A SIMPLE RE-DERIVATION OF LOGARITHMIC DISORDERING OF A DYNAMIC PLANARCRACK DUE TO SMALL RANDOM HETEROGENEITIES

Perrin and Rice [(1994) Disordering of a dynamic planar crack front in a model elastic medium of randomly variable toughness. J.,Mech. Phys. Solids 42, 1047-1064] analyzed the autocorrelation of positions along the front of a dynamic planar crack propagating in a model scalar ela stic solid through a region of small sustained fracture toughness hete rogeneities. Assuming a general stationary distribution of toughness f luctuations, they showed that the deviations from straightness, or dis order, of crack front positions and velocities diverge logarithmically with propagation distance into the zone of sustained property variati ons. The current paper presents an alternative derivation of the logar ithmic growth of crack disorder, employing a simplified approach based on a restricted distribution of fracture toughness heterogeneities. T he distribution corresponds to material granularity or discreteness in the direction of crack propagation. The final result indicates that t he crack front disorder converges to zero when the fundamental length scale of the assumed granularity vanishes. As indicated by Perrin and Rice, the same holds for any distribution of fracture toughness proper ty whose 2-D power spectrum goes to zero.