The mathematical framework and an approximate solution of surface crack propagation under hydraulic pressure loading

Material degradation and failure in rolling contact components are often caused by surface microcrack initiation and propagation. Experimental evidence shows that surface crack growth rate is higher with the presence of lubricating fluid than without, possibly due to high fluid pressure within the crack. The mathematical framework to analyze a surface crack under hydraulic pressure loading is established. A surface crack filled with incompressible, Newtonian viscous fluid is considered. The solid is considered to be linear elastic. A pressure loading history is prescribed at the mouth of the crack. The governing equations are found to be two coupled non-linear integral equations of pressure distribution and crack opening displacement distribution. An approximate solution is obtained by assuming a local pressure-opening displacement constitutive law, and by using the method of separation of variables. The results indicate that upon a sudden decrease of pressure loading at the crack mouth, the crack-tip stress intensity decreases rapidly at the beginning followed by a long tail of diminishing decreasing rate; whereas upon a sudden increase of pressure loading, an incubation time exists before the pressure can be transmitted deep into the crack. A very important parameter, the characteristic penetration time, is identified and can be used to determine whether hydraulic pressure has significant influence on surface crack propagation.