Abstract
Archard law is widely used for predicting wear volume and the rate at which adhesive wear occurs. While not explicitly stated, in processes that involve sequential loading, the Archard equation appears to be incapable of accurately predicting the wear volume. In this research, a thermodynamics-based continuum damage mechanics (CDM) procedure is applied to predict the wear coefficient for sequential loading cases in dry contact. Experimental data obtained using a pin-on-disk test rig are used to validate the model. The results show that when sequential loading is applied to a specimen, CDM method can succesfuly predict the wear coefficient. In these cases, assuming a constant value for wear coefficient results in large errors.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- \({\text{d}}A\) :
-
Real area of contact (m2)
- \({\text{d}}A_{{{\text{Di}}}}\) :
-
Real area of cracks, voids, and cavities
- \(D_{i}\) :
-
Damage after \(i\) cycles
- \(D_{{\text{c}}}\) :
-
Critical damage value
- \(E\) :
-
Young modulus
- \(E_{D}\) :
-
Effective modulus of elasticity (GPa)
- \(F_{n}\) :
-
Applied load (N)
- \(H\) :
-
Cyclic hardening modulus (GPa)
- \(K_{{{\text{Ar}}}}\) :
-
Wear coefficient (Archard)
- \(K_{{{\text{St}}}}\) :
-
Wear coefficient (Steel)
- \(K_{{\text{c}}}\) :
-
Wear coefficient (CDM)
- \(M\) :
-
Cyclic hardening exponent
- \(n\) :
-
Normal to an elemental cross section
- \(N_{{\text{w}}}\) :
-
Number of cycles to failure
- \(p\) :
-
Material flow pressure (GPa)
- \(S\) :
-
Sliding distance (m)
- \(S_{e}\) :
-
Endurance limit (GPa)
- \(T_{i}\) :
-
Boundary traction (GPa)
- \(V\) :
-
Wear volume (m3)
- \(\Delta \varepsilon_{{{\text{oi}}}}\) :
-
Threshold strain of damage increment in cycle \(i\)
- \(\Delta \varepsilon_{{{\text{pli}}}}\) :
-
Initial plastic strain in \(i\)th cycle
- \(\Delta \varepsilon_{{{\text{pmi}}}}\) :
-
Final plastic strain in \(i\)th cycle
- \(\Delta \varepsilon_{{{\text{poi}}}}\) :
-
Threshold plastic strain of damage increment in cycle \(i\)
- \(\varepsilon\) :
-
Strain
- \(\mu\) :
-
Friction coefficient
- \(\nu\) :
-
Poisson’s ratio
- \(\sigma_{{\text{f}}}\) :
-
Failure stress (GPa)
- \(\tau\) :
-
Shear stress (GPa)
- \(\varphi_{{\text{D}}}\) :
-
Partial derivative of Helmholtz free energy with respect to \(D\) (GPa)
References
Archard, J.: Contact and rubbing of flat surfaces. J. Appl. Phys. 24, 981–988 (1953)
Akbarzadeh, S., Khonsari, M.: On the applicability of miner’s rule to adhesive wear. Tribol. Lett. 63, 1–10 (2016)
Fereidouni, H., et al.: On the assessment of variable loading in adhesive wear. Tribol. Int. 129, 167–176 (2019)
Lijesh, K.P., et al.: On the integrated degradation coefficient for adhesive wear: A thermodynamic approach. Wear 408–409, 138–150 (2018)
Kachanov, L.M.: Rupture time under creep conditions (1958)
Kragelsky, I.V., Kombalov, V.S.: Calculation of value of stable roughness after running-in (elastic contact). Wear 14, 137–140 (1969)
Soda, N., et al.: Wear of some FCC metals during unlubricated sliding part IV: Effects of atmospheric pressure on wear. Wear 43, 165–174 (1977)
Lemaitre, J.: A continuous damage mechanics model for ductile fracture (1985)
Lemaitre, J., Lippmann, H.: A Course on Damage Mechanics. Springer, Berlin (1992)
Bhattacharya, B., Ellingwood, B.: A new CDM-based approach to structural deterioration. Int. J. Solids Struct. 36, 1757–1779 (1999)
Beheshti, A., Khonsari, M.M.: A thermodynamic approach for prediction of wear coefficient under unlubricated sliding condition. Tribol. Lett. 38, 347–354 (2010)
Beheshti, A., Khonsari, M.: On the prediction of fatigue crack initiation in rolling/sliding contacts with provision for loading sequence effect. Tribol. Int. 44, 1620–1628 (2011)
Beheshti, A., Khonsari, M.M.: An engineering approach for the prediction of wear in mixed lubricated contacts. Wear 308, 121–131 (2013)
Ghatrehsamani, S., Akbarzadeh, S.: Predicting the wear coefficient and friction coefficient in dry point contact using continuum damage mechanics. Proc. Inst. Mech. Eng. Part J 233, 447–455 (2019)
Ghatrehsamani, S., et al.: Experimental and numerical study of the running-in wear coefficient during dry sliding contact. Surf. Topogr. 9, 015009 (2021)
Samadani, A., Akbarzadeh, S.: Experimental and numerical prediction of wear coefficient in non-conformal lubricated rectangular contact using continuum damage mechanics. Surf. Topogr. 8, 025012 (2020)
Chow, C.L., Wei, Y.: A damage mechanics model of fatigue crack initiation in notched plates. Theoret. Appl. Fract. Mech. 16, 123–133 (1991)
Khonsari, M.M. et al.: On the running-in nature of metallic tribo-components: a review. Wear 203871 (2021)
Bhattacharya, B., Ellingwood, B.: Continuum damage mechanics analysis of fatigue crack initiation. Int. J. Fatigue 20, 631–639 (1998)
Quraishi, S.M., et al.: A thermodynamic approach for predicting fretting fatigue life. Tribol. Lett. 19, 169–175 (2005)
Wear Resistance of Steels [1], In: Totten, G.E (ed.) Friction, Lubrication, and Wear Technology. vol. 18, ASM International (2017)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ghatrehsamani, S., Akbarzadeh, S. & Khonsari, M.M. Application of Continuum Damage Mechanics to Predict Wear in Systems Subjected to Variable Loading. Tribol Lett 69, 163 (2021). https://doi.org/10.1007/s11249-021-01539-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11249-021-01539-2