The Use of a Mechano-Lattice Analogy for Determining the Abrading Stresses in Sliding Rubber

1971 ◽  
Vol 44 (3) ◽  
pp. 758-770
Author(s):  
W. O. Yandell

Abstract A rigorous mechano-lattice analogy analysis for calculating the hysteretic sliding friction of and stresses in rubber sliding on variously shaped asperities is presented. The analysis allows large strains and any Poisson's Ratio, rigidity or damping factor of the rubber. The analysis was used to calculate the distributions of minor principal stress in rubber sliding over smooth and frictional prisms with different sharpnesses and over a cylinder. The potentially disruptive stress regions were thus revealed and compared. The effect of changes in the Poisson's Ratio and of the damping factor of the rubber were also examined. It was postulated that the fine texture generates more stress-strain hysteretic heat which may lead to the more rapid abrasion observed by some workers.

1973 ◽  
Vol 13 (03) ◽  
pp. 163-174
Author(s):  
Alexander Blake ◽  
Maurice Zaslawsky

Abstract Presented here are results of experimental and theoretical investigations of the behavior of downhole pipe, surrounded by Overton sand or gravel, when subjected to shock from nuclear explosion. The principal effects investigated arelongitudinal friction between the pipe and the stemming material andresistance offered by the stemming material to transverse motion of the pipe. Introduction Stemming materials such as Overton sand and pea gravel are widely used in underground nuclear pea gravel are widely used in underground nuclear testing to ensure containment of the explosion. Present-day theories of mechanics suitable for predicting stresses and displacements within an predicting stresses and displacements within an array of particles of such materials are rather limited because of the stress-strain-time behavior and complicated boundary conditions involved. Thus, measurements representing gross effects only and linearized models of analysis must be relied upon in making the majority of engineering decisions where soil-structure interactions are encountered. Furthermore, because of the number of variables and hardware constraints present in designing deep-hole emplacement systems, the emphasis should be on obtaining experimental data on fullscale or nearly full-scale structural components in association with stemming materials of actual field quality. The experiment discussed in this paper was directed toward the development of basic mechanical properties such as modulus of elasticity, friction characteristics during axial (longitudinal) pipe motion through stemming materials, resistance pipe motion through stemming materials, resistance of stemming materials to transverse pipe displacement, and related physical phenomena that may have further bearing on the usual mechanical properties employed in various design analyses. properties employed in various design analyses. During evaluation of the basic mechanical properties, an attempt was made to develop a properties, an attempt was made to develop a Poisson's ratio type of data for the stemming Poisson's ratio type of data for the stemming materials at hand by using both specialized equipment and standard test equipment normally employed in soil mechanics. The results of the study, however, should be interpreted with due regard to the particulate nature of stemming materials, which do not represent a continuum with well defined stress-strain relationships. To obtain meaningful data on friction and transverse resistance characteristics, a special test rig was designed with particular emphasis on minimizing the scale effects and experimental errors usually encountered. In mechanics the term "friction" is the resistance to motion of two moving objects or surfaces that touch. In this paper we speak of several different types of micron, and therefore some clarification is needed. The friction between sand or gravel and the down-hole pipe as we attempt to move the pipe is one type of friction. A similar type is the friction developed between sand or gravel and the steel block it rubs against in the direct shear test apparatus. Those two examples of friction are rather straightforward, however, the following two present some confusion because they are both referred to as internal friction:Internal friction as used by engineering scientists, physicists, and metallurgists may be defined as the conversion of the mechanical energy of a vibrating solid into heat. This is also referred to as the damping capacity and corresponds to a phase difference between the applied stress and phase difference between the applied stress and its resultant strain.b soil mechanics the concept of internal friction corresponds to friction between the surfaces of individual grains of sand or gravel. In granular materials, both kinds of internal friction occur. In this paper the term "internal friction" is referred to extensively and is used exclusively in the sense of friction between particles. particles. FUNDAMENTALS OF SOIL MECHANICS The mechanical behavior of earth materials such as sand or gravel can be described by suitable physical constants reflecting certain physical constants reflecting certain stress-deformation relations that may then be applied in customary engineering predictions. In dealing with the rigidity of rocks, Young's modulus, E, and Poisson's ratio, are commonly used, and soil Poisson's ratio, are commonly used, and soil mechanics utilizes basic concepts of the theory of elasticity. By analogy to this well established practice, related concepts utilizing elastic practice, related concepts utilizing elastic constants in loading and unloading can be made applicable to stemming materials. SPEJ P. 163


2018 ◽  
Vol 140 (11) ◽  
Author(s):  
A. Delissen ◽  
G. Radaelli ◽  
L. A. Shaw ◽  
J. B. Hopkins ◽  
J. L. Herder

A great deal of engineering effort is focused on changing mechanical material properties by creating microstructural architectures instead of modifying chemical composition. This results in meta-materials, which can exhibit properties not found in natural materials and can be tuned to the needs of the user. To change Poisson's ratio and Young's modulus, many current designs exploit mechanisms and hinges to obtain the desired behavior. However, this can lead to nonlinear material properties and anisotropy, especially for large strains. In this work, we propose a new material design that makes use of curved leaf springs in a planar lattice. First, analytical ideal springs are employed to establish sufficient conditions for linear elasticity, isotropy, and a zero Poisson's ratio. Additionally, Young's modulus is directly related to the spring stiffness. Second, a design method from the literature is employed to obtain a spring, closely matching the desired properties. Next, numerical simulations of larger lattices show that the expectations hold, and a feasible material design is presented with an in-plane Young's modulus error of only 2% and Poisson's ratio of 2.78×10−3. These properties are isotropic and linear up to compressive and tensile strains of 0.12. The manufacturability and validity of the numerical model is shown by a prototype.


