# On the Connection Between the Discrete Dislocation Slip Model and the Orowan Equation

## Abstract

Within the framework of thermodynamic theory of plasticity and specific structural-variables (associated with individual dislocations), a transition has been made to an expression containing one internal variable of the averaging type--the density of glissile dislocations, N{sub g}. This expression should be considered a tensorial generalization of the well-known Orowan's equation and relates it directly to the simplest possible case of normal flow in metallic materials. Since most metals display deviations from normality in the flow rule{sup 7} it also clearly indicates that more rigorous assessment of the relation between plastic strain rate and dislocation populations is required especially for materials displaying plastic instabilities in the form of dislocation patterning, strain-softening and strain-rate softening phenomena. The obtained result could be a useful starting point in establishing such rigorous macroscopic relations from microscopic considerations associated with individual dislocations and to find useful applications in dislocation density-related constitutive modeling of plastic deformation.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 12665

- Report Number(s):
- SAND99-2290J

TRN: AH200120%%375

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Applied Physics

- Additional Journal Information:
- Other Information: Submitted to Journal of Applied Physics; PBD: 8 Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; METALS; DEFORMATION; DISLOCATIONS; PLASTICITY; SLIP; STRAIN RATE; STRAIN SOFTENING; THERMODYNAMICS; MATHEMATICAL MODELS

### Citation Formats

```
BRAGINSKY, MICHAEL V., GLAZOV, MICHAEL V., and RICHMOND, OWEN.
```*On the Connection Between the Discrete Dislocation Slip Model and the Orowan Equation*. United States: N. p., 1999.
Web.

```
BRAGINSKY, MICHAEL V., GLAZOV, MICHAEL V., & RICHMOND, OWEN.
```*On the Connection Between the Discrete Dislocation Slip Model and the Orowan Equation*. United States.

```
BRAGINSKY, MICHAEL V., GLAZOV, MICHAEL V., and RICHMOND, OWEN. Wed .
"On the Connection Between the Discrete Dislocation Slip Model and the Orowan Equation". United States. https://www.osti.gov/servlets/purl/12665.
```

```
@article{osti_12665,
```

title = {On the Connection Between the Discrete Dislocation Slip Model and the Orowan Equation},

author = {BRAGINSKY, MICHAEL V. and GLAZOV, MICHAEL V. and RICHMOND, OWEN},

abstractNote = {Within the framework of thermodynamic theory of plasticity and specific structural-variables (associated with individual dislocations), a transition has been made to an expression containing one internal variable of the averaging type--the density of glissile dislocations, N{sub g}. This expression should be considered a tensorial generalization of the well-known Orowan's equation and relates it directly to the simplest possible case of normal flow in metallic materials. Since most metals display deviations from normality in the flow rule{sup 7} it also clearly indicates that more rigorous assessment of the relation between plastic strain rate and dislocation populations is required especially for materials displaying plastic instabilities in the form of dislocation patterning, strain-softening and strain-rate softening phenomena. The obtained result could be a useful starting point in establishing such rigorous macroscopic relations from microscopic considerations associated with individual dislocations and to find useful applications in dislocation density-related constitutive modeling of plastic deformation.},

doi = {},

journal = {Journal of Applied Physics},

number = ,

volume = ,

place = {United States},

year = {1999},

month = {9}

}