Microscopic strain fields at crack tips in porous materials analyzed by a gradient-enhanced elasticity theory

The microstructural influence on the strain field at opening mode crack tips in porous materials, and especially its practical implication for understanding macroscopic failure, i.e. on a scale above, is investigated. Theoretical subscale microstrain fields are approximated using a gradient-enhanced elasticity theory and compared to microstrain fields computed in discrete high-resolution finite element microstructural models having varying pore densities but similar macroscopic geometry and boundary conditions as the theoretical gradient-enhanced model. The numerical elastic microstrain and microstress fields are non-singular in strong contrast to the singular macroscopic fields in classical linear elastic fracture theories. Experimentally approximated microstrain fields, estimated with a digital image correlation algorithm on images obtained in X-ray computational tomography fracture tests on a small wood specimen, are used to contrast the numerical analyses. A key observation is that an internal length parameter, used in the gradient-enhanced model, seems to be linked to the average pore diameter, allowing for direct bridging between scales.