scholarly journals The Interaction of Frictional Slip and Adhesion for a Stiff Sphere on a Compliant Substrate

2020 ◽  
Vol 87 (3) ◽  
Author(s):  
R. M. McMeeking ◽  
M. Ciavarella ◽  
G. Cricrì ◽  
K.-S. Kim
Keyword(s):  
Strain Energy ◽  
Elastic Strain Energy ◽  
Frictional Resistance ◽  
Linear Elastic ◽  
Adhesion Behavior ◽  
Stiff Material ◽  
Surface Microstructures ◽  
Work Done ◽  
Frictional Slip ◽  
Good Agreement

Abstract How friction affects adhesion is addressed. The problem is considered in the context of a very stiff sphere adhering to a compliant, isotropic, linear elastic substrate and experiencing adhesion and frictional slip relative to each other. The adhesion is considered to be driven by very large attractive tractions between the sphere and the substrate that can act only at very small distances between them. As a consequence, the adhesion behavior can be represented by the Johnson–Kendall–Roberts model, and this is assumed to prevail also when frictional slip is occurring. Frictional slip is considered to be resisted by a uniform, constant shear traction at the slipping interface, a model that is considered to be valid for small asperities and for compliant elastomers in contact with stiff material. A simple model for the interaction of friction and adhesion is utilized, in which some of the work done against frictional resistance is assumed to be stored reversibly. This behavior is considered to arise from surface microstructures associated with frictional slip such as interface dislocations, where these microstructures store some elastic strain energy in a reversible manner. When it is assumed that a fixed fraction of the work done against friction is stored reversibly, we obtain good agreement with data.

Buckling of Multiple-Bay Ring-Reinforced Cylindrical Shells Subject to Hydrostatic Pressure

1953 ◽  
Vol 20 (4) ◽  
pp. 469-474
Author(s):  
W. A. Nash
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Middle Surface ◽  
Elastic Buckling ◽  
Elastic Instability ◽  
Total Potential ◽  
External Forces ◽  
Work Done

Abstract An analytical solution is presented for the problem of the elastic instability of a multiple-bay ring-reinforced cylindrical shell subject to hydrostatic pressure applied in both the radial and axial directions. The method used is that of minimization of the total potential. Expressions for the elastic strain energy in the shell and also in the rings are written in terms of displacement components of a point in the middle surface of the shell. Expressions for the work done by the external forces acting on the cylinder likewise are written in terms of these displacement components. A displacement configuration for the buckled shell is introduced which is in agreement with experimental evidence, in contrast to the arbitrary patterns assumed by previous investigators. The total potential is expressed in terms of these displacement components and is then minimized. As a result of this minimization a set of linear homogeneous equations is obtained. In order that a nontrivial solution to this system of equations exists, it is necessary that the determinant of the coefficients vanish. This condition determines the critical pressure at which elastic buckling of the cylindrical shell will occur.

Linear elastic eigenstates of the compliance tensor for trigonal crystals

2000 ◽  
Vol 215 (1) ◽  
pp. 1-9 ◽  
Author(s):  
P.S. Theocaris ◽  
D.P. Sokolis
Keyword(s):  
Strain Energy ◽  
Elastic Strain Energy ◽  
Symmetric Tensor ◽  
Stress And Strain ◽  
Linear Elastic ◽  
Trigonal System ◽  
Compliance Tensor ◽  
Characteristic Values ◽  
Strain Tensors ◽  
Elastic Strain Energy Density

The spectral decomposition of the compliance fourth-rank tensor, representative of a trigonal crystalline or other anisotropic medium, is offered in this paper, and its characteristic values and idempotent fourth-rank tensors are established, with respect to the Cartesian tensor components. Consequently, it is proven that the idempotent tensors serve to analyse the second-rank symmetric tensor space into orthogonal subspaces, resolving the stress and strain tensors for the trigonal medium into their eigentensors, and, finally, decomposing the total elastic strain energy density into distinct, autonomous components. Finally, bounds on the values of the compliance tensor components for the trigonal system, dictated by the classical thermodynamical argument for the elastic potential to be positive definite, are estimated by imposing the characteristic values of the compliance tensor to be strictly positive.

