Foundations of Materials Science and Engineering
Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 17.14, Problem 39SEP
To determine

Estimate the volume of wear debris created in a 10-year period.

Expert Solution & Answer
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Answer to Problem 39SEP

The volume of wear debris created in a 10-year period is 19.24mm3.

Explanation of Solution

Express the volume of wear debris created in a 10-year period using the equation of dimensional wear factor.

 V=KWx                                                                                            (I)

Here, dimensional wear factor is K, perpendicular distance is W, volume of wear debris is V and total sliding distance is x.

Express perpendicular distance.

 W=2wbodyg2                                                                                     (II)

Here, weight of body is wbody and acceleration due to gravity is g.

Express total sliding distance in 10 years.

 x=(nyear)(nstep)14π(di)                                                                     (III)

Here, internal diameter is di, number of years is nyear and number of steps is nstep.

Conclusion:

Write the value of dimensional wear factor for UHMWPE on metal implants.

 K=107mm3/Nm

Write the value of acceleration due to gravity.

 g=9.81N/kg

Substitute 100kg for wbody and 9.81N/kg for g in Equation (II).

 W=2(100kg)[9.81N/kg2]=981N

Substitute 10 for nyear, 1000,000 for nstep and 25mm for di in Equation (III).

 x=(10)(1000,000)14π(25mm)=19.62×107mm[m103mm]=19.62×104m

Substitute 107mm3/Nm for K, 981N for W and 19.62×104m for x in Equation (I).

 V=(107mm3/Nm)(981N)(19.62×104m)=19.24mm3

Hence, the volume of wear debris created in a 10-year period is 19.24mm3.

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