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Spontaneous Stabilization and Large-Scale Oscillations of an Active Medium with Negative Dissipation 负耗散活性介质的自发稳定和大规模振荡
IF 1.8 4区 材料科学 Q2 MATERIALS SCIENCE, CHARACTERIZATION & TESTING Pub Date : 2023-12-15 DOI: 10.1134/S1029959923060024
A. E. Filippov, V. L. Popov

The paper analyzes a numerical model of an “active medium” with linear elasticity and a negative initial dissipation constant dynamically renormalized under deformation. The analysis shows that such a system, being seemingly unstable over a wide range of geometries and origins of deformation, can spontaneously reach stable dynamic modes in which its time- and space-alternating dissipation forms complex quasiperiodic patterns and its total volume (length, area) oscillates on a large scale. The results presented in the paper are of interest in academic terms and in terms of mechanical and biological application.

摘要 本文分析了一个具有线性弹性和负初始耗散常数的 "活性介质 "数值模型,该模型在变形过程中进行了动态重规范化。分析表明,这种系统在各种几何形状和变形起源下看似不稳定,但可以自发达到稳定的动态模式,在这种模式下,其时间和空间交替耗散形成复杂的准周期模式,其总体积(长度、面积)在大尺度上振荡。论文中介绍的结果在学术、机械和生物应用方面都很有意义。
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引用次数: 0
Effect of Tantalum on the Impact Toughness of 12% Cr Steels Subjected to Thermomechanical Treatment 钽对经过热机械处理的 12% 铬钢冲击韧性的影响
IF 1.8 4区 材料科学 Q2 MATERIALS SCIENCE, CHARACTERIZATION & TESTING Pub Date : 2023-12-15 DOI: 10.1134/S1029959923060097
A. Fedoseeva, A. Dolzhenko

The effect of tantalum on the impact toughness of 12% Cr steels with different tantalum content (12CrTaNb and 12CrNb) was investigated in impact tests in the temperature range from –40 to +120°C with determining the ductile-brittle transition temperature as the temperature in the middle between the upper and lower shelf energies. Both 12% Cr steels were thermomechanically treated by alternating 1050°C annealing and forging in addition to standard normalizing treatment with high-temperature tempering. It was found that for Ta-alloyed 12% Cr steel, the total fracture toughness versus temperature curve is 30–50 J/cm2 higher across the entire temperature range, including the upper and lower shelf energies, and the ductile-brittle transition temperature is 10°С lower. The main structural parameters of Ta-alloyed 12% Cr steel which can have a beneficial effect on toughness are a smaller prior austenite grain size, a larger average size but lower density of M23C6 carbide particles along low-angle martensite lath boundaries, and a larger volume fraction of VX carbonitrides.

摘要 研究了钽对不同钽含量的 12% Cr 钢(12CrTaNb 和 12CrNb)冲击韧性的影响,冲击试验的温度范围为 -40 至 +120°C,确定韧性-脆性转变温度为上架能和下架能之间的中间温度。除了高温回火的标准正火处理外,这两种 12% Cr 钢还通过 1050°C 退火和锻造交替进行热机械处理。研究发现,对于钽合金化的 12% Cr 钢,在整个温度范围内,包括上架能和下架能,总断裂韧性随温度变化曲线要高出 30-50 J/cm2,韧性-脆性转变温度要低 10°С。Ta 合金 12%Cr 钢对韧性产生有利影响的主要结构参数是:奥氏体晶粒先期尺寸较小、沿低角度马氏体板条边界的 M23C6 碳化物颗粒平均尺寸较大但密度较低、VX 碳氮化物的体积分数较大。
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引用次数: 0
A Study of the Structure and Mechanical Properties of Nb-Mo-Co-X (X = Hf, Zr, Ti) Refractory High-Entropy Alloys 铌-钼-钴-X(X = Hf、Zr、Ti)难熔高熵合金的结构和力学性能研究
IF 1.8 4区 材料科学 Q2 MATERIALS SCIENCE, CHARACTERIZATION & TESTING Pub Date : 2023-12-15 DOI: 10.1134/S1029959923060061
E. S. Panina, N. Yu. Yurchenko, A. A. Tozhibaev, M. V. Mishunin, S. V. Zherebtsov, N. D. Stepanov

