Inverse Measurement of Stiffness by the Normalization Technique for J-Integral Fracture Toughness

Abstract

The single specimen normalization technique for J-integral fracture toughness has been successfully employed by several researchers to study the strongly non-linear fracture response of ductile semicrystalline polymers. As part of the normalization technique the load and the plastic component of displacement are normalized. The normalized data is then fit with a normalization function that approximates a power law for small displacements that are dominated by blunting and smoothly transitions to a linear relationship for large displacements that are dominated by stable crack extension. Particularly for very ductile polymers the compliance term used to determine the plastic displacement can dominate the solution and small errors in determining the elastic modulus can lead to large errors in the normalization or even make it ill posed. This can be further complicated for polymers where the elastic modulus is strong strain rate dependent and simply using a “quasistatic” modulus from a dogbone measurement may not equate to the dominant strain rate in the compact tension specimen. The current work proposes directly measuring the compliance of the compact tension specimen in the solution of J-integral fracture toughness and then solving for the elastic modulus. By comparison with a range of strain rate data the dominant strain rate can then be determined.