Optical Measurement of the Plastic Strain Concentration at a Crack Tip in a Ductile Steel Plate

The shadow spot method has been established as a valuable experimental procedure for measuring elastic stress intensity factors in planar fracture specimens. It is noted here that if the crack-tip deformation field in specimens of ductile materials can be characterized by means of a single plastic intensity factor, analogous to the stress intensity factor in linear elastic fracture mechanics, then the shadow spot method has potential for use in measuring this intensity factor. The value of the J-integral is adopted as the plastic strain intensity factor, and the lateral contraction of an elastic-ideally plastic planar specimen is calculated in terms of J from the nonhardening limit of the HRR asymptotic field of elastic-plastic fracture mechanics. The theoretical caustic curve which would be generated by geometrical reflection of normally incident parallel light from points of the deformed specimen surface lying well within the plastic zone is determined, and it is shown that the value of J is proportional to the maximum transverse diameter of the shadow spot to the third power. Results of preliminary experiments, in which values of J for a given single edge notched steel plate specimen are inferred from measurements peformed separately from the elastically and plastically deforming parts of the specimen, are also reported.