The fatigue parameter n for subthreshold Vickers indentations

摘要

Models used for lifetime predictions of brittle materials use both statistical distributions of weak spots, such as Weibull statistics, and slow-crack-growth expressions. such as the power law. Local stresses, frequently present near these weak spots. are often not incorporated in these models. A Vickers indentation is used as a model system with a local stress. A radial crack is present after indentation at high loads. The local stress is then incorporated in the existing models, using the apparent fatigue parameter n' = 3/4 n + 1/2. Indentation at low loads leads to subthreshold Vickers indentations; radial cracks are not visible near the indentation site. The experimentally determined Failure stress and the apparent fatigue parameter n' of the subthreshold indentations differ significantly from the post-threshold data. Models for radial crack extension at Vickers indentations are analysed. The stress intensity factor K-1 has two minimal one at c/a approximate to 1 (crack size equal to the indentation diagonal) and the second at c/a > 1. From a combination of these curves and the power law for slow crack growth, static fatigue curves are calculated. The lower minimum largely determines the fatigue behaviour. From the stress dependence of the first minimum an expression for the apparent fatigue parameter n' for subthreshold Vickers indentations is obtained, For fused silica (n = 40) the present model predicts 8 < n' < 40 for subthreshold Vickers indentations. [References: 11]