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The crack propagation path for a system of surface and subsurface cracks and their interactions due to rolling contact fatigue

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Abstract

In this paper, the rolling contact fatigue crack growth in the presence of multiple cracks and their interactions is studied. The proposed formulation is based on linear elastic fracture mechanics and singular integral equations. The body under the rolling contact is modeled by a half-plane weakened by a set of surface, subsurface and surface–subsurface cracks. Rolling contact is simulated by translational motion of an elliptically distributed force along the half-plane boundary. Several parameters, such as the distance between cracks, the value of initial crack lengths, the value of the friction coefficient, and the initial angle between cracks and the boundary of the half-plane are studied. Results obtained from this investigation are in good agreement in a special case with those reported in the literature. It is observed that in the system of two parallel surface and subsurface cracks with equal lengths, changing the distance between the cracks changes the growth paths, and when this distance increases to a critical value, the cracks grow independently. In addition, in the case of two parallel surface cracks when the left crack is shorter, the cracks have a stronger tendency to join together, which leads to pitting phenomena on the contact surface. Furthermore, in the system of two parallel subsurface cracks, it is seen that fast fracture occurs sooner when the initial angle of the cracks increases. In the system of parallel surface and subsurface cracks, the dominant failure mode is spalling.

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Abbreviations

a :

Half of the elliptical contact zone width

\(b_{i}\, (i=1,\ldots ,N-1)\) :

Distance between origin of the local coordinate system

C :

Paris law coefficient

f :

Friction coefficient

\(h_{1n}\) :

x location of the crack center

\(h_{2n}\) :

y location of the crack center

\(j_\mathrm{c}\) :

Series counter

\({K}_{\mathrm{I}}\) :

Mode I stress intensity factor

\({K}_{\mathrm{II}}\) :

Mode II stress intensity factor

\(K_\mathrm{th}\) :

Threshold fatigue crack growth

\(K_{IC}\) :

Fracture toughness

\(K_{I\theta }\) :

Equivalent stress intensity factor

\(K_{I\theta \mathrm{max}}\) :

Maximum value of the equivalent stress intensity factor

\(L_{n}\, (n=1,\, \ldots ,\, N)\) :

Contour of each crack

n :

Paris law coefficient

\(N_{n}\) :

Normal force

\(N_\mathrm{c}\) :

Remaining life of a surface

\(P_{0}\) :

Maximum normal contact load

P(x):

Normal contact load

\(T_{n}\) :

Tangential force

\(Z_{n}^{0}\) :

Affix of the local coordinate in the global coordinate system

\(\beta \) :

Angle between the x-axes of the local and the global coordinate systems

\(\delta \) :

Normalized distance between origin of the local coordinate system

\(\Delta l_{k}\) :

Crack path construction increment

\(\theta ^{{*}}\) :

Crack propagation angle

\(\lambda \) :

Location of the contact load

\(\sigma _{\theta \theta }\) :

Circumferential stress

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  1. Department of Applied Mechanics, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, P.O. Box 19395-1999, Tehran, Iran

    A. R. Shahani & M. Babaei

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  1. A. R. Shahani
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Shahani, A.R., Babaei, M. The crack propagation path for a system of surface and subsurface cracks and their interactions due to rolling contact fatigue. Acta Mech 231, 1751–1764 (2020). https://doi.org/10.1007/s00707-019-02604-7

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  • DOI: https://doi.org/10.1007/s00707-019-02604-7

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