A Numerical Solution of a Surface Crack Under Cyclic Hydraulic Pressure Loading

Z. Q. Xu, K. J. Hsia

Research output: Contribution to journalArticlepeer-review


Material degradation and failure in rolling contact components are often associated with surface crack initiation and propagation under repeated contact loading. In the presence of lubricating fluid, the hydraulic pressure in the fluid film between the contacting surfaces may play an important role in the crack growth process. This paper presents a method to model the effect of hydraulic pressure loading on surface crack growth. The governing equations of the coupled viscous fluid/cracked solid problem are obtained, which are nonlinear integral and differential equations. The fluid is assumed to be Newtonian and incompressible. The cracked solid is considered to be linearly elastic. Pressure loading history is prescribed at the crack mouth. Finite difference methods are used to solve the governing equations. For each time step, Newton-Raphson iteration method is used to search for the root of the nonlinear equations. Both transient and steady-state pressure distributions under cyclic pressure loading are obtained using this method. A few numerical examples are given to demonstrate the reliability and effectiveness of the solution method. The solution shows that there exists a characteristic time, which determines whether pressure fluctuations at the crack mouth can be transmitted deep into the crack. The steady-state pressure distribution exhibits a phase delay from the applied cyclic loading.

Original languageEnglish (US)
Pages (from-to)637-645
Number of pages9
JournalJournal of Tribology
Issue number4
StatePublished - Oct 1997
Externally publishedYes

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Surfaces and Interfaces
  • Surfaces, Coatings and Films


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