Frictional complete contacts between elastically similar bodies subject to normal and shear load

The problem of trapezium shaped punches pressed into a frictional, elastically similar half-plane and subject to sequential normal and shear loading is studied. The initial mix of stick, slip and separation regions is described, together with the steady state response when the shearing force is cycled. Conditions for full stick are established.     

Asymptotic results for slipping complete frictional contacts

The order of singularity at the edge of a complete slipping contact depends on the material combination, the wedge angle, the coefficient of friction, and the relative direction of slip. Additionally, for a given coefficient of friction, slipping in one direction alleviates the stress state whilst slipping in the other direction, exacerbates it. However, it is known that there are material combinations for which the response cited above reverses. This paper investigates the boundary delimiting these different responses, and highlights some useful results.     

The contribution of frictional contacts to the shear strength of coarse glass bead powders and slurries

This paper investigates the use of the shear vane technique as a means of determining frictional and cohesive interparticle force contributions to the shear strength of coarse glass bead powders and slurries. To this end, the shear strength of 203-μm glass beads in air and slurried in water and kaolinite suspensions was determined as a function of vane immersion depth, vane geometry, and container size. Both vane immersion depth and container diameter are found to significantly impact the shear strength measured using the vane technique. An equation describing interparticle frictional and cohesive contributions to shear vane measurements was derived in an effort to describe the experimental results. A Janssen stress distribution model for granular materials forms the basis for this equation and appears to explain the behavior of shear strength measurements at varying immersion depths. The presence of the Janssen stress distribution can affect the interpretation of shear vane results. Rather than shear strength being a material property, as is the case with flocculated colloid slurries and polymer solutions, shear strength becomes a process property where vane depth, container size, and container material can result in significant measurement variations. Such parameters should be considered before using the shear vane results on applications involving granular material components.US Department of Energy Environmental Management Science Program project no. 90162.     

Monte Carlo simulation of self-avoiding lattice chains subject to oscillatory shear flow in polymer solution

 This paper has introduced a pseudo-potential in bond-fluctuation model to simulate oscillatory shear flow of multiple self-avoiding chains in three dimensions following our previous work under simple shear flow. The oscillatory flow field was reasonably reproduced by lattice Monte Carlo simulation using this pseudo-potential neglecting hydrodynamic interaction. By sampling the configuration distribution functions, the macroscopic viscoelasticity of semi-concentrated polymer solution was determined. Both Newtonian and non-Newtonian regimes were studied. The complex modulus and dynamic viscosity exhibit a reasonable power relation with oscillatory frequency, which is consistent with present theories and experiments. Consequently, lattice Monte Carlo simulation has been extended to model free-draining self-avoiding multi chains subject to oscillatory shear flow and to investigate associated viscoelasticity on the molecular level. Received: 1 October 1999 Accepted: 19 October 1999     

Response of an elastic Bingham fluid to oscillatory shear

The response of an elastic Bingham fluid to oscillatory strain has been modeled and compared with experiments on an oil-in-water emulsion. The newly developed model includes elastic solid deformation below the yield stress (or strain), and Newtonian flow above the yield stress. In sinusoidal oscillatory deformations at low strain amplitudes the stress response is sinusoidal and in phase with the strain. At large strain amplitudes, above the yield stress, the stress response is non-linear and is out of phase with strain because of the storage and release of elastic recoverable strain. In oscillatory deformation between parallel disks the non-uniform strain in the radial direction causes the location of the yield surface to move in-and-out during each oscillation. The radial location of the yield surface is calculated and the resulting torque on the stationary disk is determined. Torque waveforms are calculated for various strains and frequencies and compared to experiments on a model oil-in-water emulsion. Model parameters are evaluated independently: the elastic modulus of the emulsion is determined from data at low strains, the yield strain is determined from the phase shift between torque and strain, and the Bingham viscosity is determined from the frequency dependence of the torque at high strains. Using these parameters the torque waveforms are predicted quantitatively for all strains and frequencies. In accord with the model predictions the phase shift is found to depend on strain but to be independent of frequency.Notation A plate strain amplitude (parallel plates) - A _R plate strain amplitude at disk edge (parallel disks) - G elastic modulus - m torque (parallel disks) - M normalized torque (parallel disks) = 2m/R ³₀ - N ratio of viscous to elastic stresses (parallel plates) =µ A/ ₀ ratio of viscous to elastic stresses (parallel disks) =µ A _R/₀ - r normalized radial position (parallel disks) =r/R - r radial position (parallel disks) - R disk radius (parallel disks) - t normalized time = t — /2 - t time - _E elastic strain - _P plate strain (displacement of top plate or disk divided by distance between plates or disks) - _PR plate strain at disk edge (parallel disks) - ₀ yield strain - _E normalized elastic strain = _E/₀ - _P normalized plate strain = _P/₀ - _PR normalized plate strain at disk edge (parallel disks) = _PR/₀ - ₀ normalized plate strain amplitude (parallel plates) =A/ ₀ — normalized plate strain amplitude at disk edge (parallel disks) =A _R/₀ - phase shift between _P andT (parallel plates) — phase shift between _PR andM (parallel disks) - µ Bingham viscosity - stress - ₀ yield stress - T normalized stress =/ ₀ - frequency     