Refractory high-entropy alloys (HEAs) are a new class of metallic materials based on group 4–6 elements of the periodic table with possible additions of Al, Si, Re, C, or B. Some single-phase refractory HEAs can maintain high strength up to 1600°C, while multiphase compositions have more attractive specific properties at temperatures up to 1200°C. Here we examine the structure and mechanical properties of refractory HEAs Nb30Mo30Co20Hf20, Nb30Mo30Co20Zr20, and Nb30Mo30Co20Ti20 (at %). The alloys consisted of an intermetallic B2 matrix and particles of a disordered bcc phase, as well as a minor volume fraction of additional bcc (Nb30Mo30Co20Hf20 and Nb30Mo30Co20Zr20) or fcc (Nb30Mo30Co20Ti20) phases. When tested for uniaxial compression, Nb30Mo30Co20Ti20 alloy showed a higher yield strength in the temperature range of 22–1000°C than Nb30Mo30Co20Hf20 and Nb30Mo30Co20Zr20 alloys. Nb30Mo30Co20Zr20 alloy did not fail at temperatures of 22–800°C to a given 50% strain, while Nb30Mo30Co20Ti20 alloy turned out to be brittle. All alloys demonstrated high strain hardening in the temperature range of 22–800°C, and they can compete in terms of specific strength with commercial nickel and cobalt superalloys.

摘要耐火高熵合金(HEAs)是一类新的金属材料,以元素周期表中的第4-6族元素为基础,可能添加Al、Si、Re、C或B。在此,我们研究了耐火 HEA Nb30Mo30Co20Hf20、Nb30Mo30Co20Zr20 和 Nb30Mo30Co20Ti20(%)的结构和机械性能。合金由金属间 B2 基体和无序 bcc 相颗粒以及少量体积分数的额外 bcc 相(Nb30Mo30Co20Hf20 和 Nb30Mo30Co20Zr20)或 fcc 相(Nb30Mo30Co20Ti20)组成。在进行单轴压缩测试时,Nb30Mo30Co20Ti20 合金在 22-1000°C 温度范围内的屈服强度高于 Nb30Mo30Co20Hf20 和 Nb30Mo30Co20Zr20 合金。Nb30Mo30Co20Zr20 合金在 22-800°C 的温度下,在给定的 50%应变下不会失效,而 Nb30Mo30Co20Ti20 合金则变得很脆。所有合金在 22-800°C 的温度范围内都表现出很高的应变硬化,在比强度方面可与商用镍和钴超合金相媲美。
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引用次数: 0
Effect of the Local Stress State on the Fracture Mechanism of Metallic Materials with Different Lattices under Single Loads 局部应力状态对单一载荷下不同晶格金属材料断裂机制的影响
IF 1.8 4区 材料科学 Q2 MATERIALS SCIENCE, CHARACTERIZATION & TESTING Pub Date : 2023-12-15 DOI: 10.1134/S102995992306005X
G. V. Klevtsov, R. Z. Valiev, N. A. Klevtsova

The study discusses the effect of the local stress state at the crack tip on the fracture behavior of coarse- and ultrafine-grained bcc, fcc and hcp materials under single impact and static loads. The local stress state of the materials at the crack tip under impact and static loading was evaluated by the hmax/t ratio, where hmax is the maximum depth of the plastic zone under the fracture surface and t is the specimen thickness. The depth of plastic zones under the fracture surface was determined using layer-by-layer etching of the surface with subsequent X-ray diffraction analysis. The study results showed that it is not always possible to establish an unambiguous relationship between the fracture mechanisms of metallic materials and the local stress state of a material at the crack tip. Nevertheless, some particular features were found: (i) the cleavage, quasi-cleavage or intergranular brittle fracture of materials, regardless of the lattice type, is indicative of plane strain, (ii) under plane stress, all materials, regardless of the lattice type, exhibit ductile fracture with the formation of a microdimple pattern, and (iii) most fcc materials fail by a mixed mechanism in the transition region from plane strain to plane stress.

