Modeling martensitic transformation in shape memory alloys using multi-phase-field elasticity models based on partial rank-one energy relaxation on pairwise interfaces

To model the mechanically-driven phase transformations, e.g. martensitic transformation, using the phase-field theory, suitable models are needed for describing the mechanical fields of the individual non-vanishing phase-fields in the interface regions in order to obtain the mechanical driving forces of phase-field motion. Quantitative modeling requires satisfying the interfacial static equilibrium and kinematic compatibility conditions which have already been achieved in the literature for dual-phase-field materials by using the rank-one relaxation (or convexification) of the energy density. A direct generalization to the multi-phase-field case is not applicable without breaking these conditions partially. To the best of our knowledge, no existing multi-phase-field elasticity model has been able to satisfy the jump conditions between all the locally-active phase-fields on their pairwise normals in triple and higher-order junctions. In this work, we introduce a novel multi-phase-field elasticity model based on the partial rank-one relaxation of the elastic energy density defined on the pairwise interfaces...... (see PDF for the rest of the abstract

Efficient reconstruction of prior austenite grains in steel from etched light optical micrographs using deep learning and annotations from correlative microscopy

The high-temperature austenite phase is the initial state of practically all technologically relevant hot forming and heat treatment operations in steel processing. The phenomena occurring in austenite, such as recrystallization or grain growth, can have a decisive influence on the subsequent properties of the material. After the hot forming or heat treatment process, however, the austenite transforms into other microstructural constituents and information on the prior austenite morphology are no longer directly accessible. There are established methods available for reconstructing former austenite grain boundaries via metallographic etching or electron backscatter diffraction (EBSD) which both exhibit shortcomings. While etching is often difficult to reproduce and strongly depend on the investigated steel’s alloying concept, EBSD acquisition and reconstruction is rather time-consuming. But in fact, though, light optical micrographs of steels contrasted with conventional Nital etchant also contain information about the former austenite grains. However, relevant features are not directly apparent or accessible with conventional segmentation approaches. This work presents a deep learning (DL) segmentation of prior austenite grains (PAG) from Nital etched light optical micrographs. The basis for successful segmentation is a correlative characterization from EBSD, light and scanning electron microscopy to specify the ground truth required for supervised learning. The DL model shows good and robust segmentation results. While the intersection over union of 70% does not fully reflect the model performance due to the inherent uncertainty in PAG estimation, a mean error of 6.1% in mean grain size derived from the segmentation clearly shows the high quality of the result

Large scale 3-D phase-field simulation of coarsening in Ni-base superalloys

In this study we present a large scale numerical simulation of γ-γ′ microstructure evolution in Ni-base superalloy using the multi-phase field method in three dimensions. We numerically simulated precipitation hardening heat treatment cycles. Large scale three dimensional simulations are necessary in order to get sufficient statistics for predicting the morphological evolution, average γ′ precipitate size, precipitates size distribution over time and ripening exponent for a given temperature and composition. A detailed analysis of obtained result is presented emphasising the effect of elastic interaction on the coarsening kinetics in Ni-base superalloy. The study is performed using the phase-field modelling library “OpenPhase” which is based on a multi-phase field multi-component model

Modelling of flow behaviour and dynamic recrystallization during hot deformation of MS-W 1200 using the phase field framework

A new simulation environment is developed to simulate the evolution of microstructure and the corresponding flow stress during rolling. An orientation dependent crystal plasticity hardening model is coupled to grain evolution-, recovery- and recrystallization kinetics within a phase field framework. Hardening and softening kinetics are treated consecutive to differentiate between individual effects. Simulation results are compared to hot compression tests at 1373 K with a strain rate of 1 s−1

Atomistically Informed Extended Gibbs Energy Description for Phase-Field Simulation of Tempering of Martensitic Steel

In this study we propose a unified multi-scale chemo-mechanical description of the BCT (Body-Centered Tetragonal) to BCC (Body-Centered Cubic) order-disorder transition in martensitic steel by adding the mechanical degrees of freedom to the standard CALPHAD (CALculation of PHAse Diagrams) type Gibbs energy description. The model takes into account external strain, the effect of carbon composition on the lattice parameter and elastic moduli. The carbon composition effect on the lattice parameters and elastic constants is described by a sublattice model with properties obtained from DFT (Density Functional Theory) calculations; the temperature dependence of the elasticity parameters is estimated from available experimental data. This formalism is crucial for studying the kinetics of martensite tempering in realistic microstructures. The obtained extended Gibbs energy description opens the way to phase-field simulations of tempering of martensitic steel comprising microstructure evolution, carbon diffusion and lattice symmetry change due to the ordering/disordering of carbon atoms under multiaxial load

Modelling of flow behaviour and dynamic recrystallization during hot deformation of MS-W 1200 using the phase field framework

A new simulation environment is developed to simulate the evolution of microstructure and the corresponding flow stress during rolling. An orientation dependent crystal plasticity hardening model is coupled to grain evolution-, recovery- and recrystallization kinetics within a phase field framework. Hardening and softening kinetics are treated consecutive to differentiate between individual effects. Simulation results are compared to hot compression tests at 1373 K with a strain rate of 1 s−1

Multi-phase-field approach to fracture demonstrating the role of solid-solid interface energy on crack propagation

A multi-phase-field approach for crack propagation considering the contribution of the interface energy is presented. The interface energy is either the grain boundary energy or the energy between a pair of solid phases and is directly incorporated into to the Ginzburg–Landau equation for fracture. The finite difference method is utilized to solve the crack phase-field evolution equation and fast Fourier method is used to solve the mechanical equilibrium equation in three dimensions for a polycrystalline material. The importance of the interface (grain boundary) energy is analyzed numerically for various model problems. The results show how the interface energy variations change the crack trajectory between the intergranular and transgranular fracture

Parallel multiphase field simulations with OpenPhase

The open-source software project OpenPhase allows the three-dimensional simulation of microstructural evolution using the multiphase field method.The core modules of OpenPhase and their implementation as well as their parallelization for a distributed-memory setting are presented. Especially communication and load-balancing strategies are discussed. Synchronization points are avoided by an increased halo-size, i.e. additional layers of ghost cells, which allow multiple stencil operations without data exchange. Load-balancing is considered via graph-partitioning and sub-domain decomposition. Results are presented for performance benchmarks as well as fora variety of applications, e.g. grain growth in polycrystalline materials, including a large number of phase fields as well as Mg-Al alloy solidification

Microstructure Design of Tempered Martensite by Atomistically Informed Full-Field Simulation: From Quenching to Fracture

Martensitic steels form a material class with a versatile range of properties that can be selected by varying the processing chain. In order to study and design the desired processing with the minimal experimental effort, modeling tools are required. In this work, a full processing cycle from quenching over tempering to mechanical testing is simulated with a single modeling framework that combines the features of the phase-field method and a coupled chemo-mechanical approach. In order to perform the mechanical testing, the mechanical part is extended to the large deformations case and coupled to crystal plasticity and a linear damage model. The quenching process is governed by the austenite-martensite transformation. In the tempering step, carbon segregation to the grain boundaries and the resulting cementite formation occur. During mechanical testing, the obtained material sample undergoes a large deformation that leads to local failure. The initial formation of the damage zones is observed to happen next to the carbides, while the final damage morphology follows the martensite microstructure. This multi-scale approach can be applied to design optimal microstructures dependent on processing and materials composition