applied fracture mechanics

164 Applied Fracture Mechanics20 Will-be-set-by-IN-TECH5±k ⋅1041n2.521x no00 2.5 5 7.5Figure 5. The dependence of the normal stress intensity factor k + 1n on the coordinate x0 n for the case of theboundary of half-plane loaded with normal p(x 0 )=π/4 and frictional τ(x 0 )=−λp(x 0 ) stresses,y 0 n = −0.2, α n = 0, q 0 = 0: λ = 0.1 - curve marked with 1, λ = 0.2 - curve marked with 2 (after Kudishand Covitch [1]). Reprinted with permission from CRC Press.For the same loading and crack parameters the behavior of the shear stress intensity factor k ± 2nis represented in Fig. 7 and 8. It is important to observe that the shear stress intensity factorsk ± 2n are insensitive to changes of the friction coefficient λ.Fig. 5 and 6 clearly show that for subsurface cracks with angle α n = π/2 for zero or tensileresidual stress q 0 the normal stress intensity factors k ± 1n are significantly higher (by two ordersof magnitude) than the ones for α n = 0. For α n = 0 and α n = π/2 the orders of magnitudeof the shear stress intensity factors k ± 2n are the same (see Fig. 7 and 8). Moreover, from thesegraphs it is clear that the normal stress intensity factors k ± 1n are significantly influenced by thefriction coefficient λ while the shear stress intensity factors k ± 2n are insensitive to the value ofthe friction coefficient λ.Obviously, in the single-term approximation the behavior of k 0−1none of k 0+1nbetween k 0−2nand k0+2n, respectively. Generally, the difference between k0−1nand k0+2n is of the order of magnitude of δ 0 1.and k0−2n is identical to theand k0+1nas well as3.4. Lubricant-surface crack interaction. Stress intensity factors k ± 1n and k± 2nBehaviorThe process of lubricant-surface crack interaction is very complex and the details of theproblem formulation, the numerical solution approach, and a comprehensive analysis of theresults can be found in [1]. Therefore, here we will discuss only the most important features ofthis phenomenon. It is well known that the presence of lubricant between surfaces in contact