Observation of the relation between uniaxial creep and stress relaxation of filled rubber

This paper presents an experimental evaluation of the stress relaxation and creep of filled rubber. A detailed study of the influence of different test programs, where the main variable was the load sequence on the creep and relaxation processes, is discussed. The final goal of the research is to find a method to predict stress relaxation from known creep, or vice versa, in a simple way that would give sufficiently accurate results over both primary and secondary creep regions. Therefore suggestion for converting the creep test result into a stress relaxation curve and vice versa is presented. The idea is based on the assumption that both processes (creep and stress relaxation) are the result of the same viscoelastic mechanism and that the stress relaxation can be treated as creep under decreasing stress. Experimental data shows these assumptions to be correct. For the conversion of the creep parameters into stress relaxation parameters a reverse stress-strain curve is needed, therefore factors affecting the unloading stress-strain curve are also presented. Finally, the transition from the suggested conversion to the final method will be discussed.     

Complex order fractional derivatives in viscoelasticity

We introduce complex order fractional derivatives in models that describe viscoelastic materials. This cannot be carried out unrestrictedly, and therefore we derive, for the first time, real valued compatibility constraints, as well as physical constraints that lead to acceptable models. As a result, we introduce a new form of complex order fractional derivative. Also, we consider a fractional differential equation with complex derivatives, and study its solvability. Results obtained for stress relaxation and creep are illustrated by several numerical examples.     

Fractional heat conduction equation for an infinitely generalized,thermoelastic, long solid cylinder

In this work, we consider the one-dimensional problem for an infinitely long solid cylinder in the context of the theory of generalized thermoelasticity with one relaxation time. The heat conduction equation with the Caputo fractional derivative of order α is used. The curved surface of the cylinder is assumed to be in contact with a rigid surface and is subjected to constant heat flux. By means of the Laplace transform and numerical Laplace inversion the problem is solved. Numerical computations for the temperature, displacement and stress distributions are carried out and displayed graphically as well as the results are discussed comprehensively.     

马来酸酐改性天然橡胶对碳酸钙/天然橡胶复合材料力学行为的影响

以过氧化二异丙苯(DCP)为引发剂,在转矩流变仪中自制马来酸酐(MAH)接枝改性天然橡胶(NR)(MNR),将其作为超细碳酸钙/天然橡胶复合材料(CaCO3/NR)的改性剂,研究了MNR对于CaCO3/NR复合材料的力学性能、应力软化效应以及应力弛豫行为的影响。研究结果表明,MNR改性后CaCO3/NR复合材料较之未改性复合材料拉伸强度、撕裂强度和硬度等力学性能均有所提高,应力软化效应加剧,应力弛豫程度和速度降低,力学行为研究结果证实MNR可有效改善CaCO与NR基体间的界面粘合。     

Generalized thermoelastic diffusion problem for an infinitely long hollow cylinder for short times

In this work, we consider the problem of a thermoelastic infinitely long hollow cylinder in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The outer surface of the cylinder is taken traction free and subjected to a thermal shock, while the inner surface is taken to be in contact with a rigid surface and is thermally insulated. Laplace transform techniques are used. The solution is obtained in the Laplace transform domain by using a direct approach. The solution of the problem in the physical domain is obtained numerically using a numerical method for the inversion of the Laplace transform based on Fourier expansion techniques. The temperature, displacement, stress and concentration as well as the chemical potential are obtained. Numerical computations are carried out and represented graphically.     

Numerical simulation of residual stress relaxation around a cold‐expanded fastener hole under longitudinal cyclic loading using different kinematic hardening models

Cold expansion of fastener holes creates compressive residual stresses around the hole. This well‐known technique improves fatigue life by reducing tensile stress around the holes. However, cyclic loading causes these compressive residual stresses to relax, thus reducing their beneficial effect. Estimation of the fatigue life without considering the residual stress relaxation might lead to inaccurate results. In this research, numerical studies were carried out using 2D finite element (FE) models to determine the initial tangential and radial residual stress distributions generated by cold expansion and their relaxation under cyclic loading. To predict the stress relaxation, four nonlinear kinematic hardening models were applied in simulation of stress/strain path. The results obtained from the FE analysis were compared with available experimental results. A good agreement between the numerical and experimental results was observed.     

