jats:pThe behaviour of single layer graphene sections under current-stressing conditions is presented. Graphene devices are stressed to the point of failure, and it is seen that they exhibit Joule heating. Using a simple 1-D model for heat generation, we demonstrate how to extract values for the resistivity and thermal coefficient of resistance of graphene devices from their current-voltage characteristics. We also show that graphene flakes with a large number of ripples and folds have higher resistance and fail along a connected pathway of folds.</jats:p>