摘要 本研究讨论了在单次冲击和静载荷作用下,裂纹尖端的局部应力状态对粗粒和超细粒 bcc、fcc 和 hcp 材料断裂行为的影响。材料在冲击和静载荷作用下的裂纹尖端局部应力状态是通过 hmax/t 比值来评估的,其中 hmax 是断裂面下塑性区的最大深度,t 是试样厚度。断裂表面下塑性区的深度是通过逐层蚀刻表面和随后的 X 射线衍射分析确定的。研究结果表明,金属材料的断裂机制与材料在裂纹尖端的局部应力状态之间并不总是能够建立明确的关系。尽管如此,我们还是发现了一些特别的特征:(i) 无论晶格类型如何,材料的劈裂、准劈裂或晶间脆性断裂都是平面应变的表现;(ii) 在平面应力下,无论晶格类型如何,所有材料都会表现出韧性断裂,并形成微凹痕模式;(iii) 在从平面应变到平面应力的过渡区域,大多数 fcc 材料都会以混合机制断裂。
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引用次数: 0
Effect of the Tool Path on Hardness Uniformity in an Annular Zone of X20Cr13 Steel Surface-Hardened by Friction Stir Processing 刀具路径对摩擦搅拌加工表面硬化 X20Cr13 钢环形区硬度均匀性的影响
IF 1.8 4区 材料科学 Q2 MATERIALS SCIENCE, CHARACTERIZATION & TESTING Pub Date : 2023-12-15 DOI: 10.1134/S1029959923060012
V. P. Kuznetsov, A. S. Skorobogatov, E. A. Kolubaev, A. I. Dmitriev, I. Yu. Smolin, V. V. Voropaev, I. A. Vorontsov

This paper presents the numerical and experimental results of hardening of an annular zone on the flat surface of an X20Cr13 steel specimen by friction stir processing (FSP) with a WC-Co hard alloy tool moving along circular and fan-shaped paths. A finite element model of the process is proposed for predicting the temperature distribution through the width and depth of the annular zone for the considered tool paths and for detecting the reverse tempering regions. The influence of the paths of a cylindrical friction stir tool with a flat end on microhardness distribution in the surface layer of the hardened zone was studied experimentally. It was shown that FSP along the fan-shaped path provides uniform hardening of the annular zone, while processing along the circular trajectory leads to softening of the material in the regions where the friction tracks overlap. The uniformity of surface hardness in the friction stir processed annular zone of X20Cr13 steel was evaluated by calculating the “covering uniformity” (CU) index proposed by Campana. The hardening behavior is in full agreement with the results of finite element simulation of the FSP process. Hardness measurements and microstructural studies showed that the fan-shaped tool path provides surface layer hardening to a depth of 400 μm with the CU index ranging from 0.78 to 1.00. In the case of the circular path, the CU index ranges from 0.48 to 0.72 at the same depth. The proposed research methods can be applied to evaluate the FSP efficiency when using other workpiece and tool materials.

摘要 本文介绍了使用 WC-Co 硬质合金工具沿圆形和扇形路径进行摩擦搅拌加工(FSP),对 X20Cr13 钢试样平面上的环形区进行硬化的数值和实验结果。为预测所考虑的刀具路径下环形区宽度和深度的温度分布以及检测反向回火区域,提出了该过程的有限元模型。实验研究了平头圆柱形搅拌摩擦工具的路径对淬硬区表层显微硬度分布的影响。结果表明,沿扇形轨迹进行的 FSP 可使环形区域均匀硬化,而沿圆形轨迹进行的加工则会导致摩擦轨迹重叠区域的材料软化。通过计算 Campana 提出的 "覆盖均匀性"(CU)指数,对 X20Cr13 钢搅拌摩擦加工环形区的表面硬度均匀性进行了评估。硬化行为与 FSP 工艺的有限元模拟结果完全一致。硬度测量和微观结构研究表明,扇形刀具路径的表面硬化层深度为 400 μm,CU 指数在 0.78 至 1.00 之间。而圆形路径在相同深度的 CU 指数为 0.48 至 0.72。所提出的研究方法可用于评估使用其他工件和刀具材料时的 FSP 效率。
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引用次数: 0
Comparative Analysis of Weld Microstructure in Ti-6Al-4V Samples Produced by Rolling and Wire-Feed Electron Beam Additive Manufacturing 轧制和送丝电子束增材制造 Ti-6Al-4V 样品焊接微观结构的对比分析
IF 1.8 4区 材料科学 Q2 MATERIALS SCIENCE, CHARACTERIZATION & TESTING Pub Date : 2023-12-15 DOI: 10.1134/S1029959923060048
A. V. Panin, M. S. Kazachenok, K. V. Krukovsky, L. A. Kazantseva, S. A. Martynov

The microstructure and phase composition of electron beam welded Ti-6Al-4V titanium alloy were studied by optical and scanning electron microscopy, backscattered electron diffraction, and X-ray diffraction analysis. Deep-penetration electron beam welds were made in a single pass on rectangular Ti-6Al-4V samples obtained by rolling and wire-feed electron beam additive manufacturing. It was found that the weld width in the 3D printed Ti-6Al-4V samples is greater than in the rolled material. The influence of the vapor capillary on the size, shape and structure of primary β grains formed in the fusion zone was shown. The variation of the penetration coefficient, volume fraction of the residual β phase, and residual stresses along the weld length was studied for Ti-6Al-4V samples obtained by both rolling and 3D printing.