FE analysis of residual stress relaxation in a girth-welded duplex stainless steel pipe under cyclic loading

This study intends to characterize the residual stress relaxation in a girth-welded duplex stainless steel pipe exposed to cyclic loading. FE thermal simulation of the girth welding process is first performed to identify the weld-induced residual stresses. 3-D elastic–plastic FE analyses incorporated with the cyclic plasticity constitutive model which can describe the cyclic stress relaxation are next carried out to evaluate reconstruction of the residual stresses under cyclic mechanical loading. The results unveils that considerable reduction of the residual stresses in and around the girth weld occur even after the initial few loading cycles and degree of the stress relaxation is dependent on the magnitude of applied cyclic loading.     

The effect of aspect ratio on adhesion and stiffness for soft elastic fibres

The effect of aspect ratio on the pull-off stress and stiffness of soft elastic fibres is studied using elasticity and numerical analysis. The adhesive interface between a soft fibre and a smooth rigid surface is modelled using the Dugdale–Barenblatt model. Numerical simulations show that, while pull-off stress increases with decreasing aspect ratio, fibres get stiffer. Also, for sufficiently low aspect ratio fibres, failure occurs via the growth of internal cracks and pull-off stress approaches the intrinsic adhesive strength. Experiments carried out with various aspect ratio polyurethane elastomer fibres are consistent with the numerical simulations.     

Dual scale non-linear stress analysis of a fibrous metal matrix composite

Precise estimation of local stress profiles in individual phases of a fiber reinforced metal matrix composite is a crucial concern for design of composites. Stress profiles are significantly affected by plastic relaxation of soft matrix. In this work, an analytical model was developed to compute local stress profiles in individual phases of fibrous metal matrix composites. To this end, embedded cell cylindrical composite model was applied in which a layered concentric cylinder consisting of a fiber-, matrix- and homogenized composite layers was used. Mean field micromechanics was integrated into the conventional elasticity solution process so that micro-macro dual scale analysis could be performed. The algorithm was formulated in an iterative incremental structure which was able to perform plastic analysis. This also allows temperature dependence of flow stress to be considered. Taking copper-SiC system as a reference composite, stress profiles were obtained for mechanical and thermal loading cases. For comparison, independent finite element analyses were carried out for two different unit cell models. Excellent agreement between analytical and numerical solutions was found for the mechanical loading case even for plastic range. In the case of thermal loading, however, plastic solutions revealed notable difference in quantity, especially for the axial stress component.     

Influence of carbon content and carbide morphology of carbon steels on stress strain curve in vicinity of yield point

Abstract

Experimental analysis was carried out to examine the influence of carbon content on the stress–strain curve in the vicinity of yield point. Numerical analysis was then carried out to investigate the mechanism in the microstructure through which the influence occurred. Attention was focused upon the morphology of the carbide, and the homogenisation method and the elastic–plastic finite element method were used for numerical evaluation. Despite very primitive assumptions that the macroscopic stress–strain curve of extra low carbon steel applies to the ferrite in the microstructure and the carbide deforms only elastically, the numerical results have explained well the stress–strain curves obtained experimentally. Finally, TEM observations were carried out to check the validity of the result predicted by the homogenisation method. The TEM images show a concentration of dislocations in the ferrite existing between adjacent carbides lying parallel with the macroscopic loading direction. This result explains qualitatively the localisation of strain in the ferrite predicted by the homogenisation method. By using the numerical analysis inversely, it would be possible to design the morphology of the carbide so that the macroscopic mechanical behaviour of a carbon steel meets the required value in the vicinity of yield point.     

