Spatial fluctuations in transient creep deformation

Abstract

We study the spatial fluctuations of transient creep deformation of materials as a function of time, both by Digital Image Correlation (DIC) measurements of paper samples and by numerical simulations of a crystal plasticity or discrete dislocation dynamics model. This model has a jamming or yielding phase transition, around which power-law or Andrade creep is found. During primary creep, the relative strength of the strain rate fluctuations increases with time in both cases - the spatially averaged creep rate obeys the Andrade law $\epsilon_t \sim t^{-0.7}$, while the time dependence of the spatial fluctuations of the local creep rates is given by $\Delta \epsilon_t \sim t^{-0.5}$. A similar scaling for the fluctuations is found in the logarithmic creep regime that is typically observed for lower applied stresses. We review briefly some classical theories of Andrade creep from the point of view of such spatial fluctuations. We consider these phenomenological, time-dependent creep laws in terms of a description based on a non-equilibrium phase transition separating evolving and frozen states of the system when the externally applied load is varied. Such an interpretation is discussed further by the data collapse of the local deformations in the spirit of absorbing state/depinning phase transitions, as well as deformation-deformation correlations and the width of the cumulative strain distributions. The results are also compared with the order parameter fluctuations observed close to the depinning transition of the 2$d$ Linear Interface Model or the quenched Edwards-Wilkinson equation.