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Prediction of Crack Nucleation in Rough Line-Contact Fretting via Continuum Damage Mechanics Approach

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Abstract

The crack nucleation behavior of rough surfaces in line contact is investigated by means of a thermodynamically based continuum damage mechanics technique. The deterministic approach is employed to investigate the effect of roughness on the surface tractions and contact stresses. In order to treat the effect of high stress gradients, a special averaging technique, proposed previously for the case of smooth surface, is adopted in this study. The predictions of the crack nucleation life are compared with the relevant experimental data in the literature and indicate the validity of the analysis.

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Abbreviations

a :

Hertzian line-contact half-width (μm)

D :

Damage parameter

D c :

Critical damage

dA :

Undamaged elemental area (m2)

\({\text{d}}\bar{A}_{i}\) :

Damaged elemental area (m2)

E :

Nominal (undamaged) elastic modulus (GPa)

E 1, E 2 :

Modulus of elasticity for the contacting bodies 1 and 2 (GPa)

E * :

Equivalent modulus of elasticity, \(E^{*} = \left( {\frac{{1 - v_{1}^{2} }}{{E_{1} }} + \frac{{1 - v_{2}^{2} }}{{E_{2} }}} \right)^{ - 1}\) (GPa)

E′:

Effective (damaged) elastic modulus (GPa)

F n :

Dimensionless normal force, \(F_{\text{n}} = \frac{W}{{lE^{*} R}}\)

F *n :

Corrective dimensionless normal force

F **n :

Corrective dimensionless normal force corresponding to the instantaneous stick zone

F t :

Maximum dimensionless tangential force, \(F_{t} = \frac{Q}{{lE^{*} R}}\)

h g :

Hardness of the softer contacting body (GPa)

\({\mathcal{H}}\) :

Dimensionless hardness, \({\raise0.7ex\hbox{${h_{g} }$} \!\mathord{\left/ {\vphantom {{h_{g} } {E^{*} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${E^{*} }$}}\)

H c :

Cyclic hardening modulus (MPa)

H(X):

Separation between two contacting surfaces

H 0 :

Approach of two contacting bodies

l :

Contact length (mm)

M :

Cyclic hardening exponent

N :

Number of cycles to crack nucleation

N s :

Specified number of cycles to crack nucleation

n j :

Normal vector in j direction

P(X):

Dimensionless normal pressure distribution, P(X) = p(x)/p H

\(P^{*} (X)\) :

Corrective dimensionless normal pressure distribution

\(P^{**} (X)\) :

Corrective dimensionless normal pressure distribution corresponding to the instantaneous stick zone

p(x):

Normal pressure distribution (GPa)

p H :

Maximum Hertzian pressure (GPa)

Q(X):

Dimensionless tangential traction distribution in monotonic loading (associated with F t), q(x)/p H

Q cl(X):

Dimensionless tangential traction distribution in cyclic loading

q(x):

Tangential traction distribution (GPa)

R :

Radius of the cylinder in contact with a flat or effective radius of curvature (mm)

R q :

Standard deviation of the asperity heights (μm)

\(\bar{R}_{q}\) :

Dimensionless standard deviation of the asperity heights, \(\bar{R}_{q} = \frac{{R_{q} }}{R}\)

\(\partial {\mathcal{R}}\) :

Boundary of the body

S e :

Material’s endurance limit (MPa)

S y :

Material’s yield stress (MPa)

T :

Dimensionless instantaneous tangential force

T i :

Traction over the boundary

W :

Normal force (N)

x, z :

x- and z-coordinates (μm)

X :

Dimensionless x-coordinate, X = x/a

\(X_{1} ,X_{2}\) :

Dimensionless boundaries of the averaging zone

Z :

Dimensionless z-coordinate, Z = z/a

λ(X):

Surface profile (μm)

Λ(X):

Dimensionless surface profile, λ(X)/R

ɛ ij :

Strain tensor

\(\Delta \varepsilon_{li}\) :

Strain range of damage increment in cycle ith corresponding to zero stress in the hysteresis loop

\(\Delta \varepsilon_{oi}\) :

Threshold strain range of damage increment in cycle ith

\(\Delta \varepsilon_{mi}\) :

Maximum strain range of damage increment in the ith cycle

μ :

Friction coefficient

\(v_{1} ,v_{2}\) :

Poisson’s ratio for contacting bodies 1 and 2

σ :

Nominal normal stress (MPa)

σ 1 :

First principal stress (MPa)

\(\bar{\sigma }_{1}\) :

Dimensionless first principal stress, \(\bar{\sigma }_{1} = \frac{{\sigma_{1} }}{{p_{\text{H}} }}\)

σ f :

True failure stress (MPa)

σ max :

Maximum value of the cyclic stress (MPa)

σ′ :

Effective (damaged) normal stress (MPa)

ξ :

Scaling factor for the calculation of the corrective normal pressure terms

ψ :

Helmholtz free energy function

Ω c :

Contact domain

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  1. Department of Mechanical Engineering, Louisiana State University, 2508 Patrick Taylor Hall, Baton Rouge, LA, 70803, USA

    A. B. Aghdam, Ali Beheshti & M. M. Khonsari

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Aghdam, A.B., Beheshti, A. & Khonsari, M.M. Prediction of Crack Nucleation in Rough Line-Contact Fretting via Continuum Damage Mechanics Approach. Tribol Lett 53, 631–643 (2014). https://doi.org/10.1007/s11249-014-0300-9

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