Constitutive relations of strain, anisotropic degradation, and fracture of filled polymer materials in prevailing-tension processes with varying axis direction and relaxations

In the course of monotone uniaxial tension, filled polymer materials quasi-isotropic in the initial state experience increasing structure fractures (local adhesive separation and cohesive tearing) whose directions are mainly perpendicular to the tension axis. After complete unloading and relaxation, the fracture lips close, and weaker secondary bonds are formed between them. Taking into account the anisotropy of the above-described process of deterioration of the material structure and mechanical properties (degradation), we suggest to characterize the state of each elementary material fiber by its own values of the structure parameters (damage, fracture, and maximum strain), which can be calculated (according to the model equations of uniaxial tension in a constant direction) from the effective strain history of the fiber. It is determined as the product of the current values of two factors, namely, the strain intensity and the influence function, whose argument is the angle between the directions of the fiber under study and the maximum principal strain. The form of the influence function depends on the material and reflects the degree of anisotropy of the damage arising in it. As a model of uniaxial tension in a constant direction, we use the earlier-proposed version of the nonlinear endochronic theory of ageing viscoelastic materials, which, in addition, contains the secondary bond parameter (with its own equation). We show how the proposed constitutive relations permit one to describe the decrease in the resistance and the ultimate strain during the second axial tension compared with a similar tension from the initial state and to determine the dependence of these effects on the angle between the directions of the preliminary and repeated tensions.     

Constitutive relations for calculating the processes of quasistatic deformation,damage, and fracture of bodies (Including those with concentrators) made of filled polymer materials

We study composite polymer materials with a high degree of dispersion filling (several tens of percent in volume). A tensor generalization of the previously developed variant of the geroendochronic theory of viscoelastic materials is obtained, which allows us to pose and solve initialboundary value problems using this model. A numerical solution algorithm is proposed, which is realized as the UMAT subroutine for the ABAQUS finite element software package.     

Constitutive relations for the shear band evolution in granular matter under large strain

A so-called "split-bottom ring shear cell" leads to wide shear bands under slow, quasi-static deformation. Unlike normal cylindrical Couette shear cells or rheometers, the bottom plate is split such that the outer part of it can move with the outer wail, while the other part (inner disk) is immobile. From discrete element simulations (DEM), several continuum fields like the density, velocity, deformation gradient and stress are computed and evaluated with the goal to formulate objective constitutive relations for the powder flow behavior. From a single simulation, by applying time-and (local) space-averaging, a non-linear yield surface is obtained with peculiar stress dependence.The anisotropy is always smaller than the macroscopic friction coefficient. However, the lower bound of anisotropy increases with the strain rate, approaching the maximum according to a stretched exponential with a specific rate that is consistent with a shear path of about one particle diameter.     

Constitutive relations for the shear band evolution in granular matter under large strain

A so-called ＂split-bottom ring shear cell＂ leads to wide shear bands under slow, quasi-static deformation. Unlike normal cylindrical Couette shear cells or rheometers, the bottom plate is split such that the outer part of it can move with the outer wall, while the other part （inner disk） is immobile. From discrete element simulations （DEM）, several continuum fields like the density, velocity, deformation gradient and stress are computed and evaluated with the goal to formulate objective constitutive relations for the powder flow behavior. From a single simulation, by applying time- and （local） space-averaging, a non-linear yield surface is obtained with peculiar stress dependence. The anisotropy is always smaller than the macroscopic friction coefficient. However, the lower bound of anisotropy increases with the strain rate, approaching the maximum according to a stretched exponential with a specific rate that is consistent with a shear path of about one particle diameter.     

平面应变各向异性本构关系及在应力波传播模拟中的应用

为了研究平面应变条件下各向异性材料中应力波传播的特点,利用各向异性弹性Hooke定律、 Tsai-Hill屈服准则、经典塑性流动理论,引入修正的物态方程计及高压下的体积压缩非线性,建立了平面应 变条件下正交各向异性复合材料的弹塑性本构关系,并且分析了二维问题中材料变形引起的主轴旋转及客 观应力率修正问题。最后采用动态显式有限元方法自行编写程序模拟某种纤维增强复合材料碰撞过程中平 面应力波的传播,模拟结果显示,在平面应变条件下应力波在该材料的传播过程中表现出明显的二维效应、各 向异性特点及弹塑性特点。     

Competing failure mechanisms of thin metal films on polymer substrates under tension

The ductility of thin metal films on polymer substrates reported in recent experiments has a huge disparity, ranging from less than 1 % up to more than 50 %. To reveal the underpinning origins for such a large variation, this paper reports a systematic computational study of two competing failure mechanisms: metal film necking and grain boundary cracking. The quantitative results suggest that strong grain boundaries and metal/polymer interfacial adhesion are keys to achieve high ductility of polymer-supported metal films.     

Elastic-plastic strain concentrations produced by various skew holes in a flat plate under uniaxial tension

The elastic and elastic-plastic surface strain fields around circular holes drilled at various skew angles to a flat plate have been experimentally evaluated in uniaxial tension. A photoelastic coating and moiré technique were used in the low- and high-strain regions, respectively. The maximum strain-concentration factor is shown to increase markedly with horizontal skew angle and decrease slightly with increasing vertical skew angle. Plastic deformation accentuates the differences between normal and skew holes, so that the angular dependence of the strain-concentration factor increases with nominal strain.     

