Uniaxial extension and shear in combination with cyclic straining as a promising method for studying the viscoelasticity of polymers over a wide range of stresses and strains atT > T g

Simple relations are found between the fracture strains, the long-term durability and the initial values of parameters characterizing polymer rheology at deformation rates and stresses approaching zero. Fracture regimes are determined by two groups of parameters. One includes critical values of stresses. They are invariant with repect to temperature and molecular weight of the polymers; the values of critical stresses for different polymer compositions differ by a factor of 10 to 20. The second group of critical parameters includes the rates of deformation determined by the initial viscosity. The latter may vary by many orders of magnitude. There exists a universal critical value determining polymer fracture independent of linear macromolecule composition, its molecular weight, the temperature and the way of attaining a given state. This value is the recoverable strain and is equal to 0.5 according to Hencky. There exists a relation between the maximum value of recoverable strain in the transition region from the rubbery to the leathery state and the extensibility of macromolecules for polymers with various molecular weights. Quenching of the polymer near the maximum recoverable strain makes it possible to obtain high strength samples. Overspurt regimes for polymer flow have also been studied. It has been shown that this causes polymer static electrification. Simple and unique dependences of the charge density on temperature and polymer molecular weight have been established.Presented at the 28th IUPAC International Symposium on Macromolecules, June 1982, Amherst, Mass. (USA)Dedicated to Prof. Dr. Josef Schurz on the occassion of his 60th birthday     

The influence of flow confinement on the rheological properties of complex fluids

The rheological properties of plastic and viscoplastic complex fluids have been investigated using constant velocity squeeze flow rheometry at small gaps in order to examine the influence of the resulting flow confinement. The fluids investigated were aqueous carbopol suspensions and three commercial products (Tesco English mustard, Tesco value lemon curd and Heinz tomato ketchup (HTK)). The bulk rheological properties were measured using parallel plate rheometry. Rough plates were used to eliminate wall slip in both rheometric configurations. The commercial products are Herschel–Bulkley fluids and, for gaps less than a critical value of ~200 μm, the yield stresses tended to large values. There was a corresponding trend to small values for the flow consistencies except for HTK, which has a negligibly small bulk value. A possible explanation is that the micro-structural correlation lengths of these fluids are of the order of that of the critical separation. The yield stresses of the carbopol suspensions also increased sharply at the critical gap but then decreased gradually with decreasing gap separation. The transition may correspond to the formation of a jammed state with the subsequent plastic flow at smaller gap separations arising from localised shearing.     

On Stability Analysis of Ribbed Cylindrical and Conical Shells under Axial Compressive Forces

An experimental study into the stability of ribbed cylindrical and conical shells is described. It is shown that when the equivalent rigidity introduced earlier is chosen as an argument in the formula for calculation of the critical stresses at the stage of shell design, this formula has the form of a linear function.     

Determining Critical Stresses for Axially Compressed Cylindrical Shells from an Analysis of Response Characteristics

The stability of metallic and glass-reinforced plastic cylindrical shells is analyzed experimentally. It is established that if the equivalent stiffness is taken as an argument of the formula used to evaluate critical stresses in designing a shell, then the critical stresses depend linearly on its stiffness     

Loss of adhesion at the tip of an interface crack

A model is constructed to analyze adhesive bond failure at the tip of an interface crack. The model is based on the assumption that there are zones of bounded cohesive tensile and shear stresses near a crack tip. Within the context of certain broad a-priori assumptions on the distributions of certain stress and displacement components in the cohesive zones, the requirement thatall stresses in the two materials remain bounded provides a method to compute the specific details for these zones. It is assumed that bond failure occurs when the extension of the bond fiber at the crack tip exceeds a critical value. For an interface crack in a uniform tension field computations for two alternate formulations suggest that this failure criterion is independent of the precise distribution of the cohesive stresses, but rather depends only upon their averaged values. Combined loading with a dominant tensile component has also been analyzed. If the critical extension of bond fibers and the maximum value of the cohesive tensile stress are known, the model provides the maximum allowable interface stresses for given crack dimension and material parameters.     

