Feasibility of Direct Learning in Predicting Complex Flow Behavior of Metastable TiAl Intermetallics: Constitutive Analysis, Modelling and Numerical Implementation

Abstract

The deformation behavior of a TiAl alloy with a (β_o + γ) structure was studied in the temperature range of 1000 ~ 1150 °C and strain rates of 10⁰ ~ 10^–3 s⁻¹, which was characterized by intricate and irregular flow hardening/softening primarily due to the initial metastable microstructure and the onset of phase transition during deformation. As a consequence, the flow behavior was quite difficult to be modelled by the conventional constitutive relations even utilizing the highly flexible strain-compensated hyperbolic-sine law. Therefore, in this study we tried to develop an accurate constitutive model based on the multilayer feed-forward neural networks (FFNN). To this end, the FFNNs with various widths (nodes-per-layer) and depths (number of hidden layers) were constructed and evaluated. A dual-cycle training strategy was proposed to achieve the best performance for each FFNN, whereby an optimal architecture with four hidden layers and four nodes-per-layer was selected to balance the overfitting and underfitting. After systematic verification, it was demonstrated that the optimized FFNN showed superior predictivities in terms of excellent reproducibility of existing flow data, powerful interpolation and reasonable extrapolation, which notably outperformed those of the classical constitutive models. To further test the applicability of the FFNN-based model in numerical simulations, it was implemented into the finite-element (FE) code together with an efficient automatic differentiation programme. The reasonable prediction of the heterogeneous metal flow during the benchmark compression test manifested the feasibility of the multilayer FFNNs as advanced constitutive models, which were trained directly from the experimental flow data.

Graphical Abstract