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Published March 21, 2016 | public
Journal Article

Length scales and pinning of interfaces


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.

Additional Information

© 2016 The Author(s) Published by the Royal Society. Accepted: 13 November 2015. This work is financially supported by the US Army Research Office through the MURI grantW911NF-07-1-0410 and the US Air Force Office of Scientific Research through the Center of Excellence in High Rate Deformation Physics of Heterogeneous Materials (grant no.: FA 9550-12-1-0091) . We gratefully acknowledge interesting discussions with Manfred Wuttig that motivated this work. Competing interests. We declare we have no competing interests.

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