考虑平均应力的同频拉扭多轴高周疲劳寿命评价方法

目前基于临界平面理论的高周疲劳寿命预测模型, 大都充分考虑了法向平均应力对材料疲劳寿命的影响, 但是没有有效反映剪切平均应力对疲劳寿命的影响. 通过分析7075-T651铝合金的试验数据发现, 与法向拉平均应力类似, 剪切平均应力同样对材料的疲劳寿命产生不利影响. 因此, 如果寿命预测模型中忽略剪切平均应力的影响, 存在明显剪切平均应力加载工况下, 预测寿命可能偏于危险. 由此, 本文定义具有较大法向应力的最大剪应力范围平面为临界平面, 建立了一个能够同时反映法向和剪切平均应力影响的高周疲劳寿命预测模型, 并给出了模型中材料常数的确定方法. 新模型首先将基于应变的Fatemi-Socie准则, 推广到材料的高周疲劳寿命预测, 给出了Fatemi-Socie准则的应力表述形式. 然后, 引入剪切和法向Walker因子, 反映剪切和法向平均应力对材料疲劳寿命的影响. 剪切和法向Walker因子的取值都介于0和1之间, 不同取值反映了材料对剪切和法向平均应力敏感程度的不同. 新模型适用于范围内的金属塑性材料. 利用5种材料在12种存在平均应力加载工况下的试验数据, 对所建模型进行了试验验证, 结果表明预测结果与试验结果吻合良好, 绝大多数寿命预测结果分布在3倍误差带以内.      

Residual stresses in squeeze-cast aluminum rods

The longitudinal slitting technique has been applied to determining and comparing the residual stresses in as-cast and squeeze-cast aluminum rods. Residual stresses in the squeeze-cast aluminum alloy rods are found to increase with applied punch pressures under a constant die-base thermocouple reference temperature. For the variations of residual stresses with varying die-base thermocouple reference temperatures, a peak residual stress is found to occur at a die-base thermocouple reference temperature of 100° C. A semi-empirical formula is derived for the determination of the maximum longitudinal residual stress in the tapered cylindrical as-cast aluminum alloy, from which the maximum longitudinal residual stresses for squeeze cast can be determined, using the residual-stress ratios obtained experimentally     

Effective thermal conductivity of dispersed materials

Measurements have been made by the comparison method for the effective thermal conductivity of dispersed materials which consist of substances with different thermal conductivities. The applicability of existing predicting formulae is discussed in detail as comparing their predicted values with the present data. A new predicting formula is proposed through analyzing the experimental data, the numerical results, and also the data obtained with the electrolytic-bath. It is found that the proposed formula has a wider range of applicability than that of previously reported ones.     

Consistent Finite Element Calculations of Boundary and Internal Fluxes

The purpose of this paper is to develop a consistent method to calculate the fluxes or the stresses in an incompressible flow, particularly a turbulent flow. A post-processing technique has been developed such that fluxes or stresses are treated as unknown values, which are solved for, weakly, using the finite element method.

The method has been applied to calculate the Reynolds stresses in a turbulent channel flow. As a result of the new consistent method, the Reynolds stresses have shown good agreement with the DNS data confirming the momentum conservation of the finite element method.     

压电材料裂纹顶端条状电饱和区模型的力学分析

在线性压电本构方程框架下,对裂纹顶端条状电饱和区模型进行了严格的数学分析．完整地考虑了各向异性力电耦合效应．建立了电饱和区尺寸与外加电场的依赖关系．证实了当裂纹垂直极化轴时,压电材料的断裂应力随着外加正电场的增加而减小,随着外加负电场的增加而增加．当裂纹平行于极化轴时,与极化轴平行的外加电场对断裂应力无影响     

A MULTIAXIAL HIGH CYCLE FATIGUE LIFE PREDICTION MODEL CONSIDERING THE EFFECT OF MEAN STRESS FOR TENSION-TORSION LOADINGS WITH SAME FREQUENCY 1)