大型煤仓球壳的风致干扰效应研究

针对两座连续排列的大型煤仓球壳的风致干扰效应进行了风洞试验研究,并基于Reynolds时均N-S方程和RSM模型对其进行了CFD数值模拟。将数值模拟结果与风洞试验结果进行了对比分析,两者吻合较好,在此基础上探讨了煤仓球壳之间的风致静力及动力干扰效应,结果表明:静力干扰效应主要表现为阻碍效应,其结果是降低了来流动能,提高了来流湍流度;动力干扰主要表现在增大效应,当受扰建筑处于施扰建筑的下游时,动力干扰效应较大。     

Numerical integration on the sphere and its effect on the material symmetry of constitutive equations—A comparative study

In the present paper, we consider a class of constitutive models based on numerical integration on the unit sphere. The directional behaviour of the quadrature schemes and its effect on the symmetry properties of these constitutive models are studied by subjecting the set of integration points on the sphere to arbitrary rigid rotations. We investigate a number of recently proposed integration schemes in application to a full network model of rubber elasticity and to an exponential model for soft tissues. In order to assess and compare these schemes, statistical methods are presented and applied. The analysis discloses a number of integration schemes that offer a good compromise between the numerical error and the number of integration points. However, as a general result it turns out that numerical integration is prone to introduce strong anisotropy into originally isotropic constitutive equations, in particular, for highly non‐linear integrand functions. The consequences for application of the investigated class of constitutive models in finite element calculations are highlighted in a benchmark‐like numerical example. Copyright © 2009 John Wiley & Sons, Ltd.     

Relaxation behavior of neat and particulate filled polypropylene in uniaxial and multiaxial compression

The recently developed confined compression test was used to measure the viscoelastic bulk and shear relaxation moduli of neat, glass bead and talc filled polypropylene. In this paper further modifications of the test are introduced and a criterion for the assessment of the quality of experimental data is suggested. As expected, shear as well as the bulk relaxation moduli were found to increase with the addition of particles. In order to determine the pressure sensitivity of the material, unconfined compression tests were also performed and compared with the confined tests through interconversion of the measured moduli. In agreement with earlier results on other polymers, it turned out that the relaxation response is significantly retarded at higher confinement levels. It is shown that the effect of filler particles on the long-term behavior depends on the specific uniaxial or multiaxial stress state. Poisson’s ratio was calculated by interconversion from the bulk and shear relaxation modulus; these results show that with a single test in the confined configuration, a complete viscoelastic characterization of the material can be obtained.     

The effect of cold expansion on fatigue crack growth from open holes at room and high temperature

In this paper a series of residual stress measurements and fatigue crack growth tests have been carried out using aluminium alloy 2650 specimens containing cold expanded and non cold expanded holes. Residual stress measurements have been done after cold expansion and after various loading and temperature conditions. In order to measure an angular variation of residual stresses, X-ray and a new technique called the Garcia–Sachs method have been employed. Results revealed that residual stress relaxation occurred as a result of exposure at 150°C. The magnitude of relaxation was shown to be dependent on the level and the sign of externally applied load. Fatigue crack growth tests have been carried out at 20°C and 150°C for both cold expanded and non-cold expanded conditions. Fatigue crack growth rates in specimens containing cold expanded fastener holes were affected significantly by elevated temperature exposure. Depending on the exposure time and loading conditions the fatigue life improvement was found to be between one and greater than 10 for tests at 20°C.     

Effect of gate size on the melt filling behavior and residual stress of injection molded parts

This paper studies the effects of gate size on the cavity filling pattern and residual stress of injection molded parts. A total of three rectangular gates with different sizes were used. Experiments were carried out by using a dynamic visualization system. A flow visualization mold was specially designed and made for this study. A high-speed video camera was used to record the mold filling phenomena of cavities with different gate size and different processing parameters. In addition, a Stress Viewer was used to characterize the residual stress of molded samples. It was found that the undersized gate has many adverse effects on the filling behavior and residual stress of molded parts. With a larger gate, the cavity will be filled faster and residual stress of parts may be smaller. The result of the study also indicates that nozzle temperature and injection rate can significantly affect the above two aspects.     

