The main physical regularities of complex thermoviscoplastic deformation and accumulation of damage in structural materials (metals and their alloys) under various modes of cyclic combined thermomechanical loading and mathematical models of these processes are considered.
A mathematical model of the mechanics of a damaged medium has been developed, which makes it possible to simulate the cyclic viscoelastoplastic behavior and determine the resource characteristics of polycrystalline structural alloys under the combined action of degradation mechanisms that combine material fatigue and creep. The model is based on the joint integration of equations describing the kinetics of the stress-strain state and damage accumulation processes. The final relation to the model is the strength criterion, the fulfillment of which corresponds to the formation of a macrocrack.
The plasticity equations are based on the basic principles of the flow theory. To describe the creep process in the stress space, a family of equipotential creep surfaces of the corresponding radius and having a common center is introduced. The relationship between the creep equations and the thermoplasticity equations describing “instantaneous” plastic deformations is carried out at the loading stage through the stress deviator and the corresponding algorithm for determining and at the loading stage by means of certain relationships between “temporary” and “instantaneous” scalar and tensor quantities.
At the stage of development of damage scattered throughout the volume, the effect of damage on the physical and mechanical characteristics of the material is observed. This influence can be taken into account by introducing effective stresses. In the general case, stresses, plastic strains, and creep strains are determined by integrating the thermal creep equations by the four-point Runge-Kutta method with correction of the stress deviator and subsequent determination of stresses according to the thermoplasticity equations, taking into account the average creep strain rate at a new time.
The relationships that simulate the accumulation of damage are based on the energy approach to determining the resource characteristics. The kinetics of fatigue damage accumulation is based on the introduction of a scalar parameter of damage to a structural material and a unified model form for representing the degradation mechanism under fatigue and creep conditions. The influence of scattered damage on the physical and mechanical characteristics of the material is taken into account by introducing effective stresses.
The results of numerical simulation of cyclic thermoplastic deformation and accumulation of fatigue damage in heat-resistant alloys (Haynes188) under combined thermomechanical loading are presented. Particular attention is paid to the issues of modeling the processes of cyclic thermoplastic deformation and the accumulation of fatigue damage for complex deformation processes accompanied by the rotation of the main areas of stress and strain tensors.
Kinetics of Damage of Materials under Various Regimes of Re-Changeable Loads