P. Pallav, PhD

Introduction

When a particular restoration shows 150 µm of wear in 1.5 years, it is usually pretty inaccurate to say that this restoration has a wear rate of 100 µm/year.
This would only be true if the wear developed at a constant rate, such as in the Acta Wear Machine.

Wear processes in real life often develop in a non time-linear way, because the height loss hardly ever develops at a constant rate. That is, as wear proceeds, the wear rate often decreases, but of course it may also increase.

There are two reasons why a non time-linear development of wear versus time may be of interest.

• A wear rate, which decreases with time will lead to compression of the data, when the wear of different materials is compared.
• When the wear process is studied / evaluated, the data (versus time) can be compared with what would be expected.

Compression of Data

This is an unwanted property of non time-linear results. If you have the choice you will want a laboratory set up to produce time-linear wear.

When a series of different materials are compared, it is important to understand that and how non time-linearity leads to compression of the data.

This figure shows the non linearity that might occur with clinical CFA wear.
Height loss after a fixed time is the point at which the materials crosses a vertical line in the figure, where the position of the line reflects the duration of the study. In itself, this information is not relevant to material selection.
For material selection it is only relevant to know how much time it takes a material (as compared to other materials) to wear to an extent, where the material loss becomes a problem (like Dh_max). This is of course a horizontal line.

The figure shows this for two different materials; one material wears twice as fast as the other. That is, one materials takes half the time as the other, for the same amount of height loss. This is true for any horizontal line in the figure, for example one materials crosses the line (Dh_max) at 150µm of height loss after 1.5 years and the other at 3 years, a ratio of 1 : 2.

If these materials would have been tested in a clinical study, where height loss values after one and a half years would have been published, then the figure shows that these materials would have worn 150 and 100 µm respectively; the difference of 1 : 2 is compressed to only 1 : 1.5.

Evaluation of the Wear Process

When a particular setup produces non time-linear wear rates, it is very interesting to know if this caused by a change in wear type. This requires at least that a prediction is made of the development of wear versus time if there would be no change in wear mode.

Prediction of Wear vs. Time

This idea can be explained with a simple laboratory set-up.

Set-ups with a sphere and a cone with a turning or twisting motion on a wearing surface. Parameters r and h are the dimensions of the wear scar. The motion may be combined with moving up and down in between the twisting. In such a case the bodies may be immersed in some kind of erosive slurry, which is not drawn.

As wear develops, the dimensions (r and h) of the indentation will increase. The General Wear Equation implies that this will influence the wear rate, because r influences both the pressure and the velocity.

The figure to the right shows the prediction of wear versus time (Equation 3, below) for the set up with the sphere (top) and the cone (bottom)

Obviously the wear (h) controls the radius (r) of the scar in a way, which depends on the shape of the indenter.

When the force at which the sphere or cone is pushed against the surface remains constant throughout the wear experiments, the pressure will be inversely proportional to the area (p·r²) of the wear scar. Therefore, as the wear (h) increases, the pressure decreases with 1/r².

When the up, down, and / or twisting motions remain constant, the average velocity at the wear scar will increase linearly with r.

Bringing these influences on the pressure and velocity together in the General Wear Equation, we get a wear rate, which decreases during the experiments in proportion to 1/r (=r·1/r²). Combination with Equation 1 gives

For the development of the wear versus time (h_t) Equation 2 can be integrated as follows

Known Pitfall

The tricky part is when you're experimenting with a set up like this and you didn't think of a prediction. If you take the results of a few materials at 0, 1, 2, 3, and 4 years, or after 0, 100,000, 200,000, 300,000, and 400,000 cycles, whatever, you may think that the high initial wear rate in the first 100,000 cycles is caused by running-in and create a new zero-reference extrapolated from the other data.
This is of course misleading, because with a power curve, the wear will never become linear; apart from a constant factor the results will be the same after 0, 1, 2, 3, and 4 million cycles. There are ways to expand the compressed the data of course but there is no way this can be done without increasing the measurement errors and standard deviations.