Families of Stress–Strain, Relaxation and Creep Curves Generated by a Nonlinear Model for Thixotropic Viscoelastic-Plastic Media Accounting for Structure Evolution Part 2. Relaxation and Stress-Strain Curves

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

Abstract

A systematic analytical study of the mathematical properties of the previously constructed nonlinear model for shear flow of thixotropic viscoelastic-plastic media is continued. For arbitrary six material parameters and an (increasing) material function that control the model, the basic properties of the families of stress-strain curves at constant strain rates and relaxation curves generated by the model, and the features of the evolution of the structuredness under these types of loading are analytically studied. The dependences of these curves on time, shear rate, 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 and relaxation curves of structurally stable materials. In particular, it has been proved that stress-strain curves can be both increasing functions and can have decreasing sections resembling a “yield tooth” or damped oscillations, that all stress-strain curves (SSCs) possess horizontal asymptotes (steady flow stress), monotonically dependent on shear rate, and flow stress increases with shear rate growth, that the instantaneous shear modulus, on the contrary, depends on the initial structuredness, but does not depend on shear rate. Under certain restrictions on the material parameters, the model is also capable of providing a bilinear form of stress-strain curves, which is typical for an ideal elastoplastic model, but with strain rate sensitivity. It has been established that the family of stress-strain curves does not have to be increasing either in initial structuredness or in shear rate: in a certain range of shear rates, in which the equilibrium position is a “mature” focus and pronounced oscillations of stress-strain curves are observed, it is possible to intertwine stress-strain curves with different shear rates. It is proved that for any material parameters and functions, all stress relaxation curves decrease and have a common zero asymptote as time tends to infinity. 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.

Abstract Image

考虑结构演变的触变粘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 2 部分.松弛和应力-应变曲线
继续对之前构建的触变粘弹性塑性介质剪切流非线性模型的数学特性进行系统分析研究。对于控制模型的任意六个材料参数和一个(递增)材料函数,分析研究了模型产生的恒定应变速率下应力-应变曲线和松弛曲线族的基本特性,以及在这些类型的加载下结构性演变的特征。研究了这些曲线对时间、剪切速率、初始应变和材料初始结构度的依赖性,以及对材料参数和模型功能的依赖性。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-应变曲线和松弛曲线相比,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,研究证明应力-应变曲线既可以是递增函数,也可以具有类似 "屈服齿 "或阻尼振荡的递减截面;所有应力-应变曲线(SSC)都具有水平渐近线(稳定流动应力),与剪切速率单调相关,流动应力随剪切速率增长而增加;相反,瞬时剪切模量取决于初始结构度,但与剪切速率无关。在对材料参数有一定限制的情况下,该模型还能提供双线性形式的应力-应变曲线,这是理想弹塑性模型的典型形式,但具有应变速率敏感性。研究发现,应力-应变曲线族并不一定要在初始结构度或剪切速率上不断增加:在一定的剪切速率范围内,平衡位置是一个 "成熟 "的焦点,应力-应变曲线会出现明显的振荡,不同剪切速率下的应力-应变曲线有可能交织在一起。研究证明,对于任何材料参数和函数,当时间趋于无穷大时,所有应力松弛曲线都会减小,并有一个共同的零渐近线。分析证明,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、硬化)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。
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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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