Analysis of the Optical Shadow Spot Method for a Tensile Crack in a Power-Law Hardening Material

Abstract

If the crack tip deformation field in a cracked ductile solid can be characterized by means of a single plastic intensity factor, then the shadow spot method has potential as a means for direct measurement of this intensity factor. The value of the J-integral is adopted as a plasticity intensity factor, and the lateral contraction of a planar specimen of elastic-plastic power-law hardening material is calculated in terms of J from the HRR asymptotic field of elastic-plastic fracture mechanics. The theoretical caustic curve which would be generated by geometrical reflection of normally incident 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 power (3n + 2)/n, where n is the power hardening exponent. Synthetic shadow spot patterns obtained by numerical simulation of the optical reflection process are also shown.