The link between crack velocity and rupture time in creeping solids

Abstract

Within the framework of stress controlled cavity nucleation and critical damage criterion of crack advance, steady state creep crack growth rates (upsilon) under the K or C* fields are derived and linked to the creep rupture times (tr). Temperature and stress dependences of upsilon and tr are exactly opposite for the K controlled crack growth if both proceed by the same cavitation mechanism. Regardless of the dominant crack tip stress fields and the cavitation mechanism, the crack velocity is proportional to the ratio between the cavitation zone size (r) and the rupture time under the local stress sigma(r). The cavitation zone size is of the order of the characteristic distance X(c) for the K controlled growth, but of the nucleation distance r(n) for the C* controlled growth. Thus, upsilon . tr{sigma (r)} = k . r, where the proportionality constant k is a strong function of the stress exponent of creep (n). If the cavity nucleation is affected by the principal tensile stress, k is virtually independent of n for the C* controlled growth from which a Monkman-Grant type relation can be deduced. Finally, a method to estimate the crack velocity from rupture time data is proposed, and comparisons with experimental data of a Ni-based superalloy and a ferritic stainless steel are attempted.