Physics-informed machine learning for identifying gradient- <?A3B2 pi6?> <?A3B2 tlsb=-.02w?>distributed plastic parameters of the S38C axle by nano-indentation <?A3B2 tlsb?>

The S38C railway axle undergoes induction hardening, resulting in a gradient-distributed microstructure and mechanical properties. The accurate identification of gradient-distributed plastic parameters for the S38C axle remains a challenging task. To tackle this challenge, the present study proposes a novel approach for identifying the gradient-distributed plastic parameters for the S38C axle by integrating nano-indentation techniques with the machine learning method. Firstly, nano-indentation tests are conducted along the radial direction of the S38C axle to obtain the gradient-distributed load-displacement curves, nano-hardness, and elastic modulus. Subsequently, the dimensionless analysis is performed to obtain the representative stress, strain, and yield stress from load-displacement curves. These parameters are then incorporated into the machine learning method as physical information to identify the gradient-distributed plastic parameters of the S38C axle. The results indicate that the proposed method based on the physics-informed neural network and multi-fidelity neural network successfully identifies the gradient-distributed plastic parameters of the S38C axles and demonstrates superior prediction accuracy and generalization compared with the purely data-driven machine learning method.