Linear and non-linear models in damage summation theory
Abstract
Mykhalevych V., Dobraniuk Yu., Тiutiunnyk O., Kolisnyk M.
Linear and non-linear models in damage summation theory
In the article, against the background of a brief and fragmentary review of the development of the theory of deformability in the works of domestic scientists, the concepts of linear and nonlinear principles of damage summation in their connection with the corresponding scalar and tensor models are considered. The criterion relations resulting from these models are studied for the description of the ultimate plastic deformations in the processes of steady and unsteady deformation.
On the example of a two-stage process, which in each stage is a stationary process, i.e. characterized by a constant value of the stress state index, the regularities of changes of the ultimate deformations in relative coordinates are demonstrated, which reflect the dependence of the residual on the plasticity resource used. The advantages of presenting the criterion relations in these coordinates are substantiated, which consist in universality of comparisons and better reflection of changes, trends, and convenient consideration of data scales. The fundamental qualitative and quantitative difference between the criterion relations derived from models based on linear and nonlinear principles of damage aggregation in relation to the two-stage deformation process is demonstrated. In particular, it was found that when using the plasticity resource of 0.5 in the first stage, the estimated residual life according to the nonlinear criterion relation is 0.84 for the tensile-torsion process and 0.06 for the torsion-tension process, while according to the linear criterion, the residual life is 0.5 in both cases.
The analysis of the model of V.A. Ogorodnikov shows its advantages and disadvantages, which have not been sufficiently considered in the literature. It is shown for which classes of transient deformations the specified model, which reflects the nonlinear principle of damage summation, becomes identical with the simplest linear model. Thus, the recommendations concerning the limits of application of various damage summation models are clarified.
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