent tangent operator is performed through a numerical differentiation method, which avoids the determination of extensive analytical derivatives and allows the model to be easily adapted if necessary. The ability of the algorithm to solve complex transformation-induced plasticity problems is illustrated with the aid of three-dimensional analyses, in which an aggregate of single-crystal grains of retained austenite embedded in a ferrite-based matrix is subjected to uniaxial tension. Copyright © 2005 John Wiley & Sons, Ltd

Grain size effects in multiphase steels assisted by transformation-induced plasticity

The influence of the austenitic grain size on the overall stress-strain behavior in a multiphase carbon steel is analyzed through three-dimensional finite element simulations. A recently developed multiscale martensitic transformation model is combined with a plasticity model to simulate the transformation-induced plasticity effects of a grain of retained austenite embedded in a ferrite-based matrix. Grain size effects are included via a surface energy term in the Helmholtz energy. Tensile simulations for representative orientations of the grain of retained austenite show that the initial stability of the austenite increases as the grain size decreases. Consequently, the effective strength is initially higher for smaller grains. The influence of the grain size on the evolution of the transformation process strongly depends on the grain orientation. For "hard" orientations, the transformation rate is higher for larger grains. In addition, the phase transformation is partially suppressed as the grain size decreases. In contrast, for "soft" orientations, the transformation rate is lower for larger grains. The phase transformation is more homogeneous for smaller grains and, consequently, the effective transformation strain is larger. Nevertheless, in multiphase carbon steels with a relatively low percentage of retained austenite, the influence of the austenitic grain size on the overall constitutive response is smaller than the influence of the austenitic grain orientation. © 2006 Elsevier Ltd. All rights reserved

Transformation-induced plasticity in ferrous alloys

We study the mechanical behavior of a class of multiphase carbon steels where metastable austenite at room temperature is found in grains dispersed in a ferrite-based matrix. During mechanical loading, the austenite undergoes a displacive phase change and transforms into martensite. This transformation is accommodated by plastic deformations in the surrounding matrix. Experimental results show that the presence of austenite typically enhances the ductility and strength of the steel. We use a recently developed model (Turteltaub and Suiker, 2005) to analyze in detail the contribution of the martensitic transformation to the overall stress-strain response of a specimen containing a single island of austenite embedded in a ferrite-based matrix. Results show that the performance of the material depends strongly on the lattice orientation of the austenite with respect to the loading direction. More importantly, we identify cases in which the presence of austenite can in fact be detrimental in terms of strength, which is relevant information in order to improve the behavior of this class of steels. © 2005 Elsevier Ltd. All rights reserved

Crystalline damage development during martensitic transformations

A recently developed thermo-mechanical model [1] is presented that can be used to simulate the interactions between martensitic phase transformations and crystalline damage growth at the austenitic grain level. Subgrain information is included in the model via the crystallographic theory of martensitic transformations, see also [2,3]. The state of transformation for the individual transformation systems is represented by the corresponding volume fractions. The state of damage in the austenite and the martensitic transformation systems is reflected by the corresponding damaged volume fractions. The thermodynamical forces energetically conjugated to the rate of volume fraction and the rate of damaged volume fraction are the driving forces for transformation and crystalline damage, respectively. The model is used to analyse three-dimensional boundary value problems that are representative of microstructures appearing in multiphase carbon steels assisted by transformation-induced plasticity. The numerical integration of the model is performed within a finite deformation framework, using a fully implicit Euler backward method. The consistent tangent is computed numerically by consistent linearization of the updated stress, see also [4]. The analyses show that the growth of damage effectively limits the elastic stresses developing in the martensitic product phase, where the maximum value of the stress strongly depends on the toughness of the martensite. Furthermore, the generation of crystalline damage delays the phase transformation process, and may arrest it if the martensitic product phase is sufficiently brittle. The response characteristics computed with the phase-changing damage model are confirmed by experimental results.Aerospace Engineerin

Crystallographically based model for transformation-induced plasticity in multiphase carbon steels

