An algorithm for prediction of fracture toughness of titanium alloys based on uniaxial tension material properties and elastic-plastic solutions

Availability of methods for prediction of fracture toughness (K_IC) by analytical calculations derived from basic properties of the material can be important during alloy development when K_IC testing is impossible or to expedite screening. Several years ago, a work to develop such algorithm was performed by Kazan Scientific Center of Russian Academy of Sciences jointly with The Boeing Company.

The theory of strain energy density (SED) was used to approach the problem. The hypotheses of strain energy density (SED) theory are associated with the concept of a characteristic distance, a fundamental characteristic relating the processes occurring on micro- and macrostructure levels that can be identified with the fracture damage zone. A critical distance ahead of the crack tip is assumed to exist when the SED in an element reaches a certain critical value.

In this work, the critical value of the SED was measured from a uniaxial test. Two new fracture initiation parameters were proposed to establish relationships between the uniaxial tension properties and the fracture toughness of titanium alloys: (1) damage factor F_W - the ratio between the dimensionless local SED per unit volume in elastic–plastic deformation around the crack tip and the normalized total SED at standard uniaxial tension and (2) the ratio of the separation at material decohesion to crack advance. An empirical relationship was established to describe F_W as a function of normalized total SED at uniaxial tension. It was further suggested that with the knowledge of the tensile properties and of the estimated F_W ranges, the application of this method could be appropriate for predicting fracture toughness. A new automatic algorithm for fracture toughness assessment was presented based on the concept of the plastic stress intensity factor (SIF).

The presentation covers the fundamentals of employed algorithm and description of its application for a developmental titanium alloy, including obtaining experimental data, numerical analysis for determination of the I_n-integral, the dimensionless equivalent of von Mises stress, the normalized crack-tip opening displacement, the T-stress, and finally, the predicted fracture toughness values.