Coulomb friction law

Apart from the elastic stress transfer at the perfectly bonded interface, another important phenomenon that must be taken into account is the stress transfer by friction, which is governed by the Coulomb friction law after the interface bond fails. Furthermore, matrix yielding often takes place at the interface region in preference to interfacial debonding if the matrix shear yield strength, Xm is significantly smaller than the apparent interface bond strength, tb. It follows thus... 

In the debonded regions L z - (L - ) and (L - )<,z L), frictional slip occurs between the fiber and matrix and the stress transfer is governed by the Coulomb friction law for a constant coefficient of friction, p... 

Based on the Coulomb friction law, which governs the frictional stress transfer in the debonded interface, and combining Eqs. (4.12) and (4.18) yield the MAS at the interface (r = a)... 

However, some theoretical treatment considers only the special case of friction sliding of a single fiber along a mechanically bonded interface, particularly for some ceramic matrix composites, where the Coulomb friction law applies. See for example Zhou and Mai (1995) and Shetty (1988). Assuming a constant friction at the fiber-matrix interface and neglecting the Poisson effects, Shetty (1988) reported a simple force balance equation for the frictional shear strength, Tfr... 

Frictional sliding becomes an important phenomenon when cracks close and likely contributes to the macroscopic constitutive behavior of the porous material. For the sake of simphcity, a Coulomb friction law is assumed such that slip occurs when... 

For the discretization of the bulk solid and of the wall in 2-D simulation, isoparametric 8-node elements are used with a 9-GAUSSfK)int integration for the bulk solid and a 16-GAUSSpoint integration for the wall elements. The coupling between the bulk elements and the wall elements is realized with a special 6-node contact element with the assumption of a Coulomb friction law. 

Tangential contact stresses are calculated using the Amontons-Coulomb friction law, as was done for the dry contact. Subsurface stresses are calculated using a combination of FFT and MLMS [13-14]. 

For the tangential component of the contact force, a Coulomb-type friction law is used ... 

It would appear that no account of friction is complete without first stating Leonardo da Vinci s (or Amonton s) laws and Coulomb s law of friction and pointing out that, in general, polymers do not obey them. The laws are ... 

The validity of Coulomb s law has been verified also on the nanoscale Zworner et al. [484] showed that, for different carbon compound surfaces, friction does not depend on sliding velocity in the range between 0.1 /xm/s and up to 24 /xm/s. At low speeds, a weak (logarithmic) dependence of friction on speed was observed by Gnecco et al. [485] on a NaCl(lOO) surface and by Bennewitz et al. [486] on a Cu (111) surface. This can be modeled when taking into account thermal activation of the irreversible jumps in atomic stick-slip [487],... 

The second empirical law for dry, macroscopic friction is that of Coulomb Friction does not depend on the sliding velocity. 

The proportionality between the area of real contact and the applied load supplies at last a rational explanation of the well-known Amontons 1 or Coulomb s2 law of friction, that the frictional force F is directly proportional to the total load P pressing the surfaces together. The meaning of this law has long been mysterious. Under ordinary circumstances the law holds fairly accurately, i.e. there exists a nearly constant coefficient of friction, /x = F/P. The frictional force is naturally proportional to the total area of these bridges consequently the frictional force should be proportional to the load. 

Under partial slip conditions, the estimate of the stress conditions at the edge of the contacts is complicated due to the unknown frictional behaviour within the partial slip annulus. If Coulomb s friction law is assumed to apply locally within this area, some contact mechanics calculation can, however, be... 

For elastic materials, the contact problem is usually solved as a unilateral contact problem obeying Coulomb s friction law. The algorithms used here are based on those pioneered by Kalker [66]. The contact area, the stick and slip regions, the pressure and traction distributions are numerically determined first and then the stress and displacement distributions within the elastic bodies can be established at the various stages of the tangential cyclic loading. On the basis of these calculations, the occurrence of crack initiation processes can subsequently be analysed in the meridian plane of the contact, y = 0 (Fig. 12), where the cracks first initiate. As a first approach, parameters based on the amplitude of the shear stress, rm, along a particular direction and the amplitude of the tensile stress, [Pg.174]

The kinetic friction force is independent of sliding velocity (Coulomb s law). 

Such a dependence is characteristic of the dry friction, i.e. it agrees with Coulomb s friction law, Ffr = /frFN. Consequently, the model of plastic behavior of a material or disperse system may be represented by two surfaces (two plates) with a mutual friction coefficient, fx, pressed against each other with normal force, FN, causing the tangential force, Ffr, to be equal to the critical shear stress of material (Fig. IX-7). 

According to Coulomb s law of friction, the relationship among shear stress, normal stress, coefficient of friction and pore-pressure at the moment of shear slip (critical condition) due to increasing of pore-pressure are described as follow. 

Coulomb invented a torsion balance, which could measure electrostatic forces in relationship to their distance. We start with Coulomb s law that describes the relationship between force, charge, and distance. He is most famous for his discovery in electrostatics. His other fields of interest were friction phenomena. 

Merchant has proposed an analytical approach elegantly appUcable to determine the force components in orthogonal cutting (Merchant 1944). He assumes the shear plane model and Coulomb s friction law. In Fig. 12, the force... 

The force and pressure distribution between tool and workpiece in the contact area determine the resulting surface integrity (Borbe 2001). The thrust force on the cutting edge Fj is the vectorial sum of the feed and passive force Ff and Fp. Assuming a friction factor p (Coulomb s law), the normal and tangential forces on the flank Fn and Fja can be estimated at ... 

Velocity-Dependent Friction Research and development work on the numerical specification of contact and friction conditions may include mathematical formulation and implementation of friction models as well as adaptation of the numerical solution methods (Heisel et al. 2009 Neugebauer et al. 2011). Standard implementations may be illustrated using Coulomb s Law and the Friction Factor Law. These two basic models were modified using a stick-slip model. Using these models enables consideration of the relative sliding velocity between the tool and the workpiece. 

However, as seen in [392] and [393], the Amonton law and the Coulomb criterion hold when the forces of intermolecular interaction between the shifted bodies are not taken into account. This interaction was taken into consideration by Derjagin [392, 393] in a binomial friction law. Analyzing the applicability of a binomial friction law, Deijagin notes that it should be used when equilibrium conditions are considered between two adjacent bodies with large area of actual contact, which are subjected not only to the forces perpendicular to the contact surface but also to forces parallel to it. An adhesive joint is just the contact of at least two surfaces by means of adhesive that fills the microrelief and ensm-es a large area of the true contact. 

The results on crossed polymer fibers obtained by Briscoe and Kremnitzer shown in Fig. 9.16 gave good agreement with Equation (9.16). The friction force increased more rapidly than Coulomb s law predicted at low loads but approached Coulomb s law at high loads. The value of the work of adhesion W from these friction experiments was near 0.1 Jm , close to the value determined in direct adhesion experiments on the same fibers. 

---