Sub-project 6 – Microstructure simulation of solidification in the weld seam

Motivation

Solidification cracking during laser beam welding (LBW) is a complex, multiscale and multiphysical phenomenon that originates in the microstructure. Sub-project TP6 investigates the formation and propagation of solidification cracks at the microscale, using chemo-thermo-mechanical modelling. With a strongly coupled phase-field model, the evolution of stresses and strains during dendritic solidification and the subsequent solid-state transformations is predicted.

In the first funding phase, TP6 focused on austenitic stainless steels. However, these steels generally show good resistance to solidification cracking, which makes it difficult to directly correlate theoretical predictions with experimentally observed, cracked microstructures. For the second funding phase, TP6 therefore focuses on Ni-based superalloys. These alloys exhibit a significantly higher susceptibility to solidification cracking and offer a wide range of compositional variations and solidification behaviours, making them far better suited for an in-depth study of the underlying relationships between microstructure and properties.

Results from the first funding phase

Building on the work of the first phase, TP6 established several key results that form the foundation for the second phase:

• A CALPHAD-based parabolic Gibbs-energy model for the quaternary Fe-C-Cr-Ni system was formulated and validated. It reproduces the CALPHAD thermodynamics in the relevant solidification range with an accuracy of over 99 %.
• Validated 2D and 3D phase-field simulations of dendritic growth reproduced the dendritic morphology and the microsegregation of the critical alloying elements (C, Cr, Ni), including the transition from columnar to cellular dendrites and the formation of residual interdendritic liquid.
• The contribution of thermal and chemical (segregation-induced) inelastic strains to the local stress state was quantified, and an initial assessment of the probability of cracking was performed based on these thermochemical inelastic strains.
• For high-throughput solidification studies, a fully automated Kadi4Mat / KadiStudio workflow was developed that includes CALPHAD fitting, analysis of the weld pool geometry, setup of HPC simulations and automated post-processing of characteristic microstructural parameters (dendrite tip radius, arm spacing, tip velocity, etc.).

Objective

The overarching goal of the second phase is to improve the understanding and quantitative prediction of solidification cracking at the microscale in Ni-based superalloys. The main objectives are as follows:

• Extension of the strongly coupled chemo-thermo-mechanical phase-field model through a separate treatment of interstitial and substitutional elements (e.g. boron, carbon, nitrogen) and through a simulated temperature evolution, including the release of latent heat.
• Modelling of the γ → γ′ solid-state transformation and the associated transformation strains, which are decisive for the mechanical stability and crack susceptibility of Ni-based superalloys.
• Determination of the effective, temperature-dependent mechanical properties at the micro- and grain scale, based on the simulated microstructures.
• Modelling of the crack nucleation and propagation during solidification, using anisotropic critical energy release rates that depend on the depletion zone, as well as the derivation of statistical crack descriptors (crack distribution, crack fraction and crack formation rate).
• Integration of all steps into Kadi4Mat high-throughput workflows, in conjunction with AI and machine learning methods (e.g. Bayesian optimisation), to identify optimal alloy compositions and process parameters for minimising hot cracks.

Work plan

The project is divided into five interrelated work packages (WP):

1. Model extension and parameterisation – CALPHAD-based Gibbs energy functions for the Ni-based alloy, grouping of chemically similar elements into a quaternary configuration, separate treatment of interstitial and substitutional elements, and coupling of the simulated temperature evolution (input from TP3 / TP4).
2. Automated execution of solidification simulation studies – Adaptation of the Kadi4Mat workflow to the Ni-based system, high-throughput dendritic solidification studies, and automated determination of morphological descriptors (together with TP4 / TP7).
3. Modelling of the γ → γ′ solid-state transformation – Prediction of the precipitation microstructure and transformation-induced stresses at the micro- and grain scale.
4. Loading simulation studies and effective mechanical properties – Elasto-plastic (J2 plasticity, Voce hardening) simulations to derive effective, anisotropic mechanical properties and local stress concentrations from the microstructures.
5. Modelling of solidification cracking – A research group-wide work package in which a multiphase-field model for crack propagation is applied and extended to identify critical influencing factors and determine crack initiation criteria for the LBW of Ni-based superalloys.

Together, the workflows of WP2, WP3 and WP5 form a digital twin that can be used to analyse how the physical boundary conditions influence the critical factors in solidification cracking.

Interaction with the other sub-projects

TP6 receives thermal and mechanical boundary conditions from TP3 and TP4, and grain-scale microstructures from TP3. In return, TP6 supplies microscale morphological information and effective, temperature-dependent mechanical properties to TP4 and TP5, and parameterises the grain-scale solidification model in TP3. Simulated microstructures are compared with experimental results from TP1 and TP2, and all workflows, data and metadata are managed via TP7 (Kadi4Mat), following the FAIR principles.

Sub-project management

Sub-project researcher