目前基于临界平面理论的高周疲劳寿命预测模型, 大都充分考虑了法向平均应力对材料疲劳寿命的影响, 但是没有有效反映剪切平均应力对疲劳寿命的影响. 通过分析7075-T651铝合金的试验数据发现, 与法向拉平均应力类似, 剪切平均应力同样对材料的疲劳寿命产生不利影响. 因此, 如果寿命预测模型中忽略剪切平均应力的影响, 存在明显剪切平均应力加载工况下, 预测寿命可能偏于危险. 由此, 本文定义具有较大法向应力的最大剪应力范围平面为临界平面, 建立了一个能够同时反映法向和剪切平均应力影响的高周疲劳寿命预测模型, 并给出了模型中材料常数的确定方法. 新模型首先将基于应变的Fatemi-Socie准则, 推广到材料的高周疲劳寿命预测, 给出了Fatemi-Socie准则的应力表述形式. 然后, 引入剪切和法向Walker因子, 反映剪切和法向平均应力对材料疲劳寿命的影响. 剪切和法向Walker因子的取值都介于0和1之间, 不同取值反映了材料对剪切和法向平均应力敏感程度的不同. 新模型适用于范围内的金属塑性材料. 利用5种材料在12种存在平均应力加载工况下的试验数据, 对所建模型进行了试验验证, 结果表明预测结果与试验结果吻合良好, 绝大多数寿命预测结果分布在3倍误差带以内.     

CONDITIONS FOR THE APPLICATION OF THE STRESS TRANSFORMATION FORMULA 1)

斜面应力公式,即一点应力的坐标旋转变换公式,是材料力学和弹性力学里最常用的公式之一,并广泛用于固体力学和工程设计中。一个让学生感觉例外的典型例子是含V 形切口的薄板在切口尖端的应力情况,如果利用斜面应力公式和切口面的自由面条件,就会得出切口尖点处于零应力状态的结果,而这与线弹性断裂力学给出切口处应力趋于无限大的结果不符。为消除这一疑虑,考察了尖端应力的特性,指出：只有在过一点的各个斜面上的应力是单值连续的情况下,斜面应力公式才能适用,此时,该点的全部应力分量组成应力张量。在V形切口的尖端、裂纹尖端,自由面与顺其延伸至介质内侧的面上的应力不同,应力在该面上就不是单值连续的,该点的应力状态就不能用张量表示,斜面应力公式在切口或裂纹尖端就不适用了。     

Prefracture zone for longitudinal shear cracks in structured materials

We obtain simple relations for the following critical fracture parameters of elastoplastic materials: the shear stresses, the prefracture zone length, and the stress intensity factor for mode III of fracture. There is a passage to the limit from a sufficient fracture criterion to a necessary fracture criterion as the prefracture zone length tends to zero. The critical stresses obtained from the necessary and sufficient criteria are substantially different. In the framework of the proposed model, the critical stress intensity factor obtained from the sufficient criterion depends on the grain diameter and the parameters of the τ-γ diagram of the material.     

Defects in gradient micropolar elasticity—II: edge dislocation and wedge disclination

A theory of gradient micropolar elasticity based on first gradients of distortion and bend-twist tensors for an isotropic micropolar medium has been proposed in Part I of this paper. Gradient micropolar elasticity is an extension of micropolar elasticity such that in addition to double stresses double couple stresses also appear. The strain energy depends on the micropolar distortion and bend-twist terms as well as on distortion and bend-twist gradients. We use a version of this gradient theory which can be connected to Eringen's nonlocal micropolar elasticity. The theory is used to study a straight-edge dislocation and a straight-wedge disclination. As one important result, we obtained nonsingular expressions for the force and couple stresses. For the edge dislocation the components of the force stress have extremum values near the dislocation line and those of the couple stress have extremum values at the dislocation line and for the wedge disclination the components of the force stress have extremum values at the disclination line and those of the couple stress have extremum values near the disclination line.     

Suppression of edge cracking in layered ceramic composites by edge coating

A strategy is proposed to reduce surface tensile stresses that develop in ceramic microlaminate structures. As a specific example, surface stresses, which can lead to unwanted edge cracking, appear within a thin alumina/mullite layer bounded by thicker alumina layers after fabrication at some elevated temperature and subsequent cooling. A stress analysis is performed using the finite element method on a geometry in which the (edge) surface of the ceramic sandwich structure has been coated with an overlayer of the alumina/mullite material with thickness proportional to the initial buried layer thickness. These analyses show there is a critical thickness of the overlayer at which the surface tensile stresses can be reduced to zero. Stress concentration factors are calculated numerically for cracks propagating through this structure, and thus the resistance to surface cracking is quantified.     

