_{1}

^{*}

The results of the tests for a friction pair “a cylindrical specimen made of 0.45% carbon steel—a counter specimen-liner made of polytetrafluoroethyleneF4-B” during sliding friction are presented. The test results at different levels of contact load are analyzed using the Archard’s equation and are presented as a friction fatigue curve. The concept of the frictional stress intensity factor during sliding friction is introduced, and an expression that relates the wear rate to this factor and is close in shape to the Paris equation in fracture mechanics is proposed.

Among various theories of mechanical wear of solids in recent decades, fatigue theory has been widely recognized [

One characteristic of this type of wear is the material damage under the repetitive action of compressive, tensile and shear deformations during cyclic loading caused by the interaction of the polymer with the hard and blunt projections on the rough surface during sliding, which gives rise to the generation and development of cracks, and which can be assisted by the presence of defects [

According to several studies, the interaction of the abrasive particles with the polymer produces deformation and tensile, compressive and shear stresses in the worn surface layer, forming in it fatigue cracks due to the repetitive action of these interactions [

As known within the models based on contact mechanics, a model of particular relevance and broadly used is that proposed by Archard [

W = k H F N γ , (1)

where W [mm^{3}] is the worn volume, F_{N} [N] the applied normal load, γ [m] the sliding distance, k the non-dimensional wear coefficient particular to the contact pair characteristics and H [N/mm^{2}] the material hardness. When interpreting experimental situations, the hardness of the uppermost layer of material in the contact may not be known with any certainty and consequently a rather more useful quantity than the value of k alone is the ratio k/H [mm^{3}∙N^{−1}∙m^{−1}], named hereinafter as K and which is known as the dimensional wear coefficient or specific wear rate [

According to

Archard’s law referred to in Equation (1) is usually applied to the stationary stage. With the rest of the variables of the equation well known and without variation, the constant K can be considered as the characteristic wear coefficient of the wear process under study.

In this paper, the kinetic process of wear of the steel-polymer mechanical system is analyzed using fatigue fracture mechanics approaches.

Tests on sliding friction of the metal-polymer friction pair were carried out according to the shaft-liner scheme. The sample-shaft 1 made of 0.45% carbon steel with 10 mm diameter of working part was cantilevered in the spindle 2 of the upgraded testing machine UKI-6000-2 and rotated at a frequency of 3000 min^{−1} (_{N}, the value of which was set using a special tool and kept constant during the test of each pair of specimen―liner.

In the process of testing, a drip supply of a lubricant―Universal All-Seasonal Engine Oil “Lukoil Super 15W-40”―was provided and the measurement the linear wear of the friction pair using an indicator head with an accuracy of 2 μm was performed. Since the steel sample in the test pair did not wear out, all wear was obtained by a polymer liner. The liner wear equal to i_{lim} = 1000 μm was taken as the limit state.

The test results of the friction pair with the contact load F_{N} equal to 150, 180, 280, 350 and 450 N are shown in the form of kinetic graphs of the dependence of wear i [μm] on the number N of rotates [cycles] in

On the other hand, based on the fatigue theory of mechanical wear, the results of the tests can be represented as fatigue (Weller) curves in the coordinates of the contact load F_{N}―the number N of cycles before the limit state (for i_{lim} = 1000 μm) of the polymer liner (

curve consists of three branches: the left branch with a slope (this is a region of quasi-static fracture to approximately N = 7.2 × 10^{4} cycles, F_{N} = 400 - 450 N), an average line located almost vertically (this is the area of low-cycle destruction N = 7.2 × 10^{4} - 9 × 10^{4} cycles, F_{N} = 165 - 400 N), and the right one with a large slope (this is the area of multi-cycle destruction N > 1 × 10^{5} cycles, F_{N} < 165 N).

