The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 2: single-crystal plasticity

Reddy, B.
October 2011
Continuum Mechanics & Thermodynamics;Nov2011, Vol. 23 Issue 6, p551
Academic Journal
Variational formulations are constructed for rate-independent problems in small-deformation single-crystal strain-gradient plasticity. The framework, based on that of Gurtin (J Mech Phys Solids 50: 5-32, ), makes use of the flow rule expressed in terms of the dissipation function. Provision is made for energetic and dissipative microstresses. Both recoverable and non-recoverable defect energies are incorporated into the variational framework. The recoverable energies include those that depend smoothly on the slip gradients, the Burgers tensor, or on the dislocation densities (Gurtin et al. J Mech Phys Solids 55:1853-1878, ), as well as an energy proposed by Ohno and Okumura (J Mech Phys Solids 55:1879-1898, ), which leads to excellent agreement with experimental results, and which is positively homogeneous and therefore not differentiable at zero slip gradient. Furthermore, the variational formulation accommodates a non-recoverable energy due to Ohno et al. (Int J Mod Phys B 22:5937-5942, ), which is also positively homogeneous, and a function of the accumulated dislocation density. Conditions for the existence and uniqueness of solutions are established for the various examples of defect energy, with or without the presence of hardening or slip resistance.


Related Articles

  • Effect of cold rolling on the indentation deformation of AA6061 aluminum alloy. Yang, Fuqian; Du, Wenwen; Okazaki, Kenji // Journal of Materials Research;May2005, Vol. 20 Issue 5, p1172 

    The indentation behavior of cold-rolled AA6061 Al alloy was investigated. Following the approach suggested by Tabor, indentation stress-indentation strain curves were constructed and analyzed. The indentation stress required to create the same indentation strain increases with an increase in the...

  • Residual Meso Stresses in Multilevel Crystal Plasticity Models. Volegov, Pavel S.; Trusov, Peter V.; Gribov, Dmitry S. // Advanced Materials Research;2014, Issue 1040, p576 

    The problems related to the construction of multi-level mathematical models of inelastic deformation of crystalline materials based on crystal plasticity are considered. The example of the two-level model for description the severe plastic deformation of fcc polycrystals is discussed. The issues...

  • Asymptotics in discrete dislocation pile-up modelling. Voskoboinikov, R. E. // AIP Conference Proceedings;4/10/2008, Vol. 999 Issue 1, p157 

    An asymptotic methodology for analysing pile-ups of large numbers of dislocations is proposed. We provide robust proof of the interconnection between continuum and discrete approaches to dislocation description. The practical usefulness of the technique is tested on a pile-up of screw or edge...

  • Influence of the Peierls relief on size effects in plastic deformation of micro- and nanocrystals of body-centered cubic metals. Malygin, G. // Physics of the Solid State;Jun2012, Vol. 54 Issue 6, p1220 

    The influence of the Peierls relief and Peierls stresses on the size effects in micro- and nanocrystals of metals with a body-centered cubic (bcc) lattice has been theoretically discussed in the framework of the dislocation-kinetic approach. It has been found that, as compared to micro- and...

  • Dislocation-interaction-based model of strained-layer relaxation. Schwarz, Klaus W.; Tu, Yuhai // Journal of Applied Physics;Oct2009, Vol. 106 Issue 8, p083510 

    A strained layer relaxes plastically when dislocations propagate within the layer, leaving behind an array of misfit dislocations at the layer interface. We develop an analytical model of this process, based on the idea that relaxation is frustrated when propagating dislocations are trapped or...

  • ATOMISTIC STUDY OF NANOPRECIPITATES INFLUENCE ON PLASTICITY AND FRACTURE OF CRYSTALLINE METALS. Stegailov, Vladimir V.; Kuksin, Alexey Yu.; Norman, Genri E.; Yanilkin, Alexey V. // AIP Conference Proceedings;12/12/2007, Vol. 955 Issue 1, p339 

    The molecular dynamics simulation is applied to study the influence of nanoprecipitates on the microscopic mechanisms of the spall fracture initiation and corresponding plastic deformation. The systems under study are single crystals doped with nanoclusters of another metal. The calculation...

  • On the localization of plastic strain at the prefailure stage and the possibility of predicting the site and time of ductile rupture. Danilov, V.; Orlova, D.; Zuev, L.; Bolotina, I. // Technical Physics;Feb2011, Vol. 56 Issue 2, p207 

    The localization of macrodeformation during the transition from plastic flow to ductile rupture is studied for a wide class of metals. It is found that the mechanism behind this process is the same as that behind plastic deformation and as such can be described as a change in the type of...

  • Energy loss in a unidirectional flax-polyester composite subjected to multiple tensile load-unload cycles. Newman, Roger; Battley, Mark; Carpenter, James; Guen, Marie // Journal of Materials Science;Feb2012, Vol. 47 Issue 3, p1164 

    Composites reinforced with plant fibres show inelastic deformation under tensile loads. This property can be exploited in vibration-damping applications. Inelastic deformation was characterised for composites made from unsaturated polyester resin reinforced with unidirectional flax yarns. The...

  • Dislocation generation and crack growth under monotonic loading. Cherepanov, G. P.; Richter, A.; Verijenko, V. E.; Adali, S.; Sutyrin, V. // Journal of Applied Physics;11/15/1995, Vol. 78 Issue 10, p6249 

    Presents information on a study which investigated the processes of crack growth and dislocation emission induced by the crack tip in a crystal with cubic lattice of atoms under plane strain conditions. Elastic field of dislocations near a crack tip; Emission of the Nth pair of dislocations;...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics