Modelling of cyclic creep in the finite strain range using a nested split of the deformation gradient

Abstract

A new phenomenological model of cyclic creep, which is suitable for applications involving finite creep deformations of the material, is proposed. The model accounts for the effect of the transient increase of the creep strain rate upon the load reversal. In order to extend the applicability range of the model, the creep process is fully coupled to the classical Kachanov-Rabotnov damage evolution. As a result, the proposed model describes all the three stages of creep. Large strain kinematics is described in a geometrically exact manner using the assumption of a nested multiplicative split, originally proposed by Lion for finite strain plasticity. The model is thermodynamically admissible, objective, and w-invariant. The implicit time integration of the proposed evolution equations is discussed. The corresponding numerical algorithm is implemented into the commercial FEM code MSC.Marc. The model is validated using this code; the validation is based on real experimental data on cyclic torsion of a thick-walled tubular specimen made of the D16T aluminium alloy. The numerically computed stress distribution exhibits a "skeletal point" within the specimen, which simplifies the analysis of test data.

Inspection of ratcheting models for pathological error sensitivity and overparametrization

“…For simplicity, the small strain framework is implemented. However, the developed models can be generalized to large strains using the methodology from [21,33,39,34]. For phenomenological material description, three types of combined isotropic-kinematic hardening models are used here: the models of Armstrong-Frederick (AF), the first, and the second Ohno-Wang models (OW-I and OW-II).…”

Cyclic plasticity and thermomechanical alleviation in titanium alloys

“…Phenomenological models also attributed the reverse plastic flow to the presence of back-stress, e.g. (Shutov et al, 2017). However, the mechanistic basis of the strain reduction phenomenon in titanium alloys has yet to be systematically studied at the dislocation scale, notably for loading cycles containing temperature excursions.…”

Two-time-scales and time-averaging approaches for the analysis of cyclic creep based on Armstrong–Frederick type constitutive model

“…16,17 To analyze inelastic material and structural responses, efficient numerical time step and iteration algorithms are developed and utilized inside finite element codes. [18][19][20][21][22] Examples of inelastic structural analysis of power plant components are presented in the literature 4,5,13 illustrating local changes of stress state for given external thermo-mechanical loading profiles. For the analysis of structural behavior over many loading/unloading cycles, a direct numerical solution would require computationally expensive cycle-by-cycle integration with relatively small time steps.…”