A model for roughness-induced fatigue crack closure
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I.
INTRODUCTION
Basically, three mechanisms have been proposed to explain the fatigue crack closure phenomenon, i.e., plasticityinduced crack closure,[1,2,3] oxide-induced crack closure,[3,4,5] and roughness-induced crack closure.[6,7] Roughness-induced crack closure is attributed to the deflection of crack path, i.e., an irregular or rough fracture surface. At low DK (near-threshold) levels, serrated or zigzag fracture paths may be formed because of crystallographically or microstructurally sensitive crack growth.[7,8] In the case of strong crack deflection, a local mode II stress intensity factor exists at the kinked crack tip.[9,10,11] This may lead to significant mode II displacement, so that the crack becomes wedge-closed at discrete contact points along the crack facets.[4,12] Some attempts have been made to develop models for estimating the influence of fracture surface roughness parameters on roughness-induced crack closure.[7,13,14] The geometric model due to Suresh and Ritchie[7,13] addresses the contribution from both mode I and mode II displacement, leading to contact of the two mating surfaces above minimum stress intensity factor in a cycle, Kmin. The crack closing stress intensity factor, Kcl, i.e., the stress intensity at which the first contact of crack surface occurs upon unloading, is found to be proportional to the maximum stress intensity factor in a cycle, Kmax:[7,13] Kcl 5
=
2 gx K 5 1 1 2 gx max
=
x tan u K 1 1 x tan u max
[1]
where g is the ratio of height, h, to width, w, of the asperities (g 5 h/w); x is the ratio of the net mode II displacement from the peak of the fatigue cycle to the point of the first contact upon unloading, uII, to the mode I displacement at the same time, uI (x 5 uII/uI); and u is the angle of crack path deflection (u 5 arctg 2h/w). The key controlling factor ¨ LLER, SHENG-HUI WANG, Research Associate, CLEMENS MU Senior Scientist, and HANS ECKART EXNER, Professor and Head of Division, are with the Physical Metallurgy Division, Department of Materials Science, Darmstadt University of Technology, D-64287 Darmstadt, Germany. Manuscript submitted June 16, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
of crack closure related to crack surface roughness turns out to be the tilt angle. Some experimental[15] and numerical[16,17] studies support the results derived from this model. Wase´n and Karlsson[14] argued that the model of Suresh and Ritchie is geometrically oversimplified and bears no measurable relation to a real fracture surface nor does it indicate any relation to the underlying microstructure. They supposed that the statistical nature of the fracture events makes it possible to use the standard deviation of heights of the crack path profile, SH, as an effective measure of the surface roughness.[18–23] The following empirical equation was obtained:[14] Kcl 5 0.57 z E z SH1/3 (MPa =m; E in GPa; SH in m)
[2]
This equation fits the experimental values for a large number of different steels and some WC/Co alloys.[14] In contrast to the model of Suresh and
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