Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

Irani, N. (TU Delft (OLD) MSE-7)
Remmers, Joris J.C. (Eindhoven University of Technology)
Deshpande, Vikram S. (University of Cambridge)

2017

Plastic size effects in single crystals are investigated by using finite strain and small strain discrete dislocation plasticity to analyse the response of cantilever beam specimens. Crystals with both one and two active slip systems are analysed, as well as specimens with different beam aspect ratios. Over the range of specimen sizes analysed here, the bending stress versus applied tip displacement response has a strong hardening plastic component. This hardening rate increases with decreasing specimen size. The hardening rates are slightly lower when the finite strain discrete dislocation plasticity (DDP) formulation is employed as curving of the slip planes is accounted for in the finite strain formulation. This relaxes the back-stresses in the dislocation pile-ups and thereby reduces the hardening rate. Our calculations show that in line with the pure bending case, the bending stress in cantilever bending displays a plastic size dependence. However, unlike pure bending, the bending flow strength of the larger aspect ratio cantilever beams is appreciably smaller. This is attributed to the fact that for the same applied bending stress, longer beams have lower shear forces acting upon them and this results in a lower density of statistically stored dislocations.

Bending
Dislocations
Finite strain
Size effects

http://resolver.tudelft.nl/uuid:a3285250-22e8-422f-9ab8-64641ebf57be

https://doi.org/10.1007/s10409-017-0682-7

0567-7718

Acta Mechanica Sinica/Lixue Xuebao, 33 (4), 763-777

Institutional Repository

journal article

© 2017 N. Irani, Joris J.C. Remmers, Vikram S. Deshpande