Contact of crack surfaces during fatigue: Part 2. Simulations

A detailed model of the role of asperities in crack closure has been initiated in Part 1 of this article. Crack opening stress is defined as the far-field stress required to overcome the asperity-induced contact stresses along the crack. In this Part 2, the magnitude of crack opening stress is established as a function of roughness (σ₀); asperity density (N); maximum stress level (S_max/S_y) shakedown pressure (p₀^s/k), which reflects the effect of tangential tractions or friction; R ratio; and crack length. Normalizations permit application to a wide range of materials. The results, for selected levels of asperity density, are consolidated upon comparing the crack opening displacement (COD) with the roughness (σ₀) over four orders of magnitude. Specifically, a nonlinear relationship between COD/σ₀ and crack opening stress was established that can be readily used to determine crack opening stress over a broad range of conditions. The model has been utilized to predict crack opening stress levels for several materials, including 0.8 pet C steels, 9Cr-lMo steels, Ti-4Al, TJ-46A1 (γ-aluminide), and Al 2124 alloys. Experimental measurements of crack roughness and asperity density were conducted on titanium aluminide specimens using confocal microscopy, and crack closure predictions were made with the model. The predictions demonstrated very good agreement with the experimentally measured closure levels.