Length scales and pinning of interfaces

Abstract

One contribution of 11 to a theme issue 'Trends and challenges in the mechanics of complex materials' . The pinning of interfaces and free discontinuities by defects and heterogeneities plays an important role in a variety of phenomena, including grain growth, martensitic phase transitions, ferroelectricity, dislocations and fracture. We explore the role of length scale on the pinning of interfaces and show that the width of the interface relative to the length scale of the heterogeneity can have a profound effect on the pinning behaviour, and ultimately on hysteresis. When the heterogeneity is large, the pinning is strong and can lead to stick-slip behaviour as predicted by various models in the literature. However, when the heterogeneity is small, we find that the interface may not be pinned in a significant manner. This shows that a potential route to making materials with low hysteresis is to introduce heterogeneities at a length scale that is small compared with the width of the phase boundary. Finally, the intermediate setting where the length scale of the heterogeneity is comparable to that of the interface width is characterized by complex interactions, thereby giving rise to a non-monotone relationship between the relative heterogeneity size and the critical depinning stress.

Photochemical-induced phase transitions in photoactive semicrystalline polymers

“…In this case, previous study has suggested that the pinning of phase boundary by the heterogeneity can be strong [29].…”

“…There are non-photoactive heterogeneities in the semi-crystalline polymer such as the chain extender, crosslinks, residual solvents or initiators, and other precipitates. These heterogeneities can play important roles in the evolution of phase transition through pinning the phase boundaries with possible stick-slip behaviors [29,30]. We include the effect of this heterogeneity by a quenched spatial noise described in Section II.D, and now examine it in more detail.…”

Materials from mathematics

“…There are diverse thoughts about hysteresis in a large literature, 11 some of which are in fact inconsistent with the observation of rateindependent hysteresis. Ideas also include the pinning of interfaces by defects [61] and spin flips in an Ising model mediated by disorder [56]. There is also a deep mathematical literature on the modeling of hysteresis, which is not so much concerned with its origins, but rather with the accurate simulation of hysteresis loops [44].…”

Contact around a Sharp Corner with Small Scale Plasticity

“…The analysis of contact stress around these area is important in understanding the onset and propagation of those failures: it will provide guidelines for the design of contact components so that the damage can be limited [11,12,[15][16][17][18][19][20][21]. Based on experimental observations, the sliding behavior between two elastic bodies in contact can be described by three regimes on a map of tangential and normal loads: full-stick, partial-slip and gross-sliding regimes [22][23][24].…”