The Habit Plate Shift and the Morphology of ∝" Nitride Precipitate in ∝-Fe*

1982 ◽  
Vol 40 ◽  
pp. 728-729
Author(s):  
Y. C. Shih ◽  
J. W. Morris
Keyword(s):  
Surface Energy ◽  
Habit Plane ◽  
Elastic Strain ◽  
Strain Energy ◽  
Lattice Mismatch ◽  
Parent Phase ◽  
Elastic Strain Energy ◽  
Size And Shape ◽  
Linear Elastic ◽  
New Phase

A new phase which precipitates from a parent matrix has a size and shape which reflects its difference from parent phase. If the lattice mismatch is significant, the elastic strain energy is more important than the surface energy in determining the morphology and the preferred habit plane. The preferred habit of a tetragonal inclusion in a cubic matrix has been predicted by minimizing the elastic strain energy as from the Ktachaturyan linear elastic formula.

An experimental examination of the dynamical behaviour of a strut in a rigidly jointed truss framework

1963 ◽  
Vol 274 (1357) ◽  
pp. 225-238 ◽  
Keyword(s):  
Strain Energy ◽  
Elastic Strain Energy ◽  
Maximum Load ◽  
Dynamical Behaviour ◽  
Strain Rates ◽  
Axial Deformation ◽  
Jump Phenomenon ◽  
Tension Members ◽  
Work Done ◽  
Kinetic And Potential Energies

The relation between axial load and axial deformation for a strut generally involves an increase of deformation with decreasing load after the maximum load is reached. When a truss containing one or more struts is subjected to dead load, it is possible that equilibrium may be lost temporarily while the structure undergoes a ‘dynamic jump’ to a new position of equilibrium. The dynamic jump phenomenon was analyzed theoretically for a simple truss by Davies & Neal (1959). It was shown that the motion is governed by interchanges between the elastic strain energy stored in the tension members, the work done on the strut, and the kinetic and potential energies of the applied load. The present paper describes an experimental investigation into the dynamic jump phenomenon for the same simple truss system. Predictions concerning the collapse load at which the dynamic jump would occur, and the magnitude of the jump, were made using the energy method together with strut characteristics obtained previously under quasistatic conditions. It was found that the collapse loads could be predicted accurately with the aid of these characteristics. However, in order to determine the magnitude of each jump it was necessary to modify the strut characteristics markedly to allow for the effect of high strain rates during the jump in increasing the load sustained by the struts.

Thermodynamic Assessment and Determination of Spinodal Lines for Al-Zn Binary System

2014 ◽  
Vol 794-796 ◽  
pp. 634-639 ◽  
Author(s):  
Shosuke Kogo ◽  
Shoichi Hirosawa
Keyword(s):  
Free Energy ◽  
Binary System ◽  
Gibbs Free Energy ◽  
Strain Energy ◽  
Thermodynamic Assessment ◽  
Metastable Phase ◽  
Elastic Strain Energy ◽  
Miscibility Gap ◽  
Good Agreement

Calphad type thermodynamic assessment of Al-Zn binary system was performed to calculate the metastable phase diagram including not only miscibility gap but also spinodal lines. The Gibbs free energy for liquid, fcc and hcp phases was evaluated by taking into account available experimental data, and most of them were satisfactorily reproduced by our thermodynamic descriptions. Furthermore, the Gibbs free energy for GP zones was also expressed by combining the chemical energy for solid solution of fcc-Al with appropriate elastic strain energy, in good agreement with experimentally reported solubility limits. Therefore, the spinodal lines derived from the differential of the Gibbs free energy could be also reasonably estimated, although those are quite difficult to be measured experimentally.

