Continuum theory of dislocations revisited

Berdichevsky, Victor L.

doi:10.1007/s00161-006-0024-7

Cited by 90 publications

(81 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1). We apply the free energy proposed by Berdichevsky [2] to the above model (with λ, µ the elastic Lamé moduli, ε e ij = ε ij − ε p ij the elastic strains, k a material constant, ρ the dislocation density and ρ s the saturated dislocation density):…”

Section: Introductionmentioning

confidence: 99%

Plastic deformation of bicrystals within continuum dislocation theory

Kochmann¹,

Le²

2008

Proc Appl Math and Mech

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Plastic deformation of bicrystals within continuum dislocation theory

Kochmann¹,

Le²

2008

Proc Appl Math and Mech

View full text Add to dashboard Cite

show abstract

“…In the case of zero resistance for double slip system the determination of β l (y) and β r (y) reduces to the minimization of the total energy (1). Based on the analysis of a minimizing sequence [2] we obtain the energetic threshold en = 2k hbρ s | sin ϕ| | sin 2ϕ| which being exactly the same of that the single slip and clearly showing the size effect typical to problems of crystal plasticity.…”

Section: Dislocation Nucleation and Evolution At Zero Resistancementioning

confidence: 88%

“…1), and assume that the length of the strip L in z-direction is large, and the width a is much greater than the height h (L a h). For the double slip system case, we adopt the free energy formulation proposed in [1] and made modification by adding the energy of cross-slip interaction term to our model (with λ, µ the elastic Lamé moduli, ε e ij = ε ij − ε p ij the elastic strains, χ the interaction factor, k a material constant, ρ s the saturated dislocation density and ρ γ the scalar dislocation density for γ = l, r):…”

Section: Introductionmentioning

confidence: 99%

Plane constrained uniaxial extension of a single crystal strip

Sembiring

2009

Proc Appl Math and Mech

View full text Add to dashboard Cite

Within continuum dislocation theory the plane constrained uniaxial extension of a single crystal strip deforming in single or double slip is analyzed. For the single and symmetric double slip, the closed-form analytical solutions are found which exhibits the energetic and dissipative thresholds for dislocation nucleation, the Bauschinger translational work hardening, and the size effect. Numerical solutions for the non-symmetric double slip are obtained by finite element procedures.

show abstract

“…Recent results in the plasticity of metals have revealed the limitations of a quadratic potential ψ ∇ in equation (2.15), especially regarding the scaling of size effects in dislocation plasticity [47][48][49][50]63,71,72]. Two classes of nonlinear potentials are explored below motivated by the latter references.…”

Section: Nonlinear Strain Gradient Potentialsmentioning

confidence: 99%

“…Motivated by energy considerations in dislocation theory, several authors have considered logarithmic functions of scalar dislocation densities or of the norm of the dislocation density tensor [49,50,71,72]. In the present context of phenomenological metal plasticity, a logarithmic function of the norm of the gradient of the scalar plastic microstrain is proposed:…”

Section: (B) Logarithmic Potentialmentioning

confidence: 99%

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Forest¹

2016

Proc. R. Soc. A.

View full text Add to dashboard Cite

International audienceThe construction of regularization operators presented in this work is based on the introduction of strain or damage micromorphic degrees of freedom in addition to the displacement vector and of their gradients into the Helmholtz free energy function of the constitutive material model. The combination of a new balance equation for generalized stresses and of the micromorphic constitutive equations generates the regularization operator. Within the small strain framework, the choice of a quadratic potential w.r.t. the gradient term provides the widely used Helmholtz operator whose regularization properties are well known: smoothing of discontinuities at interfaces and boundary layers in hardening materials, and finite width localization bands in softening materials. The objective is to review and propose nonlinear extensions of micromorphic and strain/damage gradient models along two lines: the first one introducing nonlinear relations between generalized stresses and strains; the second one envisaging several classes of finite deformation model formulations. The generic approach is applicable to a large class of elastoviscoplastic and damage models including anisothermal and multiphysics coupling. Two standard procedures of extension of classical constitutive laws to large strains are combined with the micromorphic approach: additive split of some Lagrangian strain measure or choice of a local objective rotating frame. Three distinct operators are finally derived using the multiplicative decomposition of the deformation gradient. A new feature is that a free energy function depending solely on variables defined in the intermediate isoclinic configuration leads to the existence of additional kinematic hardening induced by the gradient of a scalar micromorphic variable

show abstract

Continuum theory of dislocations revisited

Cited by 90 publications

References 31 publications

Plastic deformation of bicrystals within continuum dislocation theory

Plastic deformation of bicrystals within continuum dislocation theory

Plane constrained uniaxial extension of a single crystal strip

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Contact Info

Product

Resources

About