Investigation of the size effect on crack propagation using finite element method and strain gradient plasticity

In this work, we have employed the strain gradient plasticity theory into the continuum mechanics to investigate the size effect of material on the crack propagation of micro-sized copper. Constitutive equation was re-formulated in terms of strain gradient and intrinsic material length. Elastic–plastic finite element method was adopted and revamped to reflect the strain gradient effect during deformation and crack propagation. We calculated the strain gradient at each element using the least square function. To demonstrate the size effect, the proposed approach has been applied to mode-I crack growth problem. It shows that as material size comes near to the intrinsic material length, the crack propagation behavior is quite different compared with that computed from the conventional plasticity theory.