Internal Structure of B19 Martensite in AuTi Shape Memory Alloy

2006 ◽  
Vol 980 ◽  
Author(s):  
Tomonari Inamura ◽  
Ryosuke Tachi ◽  
Kenji Wakashima ◽  
Hideki Hosoda
Keyword(s):  
Strain Energy ◽  
Martensite Plate ◽  
Elastic Strain Energy ◽  
Phenomenological Theory ◽  
Transmission Electron Microscopy Observation ◽  
Microscopy Observation ◽  
Invariant Plane ◽  
Transmission Electron ◽  
Transformation Geometry ◽  
Good Agreement

AbstractInternal twin of B19 martensite in equiatomic AuTi binary alloy was examined by conventional transmission electron microscopy observation and the phenomenological theory of martensite crystallography (PTMC). The crystal structure of martensite was B19 (orthorhombic) with the lattice parameters of 0.2944nm, 0.4900nm and 0.4633nm. Most of martensite plates were internally twinned by {111}typeI twin. <211>typeII twin was occasionally observed and {011}compound-twin relationship was observed at boundaries between adjacent martensite plates. However, no martensite plate entirely twinned by the <211>typeII twinning or the {011}compound twinning was observed. PTMC analysis showed that the invariant plane is formed only by the introduction of the internal twin of {111}typeI or <211>typeII twin in the present geometry of the transformation. Geometry of a typical martensite plate with internal twin of {111}typeI twin was in good agreement with that required for the formation of habit plane with the invariant plane character. The observed {111}typeI twin is, therefore, considered to be the lattice invariant shear to minimize the elastic strain energy due to the transformation.

scholarly journals Discussions on the Complete Strain Energy Characteristics of Deep Granite and Assessment of Rockburst Tendency

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Lu Chen ◽  
Lijie Guo
Keyword(s):  
Time Delay ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Confining Pressure ◽  
Strain Effect ◽  
Peak Strain ◽  
Rockburst Hazard ◽  
Linear Elastic ◽  
Loading And Unloading

In deep mining, the rockburst hazard has become a prominent problem. Rockburst is difficult to be predicted, and it gives a severe threat to mining safety. In this paper, the triaxial compressive tests with an acoustic emission (AE) device and full cyclic loading and unloading tests were carried out, respectively, to present characteristics of linear elastic strain energy and peak strain energy. Also, to consider the time-delay strain characteristics of granite found in the abovementioned tests, a new stage loading and unloading test with dual monitoring systems was designed and performed. Through 20 days’ time-delay strain monitoring, the peak-strength strain energy was further modified. The results showed that the peak strain energy is approximate 1.2-1.3 times than linear elastic strain energy under the same confining pressure, and after considering the time-delay strain effect, the modified maximal strain energy value of the deep granite significantly increased. The peak strain energy values are further enhanced from 1.0 × 104 J/m3 to 1.8 × 104 J/m3, respectively. At last, by taking advantage of the strain energy index model of rockburst, the tendency and intensity of rockburst were assessed contrastively.

Latent Elastic Strain Energy Due to the Residual Stresses in a Plastically Deformed Polycrystal

1967 ◽  
Vol 34 (3) ◽  
pp. 606-611 ◽  
Author(s):  
T. H. Lin ◽  
Marvin Ito
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Residual Stress Field ◽  
Latent Energy ◽  
Energy Part ◽  
Crystallographic Slip ◽  
Work Done

A part of the work done on a plastically deformed metal reappears in the form of heat and the remaining part remains latent in the metal, known as latent energy. Part of this latent energy is the elastic strain energy of the residual stresses of the plastically deformed metal. In this paper, this strain energy in a polycrystal is calculated from the crystallographic slip properties of single crystals. The polycrystalline aggregate is composed of differently oriented cube-shaped crystals, each with one slip plane on which there are three slip directions. Neglecting the inhomogeneity and anisotropy of elastic constants, the polycrystal is taken to be elastically homogeneous and isotropic. The analogy between plastic strain gradient and body force in an infinite elastic medium is used to calculate the residual stress field. The residual stress calculation satisfies the condition of continuity, the equilibrium condition, and the single crystal stress-strain relationship throughout the aggregate. The variation of the latent elastic strain energy with the aggregate stress is shown. A similar method may be used to calculate the latent elastic strain energy of f.c.c. and b.c.c. polycrystals.

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