Law of damage accumulation and fracture criteria in highly filled polymer materials

We present the results of a large series of experiments aimed at the study of laws of damage accumulation and fracture in highly filled polymer materials under loading conditions of various types: monotone, repeated, low- and high-cycle, with varying type of stress state, dynamic (in general, more than 50 programs implemented on specimens from one lot of material). The data obtained in these test allow one to make conclusions about the constitutive role of the attained maximum of strain intensity when estimating the accumulated damage in the process of uniaxial tension by various programs (in particular, an additional cyclic deformation below the preliminary attained strain maximum does not affect the limit values of strain and stress in the subsequent active extension), about the strong influence of the stress state on the deformation and fracture, about the specific features of the nonlinear behavior of the material under the shock loading conditions and its influence on the repeated deformation. All tests are described (with an accuracy acceptable in practical calculations, both with respect to stresses and strains in the process of loading and at the moment of fracture) in the framework of the same model of nonlinear viscoelasticity with the same set of constants. The constants of the proposed model are calculated according to a relatively simple algorithm by using the results of standard uniaxial tension tests with constant values of the strain rate and hydrostatic pressure (each test for 2–3 levels of these parameters chosen from the ranges proposed in applications, each loading lasts until the fracture occurs, and one of the tests contains an intermediate interval of total loading and repeated loading) and one axial shock compression test if there are dynamic problems in the applications. The model is based on the use of the criterion fracture parameter which, in the class of proportional loading processes, is the sum of partial increments of the strain intensity on active segments of the process (where the strain intensity is at its historical maximum) with the form of the stress state and the intensity of strain rates taken into account.     

Damping characteristics of pipes vibrating in flexure and filled with various materials

Tanks and pipes vibrating in flexure and filled with various materials have been a problem in power plants, factories, airplanes and tankers. The present experimental investigation was carried out on a pipe vibrating in flexure and filled with various materials, both liquid and solid. The tests showed that, in general, filling a pipe in flexure with any material, liquid or solid, increases its damping characteristics. An increase in the kinematic viscosity of the filling liquid, or a decrease in the size of the particles of the filling solid, will result in a corresponding increase in the equivalent damping factor of the system.     

Optimization of hole shapes in circular cylindrical shells under axial tension

Hole shapes are optimized in circular cylindrical shells subjected to axial load considering only the predominantly large membrane stresses present around the holes. Two-dimensional photoelastic isochromatics obtained with a special-purpose polariscope are utilized for the optimization process. The process leads to a significant decrease in the membrane stress-concentration factor and a modest decrease in weight, thus yielding a considerable increase in strength-to-weight ratio. This paper presents results for certain typical ratios of hole diameter to shell diameter. Previous theoretical and experimental studies for the circular hole have also been verified     

Numerical simulation of plastic deformation and damage accumulation in structural materials under various low-cycle loading conditions

This paper presents the results of a finite-element study of elastic-plastic deformation and damage accumulation in structural materials under various cyclic loading conditions. Material behavior is described by the relations of damage mechanics using thermoplastic model which takes into account the plastic deformation of material under cyclic loading and the kinetic equations of the energy theory of damage accumulation. The basic laws of plastic deformation and development of damage in materials under hard, soft, symmetric, and asymmetric low-cycle loading are established.     

Uniqueness and stability of rigid-plastic cylinders under internal pressure and axial tension

Uniqueness of deformation and stability of the equilibrium configuration of a long closed-ended cylinder of rigid-plastic material, obeying the von Mises yield criterion, are examined under internal pressure and axial tensile load. Sufficient conditions are derived for uniqueness of the current state of the finitely deformed cylinder. By considering a material model of the Ramberg-Osgood type, it is shown that uniqueness is guaranteed up to a stage when either of the loads (or both) attains a maximum. For such a material model, “pressure-tension interaction curves” are obtained for some values of the wall-ratio and the strain-hardening index. Under internal pressure and small tension, however, the possibility of a bifurcation preceding a stability loss is shown to exist for certain cylinder geometry and material hardening properties.     

Failure analysis of unidirectional fiber composites under combined axial tension and shear

A method of analysis is proposed for investigating the mechanics of failure of unidirectional, fiber composite materials subjected to axial tension and shear. The mechanisms of failure are assumed to result from the interaction of the applied shear stress and local matrix shear stress concentrations which arise as a result of the scattered fiber breaks that occur throughout the material. Two modes of failure are identified. One is associated with the unstable growth of shear failure regions in the matrix. The other is primarily a tensile failure mode which is influenced by the applied shear. The analysis predicts that a variety of shear-tensile stress failure surfaces are possible, depending on material properties. The results suggest that radical changes in the shape of failure surfaces can occur as the result of environmental effects. This has significant implications for reliability.     

Yield conditions for incompressible isotropic and orthotropic materials with different yield stress in tension and compression

Summary Two modified Tresca yield conditions are proposed for plastically incompressible isotropic and orthotropic materials with different yield stress in tension and compression.

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Sommario Dimostrata la non necessarietà d'introduzione dei termini idrostatici nella condizione di plasticità dei materiali dotati di differente resistenza a trazione e compressione vengono proposti due criteri di plasticità di cui uno per i materiali isotropi ed uno per i materiali ortotropi.

     

Identification of the model of nonlinear viscoelasticity of filled polymer materials in millisecond time range

Determination of mechanical characteristics of filled polymer materials in shock wave processes is of interest in calculations of the strength of these materials. The standard computation methods are based on the use of the linear theory of viscoelasticity, where there is no distinction between the active and passive deformation processes. In the present paper, dynamical experiment and theoretical modeling are used to illustrate the important role played by the sharp decrease in the resistance of a filled polymer material in unloading (in the millisecond time range). The higher the degree of filling of this material, the more significant this effect is.