摘要 通过光学显微镜、扫描电子显微镜、背散射电子衍射和 X 射线衍射分析研究了电子束焊接 Ti-6Al-4V 钛合金的微观结构和相组成。在通过轧制和送丝电子束增材制造获得的矩形 Ti-6Al-4V 样品上,进行了一次深穿透电子束焊接。结果发现,三维打印 Ti-6Al-4V 样品的焊缝宽度大于轧制材料。研究显示了蒸汽毛细管对熔合区形成的初级β晶粒的尺寸、形状和结构的影响。研究了通过轧制和三维打印获得的 Ti-6Al-4V 样品沿焊接长度方向的渗透系数、残余 β 相体积分数和残余应力的变化。
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引用次数: 0
Structure, and Mechanical and Tribological Properties of Ti–Cr–C–Ni–Fe Composite Coatings 钛-铬-碳-镍-铁复合涂层的结构、机械性能和摩擦学性能
IF 1.8 4区 材料科学 Q2 MATERIALS SCIENCE, CHARACTERIZATION & TESTING Pub Date : 2023-12-15 DOI: 10.1134/S1029959923060085
M. S. Antipov, P. M. Bazhin, A. S. Konstantinov, A. P. Chizhikov, A. O. Zhidovich, A. M. Stolin

The paper analyzes the structure, and the mechanical and tribological properties of Ti–Cr–C–Ni–Fe coatings formed on R6M5 high-speed steel in four modes of electrospark deposition (ESD) using TiC–NiCr electrodes manufactured by extrusion in combination with self-propagating high-temperature synthesis (SHS). The analysis shows that the coatings formed in the four ESD modes at a discharge energy of 0.2, 0.3, 0.6, and 1.0 J are composed mainly of Cr–Ni–Fe–Csolid and Fe0.7Ni0.3 matrix phases strengthened with Ti0.8Cr0.2C particles the size of which decreases to less than 100 nm in going from the coating surface to the substrate. In the SHS electrode during the deposition, most carbide particles are melted. Increasing the discharge energy increases the fraction of solid grains transferred to the substrate by a factor of up to 9. The dependences of the total anode mass loss and total cathode mass gain on the ESD time in the four modes have a classical form. Also considered are the discharge energy dependences of the SHS electrode transfer coefficient, coating run-in length, and wear of the coating and counterbody. The coating hardness measures 10.6–13.5 GPa.

摘要 本文分析了在四种电火花沉积(ESD)模式下,使用挤压法制造的TiC-NiCr电极结合自蔓延高温合成(SHS)在R6M5高速钢上形成的Ti-Cr-C-Ni-Fe涂层的结构、机械性能和摩擦学性能。分析表明,在放电能量为 0.2、0.3、0.6 和 1.0 J 时的四种静电放电模式下形成的涂层主要由 Cr-Ni-Fe-C 固相和 Fe0.7Ni0.3 基体相组成,并由 Ti0.8Cr0.2C 颗粒强化。在沉积过程中,SHS 电极中的大部分碳化物颗粒被熔化。增加放电能量可使转移到基底的固体颗粒的比例增加 9 倍。在四种模式下,阳极总质量损失和阴极总质量增加与静电放电时间的关系具有经典形式。此外,还考虑了 SHS 电极传递系数、涂层磨合长度以及涂层和基体磨损的放电能量相关性。涂层硬度为 10.6-13.5 GPa。
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引用次数: 0
A Study of Deformation and Fracture of the Eutectic in an Additively Manufactured Al-Si Composite Alloy 关于添加式制造的铝硅复合材料共晶变形和断裂的研究
IF 1.8 4区 材料科学 Q2 MATERIALS SCIENCE, CHARACTERIZATION & TESTING Pub Date : 2023-12-15 DOI: 10.1134/S1029959923060073
A. V. Zemlyanov, D. D. Gatiyatullina, V. R. Utyaganova, E. Dymnich, N. N. Shamarin, S. Yu. Nikonov, V. A. Romanova, A. S. Kulkov, R. R. Balokhonov

