LOGARITHM STRAIN SINGULARITY AT TIP OF MODE-I GROWING CRACK IN ELASTIC AND PERFECTLY-PLASTIC MATERIAL

Reanalyzed in detail is the stress and strain distribution near the ti p of a Mode I steadily growing crack in an elastic and perfectly-plast ic material. The crack tip region is divided into five angular sectors , one of which is singular in character and represents a rapid transit ion zone that becomes a line of strain discontinuity in the limit as c rack tip is approached. It is shown for an incompressible material (nu = 0.5) under plane strain that the local strain in all the angular se ctors possesses the same logarithm singularity, i.e., In r where r is the radial distance measured from the crack tip. This result also prev ails for the compressible material (nu < 0.5) and resolves a long stan ding controversy concerning the strain singularity in the sector just ahead of the crack tip.