Creep or aging induced by temperature changes

B. Blanc, E. Bertin, H. Gayvallet, T. Divoux and J.-C. Géminard

Collaboration : L. Pugnaloni (IFLYSIB, La Plata)

The literature canonically presents granular materials as a bunch of athermal particles. Indeed, the energy necessary for the grains to hop one over another (a few tenths of a millimeter, for instance) is roughly 10 orders of magnitude higher than the ambient thermal agitation kT. This is probably one of the reasons why the behavior of a granular assembly submitted to temperature fluctuations has received so little attention. Nonetheless, uncontrolled thermal dilations of a granular pile have been reported to generate stress fluctuations large enough to hinder reproducible measurements of the stress field inside the pile, and are even suspected of being the driving factor leading to large-scale "static avalanches". Indeed, the slow relaxation and compaction of a granular material, which has been hitherto produced by the input of mechanical energy, can be induced by periodically raising and then lowering the temperature of the granular assembly, as recently brought to the fore by Chen and co-workers. However, the compaction dynamics as well as the basic mechanisms at stake remain unknown. We address the following questions: What is the dynamic of the top of a granular column submitted to thermal cycling? Does this compaction process exhibit features analogous to aging, as other compaction processes (e.g., tapping, cyclic shear. . .) do? And finally, what is the behavior of the grain assembly in the limit of low amplitude temperaturecycles, i.e., well below a cycling amplitude of 40°C. 

First, we report a time-resolved study of the dynamics associated with the slow compaction of a granular column submitted to thermal cycles. The column height displays a complex behavior: for a large amplitude of the temperature cycles, the granular column settles continuously, experiencing a small settling at each cycle. By contrast, for a small-enough amplitude, the column exhibits a discontinuous and intermittent activity: successive collapses are separated by quiescent periods whose duration is exponentially distributed. We then discuss potential mechanisms which would account for both the compaction and the transition at finite amplitude [Divoux, 2008 & 2009; Blanc, 2013]. 

Second, we evaluate in a simple model the ability for the temperature changes to lead to aging of the frictional contact between solids. The dry frictional contact between two solid surfaces is well known to obey Coulomb friction laws. In particular, the static friction force resisting the relative lateral tangential motion of solid surfaces, initially at rest, is known to be proportional to the normal force and independent of the area of the macroscopic surfaces in contact. Experimentally, the static friction force has been observed to slightly depend on time. Such an aging phenomenon has been accounted for either by the creep of the material or by the condensation of water bridges at the microscopic contact points. By studying a toy model, we show that the small uncontrolled temperature changes of the system can also lead to a significant increase of the static friction force [Géminard, 2010]. 

Finally, we report on the dynamics of a model frictional system submitted to minute external perturbations. The system consists of a chain of sliders connected through elastic springs that rest on an incline [Blanc, 2011]. By introducing cyclic expansions and contractions of the springs we observe a reptation of the chain. We account for the average reptation velocity theoretically. The velocity of small systems exhibits a series of plateaus as a function of the incline angle. Due to elastic effects, there exists a critical amplitude below which the reptation is expected to cease. However, rather than a full stop of the creep, we observe in numerical simulations a transition between a continuous-creep and an irregular-creep regime when the critical amplitude is approached. The latter transition is reminiscent of the transition between the continuous and the irregular compaction of granular matter submitted to periodic temperature changes. 

Creep motion of a granular pile induced by thermal cycling,
T. Divoux, H. Gayvallet and J.-C. Géminard, Phys. Rev. Lett. 101 (2008) 148303. 

Aging of a granular pile induced by thermal cycling,
T. Divoux, I. Vassilief, H. Gayvallet and J.-C. Géminard,
6th International Conference on the Micromechanics of Granular Media, JUL 13-17, 2009 Golden, CO
POWDERS AND GRAINS 2009, AIP Conference Proceedings 1145 (2009) 473-476. 

Aging of the frictional properties induced by temperature variations,
J.-C. Géminard and E. Bertin, Phys. Rev. E 82, (2010) 056108. 

Creep motion of a model frictional system,
B. Blanc, L.A. Pugnaloni and J.-C. Géminard, Phys. Rev. E 84 (2011) 061303. 

Intrinsic creep of a granular column subjected to temperature changes,
B. Blanc and J.-C. Géminard, Phys. Rev. E 88, 022201 (2013)