2019 ◽  
Vol 92 ◽  
pp. 15003
Author(s):  
Teruo Nakai ◽  
Hossain Md. Shahin ◽  
Akira Ishikawa

A simple and rigorous formulation of elastic component of elastoplastic model for geomaterials is presented. Although linear relation between elastic volumetric strain and mean principal stress in log scale is assumed in most of the usual models, linear relation between each principal stress and the corresponding principal elastic strain in log scale is assumed. Incorporating Poisson's ratio, three principal stresses vs. three elastic principal strain relation is obtained. Also, assuming coaxially between stresses and elastic strains, this relation can be transformed to stress- elastic strain relation in general coordinate. The material parameters of the proposed model of the elastic component are the same as those of the usual models, i.e., swelling index κ and Poisson's ratio ν. This proposed model can describe typical unloading behaviour of various shear tests and constant stress ratio unloading tests reported before.


1969 ◽  
Vol 6 (6) ◽  
pp. 1415-1419 ◽  
Author(s):  
P. E. Gretener

Diabase sills contain material originating from the base of the crust or the upper mantle. As a result they must be fed by dike- or plug-like bodies. The formation of a sill thus represents a major reorientation of the form of the intrusion. Tabular intrusive bodies tend to orient themselves perpendicular to the least compressive principal stress axis as shown by E. M. Anderson. It is suggested that diabase sills form under sedimentary strata in which the two horizontal principal stresses exceed the vertical stress (Sx > Sy > Sz). Such strata act as stress barriers and prevent further ascent of the magma, In order for this situation to occur the sediments must be in compression in the x-direction and confined in the y-direction. The parameter of importance to produce the above state of stress is the effective Poisson's ratio.


1983 ◽  
Vol 20 (1) ◽  
pp. 120-130 ◽  
Author(s):  
L. V. Medeiros ◽  
Z. Eisenstein

Laboratory investigation of the stress–strain behaviour of glacial till (stiff silty clay) and dense preglacial sand have been carried out. Special attention has been devoted to investigation of the influence of different stress paths on the stress–strain response of these materials. Since these tests were performed primarily for an analytical study of the behaviour of a deep retaining structure, the stress paths chosen for testing were typical of stress conditions for this field situation. Triaxial and plane strain drained tests on till were run in passive compression (with increasing major principal stress and constant minor principal stress) and in active compression (with constant major principal stress and decreasing minor principal stress). On the sand, only triaxial tests were carried out. These experiments were in passive compression and in active extension (with decreasing major principal stress and constant minor principal stress).The results of different tests were compared at corresponding stress and strain levels. They indicated an appreciably decreased stiffness along the passive compression stress path compared with that in the active compression and active extension tests. Also, a comparison between the triaxial and plane strain tests for the till showed a marked influence of the intermediate principal stress. Although the results were intended for use in a stress path dependent, nonlinear elastic analysis they are discussed and explained in terms of a more general elastoplastic model of soil behaviour. Keywords: stress–strain relationship, stress path, laboratory testing, stiff clay, dense sand.


1946 ◽  
Vol 37 (4) ◽  
pp. 211 ◽  
Author(s):  
A.H. Stang ◽  
M. Greenspan ◽  
S.B. Newman

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Aizhong Lu ◽  
Ning Zhang ◽  
Guisen Zeng

Under the triaxial compressive state, the compressive strain is supposed to happen in the direction of the maximum principal stress, but tensile strain happens in the direction of the minimum principal stress. Moreover, as the intermediate principal stress is not too high, the corresponding strain can also be tensile. If the brittle rock is assumed as linear elastic in the prefailure stage, a new strength criterion based on the sum of the two tensile strains was presented. The new criterion considers the differences in mechanical parameters (i.e., elastic modulus and Poisson’s ratio) under tension and compression. The parameters of the criterion only include Poisson’s ratio and uniaxial strength. And the effect of the intermediate principal stress σ 2 can be reflected. Certain featured failure phenomenon of rock material can be explained well by the proposed criterion. The results of conventional and true triaxial tests can verify the criterion well. Finally, the criterion is compared with the Mohr–Coulomb and Drucker–Prager criteria.


Aerospace ◽  
2004 ◽  
Author(s):  
Paolo Pastorino ◽  
Fabrizio Scarpa

The paper describes the manufacturing and tensile testing of auxetic (negative Poisson’s ratio) thermoplastic polyurethane foams. The foams are produced from conventional flexible polyurethane basis following a manufacturing route developed in previous works. The Poisson’s ratio behavior over tensile strain has been analyzed using an Image Data processing technique based on Edge Detection from digital images recorded during quasi-static tensile test. The samples have been subjected to tensile and compressive tests at quasi-static and constant strain-rate values (up to 12 s−1). Analogous tests have been performed over iso-volumetric foams samples, i.e., foams subjected to the same volumetric compression of the auxetic ones, without exhibiting a negative Poisson’s ratio behavior. A model describing the compressive stress-strain behavior of the auxetic foams has been developed considering the stress-strain performance of single unit cell and making use of statistical distributions of relative densities and buckling loads on auxetic foam cells during loading.


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