Spatial fluctuations in transient creep deformation

Abstract

We study the spatial fluctuations of transient creep deformation of materials as a functionof time, both by digital image correlation (DIC) measurements of paper samples and bynumerical simulations of a crystal plasticity or discrete dislocation dynamics model. Thismodel has a jamming or yielding phase transition, around which power law or Andradecreep is found. During primary creep, the relative strength of the strain rate fluctuationsincreases with time in both cases—the spatially averaged creep rate obeys the Andrade lawϵt ∼ t − 0.7, while the time dependence of the spatial fluctuations of the local creep rates is given byΔϵt ∼ t − 0.5. A similar scaling for the fluctuations is found in the logarithmic creep regime that istypically observed for lower applied stresses. We review briefly some classical theories ofAndrade creep from the point of view of such spatial fluctuations. We consider thesephenomenological, time-dependent creep laws in terms of a description based on anon-equilibrium phase transition separating evolving and frozen states of the systemwhen the externally applied load is varied. Such an interpretation is discussedfurther by the data collapse of the local deformations in the spirit of absorbingstate/depinning phase transitions, as well as deformation–deformation correlations andthe width of the cumulative strain distributions. The results are also comparedwith the order parameter fluctuations observed close to the depinning transitionof the 2d linear interface model or the quenched Edwards–Wilkinson equation.