Investigation of bed shear stresses subject to external turbulence

The fluctuating bed shear stress has largely been investigated only for uniform channel flows and boundary layers. In practical engineering, the flow conditions are often modified due to the presence of various hydraulic structures. To what extent the modification affects the known characteristics of the bed shear stress is not clear. This study presents experimental results of the bed shear stress fluctuations, which are obviously subjected to external turbulence generated by superimposing artificial structures in the open channel flows. The statistical analysis of the measurements shows that the probability density function of the bed shear stress can be described by the lognormal function. Some associated relations concerning higher-order moments, skewness and kurtosis, which are derived from the lognormal function, are further compared with the experimental data. Physical implication of the skewed probability density distribution is finally discussed.     

Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium

The present study aims to investigate the salient features of incompressible,hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat transfer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two-and three-dimensional flow phenomena are also shown through graphical results.     

Cyclic multiaxial and shear finite deformation response of OFHC: Part I,experimental results

A series of experiments has been conducted on oxygen free high conductivity (OFHC) copper hollow cylinders under cyclic free-end torsion and biaxial tension–torsion at large strains. In addition, equations are developed to account for the finite rotation and strains in electrical resistance strain gages. In free-end cyclic torsion experiments with shear strain range equal to 23%, a significant strain in the axial direction is observed and it accumulates with a constant rate cycle by cycle. In the biaxial tension–torsion (multiaxial ratchetting) experiments, in which the primary (constant) axial stress is larger than the initial yield stress of the material, the loading conditions are varied to determine the influence of primary axial stress, cyclic shear strain range, pre-cyclic hardening and loading sequence on multiaxial ratchetting. Some important experimental features are high-lighted and recommended to help modeling efforts later.     

The role of dislocation walls for nanoindentation to shallow depths

Dislocation events are seen as excursions or pop-in events in the load–displacement curve of nanoindentation experiments. Two nanoindenters have been used to examine the difference between quasi-static and dynamic loading during indentation. Yield excursions were present in the load–displacement curves of both the statically and dynamically loaded single crystal nickel samples. Only one major excursion occurred in each quasi-static indent, nominally loaded at 100 μN/s while staircase yielding was observed under dynamic loading indentation with a 45 Hz oscillation of 2 nm superimposed on a 60 μN/s loading rate. Thermal activation analysis is used to explain the arrest and reinitiation of the yielding with activation volumes being modeled. For nanoindentation experiments differences between quasi-static and dynamic loading are described by the models presented. It is proposed that insight into the plastic deformation mechanisms associated with such plastic instabilities will provide one of the keys to length scale effects necessary to understanding nanostructures.     

An asymptotic approach to crack initiation in fretting fatigue of complete contacts

The stress state near the corner of a complete contact subject to fretting action is studied using an asymptotic analysis. The spatial distribution of stress, together with the generalised stress intensity factor defining the severity of the stress state are found, and the implications for experimental determination of crack initiation conditions discussed.     

Newtonian drop in a Newtonian matrix subjected to large amplitude oscillatory shear flows

The dynamics of a single Newtonian drop immersed in a Newtonian matrix subjected to large-amplitude oscillatory shear flow is investigated. The ratio of the drop and matrix viscosity is above criticality, and thus break-up is absent under constant shear flow. At small forcing amplitudes the drop shape follows a regular oscillation. As the forcing amplitude increases, multipeaked oscillations of drop shape and orientation are observed. Experimental results are compared with predictions obtained with a phenomenological model. Model predictions are in qualitative good agreement with experimental data. The model suggests that the appearance of higher harmonics in the drop response is mainly due to flow nonaffinity.     

Thermodynamic based model for the evolution equation of the backstress in cyclic plasticity

A nonlinear kinematic hardening rule is developed here within the framework of thermodynamic principles. The derived kinematic hardening evolution equation has three distinct terms: two strain hardening terms and a dynamic recovery term that operates at all times. The proposed hardening rule, which is referred in this paper as the FAPC (Fredrick and Armstrong–Phillips–Chaboche) kinematic hardening rule, shows a combined form of the Frederick and Armstrong backstress evolution equation, Phillips evolution equation, and Chaboche series rule. A new term is incorporated into the Frederick and Armstrong evolution equation that appears to have agreement with the experimental observations that show the motion of the center of the yield surface in the stress space is directed between the gradient to the surface at the stress point and the stress rate direction at that point. The model is further modified in order to simulate nonproportional cyclic hardening by proposing a measure representing the degree of nonproportionality of loading. This measure represents the topology of the incremental stress path. Numerically, it represents the angle between the current stress increment and the previous stress increment, which is interpreted through the material constants of the kinematic hardening evolution equation. This new kinematic hardening rule is incorporated in a material constitutive model based on the von Mises plasticity type and the Chaboche isotropic hardening type. Numerical integration of the incremental elasto-plastic constitutive equations is based on a simple semi-implicit return-mapping algorithm and the full Newton–Raphson iterative method is used to solve the resulting nonlinear equations. Experimental simulations are conducted for proportional and non-proportional cyclic loadings. The model shows good correlation with the experimental results.     