The microstructure of multiphase steels assisted by transformation-induced plasticity consists of grains of retained austenite embedded in a ferrite-based matrix. Upon mechanical loading, retained austenite may transform into martensite, as a result of which plastic deformations are induced in the surrounding phases, i.e., the ferrite-based matrix and the untransformed austenite. In the present work, a crystallographically based model is developed to describe the elastoplastic transformation process in the austenitic region. The model is formulated within a large-deformation framework where the transformation kinematics is connected to the crystallographic theory of martensitic transformations. The effective elastic stiffness accounts for anisotropy arising from crystallographic orientations as well as for dilation effects due to the transformation. The transformation model is coupled to a single-crystal plasticity model for a face-centered cubic lattice to quantify the plastic deformations in the untransformed austenite. The driving forces for transformation and plasticity are derived from thermodynamical principles and include lower-length-scale contributions from surface and defect energies associated to, respectively, habit planes and dislocations. In order to demonstrate the essential features of the model, simulations are carried out for austenitic single crystals subjected to basic loading modes. To describe the elastoplastic response of the ferritic matrix in a multiphase steel, a crystal plasticity model for a body-centered cubic lattice is adopted. This model includes the effect of nonglide stresses in order to reproduce the asymmetry of slips in the twinning and antitwinning directions that characterizes the behavior of this type of lattices. The models for austenite and ferrite are combined to simulate the microstructural behavior of a multiphase steel. The results of the simulations show the relevance of including plastic deformations in the austenite in order to predict a more realistic evolution of the transformation process

Oxide growth and damage evolution in thermal barrier coatings

Cracking in thermal barrier coatings (TBC) is triggered by the development of a thermally-grown oxide (TGO) layer that develops during thermal cycling from the oxidation of aluminum present in the bond coat (BC). In the present communication a numerical model is presented that describes the interactive development of the TGO morphology and the fracture processes in TBC systems in a mesh-independent way. The evolution of the TGO-BC mixture zone is described by an oxygen diffusion-reaction model. The partition-of-unity method is employed for the simulation of discrete cracking, where cracks can nucleate and propagate across finite elements at arbitrary locations and orientations. The validity of the model is demonstrated through the analysis of a representative TBC system subjected to a specific thermal cycling process. A parametric analysis demonstrates the sensitivity of the response of the TBC system to the fracture strength of the top coat. The simulation results indicate that cracks appear primarily at the current location of the BC-TGO interface and may nucleate at early stages of thermal cycling. These results are in good agreement with recent experimental observations reported in the literature. © 2011 Elsevier Ltd

Coupled thermomechanical analysis of transformation-induced plasticity in multiphase steels

The thermomechanical response of low-alloyed multiphase steels assisted by transformation-induced plasticity (TRIP steels) is analyzed taking into account the coupling between the thermal and mechanical fields. The thermomechanical coupling is particularly relevant since in TRIP steels the phase transformation that occurs during mechanical loading is accompanied by the release of a considerable amount of energy (latent heat) that, in turn, affects the mechanical response of the material. The internal generation of heat associated with the martensitic phase transformation and the plastic deformation are modeled explicitly in the balance of energy. The momentum and energy equations are solved simultaneously by using a fully-implicit numerical scheme. The simulations are conducted using a micromechanical formulation for single crystals of austenite and ferrite. The characteristics of the model are illustrated by means of simulations for a single crystal of austenite and an aggregate of austenitic and ferritic grains. For a single crystal of austenite, it is found that the increase in local temperature due to transformation actually hinders further transformation and, instead, promotes plastic deformation. However, for an aggregate of austenitic and ferritic grains in a multiphase steel, the increase in temperature due to transformation is limited since the heat generated in the austenite is conducted to the ferritic matrix, effectively lowering the temperature in the austenitic phase

Microcrack nucleation in thermal barrier coating systems

Crack nucleation in thermal-barrier coating (TBC) systems subjected to a monotonic cooling process is studied. The TBC system is modeled using the finite element method, where cracks are represented as discrete discontinuities across continuum elements using the partition-of-unity method. The numerical implementation used for crack nucleation is based on an algorithm where, at insertion of a discontinuity, the traction response is derived from a cohesive zone model that has been modified to (i) behave like an initially rigid cohesive model, and to (ii) ensure smoothness of the traction-separation law at zero crack opening. Accordingly, an adequate convergence behavior of the numerical formulation can be warranted in boundary value problems of systems with relatively complex geometries. In the present numerical study, a comparison is made between TBC systems composed of different constitutive models. The fracture patterns and evolutions of the overall crack growth resulting from the simulations clearly illustrate the importance of accounting for the effects of plasticity in the bond coating and anisotropy in the top coating. The computed fracture profile is in good correspondence with experimental observations reported in the literature. © 2008 Elsevier Ltd. All rights reserved