Electrochemical Simulation of the Current and Potential Response in Sliding Tribocorrosion

Abstract

Valuable insights into the wear-corrosion behavior of metals, as well as into the tribocorrosion field through the development of simulation models of tribocorrosion experiments, can contribute in rationalizing wear-accelerated experiments and their open circuit potential (OCP) behavior under rubbing. These results demonstrate that mathematical models of controlled tribo-electrochemical contacts can complement the physical experiment and add valuable understanding to the tribological behavior of metals, alloys, and generally to materials in an electrochemically active environment. The excellent agreement of experimental wear data and the experimental OCP curves with the OCP simulations with time establishes the concepts underlying the galvanic coupling model as a valid methodological approach toward a quantitative description and mechanistic understanding of the tribo-electrochemical experiment. Besides analyzing stellite tribocorrosion, application of the model to Al alloy data has helped us quantify the relative contributions of chemical and mechanical wear and reveal the underlying synergy. Ti metal tribocorrosion under variable load has revealed that the contact pressure P _av, can reach much lower values within the experimental time domain and finally be the cause of interruption of the initial wear mechanism.

Appendix

1.1 Hertz Pressure

Hertz’s theory is used to calculate the average pressure and maximum pressure between two non-conforming contacts. This theory was used to assess changes in maximum pressure during wear. For this purpose, the equations established by Hamrock and Dowson [23] were assumed. Therefore, the dimensions of contact (assumed elliptical) are given by Eq. I, where a is the semimajor axis and b the semiminor axis of the contact.

$$ \begin{aligned} & a = \left( {\frac{{6\bar{k}^2\bar{\varepsilon}}WR^{\prime}}{{\pi E^{\prime}}}}\right)^{1/3} \\ & b = \left({\frac{{6\bar{\varepsilon}WR^{\prime}}}{{\pi \bar{k}E^{\prime} }}}\right)^{1/3} \\ \end{aligned} $$

(I)

where $\bar{\varepsilon }$ is a simplified integration parameter and $\bar{k}$ a parameter of ellipticity given by

$$ \begin{gathered} \bar{\varepsilon } = 1. 0 0 0 3+0.5968\frac{{R_{x} }}{{R_{y} }} \hfill \\ \bar{k} = 1. 0 3 39\left( {\frac{{R_{y} }}{{R_{x} }}} \right)^{0.636} \hfill \\\end{gathered} $$

(II)

where E′ is the reduced Young’s modulus, R′ is the radius of reduced curvature, and R _x and R _y are the reduced radii in the x-direction and the y-direction, respectively. The x and y axes are defined as the axes of the plane of the contact, respectively, along the major axis and minor axis of the ellipse formed by it. These values are defined as

$$ \frac{1}{{E^{'} }}\, = \,\frac{1}{2}\,\left( {\frac{{1 - v_{\text{a}}^{2} }}{{E_{\text{a}} }}\, + \,\frac{{1 - v_{\text{b}}^{2} }}{{E_{b} }}} \right) $$

$$ \frac{1}{{R_{x} }} = \frac{1}{{R_{{{\text{b}}x}} }} + \frac{1}{{R_{{{\text{a}}x}} }} $$

$$ \frac{1}{{R_{y} }} = \frac{1}{{R_{{{\text{b}}y}} }} + \frac{1}{{R_{{{\text{a}}y}} }} $$

$$ \frac{1}{{R^{ '} }} = \frac{1}{{R_{y} }} + \frac{1}{{R_{x} }} $$

where E _a and E _b are the Young’s modulus values of the material of body a and body b; n _a and n _b their respective Poisson coefficients; R _ax , R _bx , R _ay, and R _by are the radii of curvatures of the body a along the x axis, the body b along the x axis, and body a along the y axis, and body b along this same axis, respectively.

In the case studied, it was assumed that the contact is between the sphere (i.e., the ball) and the concave track surface having a radius of curvature R _by , which is considered here only slightly larger than the curvature of the ball of radius R = R _ax  = R _ay.

According to Eq. I and II of the above method, the average contact pressure exerted by the sphere onto the concave track, under force W, is given by

$$ P_{\text{av}} = \, W/\pi \,a \, b $$

(III)

Using the definitions declared in the Sect. 4 and substituting Eq. I, II into Eq. III we have

$$ P_{{\text{av}}@{ \lim }} = \left( {\frac {{E^{'} W}}{6\pi {\bar{\varepsilon}} R a}} \right)^{ 1/ 2} $$

where a = 0.5 a_@lim and a_@lim is the wear track's width.