On the relationship between the work of adhesion and the critical shear stress for the onset of flow instabilities

The relationship between the critical shear stress for the onset of flow instabilities and the work of adhesion at the interface has been evaluated experimentally for a series of polyolefins on several steels, brasses, and coated steels. The critical shear stress was considerably affected by the chemical nature of the die. Low-surface-energy materials were found to produce smooth extrudates presumably by inducing slippage at the wall. Steel, tungsten carbide, and brass surfaces promoted sharkskin defect at shear stresses above the first critical shear stress. A linear relationship between the critical shear stress and the work of adhesion was found to be valid for values of work of adhesion smaller than approximately 30 mN/m. This indicates that slippage occurs due to a breakdown of the adhesion at the interface. For values of work of adhesion greater than approximately 30 mN/m a stronger interaction at the interface may induce a cohesive failure at the interface and subsequently, extrudate distortions.     

Some features of the buckling of stringer shells

A technique for stability analysis of stringer shells is proposed. It is used to analyze the minimum critical stresses. The dependence of the dimensionless parameters σ_cr/σ_cl on the number of stringers is plotted. The linear and nonlinear theories of ribbed shells are used to examine the features of how stringer shells lose stability. It is shown that the minimum critical stresses determined using the theory of ribbed shells and a structurally orthotropic model are close within the range of stiffness parameters considered __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 59–64, February 2006.     

水平均布荷载作用在地基内部时的土中应力公式

本文根据半无限体内受水平集中力作用的明德林公式，通过积分而首次完整地推导出水平矩形均布荷载作用在地基内部时的土中应力分量的解析表达式，以便工程设计人员在设计时使用。     

Effect of the pattern of initial perturbations on the steady pipe flow regime

The influence of the inlet flow formation mode on the steady flow regime in a circular pipe has been investigated experimentally. For a given inlet flow formation mode the Reynolds number Re* at which the transition from laminar to turbulent steady flow occurred was determined. With decrease in the Reynolds number the difference between the resistance coefficients for laminar and turbulent flows decreases. At a Reynolds number approximately equal to 1000 the resistance coefficients calculated from the Hagen-Poiseuille formula for laminar steady flow and from the Prandtl formula for turbulent steady flow are equal. Therefore, we may assume that at Re > 1000 steady pipe flow can only be laminar and in this case it is meaningless to speak of a transition from one steady pipe flow regime to the other. The previously published results [1–9] show that the Reynolds number at which laminar goes over into turbulent steady flow decreases with increase in the intensity of the inlet pulsations. However, at the highest inlet pulsation intensities realized experimentally, turbulent flow was observed only at Reynolds numbers higher than a certain value, which in different experiments varied over the range 1900–2320 [10]. In spite of this scatter, it has been assumed that in the experiments a so-called lower critical Reynolds number was determined, such that at higher Reynolds numbers turbulent flow can be observed and at lower Reynolds numbers for any inlet perturbations only steady laminar flow can be realized. In contrast to the lower critical Reynolds number, the Re* values obtained in the present study, were determined for given (not arbitrary) inlet flow formation modes. In this study, it is experimentally shown that the Re* values depend not only on the pipe inlet pulsation intensity but also on the pulsation flow pattern. This result suggests that in the previous experiments the Re* values were determined and that their scatter is related with the different pulsation flow patterns at the pipe inlet. The experimental data so far obtained are insufficient either to determine the lower critical Reynolds number or even to assert that this number exists for a pipe at all.     

Automated Stress Separation Along Stress Trajectories

A procedure for the separation of principal stresses in automated photoelasticity is presented. It is based on the integration of indefinite equations of equilibrium along stress trajectories, also known as Lamè–Maxwell equations. A new algorithm for precise and reliable stress trajectory calculation, which is an essential feature of the procedure, has also been developed. Automated stress separation is carried out along stress trajectories starting from free boundaries. Experimental tests were performed on a disc in diametral compression and on a ring with internally applied pressure. Full-field principal stress values were obtained and results were compared with those from the theory of elasticity and with those obtained from the classical shear difference method. It was shown that the proposed method is more accurate and less affected by the presence of residual stresses or experimental errors at the boundaries than the shear difference method. In addition, the method requires little human interaction and is therefore well-suited for automated photoelasticity.