We thank Dr. Abdel-Aal for his interest in our paper and for providing an interesting discussion. The premise of this discussion is to further develop the entropy concept to account for the running-in (transient) period. The idea is to consider the variation of hardness as a function of temperature.

As pointed out in the paper (see Eq. (4) and its associated discussion), the analysis presented pertains to the steady state condition where the entropy generation and entropy flow are in balance. In the transient regime the total entropy of the system, which includes entropy flow and entropy generation, should be considered (see Eq. (1) in the original paper). The realization of connecting the entropy generation and entropy flow to degradation processes involving wear and fatigue has been a subject of intense research. Interested readers may refer to Refs. [1,2,3,4,5,6] for detailed discussions.

Dr. Abdel-Aal’s derivation of Eq. (5) includes two terms: TS· and μlNT·/T'. Considering the notation used in the paper, the term TS· plays the role of entropy flow while the term μlNT·/T' can be considered as the entropy generation. The latter term includes μlN, which is the energy dissipation by the friction force (μN) during a sliding distance of l. This equation takes into account the role of both entropy generation and entropy flow during the running-in period. However, it is important to note that during the running-in period, the coefficient of friction μ, (or in a similar way, the wear coefficient K) changes with time until a steady state is reached. This has been analytically and experimentally demonstrated. See, for example, Refs. [7,8].

References

References
1.
Bryant
,
M. D.
,
Khonsari
,
M. M.
, and
Ling
,
F. F.
, 2008, “
On the Thermodynamics of Degradation
,”
Proc. R. Soc. London
,
464
, pp.
2001
2014
.
2.
Amiri
,
M.
,
Naderi
,
M.
, and
Khonsari
,
M. M.
, 2011, “
An Experimental Approach to Evaluate the Critical Damage
,”
Int. J. Damage Mechanics
,
20
, pp.
89
112
.
3.
Amiri
,
M.
, and
Khonsari
,
M. M.
, 2012, “
On the Role of Entropy Generation in Processes Involving Fatigue
,”
Entropy
,
14
, pp.
24
31
.
4.
Naderi
,
M.
, and
Khonsari
,
M. M.
, 2010, “
An Experimental Approach to Low-Cycle Fatigue Damage Based on Thermodynamic Entropy
,”
Int. J. Solids Struct.
,
4
, pp.
875
880
.
5.
Beheshti
,
A.
, and
Khonsari
,
M. M.
, 2010, “
A Thermodynamic Approach for Prediction of Wear Coefficient Under Unlubricated Sliding Condition
,”
Tribol. Lett
,
38
, pp.
347
354
.
6.
Agdam
,
A. B.
, and
Khonsari.
M. M.
, 2011, “
On the Correlation Between Wear and Entropy in Dry Sliding Contact, Wear
,” 270, pp. 781–790.
7.
Akbarzadeh
,
S.
, and
Khonsari
,
M. M.
, 2010, “
Experimental and Theoretical Investigation of Running-In
,”
Tribol. Int.
,
22
, pp.
92
100
.
8.
Akbarzadeh
,
S.
, and
Khonsari
,
M. M.
, 2010, “
On the Prediction of Running-In Behavior in Mixed-Lubrication Line Contact
,”
ASME J. Tribol.
,
132
, p.
032102
.