Non-planar cracks, propagating along crystallographic directions during the cleavage fracture of brittle materials and fluctuating about a mean plane, were represented in a simple model by means of a distribution of sinusoidal edge dislocations in a linear elastic medium. The dislocations were perpendicular to the crack propagation direction. Opening mode-I loading was assumed. It was shown that, at the front of the sinusoidal crack and out of the mean fracture plane, the stresses were bounded and the derivative of the energy decrease of the system with respect to the crack area was equal to zero. Only the positions of the crack front located on the mean fracture plane were associated with a non-zero value. It was concluded that the sinusoidal crack could not start to propagate from positions on the crack front that were out of the mean fracture plane. Crack propagation could begin very near to the intersection of the crack front with the mean fracture plane only if certain assumptions were made concerning the anisotropy of the surface energy.

A Non-Planar Crack Analysis using Continuously Distributed Sinusoidal Edge Dislocations and Linear Elasticity. P.N.B.Anongba: Physica Status Solidi B, 1996, 194[2], 443-52