A simplified formula to estimate the size of the cyclic plastic zone in metals containing elastic particles

The applicability of Irwin's estimate to metals containing particles becomes dubious when the plastic zone (PZ) size is comparable to the particle spacing. Therefore, a multiscale model is used to investigate the crack tip plasticity in a cyclically loaded elastic-perfectly plastic matrix containing a realistic distribution of spherical particles.

Homogenization and dimensional analysis demonstrate that the PZ shape differs from what is expected based on von Mises plasticity. The scaling of the PZ size with the square of the stress intensity factor is confirmed, but the proportionality coefficient is strongly affected by the particle volume fraction.

Consequently, a new compact formula for the PZ size is proposed, which holds for material properties ranging from metal matrix composites to cast irons and is robust to minor particle deviations from the spherical shape.