Experimental and numerical studies were conducted on AlSi12 alloy fabricated by wire-feed electron beam additive manufacturing to examine the structure, thermomechanical behavior and fracture of a eutectic microvolume at the scale of several microns. Dynamic boundary value problems were solved under plane strain conditions. The composite structure of the eutectic phase consisting of an aluminum matrix and silicon particles was taken into account explicitly in the calculations. Isotropic models of the thermoelastoplastic matrix and elastic-brittle particles were implemented in ABAQUS/Explicit. Composite deformation was calculated both with and without allowance for residual stresses caused by cooling of the composite after its fabrication. It was shown that after the cooling of the eutectic, silicon particles are compressed, and the aluminum matrix is under both bulk compressive and tensile as well as under pure shear stresses. It was found that residual stresses play a negative role at the stages of intense deformation of the composite. The fracture strain of the eutectic strongly depends on the yield point of the matrix, while the ultimate fracture stress varies but only slightly. Favorable morphology of silicon particles was determined which prevents early fracture of the eutectic.

摘要 对采用线进电子束增材制造技术制造的 AlSi12 合金进行了实验和数值研究,以考察几个微米尺度的共晶微体积的结构、热力学行为和断裂情况。在平面应变条件下求解了动态边界值问题。计算中明确考虑了由铝基体和硅颗粒组成的共晶相的复合结构。在 ABAQUS/Explicit 中实现了热塑基体和弹脆颗粒的各向同性模型。在计算复合材料变形时,既考虑到了复合材料制造后冷却所产生的残余应力,也考虑到了未考虑的残余应力。结果表明,共晶冷却后,硅颗粒受到压缩,铝基体受到体积压应力、拉应力和纯剪应力。研究发现,残余应力在复合材料剧烈变形阶段起着负面作用。共晶的断裂应变在很大程度上取决于基体的屈服点,而极限断裂应力仅略有不同。硅颗粒的良好形态可防止共晶的早期断裂。
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引用次数: 0
Structure Formation in Surface Layers of Aluminum and Titanium Alloys during Plasma Cutting 等离子切割过程中铝和钛合金表面层的结构形成
IF 1.8 4区 材料科学 Q2 MATERIALS SCIENCE, CHARACTERIZATION & TESTING Pub Date : 2023-12-15 DOI: 10.1134/S1029959923060103
A. V. Chumaevskii, A. V. Nikolaeva, A. V. Grinenko, A. O. Panfilov, E. O. Knyazhev, A. M. Cheremnov, V. R. Utyaganova, V. A. Beloborodov, P. S. Sokolov, D. A. Gurianov, E. A. Kolubaev

This paper explores the structure and changes in the mechanical properties, chemical composition and surface morphology of aluminum alloys AA5056, AA2024 and Grade 2 titanium alloy after high energy impact during plasma cutting. The studies show that plasma cutting causes the formation of a subsurface layer with a dendritic structure typical of cast material and with a partially altered chemical composition. The subsurface layer material is significantly softened when cutting heat treated alloy AA2024, but changes slightly when cutting AA5056 alloy. During plasma cutting of Grade 2 titanium alloy in shielding atmosphere, the presence of even a small amount of atmospheric oxygen leads to the formation of oxides in the layer closest to the surface, which have microhardness values more than 5–7 times higher than the base metal hardness. Below the surface layer with a molten structure, a heat-affected zone is formed where the structure of the base metal is changed as a result of thermal influence. Significant changes in this zone are characteristic only for heat treated alloy AA2024. Metal flow in the cutting zone initiated by the plasma jet and shielding gas flow occurs in both the laminar and vortex modes. Nonuniform metal flow in the cutting zone and nonoptimal process parameters lead to the formation of structural heterogeneities and defects of different structural and scale levels on the surface of the samples.

