  When subjected to large amplitude oscillatory shear stress, aqueous Laponite
suspensions show an abrupt solidification transition after a long delay time
tc. We measure the dependence of tc on stress amplitude, frequency, and on the
age-dependent initial loss modulus. At first sight our observations appear
quantitatively consistent with a simple soft-glassy rheology (SGR)-type model,
in which barrier crossings by mesoscopic elements are purely strain-induced.
For a given strain amplitude {\gamma}0 each element can be classified as fluid
or solid according to whether its local yield strain exceeds {\gamma}0. Each
cycle, the barrier heights E of yielded elements are reassigned according to a
fixed prior distribution {\rho}(E): this fixes the per-cycle probability
R({\gamma}0) of a fluid elements becoming solid. As the fraction of solid
elements builds up, {\gamma}0 falls (at constant stress amplitude), so
R({\gamma}0) increases. This positive feedback accounts for the sudden
solidification after a long delay. The model thus appears to directly link
macroscopic rheology with mesoscopic barrier height statistics: within its
precepts, our data point towards a power law for {\rho}(E) rather than the
exponential form usually assumed in SGR. However, despite this apparent
success, closer investigation shows that the assumptions of the model cannot be
reconciled with the extremely large strain amplitudes arising in our
experiments. The quantitative explanation of delayed solidification in Laponite
therefore remains an open theoretical challenge.
