Modeling the kinetics of stress–strain state and damage accumulation in structural alloys under the mutual influence of fatigue and creep

IF 1.9 4区工程技术 Q3 MECHANICS

Continuum Mechanics and Thermodynamics Pub Date : 2025-03-12 DOI:10.1007/s00161-025-01371-2

L. A. Igumnov, I. A. Volkov, A. I. Yudintseva, A. I. Volkov

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Abstract

The corresponding mathematical model of cyclic viscoplastic deformation of damaged material, a structural element counteracting multiaxial disproportionate modes of hybrid thermomechanical loading, is considered. The model is determined by the relations between viscoplastic deformation and failure, as well as the evolution equations of damage accumulation kinetics and the material strength criterion. The description of viscoplastic deformation is based on the existence of plasticity and creep surfaces in the stress space and the principle of gradient of the velocity vectors of the corresponding deformations at the loading point. Such a description distinguishes the main effects of the cyclic behaviour of the material for complex loading trajectories. The description of kinetic damage accumulation is based on the scalar damage parameter. The formation, growth and coalescence of micro-defects are considered. A coupled formulation of the evolution equations for low-cycle fatigue and long-term strength is proposed. The condition that the damage value reaches a critical value is taken as the strength criterion. In the work, material parameters and scalar functions of the mathematical model are obtained. Based on the model, the results of the numerical simulation of the behaviour of the alloys are presented. It is shown that the model describes the durability of the materials with practical reliability.

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建立了疲劳和蠕变共同作用下结构合金应力-应变状态和损伤积累动力学模型

考虑了损伤材料的循环粘塑性变形的数学模型，这是一种抵消混合热-机械加载多轴不成比例模式的结构单元。该模型由粘塑性变形与破坏关系、损伤积累动力学演化方程和材料强度准则确定。粘塑性变形的描述是基于应力空间中塑性面和蠕变面的存在以及相应变形在加载点处速度矢量的梯度原理。这种描述区分了复杂加载轨迹下材料循环行为的主要影响。动能损伤累积的描述是基于标量损伤参数的。考虑了微缺陷的形成、生长和聚并。提出了低周疲劳与长期强度演化方程的耦合表达式。以损伤值达到某一临界值为强度判据。在工作中，得到了数学模型的材料参数和标量函数。基于该模型，给出了合金行为的数值模拟结果。结果表明，该模型能较好地描述材料的耐久性，具有实际的可靠性。

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来源期刊

Continuum Mechanics and Thermodynamics 物理-力学

CiteScore

5.30

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena. Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.