# Identification of Dynamic Recrystallization Model Parameters for 40CrMnMoA Alloy Steel Using the Inverse Optimization Method

## TL;DR

This paper introduces a new inverse optimization method to accurately determine dynamic recrystallization model parameters for 40CrMnMoA steel, improving predictions of microstructure evolution during hot forging.

## Contribution

The novel inverse optimization method using adaptive simulated annealing improves DRX model parameter accuracy for 40CrMnMoA steel.

## Key findings

- The optimized DRX model achieved an R-value of 0.992 with significant reductions in AARE and RMSE.
- Simulation results showed a relative error of less than 3% compared to actual samples.

## Abstract

The microstructure of 40CrMnMoA during hot forging determines its macroscopic mechanical properties. Dynamic recrystallization (DRX) behavior is commonly used to refine grains and improve the microstructure of materials; therefore, it is important to be able to predict mechanical behavior during hot forging and the microstructure evolution during dynamic recrystallization. In order to accurately determine the DRX model parameters of 40CrMnMoA steel, an inverse optimization method is proposed in this work. The uniaxial isothermal compression experiment of 40CrMnMoA steel was carried out on a Gleeble-1500D thermal simulation tester (Dynamic Systems Inc. (DSI), Poestenkill, NY, USA) under the temperature range of 900~1200 °C and the strain rate range of 0.005 to 5 s−1. Based on the true stress–strain data obtained by a compression test, the DRX model of 40CrMnMoA was initially established using the traditional averaging method. Subsequently, the DRX model parameters calculated by the conventional averaging method were used as the initial values, the mean-square error between the experimental and calculated values of the DRX volume fraction was set as the objective function, and the DRX model parameters were optimized by the adaptive simulated annealing (ASA) algorithm. By comparing the correlation coefficient R, average absolute relative error (AARE), and the root mean square error (RMSE) of the predicted DRX percentage with the experimental values before and after optimization, it was found that the optimized model achieved an R-value of 0.992, with AARE and RMSE decreased by 34% and 2%, respectively, which verified the accuracy of the optimized DRX model. Through the program’s secondary development, the optimized DRX model of 40CrMnMoA was integrated into finite element software Forge® 3.2 to simulate the isothermal compression process. The comparison between grain size from the central region of simulation results and actual samples revealed that the relative error is less than 3%. This result demonstrated that the inverse optimization method can accurately identify the DRX model parameters of 40CrMnMoA alloy steel.