Ductile crack propagation at the micron scale

The asymptotic fields near the tip of a crack steadily propagating in a ductile material under Mode III loading conditions are investigated by adopting an incremental version of the indeterminate theory of couple stress plasticity displaying linear and isotropic strain hardening. The adopted constitutive model is able to account for the microstructure of the material by incorporating two distinct material characteristic lengths. It can also capture the strong size effects arising at small scales, which results from the underlying microstructures. The effects of microstructure on Mode III crack tip fields mainly consist in a switch in the sign of tractions and displacement and in a substantial increase in the singularity of tractions ahead of the crack-tip, with respect to the classical solution of LEFM and EPFM. The increase in the stress singularity is essentially due to the skew-symmetric stress field, since the symmetric stress field turns out to be non-singular. Moreover, the obtained results show that the ratio between the characteristic lengths has a limited effect on the strength of the stress singularity. However, it displays a strong influence on the angular distribution of the asymptotic crack tip fields.