Stress Assisted Tribofilm Growth: A New Model

Tribofilm Growth - AFM Data

Under extreme conditions the lubricant film fails to separate the rubbing surfaces and solid-to-solid contact occurs. To prevent excessive wear of the base materials anti-wear additives are used in these cases. The additives create a protective layer which is worn instead of the base materials and allows to control the friction and wear developed in the system. The key here is to ensure that the growth rate of the tribofilm is larger than the rate of its removal. On the other hand, the tribofilms do not grow infinitely and stabilize at a certain thickness. These two effects were addressed in the current study.

One of the most frequently used anti-wear additives is the Zincdialkyldithiophosphate (ZDDP). Recent Atomic Force Microscopy study clearly showed that the growth rate of ZDDP tribofilm is determined by the shear stress and temperature according to the following equation:

(1)    \begin{eqnarray*} \frac{\partial h_g}{\partial t} = \tilde{\Gamma}_0 e^{\frac{\Delta U_{act} - \tau \Delta V_{act}}{K_B T}} \\ \end{eqnarray*}

where  \tilde{\Gamma}_0, \Delta U_{act}, \Delta V_{act} are the reaction constants,  \tau, T are the shear stress and temperature,  K_B is the Boltzmann constant.


In the recent study in Surface Technology and Tribology group of University of Twente, equation (1) was combined with a simple wear equation to predict the growth and wear of the tribofilm, its self-limitation and wear of the base materials in a rough sliding contact. The wear equation had the following simple from:

(2)    \begin{eqnarray*} \frac{\partial h_w}{\partial t} = \alpha h \\ \end{eqnarray*}

where  \alpha is an empirical wear coefficient. Overall, the tribofilm growth equation give the equation to calculate the tribofilm growth rate at given contact shear stress and temperature according to the simple equation:

(3)    \begin{eqnarray*} \frac{\partial h}{\partial t} = \frac{\partial h_g}{\partial t} - \frac{\partial h_w}{\partial t}  \\ \end{eqnarray*}


The model was validated using experimental data at various temperatures found in the literature:

Tribofilm Growth Model
Fig. 1. Tribofilm thickness evolution (left) and tribofilm wear rate (right). Reprinted from [1].
The model was also applied to simulate base material removal and a good agreement with the experimental data was observed. As can be seen from the Fig. 2, the substrate material removal is maximum at 60C, while the overall tribofilm wear rate is maximum at 100C (see Fig. 1, right). This feature emphasizes the sacrificial nature of the tribofilm: at 100C the tribofilm grows faster and even though the overall wear rate is larger, the base material removal is less.
Tribofilm Growth Model - Material Wear
Fig. 2. Base material removal rate. Reprinted from [1].

Further details can be found in the original article: A. Akchurin, R. Bosman, A Deterministic Stress-Activated Model for Tribo-Film Growth and Wear Simulation, doi:10.1007/s11249-017-0842-8.

[1]. A. Akchurin, R. Bosman, A Deterministic Stress-Activated Model for Tribo-Film Growth and Wear Simulation, Tribology Letters, , 65:59.

Administration of the project


  1. It is truly remarkable to see the efforts still dedicated to modeling the late Herbert C. Freuler’s 1941 creation (ZDDP, patented in 1944), especially in light of the fact that its synthesis and thermal decomposition involve the likes of H₂S.

    Two quick thoughts…

    If the mechanism hasn’t been fully elucidated since 1944, time to work on something else.

    If it involves – in any way whatsoever – H₂S, time to work on something else.

  2. I think that it actually does not matter what kind of additive is in the oil, until it behaves in accordance to the Arrhenius equation. This equation is frequently used to describe the reaction rates, so there is a high chance that the approach used here can be applied to another additive.

    • Yes Aydar, the ZDDP (Arrhenius model) approach can be applied to “other” AW additives, such as all those thermally-activated tribofilm-forming organophosphates; these additives producing films from their thermal decomposition products that contain the same nasty elements as ZDDP.

      These “other” thermally-activated additives (such as TPPT (triphenyl phosphorothionate), MoDTC (molybdenum dialkyldithiocarbamate) and ZP (zinc phosphate), etc.), all involve the same usual suspects and are not any type of meaningful alternative to ZDDP.

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