An optimal control approach to the analysis of inelastic structures under cyclic loading

Optimal control theory is used to study the asymptotic behaviour of elasto-viscoplastic structures under cyclic loading. With this approach, the asymptotic state is found as the solution of a minimization problem. General properties of this method are established. A simple thermomechanical problem is studied to illustrate and validate this approach. An interest of the proposed method lies in its capacity to handle other nonlinearities than plasticity. To illustrate this point, the approach is extended to the coupled viscoplasticity/frictionless contact problem. Some numerical results are given for an elasto-viscoplastic half-plane under cyclic frictionless indentation.     

Torsional buckling of cross-ply laminated orthotropic composite cylindrical shells subject to dynamic loading

This study considers torsional buckling of cross-ply laminated orthotropic composite cylindrical thin shells under loads, which is a power function of time. The modified Donnell type dynamic stability and compatibility equations are obtained first. These equations are subsequently reduced to a time dependent differential equation with variable coefficients by using Galerkin's method. The critical parameters are found analytically by applying the Ritz type variational method. According to theoretical solutions, numerical analyses are done.     

Numerical simulation of the dynamics of a reinforced shell subject to nonstationary load

A numerical algorithm to determine the stress-strain state of a reinforced cylindrical shell subject to impulsive loading is elaborated. Results from a numerical analysis of the dynamic behavior of a reinforced elastoplastic shell under explosive loading are presented __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 83–90, July 2008.     

The application of asymptotic solutions to characterising the process zone in almost complete frictionless contacts

A method is developed for characterising the nature of the plastic zone which develops along the boundary of any notionally complete frictionless contact but where, in practice, there is some small rounding. The approach consists of an outer asymptote, the solution for a semi-infinite square ended rigid punch, whose validity sets the upper limit to the load, and a nested inner asymptote, the solution for a semi-infinite rounded punch, which sets the lower limit to the load. The technique is applied, as an example, to a circular punch, and explicit values of the load given to ensure that the singular field characterises the local stress field to within a given degree of accuracy.     

A method for the evaluation of design limits for structural materials in a cyclic state of creep

The purpose of the present paper is to demonstrate how the minimum theorems proposed in an accompanying paper (Ponter and Boulbibane, 2002) can be utilised in the prediction of the deformation and life assessment of structures subjected to cyclic mechanical and thermal loadings. The developed method, which is based upon bounding theorems and an associate programming method, the Linear Matching method, takes into account the changes in residual stress field occurring within a cycle. Although the solution provided a bound on the inelastic work, it also appears that generally the displacements predicted by this solution are smaller than those that would be predicted by the rapid cycle solution. By way of illustration a simple non-linear viscous model is adopted and a number of solutions are presented involving a Bree plate problem subjected to cyclic histories of load and temperature. An elastic follow-up factor is identified as a key design parameter for high temperature dwell periods.     

Dynamic response of a half-space to radial shear surface loadings

Summary The axisymmetric response of an elastic half-space to the sudden application of radial shear surface loadings is investigated in this paper. Exact expressions for the surface displacement components are developed by means of integral transforms and complex functions. Numerical results are presented in diagrams to show the wave propagation on the surface due to the dynamic loadings, and the wave front singularities in the displacement components are particularly discussed. It is found that, for a given point on the half-space surface, Rayleigh surface waves issued from the nearest and farthest disturbances give rise to a jump or a two-sided logarithmic singularity in the displacement components.     

Fluid pressure response in poroelastic materials subjected to cyclic loading

When cyclic loading is applied to poroelastic materials, a transient stage of interstitial fluid pressure occurs, preceding a steady state. In each stage, the fluid pressure exhibits a characteristic mechanical behavior. In this study, an analytical solution for fluid pressure in two-dimensional poroelastic materials, which is assumed to be isotropic, under cyclic axial and bending loading is presented, based on poroelasticity. The obtained analytical solution contains transient and steady-state responses. Both of these depend on three dimensionless parameters: the dimensionless stress coefficient; the dimensionless frequency; and, the axial-bending loading ratio. We focus particularly on the transient behavior of interstitial fluid pressure with changes in the dimensionless frequency and the axial-bending loading ratio. The transient properties, such as half-value period and contribution factor, depend largely on the dimensionless frequency and have peak values when its value is about 10. This suggests that, under these conditions, the transient response can significantly affect the mechanical behavior of poroelastic materials.