Prediction of stress-strain curves for aluminium alloys using symbolic regression

An in-depth understanding of material flow behaviour is crucial for numerical simulation of plastic deformation processes. In present work, we use a Symbolic Regression method in combination with Genetic Programming for modelling flow stress curves. In contrast to classical regression methods that fit parameters to an equation of a given form, symbolic regression searches for both numerical parameters and the equation form simultaneously; therefore, no prior assumption on a flow model is required. This identification process is done by generating and adapting equations iteratively using a genetic algorithm. The constitutive model is derived for two aluminium wrought alloys: a conventional AA6082 and modified Cu-containing AA7000 alloy. The required dataset is created by performing a series of hot compression tests at temperatures between 350 °C and 500 °C and strain rates from 10⁻³ to 10 s⁻¹ using a deformation dilatometer. The measured data, experimental set-up parameters as well as the material process history and its chemical composition are stored in a SQL database using a python^™ script. To correct raw measured data, e.g. minimize the noise, an in-house Flow Stress Analysis Toolkit was used. The obtained results represent a data-driven free-form constitutive model and are compared to a physics-based model, which describes the flow stress in terms of internal state parameters (herein, mean dislocation density). We find that both models reproduce reasonably well the measured data, while for modeling using symbolic regression no prior knowledge on materials behavior was required.