Asymptotic behaviour of the crack tip fields under creep regime taking into account damage accumulation processes

The aim of the study is to identify the asymptotic stress, creep strain rate and continuity fields behavior in the proximity of the crack tip under creep conditions, taking into account the damage accumulation process, based on the finite element analysis of the stress-strain state at the crack tip in the finite element software SIMULIA Abaqus using the UMAT procedure, which allows us to describe constitutive equations that are absent in the standard set of defining equations of the FEM complex, and incorporate the damage accumulation processes into the design scheme of the FEM software. The damage accumulation phenomenon is described using the classical Kachanov - Rabotnov model, which postulates a power law linking creep strain rates and stresses, and a power law of damage accumulation, in a coupled formulation. Finite element modeling of loading of a plate with a central horizontal and inclined crack under conditions of steady state creep is performed under the assumption of the realization of a plane stress state. It is shown that in the case of steady-state creep without taking into account the process of damage accumulation, the finite element solution clearly has the asymptotic behavior of the classical Hutchinson - Rice - Rosengren solution. With the help of the developed user procedure UMAT, the coupling of two processes is realized in the computational scheme of the finite element method: the evolution of mechanical fields and the increase of damage in the vicinity of the crack tip in accordance with the canonical Kachanov - Rabotnov damage evolution model. On the basis of the analysis of the stress field obtained by finite element computations, in the vicinity of the crack tip, taking into account the damage, a new asymptotic of stress fields near the crack tip in a plate under uniaxial tension conditions was revealed, different from the asymptotic corresponding to the Hutchinson-Rice-Rosengren solution.