A conventional theory of strain gradient crystal plasticity based on the Taylor dislocation model

H. Wang, K. C. Hwang, Y. Huang*, P. D. Wu, B. Liu, G. Ravichandran, C. S. Han, H. Gao

*Corresponding author for this work

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

Single crystal metallic materials display strong size effects when the characteristic length of plastic deformation is on the order of microns. The classical crystal plasticity theory cannot explain the size effects since its constitutive model possesses no intrinsic material length. The strain gradient crystal plasticity theory [Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005a. Mechanism-based strain gradient crystal plasticity - I. Theory. Journal of the Mechanics and Physics of Solids 53, 1188-1203; Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005b. Mechanism-based strain gradient crystal plasticity - II. Analysis. Journal of the Mechanics and Physics of Solids 53, 1204-1222] has been modified to incorporate a new quasi rate-independent formulation for the slip rate. Its major advantage is that it is not necessary to distinguish plastic loading and unloading in a rate-independent formulation, and therefore avoids the complexity of determining the set of active slip systems in single crystals. The intrinsic material length is identified from the Taylor dislocation model as l = α 2 (frac(μ, τ 0 )) 2 b, where μ is the shear modulus, τ 0 is the initial yield stress (critical resolved shear stress) in slip systems, b is the magnitude of Burgers vector, and α is an empirical coefficient between 0.3 and 0.5. For non-uniform plastic deformation with the characteristic length of deformation comparable to the intrinsic material length l, the present theory gives higher plastic work hardening than the classical crystal plasticity theory due to geometrically necessary dislocations.

Original languageEnglish (US)
Pages (from-to)1540-1554
Number of pages15
JournalInternational journal of plasticity
Volume23
Issue number9
DOIs
StatePublished - Sep 1 2007

Fingerprint

Dislocations (crystals)
Plasticity
Crystals
Plastic deformation
Mechanics
Physics
Single crystals
Plastics
Burgers vector
Constitutive models
Unloading
Strain hardening
Yield stress
Shear stress
Elastic moduli

Keywords

  • Constitutive behavior
  • Crystal plasticity
  • Strain gradient
  • Taylor dislocation model

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Wang, H. ; Hwang, K. C. ; Huang, Y. ; Wu, P. D. ; Liu, B. ; Ravichandran, G. ; Han, C. S. ; Gao, H. / A conventional theory of strain gradient crystal plasticity based on the Taylor dislocation model. In: International journal of plasticity. 2007 ; Vol. 23, No. 9. pp. 1540-1554.
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abstract = "Single crystal metallic materials display strong size effects when the characteristic length of plastic deformation is on the order of microns. The classical crystal plasticity theory cannot explain the size effects since its constitutive model possesses no intrinsic material length. The strain gradient crystal plasticity theory [Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005a. Mechanism-based strain gradient crystal plasticity - I. Theory. Journal of the Mechanics and Physics of Solids 53, 1188-1203; Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005b. Mechanism-based strain gradient crystal plasticity - II. Analysis. Journal of the Mechanics and Physics of Solids 53, 1204-1222] has been modified to incorporate a new quasi rate-independent formulation for the slip rate. Its major advantage is that it is not necessary to distinguish plastic loading and unloading in a rate-independent formulation, and therefore avoids the complexity of determining the set of active slip systems in single crystals. The intrinsic material length is identified from the Taylor dislocation model as l = α 2 (frac(μ, τ 0 )) 2 b, where μ is the shear modulus, τ 0 is the initial yield stress (critical resolved shear stress) in slip systems, b is the magnitude of Burgers vector, and α is an empirical coefficient between 0.3 and 0.5. For non-uniform plastic deformation with the characteristic length of deformation comparable to the intrinsic material length l, the present theory gives higher plastic work hardening than the classical crystal plasticity theory due to geometrically necessary dislocations.",
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A conventional theory of strain gradient crystal plasticity based on the Taylor dislocation model. / Wang, H.; Hwang, K. C.; Huang, Y.; Wu, P. D.; Liu, B.; Ravichandran, G.; Han, C. S.; Gao, H.

In: International journal of plasticity, Vol. 23, No. 9, 01.09.2007, p. 1540-1554.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A conventional theory of strain gradient crystal plasticity based on the Taylor dislocation model

AU - Wang, H.

AU - Hwang, K. C.

AU - Huang, Y.

AU - Wu, P. D.

AU - Liu, B.

AU - Ravichandran, G.

AU - Han, C. S.

AU - Gao, H.

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Y1 - 2007/9/1

N2 - Single crystal metallic materials display strong size effects when the characteristic length of plastic deformation is on the order of microns. The classical crystal plasticity theory cannot explain the size effects since its constitutive model possesses no intrinsic material length. The strain gradient crystal plasticity theory [Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005a. Mechanism-based strain gradient crystal plasticity - I. Theory. Journal of the Mechanics and Physics of Solids 53, 1188-1203; Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005b. Mechanism-based strain gradient crystal plasticity - II. Analysis. Journal of the Mechanics and Physics of Solids 53, 1204-1222] has been modified to incorporate a new quasi rate-independent formulation for the slip rate. Its major advantage is that it is not necessary to distinguish plastic loading and unloading in a rate-independent formulation, and therefore avoids the complexity of determining the set of active slip systems in single crystals. The intrinsic material length is identified from the Taylor dislocation model as l = α 2 (frac(μ, τ 0 )) 2 b, where μ is the shear modulus, τ 0 is the initial yield stress (critical resolved shear stress) in slip systems, b is the magnitude of Burgers vector, and α is an empirical coefficient between 0.3 and 0.5. For non-uniform plastic deformation with the characteristic length of deformation comparable to the intrinsic material length l, the present theory gives higher plastic work hardening than the classical crystal plasticity theory due to geometrically necessary dislocations.

AB - Single crystal metallic materials display strong size effects when the characteristic length of plastic deformation is on the order of microns. The classical crystal plasticity theory cannot explain the size effects since its constitutive model possesses no intrinsic material length. The strain gradient crystal plasticity theory [Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005a. Mechanism-based strain gradient crystal plasticity - I. Theory. Journal of the Mechanics and Physics of Solids 53, 1188-1203; Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005b. Mechanism-based strain gradient crystal plasticity - II. Analysis. Journal of the Mechanics and Physics of Solids 53, 1204-1222] has been modified to incorporate a new quasi rate-independent formulation for the slip rate. Its major advantage is that it is not necessary to distinguish plastic loading and unloading in a rate-independent formulation, and therefore avoids the complexity of determining the set of active slip systems in single crystals. The intrinsic material length is identified from the Taylor dislocation model as l = α 2 (frac(μ, τ 0 )) 2 b, where μ is the shear modulus, τ 0 is the initial yield stress (critical resolved shear stress) in slip systems, b is the magnitude of Burgers vector, and α is an empirical coefficient between 0.3 and 0.5. For non-uniform plastic deformation with the characteristic length of deformation comparable to the intrinsic material length l, the present theory gives higher plastic work hardening than the classical crystal plasticity theory due to geometrically necessary dislocations.

KW - Constitutive behavior

KW - Crystal plasticity

KW - Strain gradient

KW - Taylor dislocation model

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