Abstract: The Problem of dislocations emitted from a semi-infinite crack in mode Ⅱ or Ⅲ loading and blocked by a penetrable barrier(grain boundary),or many such epually spaced barriers,is studied.Analytical solutions for the continuous distribution of dislocations between the crack tip and a barrier is obtained.The case of multiple barriers is studied by computer simulation.The results are used to understand the effect of grain size on fracture toughness.For the same applied stress intensity factor,the toughness is found to increase with increasing grain size.By using a power-law relation,the exponent varies between 0 and 1.5 depending on the ratio of the lattice friction for dislocation motion to the grain-boundary strength.Together with the Petch relation for the dependence of grain size on fracture stress,a relation is suggested between the grain size and the critical stress intensity factor for crack propagation.