Let’s try to describe the test results using the Archard’s equation. In this case, in Equation (1) we write linear wear i instead of volume wear W, since they are proportional to each other. The sliding distance γ is replaced by the number N of loading cycles (these quantities are also proportional to each other). In

shows graphs of the ratio i/F_{N} against the number N of loading cycles, plotted in logarithmic coordinates according to the test results of the friction pair under study.

As can be seen from _{N} versus N, each graph can be represented as consisting of two linear dependencies, the values of the parameters a and b of the equations of which are shown in

Analysis of graphs in

Some authors, such as Martinez et al. [

Regarding the fatigue crack process,

which the fatigue crack growth behavior is divided for a polymer [_{0}, hence no mechanical crack growth occurs. In region II, the region of slow crack growth, the crack growth is dependent on both ozone and mechanical factors in an additive way. In region III, a power law dependency between the crack growth rate and the tearing energy is found as follows:

d a d N = B G β , (2)

where a [mm] is the crack length, N is the number of cycles, B and β are material constants. Depending on the polymer type, the value of β lies between 1.5 and 6; in this region, stable crack growth takes place. Region IV corresponds to a rapid and unstable crack growth and therefore to the region of catastrophic failure.

In addition to the energy G, the stress intensity factor proportional to the value of G is often used as a control parameter for crack growth in fracture mechanics. As known, for a sample with limited dimensions the crack growth under the action of shear stresses τ is controlled by the shear stress intensity factor

K τ = Y τ π a , (3)

where Y is the correction function that takes into account the geometry of the sample and its loading circuit.

In the case of volumetric damage during mechanical fatigue the crack size a characterizes the degree of material damage, while the surface damage caused by sliding friction is characterized by the value i of wear. Instead of tangential shear stress τ under friction, we can apply the so-called specific friction force or friction stress τ_{w} equal to [

τ w = f p a = f F N A a , (4)

where f is the friction coefficient; p_{a} is the average contact pressure; A_{a} is the nominal contact area. Consequently, with reference to sliding friction, taking into account the assumptions made and (4), expression (3) can be written as

K τ w ~ τ w i ~ p a i ~ F N A a i . (5)

Thus, using expression (5), it is possible to estimate the frictional stresses intensity factor under sliding friction. Obviously, the damage rate Δa/ΔN with the growth of fatigue cracks can be matched to the wear rate Δi/ΔN (in discrete form). Then for the wear rate during sliding friction, we obtain an expression close in form to (2):

Δ i Δ N = B * K τ w β * ~ B * ( F N A a i ) β * , (6)

where B^{*} and β^{*} are material constants characterizing the steady-state stage of the wear process.

The analysis of experimental data on the expression (6) showed their satisfactory compliance. In _{τw} for the contact load 280 N is plotted.

The generalized graph lg(Δi/ΔN) − lgK_{τw} for the test results for all levels of contact load is presented in

(^{*} = 1.122 × 10^{−6}, β^{*} = 2.21. Note that for a number of polymers β = 1.5 ∙∙∙ 3.0 [

Obviously with contact loads smaller than 180 N, we will have a stage of low wear rates (

Therefore, and according to the expressions stated in Equations (4)-(6), a clear analogy between the wear and the crack growth phenomena can be established, obtaining similar wear and crack growth rates, respectively. This is true for the friction pair studied as applied to the specified test conditions.

However, it is necessary to conduct additional experiments with other contact loads, other test conditions and other materials of a friction pair in order to assess the validity of the proposed approach to the description of wear kinetics during sliding friction. In addition, it is necessary to give a clear physical meaning to the parameters B^{*} and β^{*} of Equation (6).

The author declares no conflicts of interest regarding the publication of this paper.

Bogdanovich, A.V. (2019) Lows of Wear Process of the Friction Pair “0.45% Carbon Steel―Polyte- trafluoroethylene” during Sliding from the Position of Fracture Mechanics. World Journal of Mechanics, 9, 95-104. https://doi.org/10.4236/wjm.2019.95007