RESEARCH PAPER
Multi-Objective NSGA-II Optimization with Arrhenius and Johnson–Cook Constitutive Modeling of Ductile Cast Iron at Elevated Temperature
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1
Mechanical engineering department, Faculty of Engineering, Qena University, Egypt
2
Mechanical Engineering Department, College of Engineering, Alasala Colleges, Saudi Arabia
3
Mechanical Engineering Department,, College of Engineering and Architecture, Umm Al-Qura University, Saudi Arabia
These authors had equal contribution to this work
Submission date: 2026-01-16
Final revision date: 2026-07-12
Acceptance date: 2026-07-12
Publication date: 2026-09-25
Corresponding author
Mohammed Y. ABDELLAH
Mechanical engineering department, Faculty of Engineering, Qena University, Maabar shabab, 83523, Qena, Egypt
Acta Mechanica et Automatica 2026;20(3):755-770
HIGHLIGHTS
- Enhanced high-temperature ductility observed experimentally
- Accurate constitutive modeling across wide temperature and rate conditions
- Effective multi-objective optimization using NSGA-II
KEYWORDS
TOPICS
ABSTRACT
Temperature and strain rate exert a profound influence on the thermo-mechanical behavior and structural integrity of ductile cast iron operating under elevated-temperature service conditions. In this study, an experimental investigation was conducted over temperatures ranging from 25 to 850 °C and strain rates of 1.8 × 10⁻⁴, 9 × 10⁻⁴, and 4.5 × 10⁻³ s⁻¹. Tensile testing revealed pronounced thermal softening, with ultimate tensile strength decreasing from 761.5 MPa at room temperature to below 100 MPa at 850 °C, while fracture strain increased to a maximum of 2.2%, indicating enhanced ductility at elevated temperatures. Fracture toughness was evaluated using experimentally validated XFEM simulations, showing a substantial reduction from 54.66 kJ/m² at room temperature to 23.9 kJ/m² at 850 °C. To establish predictive relationships between processing conditions and mechanical performance, Arrhenius-type and Johnson–Cook constitutive models were calibrated and systematically compared. The Johnson–Cook formulation demonstrated significantly superior predictive capability, achieving coefficients of determination of R² = 0.91 and 0.92 for ultimate and yield strengths, respectively, compared with R² values below 0.52 for the Arrhenius model. Building on the vali-dated constitutive framework, a multi-objective optimization strategy based on the
Non-dominated Sorting Genetic Algorithm II (NSGA-II) was developed to simultaneously optimize strength, ductility, and fracture toughness. The resulting Pareto fronts quantified the inherent trade-offs among competing mechanical properties and enabled the identification
of optimal thermo-mechanical processing windows. The proposed integrated experimental–computational framework provides a validated meth-odology for constitutive characterization, performance prediction, and materials design optimization of ductile cast iron under severe thermo-mechanical environments. The findings demonstrate the potential of combining constitutive modeling, fracture mechanics, and
evolutionary multi-objective optimization to accelerate the development of high-performance engineering alloys.
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