考虑结构演变的触变粘弹性-弹性介质非线性模型生成的应力-应变、松弛和蠕变曲线族 第 3 部分.蠕变曲线

IF 1.5 4区 材料科学 Q4 MATERIALS SCIENCE, COMPOSITES
A. V. Khokhlov, V. V. Gulin
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引用次数: 0

摘要

我们继续对之前构建的触变粘弹塑性介质剪切流非线性模型的数学特性进行了系统的分析研究,该模型考虑了变形过程和结构演变的相互影响。得到了描述恒定速率剪切和应力松弛过程的两个非线性微分方程组。导出了描述蠕变的方程组;以显式形式构建了方程组的考奇问题的一般解(导出了蠕变和结构度曲线的方程组)。对于支配模型的任意六个材料参数和(递增)材料函数,分析研究了恒定应变速率下的应力-应变曲线族、应力松弛曲线和模型生成的蠕变曲线的基本特性,以及在这些类型的加载下结构度演变的特征。研究了这些曲线与时间、剪切速率、应力水平、初始应变和材料初始结构度的关系,以及与材料参数和模型功能的关系。发现了模型适用性的几个指标,便于与实验数据进行核对。与结构稳定材料的典型应力-应变曲线、松弛曲线和蠕变曲线相比,研究了该模型可以描述粘弹性-塑性介质的哪些典型效应,以及结构度变化会产生哪些异常效应(异常特性)。特别是,研究证明,蠕变曲线总是随时间而增加,并具有斜渐近线,而恒定应力下的结构度总是单调的(与其他加载模式不同),但可根据应力水平和初始结构度之间的关系而减小或增大。同样的条件控制着蠕变曲线的上凸或下凸:在一定的(计算的)临界载荷下,蠕变曲线从上凸(在较小载荷下)变为下凸,结构度从下降变为上升。分析表明,该模型不仅能描述液态粘弹性介质的行为,还能描述固态(增厚、硬化、淬火)介质的行为:蠕变、松弛、恢复、实验松弛曲线的一些典型特性、蠕变和应力-应变曲线、应变速率和应变硬化、恒定应力下的流动等。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Families of Stress-Strain, Relaxation, and Creep Curves Generated by a Nonlinear Model for Thixotropic Viscoelastic-Plastic Media Accounting for Structure Evolution Part 3. Creep Curves

Families of Stress-Strain, Relaxation, and Creep Curves Generated by a Nonlinear Model for Thixotropic Viscoelastic-Plastic Media Accounting for Structure Evolution Part 3. Creep Curves

A systematic analytical study of the mathematical properties of the previously constructed nonlinear model for shear flow of thixotropic viscoelastic-plastic media, which takes into account the mutual influence of the deformation process and structure evolution, is continued. A set of two nonlinear differential equations describing the processes of shear at a constant rate and stress relaxation is obtained. Equation set describing creep is derived; a general solution of the Cauchy problem for the set is constructed in an explicit form (the equations of the families of creep, and structuredness curves are derived). For arbitrary six material parameters and (increasing) material function that govern the model, basic properties of the families stress-strain curves at constant strain rates, stress relaxation curves and creep curves generated by the model, and the features of structuredness evolution under these types of loading are analytically studied. The dependences of these curves on time, shear rate, stress level, initial strain, and initial structuredness of the material, as well as on the material parameters and function of the model, are studied. Several indicators of the applicability of the model are found which are convenient to check with experimental data. It was examined what effects typical for viscoelastic-plastic media can be described by the model and what unusual effects (unusual properties) are generated by a change in structuredness in comparison with typical stress-strain curves, relaxation curves, and creep curves of structurally stable materials. In particular, it is proved that creep curves always increase in time and have oblique asymptote, and structuredness under constant stress is always monotonous (unlike other loading modes), but can decrease or increase depending on the relation between the stress level and initial structuredness. The same condition controls creep curves to be convex up or down: at a certain (calculated) critical load creep curves change from convexity up (under smaller loads) to convexity down, and the structuredness becomes ascending instead of descending. The analysis proved the ability of the model to describe behavior of not only liquid-like viscoelastoplastic media, but also solid-like (thickening, hardening, hardened) media: creep, relaxation, recovery, a number of typical properties of experimental relaxation curves, creep and stress-strain curves, strain rate and strain hardening, flow under constant stress and so on.

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来源期刊
Mechanics of Composite Materials
Mechanics of Composite Materials 工程技术-材料科学:复合
CiteScore
2.90
自引率
17.60%
发文量
73
审稿时长
12 months
期刊介绍: Mechanics of Composite Materials is a peer-reviewed international journal that encourages publication of original experimental and theoretical research on the mechanical properties of composite materials and their constituents including, but not limited to: damage, failure, fatigue, and long-term strength; methods of optimum design of materials and structures; prediction of long-term properties and aging problems; nondestructive testing; mechanical aspects of technology; mechanics of nanocomposites; mechanics of biocomposites; composites in aerospace and wind-power engineering; composites in civil engineering and infrastructure and other composites applications.
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