摘要 本文探讨了铝合金 AA5056、AA2024 和 2 级钛合金在等离子切割过程中受到高能量冲击后的结构及其机械性能、化学成分和表面形态的变化。研究表明,等离子切割会形成具有典型铸造材料树枝状结构的次表层,其化学成分也会发生部分改变。在切割经热处理的 AA2024 合金时,次表层材料明显软化,但在切割 AA5056 合金时,次表层材料略有变化。在屏蔽气氛中对 2 级钛合金进行等离子切割时,即使存在少量大气氧,也会在最接近表面的层中形成氧化物,其显微硬度值比基体金属硬度高 5-7 倍以上。在具有熔融结构的表层下面,会形成一个热影响区,由于热影响,基体金属的结构会发生变化。只有 AA2024 热处理合金才会在这一区域发生显著变化。由等离子射流和保护气流引发的切割区金属流既有层流模式,也有涡流模式。切割区内不均匀的金属流动和非最佳工艺参数导致样品表面形成不同结构和尺度的结构异质性和缺陷。
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引用次数: 0
Analysis of the Properties of a Nonlinear Model for Shear Flow of Thixotropic Media Taking into Account the Mutual Influence of Structural Evolution and Deformation 考虑结构演变和变形相互影响的触变介质剪切流非线性模型的特性分析
IF 1.8 4区 材料科学 Q2 MATERIALS SCIENCE, CHARACTERIZATION & TESTING Pub Date : 2023-12-15 DOI: 10.1134/S1029959923060036
A. V. Khokhlov, V. V. Gulin

A systematic analytical study was conducted on the mathematical properties of a previously proposed prototype of a nonlinear Maxwell-type constitutive equation for describing the shear flow of thixotropic substances (viscous liquid polymers, viscoelastic melts, concentrated solutions, pastes, emulsions). The equation takes into account the mutual influence of deformation and structural evolution (the kinetics of intermolecular bond formation and breaking) on viscosity and shear modulus and the effect of deformation on this kinetics. In the uniaxial case, the constitutive equation is governed by a nondecreasing material function and six positive parameters. The equation is reduced to a set of two nonlinear autonomous differential equations for the stress and the crosslinking degree. It is proved that the equilibrium point of this set is unique. The dependences of the point coordinates on all material parameters and on the shear rate for an arbitrary nondecreasing material function are investigated in general form, and all the dependences are proved to be monotonic. Equations for the flow and viscosity curves are derived and investigated. It is proved that the model leads to an increasing shear rate dependence of the equilibrium stress and to a decreasing apparent viscosity curve, which reflect the typical properties of the experimental flow curves of pseudoplastic materials. Using six arbitrary governing material parameters and the governing material function, we analytically study the phase portrait of the nonlinear set of two differential equations, to which the model is reduced, for dimensionless stress and crosslinking degree near its only equilibrium point. It is proved that the equilibrium point is always stable and can be of three types only: a stable node, a degenerate node, or a stable focus. The existence criteria for each type are found in the form of explicit constraints on the material function, model parameters, and shear rate. A stable focus indicates the nonmonotonicity of the set solutions and the existence of deformation modes with damped oscillations of stress and crosslinking degree upon reaching steady-state values. The influence of the material parameters and material function on the type of equilibrium point and on the behavior of the model integral curves is analyzed.

摘要 对以前提出的用于描述触变性物质(粘性液态聚合物、粘弹性熔体、浓溶液、糊剂、乳剂)剪切流动的非线性麦克斯韦式结构方程原型的数学特性进行了系统的分析研究。该方程考虑了变形和结构演变(分子间键的形成和断裂动力学)对粘度和剪切模量的相互影响,以及变形对这一动力学的影响。在单轴情况下,构成方程由一个非递减材料函数和六个正参数控制。该方程简化为应力和交联度的两个非线性自主微分方程组。该方程组的平衡点是唯一的。对于任意非递减材料函数,以一般形式研究了点坐标对所有材料参数和剪切率的依赖关系,并证明所有依赖关系都是单调的。推导并研究了流动和粘度曲线方程。研究证明,该模型导致平衡应力随剪切速率的增加而增加,表观粘度曲线随剪切速率的减小而减小,这反映了假塑性材料实验流动曲线的典型特性。利用六个任意的控制材料参数和控制材料函数,我们分析研究了非线性两微分方程组的相位图,该模型被简化为无量纲应力和交联度在其唯一平衡点附近的相位图。研究证明,平衡点总是稳定的,并且只能有三种类型:稳定节点、退化节点或稳定焦点。通过对材料函数、模型参数和剪切速率的明确约束,找到了每种类型的存在标准。稳定焦点表示集合解的非单调性,以及在达到稳态值时应力和交联度存在阻尼振荡的变形模式。分析了材料参数和材料函数对平衡点类型和模型积分曲线行为的影响。
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引用次数: 0
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Physical Mesomechanics
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