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

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

Multi-phase-field simulation of microstructure evolution in metallic foams

This paper represents a model for microstructure formation in metallic foams based on the multi-phase-field approach. The model allows to naturally account for the effect of additives which prevent two gas bubbles from coalescence. By applying a non-merging criterion to the phase fields and at the same time raising the free energy penalty associated with additives, it is possible to completely prevent coalescence of bubbles in the time window of interest and thus focus on the formation of a closed porous microstructure. On the other hand, using a modification of this criterion along with lower free energy barriers we investigate with this model initiation of coalescence and the evolution of open structures. The method is validated and used to simulate foam structure formation both in two and three dimensions

Microstructure design of tempered martensite by atomistically informed full-field simulation

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

Microstructure property classification of nickel-based superalloys using deep learning

Nickel-based superalloys have a wide range of applications in high temperature and stress domains due to their unique mechanical properties. Under mechanical loading at high temperatures, rafting occurs, which reduces the service life of these materials. Rafting is heavily affected by the loading conditions associated with plastic strain; therefore, understanding plastic strain evolution can help understand these material's service life. This research classifies nickel-based superalloys with respect to creep strain with deep learning techniques, a technique that eliminates the need for manual feature extraction of complex microstructures. Phase-field simulation data that displayed similar results to experiments were used to build a model with pre-trained neural networks with several convolutional neural network architectures and hyper-parameters. The optimized hyper-parameters were transferred to scanning electron microscopy images of nickel-based superalloys to build a new model. This fine-tuning process helped mitigate the effect of a small experimental dataset. The built models achieved a classification accuracy of 97.74% on phase-field data and 100% accuracy on experimental data after fine-tuning

On crystal mosaicity in single crystal Ni-based superalloys

In the present work, we investigate the evolution of mosaicity during seeded Bridgman processing of technical Ni-based single crystal superalloys (SXs). For this purpose, we combine solidification experiments performed at different withdrawal rates between 45 and 720 mm/h with advanced optical microscopy and quantitative image analysis. The results obtained in the present work suggest that crystal mosaicity represents an inherent feature of SXs, which is related to elementary stochastic processes which govern dendritic solidification. In SXs, mosaicity is related to two factors: inherited mosaicity of the seed crystal and dendrite deformation. Individual SXs have unique mosaicity fingerprints. Most crystals differ in this respect, even when they were produced using identical processing conditions. Small differences in the orientation spread of the seed crystals and small stochastic orientation deviations continuously accumulate during dendritic solidification. Direct evidence for dendrite bending in a seeded Bridgman growth process is provided. It was observed that continuous or sudden bending affects the growth directions of dendrites. We provide evidence which shows that some dendrites continuously bend by 1.7° over a solidification distance of 25 mm