### STP605: Relationship Between the Fracture Toughness and the Crack Tip Radius

Taggart, R

*Professor, University of Washington, Seattle, Wash*

Wahi, KK

*Senior engineer, Science Applications Inc., Oakland, Calif*

Beeuwkes, R

*Research engineer, Army Mechanics and Materials Research Center, Watertown Arsenal, Mass.*

Pages: 9 Published: Jan 1976

**Abstract**

The conditions that surround the tip of a sharp crack in a ductile metallic material dictate the onset of plastic flow and crack extension. The problem of predicting the onset of unstable fracture is related directly to the difficulty of measuring or calculating the actual stresses and strains within the plastic enclave that encompasses the crack tip. Beeuwkes has obtained an approximate solution for the elastic-plastic state in the vicinity of the crack tip and concludes that the crack tip radius after deformation together with the fracture strength at nil ductility of the material form the basis for a fracture criterion.

In this study measurements have been made of the crack opening of fatigue cracked double cantilever beam specimens of 6061-T6 and annealed 4340VM steel. The crack opening measurements have been used to compute the crack tip radius at different loads by fitting the experimental data with an *n*^{th} order polynomial (*n* = 2, 4, 6, and 8). The polynomial for which the average deviation in the computed values is a minimum with respect to the measured values was chosen to represent the crack geometry. The values of the crack tip radius as given by this polynomial were plotted against the stress intensity factor.

It has been found for both the selected materials that the stress intensity factor and the crack tip radius follow a linear relation when plotted on a log-log basis. The stress intensity factor and the ratio of the crack tip radius to a critical crack tip radius also plot as a straight line on a log-log basis.

It is concluded that the concept of a critical crack tip radius is consistent with a crack extension model that depends on void coalescence and growth. The data also support the fracture criterion based on the elastic-plastic analysis proposed by Beeuwkes.

**Keywords:**

fracture properties, crack propagation, plastic deformation, toughness, fracture strength

**Paper ID:** STP27800S

**Committee/Subcommittee:** E08.08

**DOI:** 10.1520/STP27800S

ASTM International is a member of CrossRef.