Inspection of free energy functions in gradient crystal plasticity

Forest, Samuel; Guéninchault, Nicolas

doi:10.1007/s10409-013-0088-0

Cited by 53 publications

(36 citation statements)

References 48 publications

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“…There are arguments pointing toward a gradient energy which is closer to linear rather than quadratic (Evans and Hutchinson, 2009, see Section 5). A free energy potential linear in the slip gradients was investigated by Ohno and Okumara (2007) and Forest and Guéninchault (2013). Here, a generalization from the quadratic form of the gradient energy in Eq.…”

Section: Back Stress Formulations and Resultsmentioning

confidence: 99%

On modeling micro-structural evolution using a higher order strain gradient continuum theory

El-Naaman

Nielsen

Niordson

2016

International Journal of Plasticity

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Published experimental measurements on deformed metal crystals show distinct pattern formation, in which dislocations are arranged in wall and cell structures. The distribution of dislocations is highly non-uniform, which produces discontinuities in the lattice rotations. Modeling the experimentally observed micro-structural behavior, within a framework based on continuous field quantities, poses obvious challenges, since the evolution of dislocation structures is inherently a discrete and discontinuous process. This challenge, in particular, motivates the present study, and the aim is to improve the micro-structural response predicted using strain gradient crystal plasticity within a continuum mechanics framework. One approach to modeling the dislocation structures observed is through a back stress formulation, which can be related directly to the strain gradient energy. The present work offers an investigation of constitutive equations for the back stress based on both considerations of the gradient energy, but also includes results obtained from a purely phenomenological starting point. The influence of model parameters is brought out in a parametric study, and it is demonstrated how a proper treatment of the back stress enables dislocation wall and cell structure * Tel: +45 4525-4020, Fax: +45 4593-1475 URL: saeln@mek.dtu.dk (S.A. El-Naaman)

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Section: Back Stress Formulations and Resultsmentioning

confidence: 99%

On modeling micro-structural evolution using a higher order strain gradient continuum theory

El-Naaman

Nielsen

Niordson

2016

International Journal of Plasticity

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“…The case m = 1 leads to the condition p = χ and no extra-hardening. This leaves the possibility of localization of plastic strain and plastic strain gradient in the form of interface dislocations as discussed in [49,50]. The corresponding singular distribution of plastic microstrain in conjunction with the relation (3.15) was shown in the latter reference to lead to a size-dependent overall increase of the apparent yield stress and to no extra-hardening.…”

Section: (B) Logarithmic Potentialmentioning

confidence: 89%

“…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%

“…The logarithmic potential (3.14), the associated regularization operator (3.18) and the enhanced hardening law (3.19) are now specialized to the one-dimensional case: example given in gradient plasticity in reference [49]. The logarithmic potential is inspired from strain gradient crystal plasticity models emerging from the statistical theory of dislocations [49].…”

Section: (B) Logarithmic Potentialmentioning

confidence: 99%

“…The logarithmic potential is inspired from strain gradient crystal plasticity models emerging from the statistical theory of dislocations [49]. It has the advantage with respect to the m = 1 case that it can account for both enhanced strength and hardening at small sizes, as demonstrated in [50].…”

Section: (B) Logarithmic Potentialmentioning

confidence: 99%

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

Forest¹

2016

Proc. R. Soc. A.

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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

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Simulation of Hot Isostatic Pressing in a Single‐Crystal Ni Base Superalloy with the Theory of Continuously Distributed Dislocations Combined with Vacancy Diffusion

2022

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Single‐crystal components made of nickel base superalloys contain pores after casting and homogenization heat treatment. Hot isostatic pressing (HIP), which is carried above the γ′‐solvus temperature of the alloy, is industrially applied to reduce porosity. A modeling of HIP based on continuously distributed dislocations is developed in a 2D setting. Glide and climb of straight‐edge dislocations, as well as vacancy diffusion, are the deformation mechanisms taken into account. Thereby, dislocation glide is controlled by dragging a cloud of large atoms, and climb is controlled by vacancy diffusion. Relying on previous investigations of the creep behavior at HIP temperatures, it is assumed that new dislocations are nucleated at low‐angle boundaries (LAB) and move through subgrains until they either reach the opposite LABs or react with other dislocations and annihilate. Vacancies are created at the pore surface and diffuse through the alloy until they are either consumed by climbing dislocations or disappear at the LABs. The field equations are solved by finite elements. It is shown that pore shrinking is mostly controlled by vacancy diffusion as the shear stresses at the LABs are too low to nucleate a sufficient amount of dislocations.

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Inspection of free energy functions in gradient crystal plasticity

Cited by 53 publications

References 48 publications

On modeling micro-structural evolution using a higher order strain gradient continuum theory

On modeling micro-structural evolution using a higher order strain gradient continuum theory

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

Simulation of Hot Isostatic Pressing in a Single‐Crystal Ni Base Superalloy with the Theory of Continuously Distributed Dislocations Combined with Vacancy Diffusion

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