Precise prediction of plastic flow patterns during indentation is difficult, due to the presence of many possible slip systems and the complexity of dislocation interactions. However, some general patterns of behaviour are observed, in particular a transition from laminar flow to rotational flow as the indentation progresses, and the major features can be predicted without detailed crystallographic knowledge. Here we present a model for rotational flow under spherical indenters, based on the slip circle construction which has already been applied to pyramidal indenters. By using the magnitude of a representative Burgers vector as a scale parameter, it is also possible to estimate the approximate size at which the transition from laminar to rotational flow occurs. We find that this straightforward model produces predictions which agree well with the available hardness data for spherical indenters.
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