Predicting dislocation patterns and discovering the law of similitude: Machine learning based on fully reversed fatigue of FCC metals

Abstract

Dislocation patterns reflect the complex self-organization nature of dislocations and have strong influence on the mechanical properties of crystalline materials. Although the law of similitude has been widely accepted to quantify the relation between saturation resolved shear stress and pattern wavelength, it remains a big challenge to link the major inputs (e.g. saturation resolved shear stress, crystal orientation and applied strain amplitude) and major outputs (e.g. wave-type and wave-length) of dislocation patterns. In the present work, we develop two black-box machine learning methods to predict the wave-type and wave-length, as well as two white-box machine learning methods to discover explicit formulas linking major inputs and wave-length of dislocation patterns, based on the experimental data of room temperature fully reversed fatigue of FCC metals. Data of single crystal Cu are used for training and validation, and data of bicrystal Cu and polycrystal Ni are used for testing. The results show that the black-box machine learning methods can well predict over twenty types of patterns consisting of five constitutive patterns (i.e. wall, vein, ladder, labyrinth and cell structures) and their wavelengths. The traditional law of similitude, as well as an improved version that additionally incorporates crystal orientation, are surprisingly discovered from experimental data under the guidance of expert knowledge and physical constraints in the white-box machine learning methods. This improved formulation represents a significant advancement toward establishing a more comprehensive law of similitude.