Creep crack growth in brittle materials

Abstract

During steady state crack growth by diffusive cavitation at grain boundaries, crack tip fields are relaxed due to the presence of a cavitation zone. In the present analysis, analytic solutions for the actual crack rip stress fields and the crack velocity in the presence of cavitation zone consisting of continuously distributed cavities ahead of the crack tip are derived using the smeared volume concept. Results indicate that the r(-1/2) singularity is now attenuated to r(-1/2+theta)(0 < theta < 1/2) singularity. The singularity attenuation parameter theta is a function of the crack velocity and material parameters. The crack growth rate v is related to the mode I stress intensity factor K by v proportional to K-2 at relatively high load, v proportional to K-n at intermediate load, and approaches zero at small load near K-th. Meanwhile, the cavitation zone extends further into the material due to the stress relaxation at the crack tip and the subsequent stress redistribution. Such relaxation effects become very distinct at low crack velocity and low applied load.