Arun K. Singh

Simulation of Frictional Strength and Steady Relaxation Using the Rate and State Dependent Friction Model

In this paper, frictional strength of hard solids, such as rock–rock sliding surfaces, is studied as a function of waiting time and shearing velocity. A one dimensional spring–mass sliding system is numerically simulated under the quasistatic condition using the rate and state dependent friction model. It is established that frictional strength varies linearly with the logarithm of waiting time (also known as time of stationary contact or relaxation time, etc.) as well as logarithm of shearing velocity. Analytical expression developed for frictional strength is found to be valid only in the case of high stiffness of the connecting spring. In the steady relaxation simulation, a steadily sliding mass is suddenly brought to zero velocity and relaxation of the interfacial stress and corresponding velocity at the sliding interface is studied as a function of relaxation time in the velocity strengthening regime of friction. A mathematical relation is derived between state variable and waiting time using the concept of steady relaxation. The relaxation model is also compared with the experimental data from the literature. Finally, the present study enables one to unify the slide–hold–slide friction experiments.

Steady dynamic friction at elastomer–hard solid interface: A model based on population balance of bonds

We present a model for the steady dynamic friction of a block of an elastomer, sliding steadily on a hard surface. The model uses population balance of the bonds between the hard surface and the polymer chains of the elastomer to estimate the force of friction. Although the basic premises of the present model are the same as those of the Schallamach model for dynamic friction (1963), the present formulation is a clearer representation of the phenomena involved. Moreover, the model is not based on the ergodic hypothesis and is therefore more versatile. It also allows us to correct the error in the expression for the force of friction in the Schallamach model. The present model exhibits the same qualitative trends as the Schallamach model. However, there are significant quantitative differences between the two models. We also show that our expression for the force of friction is equivalent to that obtained by the Chernyak and Leonov (1986) model, which is based on the ergodic hypothesis. The model is further modified to account for both the non-Hookean extension of the bonded chains and the viscous retardation effect. The model is validated using the experimental data of Vorvolakos and Chaudhury (2003) on sliding of crosslinked PDMS solid on silane coated silicon wafer. From this analysis, scaling laws, which relate the model parameters to the molecular weight of the polymer chains and the temperature, are derived and justified.

Scaling laws of gelatin hydrogels for steady dynamic friction

In this article, we use population balance based dynamic friction model for steady sliding to develop scaling laws in the terms of mesh size of gelatin hydrogels. First of all, it is observed in the sliding experiments that shear modulus of gelatin hydrogels depends on sliding velocity. This dependence is more evident in the case of low sliding velocity. Moreover, relaxation time constant of a dangling chain at the sliding interface scales with the same exponent as its stiffness. The scaling law is also developed for chain density and viscous retardation at the sliding interface. It is also established that the Hookean-based dynamic friction model is sufficient to study frictional behaviour of hydrogels. The reason for this observation is attributed to the weak bonding between a gelatin hydrogel and glass interface.

Stress relaxation at a gelatin hydrogel–glass interface in direct shear sliding

In this paper, we study experimentally the stress relaxation behavior of soft solids such as gelatin hydrogels on a smooth glass surface in direct shear sliding. It is observed experimentally that irrespective of pulling velocity, the sliding block relaxes to the same level of nonzero residual stress. However, residual stress increases with increasing gelatin concentration in the hydrogels. We have also validated a friction model for strong bond formation during steady relaxation in light of the experimental observations. Our theoretical analysis establishes that population of dangling chains at the sliding interface significantly affects the relaxation process. As a result, residual stress increases with increasing gelatin concentration or decreasing mesh size of the three-dimensional structures in the hydrogels. It is also found that the transition time, at which a weak bond converts to strong bond, increases with increasing mesh size of the hydrogels. Moreover, relaxation time constant of a strong bond...

Energy release rate of gelatin hydrogels on glass surface in direct shear sliding experiments

Abstract In this article, we determine experimentally the energy release rate (ERR) of gelatin hydrogels on a smooth glass surface in the direct shear mode using slide-hold-slide (SHS) experiments. The crack lengths and corresponding forces measured in SHS experiment are ultimately used to estimate ERR of the sliding surfaces. The ERR at static, dynamic and residual strengths are physically correlated in terms of work of rupture , work of steady sliding and work of adhesion respectively. Moreover, it is observed that and increase with pulling velocity, normal stress and gelatin concentrations. Although at the residual strength remains independent of pulling velocity, the same increases with the normal stress and gelatin concentrations. The novelty of the present study is that the frictional properties of gelatin hydrogels on glass surface is now correlated with fracture mechanics.

The Effect of Carbon Nanotubes Based Nanolubricant on Stick–Slip Behavior

In this article, stick–slip behavior of a metal–metal interface is investigated in presence of a lubricant mixed with multiwalled carbon nanotubes (MWCNTs). The friction experiments are carried out to determine the critical pulling velocity at which stick–slip motion disappears and steady sliding follows thereafter. The sliding experiments show that the critical velocity decreases with increase in concentration of MWCNTs in the lubricant up to 1.6% (wt./vol.), but further addition of the nanoparticles in the lubricant leads to increase in the critical velocity. Also, the critical velocity is found to be nearly independent of normal stress at the optimal concentration of the nanoparticles. Moreover, amplitude of stick–slip motion decreases with increase in concentration of MWCNTs up to the optimal value at a fixed velocity but the same begin to increase after the optimal concentration. The results are explained in light of the rolling-sliding mechanism of the spherical or cylindrical nanoparticles reported in literature. The present study reveals that the stick–slip instability can also be eliminated by using an optimal concentration of the nanoparticles in the lubricant.

Dynamic Stability of the Rate, State, Temperature, and Pore Pressure Friction Model at a Rock Interface

In this article, we study numerically the dynamic stability of the rate, state, temperature, and pore pressure friction (RSTPF) model at a rock interface using standard spring-mass sliding system. This particular friction model is a basically modified form of the previously studied friction model namely the rate, state, and temperature friction (RSTF). The RSTPF takes into account the role of thermal pressurization including dilatancy and permeability of the pore fluid due to shear heating at the slip interface. The linear stability analysis shows that the critical stiffness, at which the sliding becomes stable to unstable or vice versa, increases with the coefficient of thermal pressurization. Critical stiffness, on the other hand, remains constant for small values of either dilatancy factor or hydraulic diffusivity, but the same decreases as their values are increased further from dilatancy factor

Ergonomic Study and Design of the Pulpit of a Wire Rod Mill at an Integrated Steel Plant

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