Modeling and Prediction of Thermal Cycle Induced Failure in Epoxy-Silica Composites

Epoxy resins filled with dielectric mineral particles are frequently used as insulating materials in power industry applications. Due to their excellent dielectric properties and relatively good thermal performance (resistance, ageing and conductivity) their usability is common and extensive. However, the mechanical performance of the resins is influenced by several factors such as resistance to crack propagation, especially in low temperature applications. This phenomenon is normally linked with appearance of two phase systems where particle filled epoxy material interacts with metallic inserts having significantly different thermal expansion coefficients. This kind of epoxy-metal interface can produce relatively high stresses in the product structure during thermal cycle loading. The paper deals with mechanical problems of power industry products and introduces the methodology for numerical modeling of failure in silica filled epoxy systems subjected to severe temperature gradients. Various aspects of material behavior modeling are covered in this article, including polymerization process, viscoelastic stress relaxation as well as stochastic cracking.     

Bending behavior of aluminum foam-filled double cylindrical tubes

Quasi-static experiments and numerical simulations are carried out to study three-point bending behavior of a new kind of structures, i.e., double cylindrical tubes filled with closed-cell aluminum foam. The deformation and failure mechanism of this new structure were observed and analyzed numerically using the finite element method. It is revealed that the stress distribution and fracture of the foam-filled double-tube structure are different from those of an empty tube and foam-filled single tube. Two cracks were found experimentally, and both experiments and numerical simulation show that cracks initiated in the aluminum foam. In comparison with empty and foam-filled single tubes, the load-carrying capacity of this new structure is much steadier, the bending resistance is enhanced, and the weight efficiency of energy absorption is higher. Parameters affecting the performance of the foam-filled double-tube structures are also studied.     

A micromechanical analysis to predict the cord-rubber composite properties

Both three- and two-dimensional generalized plane strain finite element analyses based on a micromechanics approach were carried out to investigate the linear and nonlinear effective composite properties as well as the stress fields. A unit cell model of cord-rubber composite subjected to different loadings was studied to predict the effective composite properties. The numerical results of effective composite properties obtained from 2D and 3D finite element analyses were compared with experimental data and other finite element results available in the literature. The effects of rubber material nonlinearity and large deformation on the effective composite properties and interface stress distributions are presented and discussed.     

Stress relaxation characteristics of warm frozen clay under triaxial conditions

Stress relaxation is one of the main concerns in geotechnical engineering, especially in permafrost regions with warm frozen soil. This paper investigated the mechanical behaviors of a warm frozen soil during relaxation process. A series of triaxial relaxation tests were carried out on the warm frozen soil samples under the temperature from − 1.0 °C to − 0.2 °C and confining pressure of 0.5 MPa to 3.0 MPa. Three stages were observed during the whole stress relaxation process, i.e. instantaneous relaxation, intense relaxation and slow relaxation. Relationship between deviatoric stress and time was described by a hyperbolic relationship. With relatively small pre-strain (3% and 4%), volumetric changes during stress relaxation contracted initially followed by expansion, but contraction dominates the relaxation process with the magnitude of pre-strain over 6%. Characteristic parameters such as the instantaneous stress relaxation, the critical relaxation duration and relaxation rate are defined and analyzed. It is found that the parameters are all dependent on soil temperature, confining pressure and magnitude of pre-strain.     

冷轧带肋钢筋应力松弛试验机的研制

针对冷轧带肋钢筋材料在高应力(高于松弛下限)作用下会产生流变(晶格变形、滑移),应力将随时间衰减的特性,研制该电子应力松弛试验机。该机采用MaxTest标准化模块软件系统进行应力、变形和位移闭环的自动控制,同时在结构设计上通过使用三爪夹具保证防滑,通过结构力学的核算来保证其刚度,从而具有防止试样打滑、精确地负荷和形变控制、连续并适时地绘制松驰力-试验时间曲线的特点,并设计在意外因素(停电、断电)下继续进行试验的措施,充分满足标准要求和实际工作需要。