### Abstract

In this work, we discuss a thermodynamic theory of plasticity for self-organization of collective dislocations in FCC metals. The theory is described by geometrical tensor of crystal defect fields such as dislocation density tensor, representing net mobile dislocation density and geometrically necessary boundaries, and the incompatibility tensor representing immobile dislocation density. Conservation laws for the two kinds of dislocation density are formulated with dislocation products and interactions terms. Based on the second law of thermodynamics, we drive basic constitutive equations for the dislocation flux, production and interaction terms of dislocations. We also derive a set of reaction-diffusion equations for the dislocation density tensor and incompatibility tensor which describes the vein and persistent slip band (PSB) ladders structures. These equations are analyzed using linear stability and bifurcation analysis. An intrinsic mesoscopic length scale is determined which provides an estimate for the wavelength of the PSBs. The basic aspects of the model are motivated and substantiated by analyzing the stress fields of various possible dislocation configurations using discrete dislocation dynamics.

Original language | English |
---|---|

Pages (from-to) | 416-419 |

Number of pages | 4 |

Journal | Materials Science and Engineering A |

Volume | 309-310 |

DOIs | |

Publication status | Published - 2001 Jul 15 |

### Fingerprint

### Keywords

- Dislocation density
- PSB
- Thermodynamics

### ASJC Scopus subject areas

- Materials Science(all)

### Cite this

*Materials Science and Engineering A*,

*309-310*, 416-419. https://doi.org/10.1016/S0921-5093(00)01630-0

**A strain-gradient thermodynamic theory of plasticity based on dislocation density and incompatibility tensors.** / Shizawa, Kazuyuki; Kikuchi, Kanto; Zbib, Hussein M.

Research output: Contribution to journal › Article

*Materials Science and Engineering A*, vol. 309-310, pp. 416-419. https://doi.org/10.1016/S0921-5093(00)01630-0

}

TY - JOUR

T1 - A strain-gradient thermodynamic theory of plasticity based on dislocation density and incompatibility tensors

AU - Shizawa, Kazuyuki

AU - Kikuchi, Kanto

AU - Zbib, Hussein M.

PY - 2001/7/15

Y1 - 2001/7/15

N2 - In this work, we discuss a thermodynamic theory of plasticity for self-organization of collective dislocations in FCC metals. The theory is described by geometrical tensor of crystal defect fields such as dislocation density tensor, representing net mobile dislocation density and geometrically necessary boundaries, and the incompatibility tensor representing immobile dislocation density. Conservation laws for the two kinds of dislocation density are formulated with dislocation products and interactions terms. Based on the second law of thermodynamics, we drive basic constitutive equations for the dislocation flux, production and interaction terms of dislocations. We also derive a set of reaction-diffusion equations for the dislocation density tensor and incompatibility tensor which describes the vein and persistent slip band (PSB) ladders structures. These equations are analyzed using linear stability and bifurcation analysis. An intrinsic mesoscopic length scale is determined which provides an estimate for the wavelength of the PSBs. The basic aspects of the model are motivated and substantiated by analyzing the stress fields of various possible dislocation configurations using discrete dislocation dynamics.

AB - In this work, we discuss a thermodynamic theory of plasticity for self-organization of collective dislocations in FCC metals. The theory is described by geometrical tensor of crystal defect fields such as dislocation density tensor, representing net mobile dislocation density and geometrically necessary boundaries, and the incompatibility tensor representing immobile dislocation density. Conservation laws for the two kinds of dislocation density are formulated with dislocation products and interactions terms. Based on the second law of thermodynamics, we drive basic constitutive equations for the dislocation flux, production and interaction terms of dislocations. We also derive a set of reaction-diffusion equations for the dislocation density tensor and incompatibility tensor which describes the vein and persistent slip band (PSB) ladders structures. These equations are analyzed using linear stability and bifurcation analysis. An intrinsic mesoscopic length scale is determined which provides an estimate for the wavelength of the PSBs. The basic aspects of the model are motivated and substantiated by analyzing the stress fields of various possible dislocation configurations using discrete dislocation dynamics.

KW - Dislocation density

KW - PSB

KW - Thermodynamics

UR - http://www.scopus.com/inward/record.url?scp=0035879806&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035879806&partnerID=8YFLogxK

U2 - 10.1016/S0921-5093(00)01630-0

DO - 10.1016/S0921-5093(00)01630-0

M3 - Article

VL - 309-310

SP - 416

EP - 419

JO - Materials Science & Engineering A: Structural Materials: Properties, Microstructure and Processing

JF - Materials Science & Engineering A: Structural Materials: Properties, Microstructure and Processing

SN - 0921-5093

ER -