Finite element analysis of the modified ring test for determining mode I fracture toughness

Abstract

Plane strain fracture toughness ( K Ic) values are determined for the modified ring (MR) test through numerical simulation of crack growth to highlight the sensitivity of MR K Ic values on applied displacement or force boundary conditions, slip conditions at the specimen-platen interface, and the Poisson ratio (v) of the test material. Numerical calculation of fracture toughness in the MR test is traditionally conducted assuming a uniform force along the specimen loading surfaces and no slip between the specimen and the loading platens. Under these conditions K Ic increases by 30–40% as v decreases from 0.4 to 0.1. When slip is allowed at the specimen-platen interface under a uniform force, K Ic values are independent of v, and for any given v, are 5–25% less than those determined under a no-slip boundary condition. Under a uniform displacement of the specimen loading surfaces, K Ic is essentially independent of v, regardless of specimen-platen interaction. Moreover, although K Ic values determined under unifor displacement and no-slip boundary conditions are always higher than those determined under uniform displacement and slip-allowed boundary conditions, the average difference in K Ic for these two methods is less than 5% for the two specimen geometries examined. This suggests that under uniform displacement conditions, K Ic is essentially independent of specimen-platen interaction. Because K Ic values determined from MR testing are strongly dependent on the modeling procedure, future reports of K Ic determined from this test should be accompanied by detailed reports of the modeling procedure. Until further testing reveals the most accurate simulation technique, we advocate use of a uniform displacement formulation for K Ic determination from MR testing because results from this method are insensitive to most modeling parameters. Numerical results from models conducted under uniform force, no-slip boundary conditions should be viewed as an upper bound to K Ic.