Efficient multiscale design of microstructure evolution in shape rolling: a validated FEM-FCA framework

The International Journal of Advanced Manufacturing Technology https://doi.org/10.1007/s00170-026-18419-5 ORIGINAL ARTICLE Efficient multiscale design of microstructure evolution in shape rolling: a validated FEM-FCA framework Łukasz Łach1 · Jarosław Nowak1 · Dmytro Svyetlichnyy1 Received: 4 February 2026 / Accepted: 27 May 2026 © The Author(s) 2026 Abstract Accurate prediction and design of microstructure evolution are essential for optimizing the mechanical performance of shape-rolled components. This work presents an efficient multiscale FEM–FCA computational framework that enables proactive microstructure design in shape rolling processes. The framework integrates Finite Element Method (FEM)derived thermomechanical fields with a computationally efficient Frontal Cellular Automata (FCA) approach that captures grain nucleation, growth, and static recrystallization (SRX). Unlike traditional CA methods that suffer from excessive computational costs, the FCA approach reduces simulation time by an order of magnitude while maintaining physical accuracy through front-tracking mechanisms. Originally validated for flat rolling, the framework has been extended to complex shape rolling geometries (square–oval–round sequences) through seamless multiscale data coupling. Comprehensive validation against experimental data from AISI 304 L stainless steel demonstrates excellent predictive capability, achieving RMSE of 1.099 μm (8.12%) for grain size and accurate flow stress evolution. This validated framework bridges the gap between detailed microstructural modeling and industrial applicability, offering a scalable tool for process optimization across diverse rolling operations and materials. Keywords Frontal cellular automata · Finite element method · Microstructure evolution · Shape rolling 1 Introduction Accurate prediction of microstructure evolution during metal forming processes is critical to optimize material properties and reduce industrial manufacturing costs. Shape rolling, in particular, presents unique challenges due to complex deformation patterns and varying thermomechanical conditions throughout the process. AISI 304 L stainless steel serves as an ideal test material for microstructure modeling validation due to its widespread industrial applications in automotive [1], aerospace [2, 3], and other industrial sectors [4, 5], where controlled grain refinement directly impacts mechanical performance through Hall-Petch strengthening [6, 7], corrosion resistance [8], and service life. The ability to predict and control microstructural evolution in Łukasz Łach 1 Faculty of Metals Engineering and Industrial Computer Science, AGH University of Krakow, al. Mickiewicza 30, Krakow 30-059, Poland shape rolling processes enables manufacturers to optimize processing parameters, reduce material waste, and achieve desired mechanical properties without extensive trial-anderror experimentation [9, 10]. Current approaches to microstructure evolution modeling encompass several computational methods, each with distinct advantages and limitations. The Finite Element Method (FEM) provides accurate thermomechanical field predictions but lacks microstructural detail [11, 12]. Traditional Cellular Automata (CA) models offer detailed grainlevel evolution, but suffer from high computational costs and poor scalability [13–16]. Phase Field Methods (PFM) provide high-resolution interface tracking, but are computationally prohibitive for industrial-scale applications [17– 19]. Level Set (LS) methods provide efficient front tracking but struggle with complex topological changes during recrystallization [20, 21]. Monte Carlo (MC) approaches offer statistical accuracy, but lack the deterministic predictability required for process control [22–24]. A critical gap exists in current modeling frameworks: the lack of computationally efficient multiscale integration that combines accurate thermomechanical predictions with detailed The International Journal of Advanced Manufacturing Technology microstructural evolution while maintaining industrial applicability. Furthermore, most existing models focus on flat rolling conditions, leaving shape rolling processes with complex deformation patterns inadequately addressed. The combination of FEM with Frontal Cellular Automata (FCA) addresses these limitations through a novel multiscale integration strategy. Unlike traditional CA models that require full-field calculations across the entire domain, FCA focuses computational resources only on active recrystallization fronts, dramatically reducing computational overhead while maintaining physical accuracy [25, 26]. This approach leverages the strength of the FEM to provide accurate thermomechanical fields (temperature, strain, strain rate) as input conditions for FCA-based microstructural evolution. The FCA method inherently accounts for both the nucleation and grain growth mechanisms during and after deformation, offering a unified perspective on static recrystallization that eliminates the need for separate dynamic and static models. Previous validation in flat rolling processes [27] demonstrated the accuracy and computational efficiency of the model, establishing a solid foundation for extension to the more complex conditions of the shape rolling. The independent modeling scheme (FEM → FCA without feedback) is justified by the dominance of the deformation parameters over the microstructural effects on the metal flow during the rolling conditions studied. Fig. 1 Modeling system for shape rolling 13 This study presents and validates a computationally efficient multiscale FEM–FCA framework for predicting microstructure evolution in AISI 304 L stainless steel during shape rolling. The framework extends a previously validated flat-rolling model to complex shape rolling geometries, specifically focusing on square-oval-round pass sequences commonly used in industrial applications. Validation is achieved through a comprehensive comparison with experimental data from laboratory-scale rolling tests, including grain size measurements and flow stress analysis. The developed framework advances process-aware microstructure modeling by improving both predictive accuracy and computational efficiency, offering an adaptable tool for industrial process optimization. 2 Shape rolling modeling system The comprehensive modeling system dedicated to shape rolling is presented in Fig. 1. Experimental studies, numerical simulations, and data from the literature are the main elements of information used during system development. Microscopic studies are basic research carried out in the field of experimental studies. The experimental findings and information from the existing literature serve as the basis for identifying and validating the model parameters. The International Journal of Advanced Manufacturing Technology In particular, flow stress data, recrystallization kinetics, and thermal properties of AISI 304 L were ado (...truncated)