Steady-State Crack Growth in Nanostructured Quasi-Brittle Materials Governed by Second Gradient Elastodynamics

Abstract

The elastodynamic stress field near a crack tip propagating at a constant speed in isotropic quasi-brittle material was investigated, taking into account the strain gradient and inertia gradient effects. An asymptotic solution for a steady-state Mode-I crack was developed within the simplified strain gradient elasticity by using a representation of the general solution in terms of Lamé potentials in the moving framework. It was shown that the derived solution predicts the nonsingular stress state and smooth opening profile for the growing cracks that can be related to the presence of the fracture process zone in the micro-/nanostructured quasi-brittle materials. Note that similar asymptotic solutions have been derived previously only for Mode-III cracks (under antiplane shear loading). Thus, the aim of this study is to show the possibility of analytical assessments on the elastodynamic crack tip fields for in-plane loading within gradient theories. By using the derived solution, we also performed analysis of the angular distribution of stresses and tractions for the moderate speed of cracks. It was shown that the usage of the maximum principal stress criterion within second gradient elastodynamics allows us to describe a directional stability of Mode-I crack growth and an increase in the dynamic fracture toughness with the crack propagation speed that were observed in the experiments with quasi-brittle materials. Therefore, the possibility of the effective application of regularized solutions of strain gradient elasticity for the refined analysis of dynamic fracture processes in the quasi-brittle materials with phenomenological assessments on the cohesive zone effects is shown.

Higher-order asymptotic crack-tip fields in simplified strain gradient elasticity

“…The cohesive effects arise naturally in SGE solutions due to more general definition of surface tractions that takes into account the balance of stresses and hyper-stresses [19][20][21]. For the problems of growing cracks it was also shown that gradient theories allow to describe the stabilizing and crack tip shielding effects [22][23][24] in quasi-brittle materials. Implementation of SGE models in the advanced numerical methods allowed to obtain the refined and mesh-independent solutions for the problems of crack propagation [25][26][27][28][29].…”