Deep learning for characterizing fracture toughness from the nanoindentation image of a complex heterogeneous medium

Abstract

Fracture toughness is a fundamental property characterized using nanoindentation, and it typically requires elastic modulus, applied load, and crack length. This study demonstrates that deep learning can predict fracture toughness using only nanoindentation images. A deep-learning model is designed, incorporating a pretrained Visual Geometry Group model with 16 layers (VGG16) and fully connected layers. The study augments 3,546 original nanoindentation images of shale to increase them to 21,276 images and employs the adaptive momentum (Adam) solver with a learning rate of 0.0002. The nanoindentation images contain complex patterns distinct from the simple topologies of homogeneous media, such as pure silica. Results show that the model accurately determines normalized fracture toughness, with a mean squared error (MSE) of 0.0014, indicating that the model effectively learns to interpret the underlying features. Additionally, once trained, the model predicts fracture toughness much faster than the existing approach based on K-means clustering. More importantly, this study suggests that nanoindentation images of complex porous media convey crucial information, including elastic modulus, applied load, and hardness. The results and the proposed model have applications in characterizing heterogeneous media with complex structures.