# Wear coefficient

The wear coefficient is a physical coefficient used to measure, characterize and correlate the wear of materials.

## Background

Traditionally, the wear of materials has been characterized by weight loss and wear rate. However, studies have found that wear coefficient is more suitable. The reason being that it takes the wear rate, the applied load, and the hardness of the wear pin into account. Although, measurement variations by an order of 10-1 have been observed, the variations can be minimized if suitable precautions are taken.[1][2]

A wear volume versus distance curve can be divided into at least two regimes, the transient wear regime and the steady-state wear regime. The volume or weight loss is initially curvilinear. The wear rate per unit sliding distance in the transient wear regime decreases until it has reached a constant value in the steady-state wear regime. Hence the standard wear coefficient value obtained from a volume loss versus distance curve is a function of the sliding distance.[3]

## Measurement

Table 1: K values for various materials
Material K
Mild steel (on mild steel) 7×10−3
α- / β-brass[N 1] 6×10−4
PTFE 2.5×10−5
Copper-beryllium 3.7×10−5
Hard tool steel 1.3×10−4
Ferritic stainless steel 1.7×10−5
Polythene 1.3×10−7
PMMA 7×10−6

The steady-state wear equation was proposed as:[2]

${\displaystyle V=K{\frac {PL}{3H}}}$

where ${\displaystyle H}$ is the Brinell hardness, ${\displaystyle V}$ is the volumetric loss, ${\displaystyle P}$ is the normal load, and ${\displaystyle L}$ is the sliding distance. ${\displaystyle K}$ is the dimensionless standard wear coefficient.

Therefore, the wear coefficient ${\displaystyle K}$ in the abrasive model is defined as:[2]

${\displaystyle K={\frac {3HV}{PL}}}$

As ${\displaystyle V}$ can be estimated from weight loss ${\displaystyle W}$ and the density ${\displaystyle \rho }$, the wear coefficient can also be expressed as:[2]

${\displaystyle K={\frac {3HW}{PL\rho }}}$

As the standard method uses the total volume loss and the total sliding distance, there is a need to define the net steady-state wear coefficient:

${\displaystyle K_{N}={\frac {3HV_{s}}{PL_{s}}}}$

where ${\displaystyle L_{s}}$ is the steady-state sliding distance, and ${\displaystyle V_{s}}$ is the steady-state wear volume.

With regard to the sliding wear model K can be expressed as:[4]

${\displaystyle K={\frac {V}{A_{p}L}}}$

where ${\displaystyle A_{p}}$ is the plastically deformed zone.

If the coefficient of friction is defined as:[4]

${\displaystyle \mu ={\frac {F_{t}}{P}}}$

where ${\displaystyle F_{t}}$ is the tangential force. Then K can be defined for abrasive wear as work done to create abrasive wear particles by cutting ${\displaystyle Vu}$ to external work done ${\displaystyle FL}$:[4]

${\displaystyle K={\frac {3\mu HV}{\mu PL}}=3\mu {\frac {Vu}{FL}}\approx {\frac {Vu}{FL}}}$

In an experimental situation the hardness of the uppermost layer of material in the contact may not be known with any certainty, consequently, the ratio ${\displaystyle {\frac {K}{H}}}$ is more useful; this is known as the dimensional wear coefficient or the specific wear rate. This is usually quoted in units of mm3 N−1 m−1.[5]

### Composite material

As metal matrix composite (MMC) materials have become to be used more often due to their better physical, mechanical and tribological properties compared to matrix materials it is necessary to adjust the equation.

The proposed equation is:[2]

${\displaystyle K={\frac {3g_{1}d(1-f_{v})}{g_{3}f_{v}L}}\left[1-exp\left({\frac {-g_{3}f_{v}L}{d(1-f_{v})}}\right)\right]}$

where ${\displaystyle g_{3}}$ is a function of the average particle diameter ${\displaystyle d}$, ${\displaystyle f_{v}}$ is the volume fraction of particles. ${\displaystyle g_{1}}$ is a function of the applied load ${\displaystyle P}$, the pin hardness ${\displaystyle H}$ and the gradient ${\displaystyle m_{A}}$ of the ${\displaystyle V_{c}}$ curve at ${\displaystyle L=0}$.

${\displaystyle g_{1}={\frac {Hm_{A}}{P}}}$

Therefore, the effects of load and pin hardness can be shown:[2]

${\displaystyle K={\frac {3Hm_{A}d(1-f_{v})}{PLg_{3}f_{v}L}}\left[1-exp\left({\frac {-g_{3}f_{v}L}{d(1-f_{v})}}\right)\right]}$

As wear testing is a time consuming process it was shown to be possible to save time by using a predictable method.[3]

## References

1. ^ Peter J. Blau, R. G. Bayer (2003). Wear of Materials. Elsevier. p. 579. ISBN 9780080443010.
2. L.J. Yang (January 2003). "Wear coefficient equation for aluminium-based matrix composites against steel disc". Wear. 255 (1–6): 579–592. doi:10.1016/S0043-1648(03)00191-1.
3. ^ a b L.J. Yang (May 15, 2005). "A methodology for the prediction of standard steady-state wear coefficient in an aluminium-based matrix composite reinforced with alumina particles". Journal of Materials Processing Technology. 162–163: 139–148. doi:10.1016/j.jmatprotec.2005.02.082.
4. ^ a b c Nam Pyo Suh, Nannaji Saka (2004), Tribology (PDF)
5. ^ J.A. Williams (April 1999). "Wear modelling: analytical, computational and mapping: a continuum mechanics approach" (PDF). Wear. 225–229: 1–17. doi:10.1016/S0043-1648(99)00060-5.

### Notes

1. ^ Cu/Zn with 30-45% Zn