Size effects in single crystal thin films: nonlocal crystal plasticity simulations

Yefimov, Serge; Giessen, van der Erik

doi:10.1016/j.euromechsol.2005.01.002

Cited by 32 publications

(28 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above form for the back stress nicely converges to the single-slip theory of Groma et al [11][12][13][14]25 The cos͑ ij ͒ coupling between slip systems should come as no surprise. The angular dependence of the back stress must emerge from the symmetry of the potential.…”

Section: ͑50͒mentioning

confidence: 61%

“…Using the knowledge of the pair correlation functions, we obtain a complete description of the back stress as a function of slip orientationssomething that has not been achieved in the Groma-Zaiser approach but which had been previously incorporated in the multiple-slip theory using the ad hoc phenomenological considerations. 14,25 Finally in Sec. VII, we contrast our theory with the multiple-slip theory of Yefimov and Van der Giessen.…”

Section: Introductionmentioning

confidence: 99%

“…VII, we contrast our theory with the multiple-slip theory of Yefimov and Van der Giessen. 14,25 While both theories propose that interactions among slip systems solely depend on relative angles of slip orientations, the functional forms are different. We attribute the failure of the earlier theory in explaining size effects in single-crystal thin films partly to this difference and partly to the treatment of dislocation nucleation in the theory.…”

Section: Introductionmentioning

confidence: 99%

“…While the theory successfully captured most features observed in discrete dislocation simulations, its ad hoc extension to multiple-slip systems failed to explain the size effects in single-crystal thin films. 14 The main goals of this paper are ͑1͒ to correctly describe and obtain analytical expressions for dislocation pair correlations and ͑2͒ to systematically generalize the approach of Groma et al to multiple-slip systems.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Statistical approach to dislocation dynamics: From dislocation correlations to a multiple-slip continuum theory of plasticity

Limkumnerd

Giessen

2008

Phys. Rev. B

View full text Add to dashboard Cite

Due to recent successes of a statistical-based nonlocal continuum crystal plasticity theory for single-glide in explaining various aspects such as dislocation patterning and size-dependent plasticity, several attempts have been made to extend the theory to describe crystals with multiple slip systems using ad-hoc assumptions. We present here a mesoscale continuum theory of plasticity for multiple slip systems of parallel edge dislocations. We begin by constructing the Bogolyubov-Born-Green-Yvon-Kirkwood (BBGYK) integral equations relating different orders of dislocation correlation functions in a grand canonical ensemble. Approximate pair correlation functions are obtained for single-slip systems with two types of dislocations and, subsequently, for general multiple-slip systems of both charges. The effect of the correlations manifests itself in the form of an entropic force in addition to the external stress and the self-consistent internal stress. Comparisons with a previous multiple-slip theory based on phenomenological considerations shall be discussed.

show abstract

Section: ͑50͒mentioning

confidence: 61%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Statistical approach to dislocation dynamics: From dislocation correlations to a multiple-slip continuum theory of plasticity

Limkumnerd

Giessen

2008

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…How to generalise the continuum model to multiple slip is being studied intensively [66,67]. At the moment the theory is far from being fully developed.…”

Section: Application To Metal-matrix Compositementioning

confidence: 99%

Statistical physical approach to describe the collective properties of dislocations

Groma

2010

Multiscale Modelling of Plasticity and Fracture by Means of Dislocation Mechanics

View full text Add to dashboard Cite

On a Proper Account of First‐ and Second‐Order Size Effects in Crystal Plasticity

et al. 2009

View full text Add to dashboard Cite

This paper addresses two important aspects of engineering size effects in miniaturizing metallic components and the modeling thereof. The critical role of processing induced size effects is emphasized, which tend to be easily forgotten in experimental work or engineering interpretations of size effects. The second aspect is related to the need for a rigorous strain gradient enrichment in crystal plasticity modeling, as the result of coarse graining the interaction between discrete dislocations. The physical origin of the energetic enrichment is discussed and its deterministic derivation is briefly confronted with the analogous result obtained from a statistical mechanics analysis.In the past decade, industry is increasingly focusing on the behavior of materials in micro and nano-systems. At the level of many microsystems, metallic structures, and films are used ranging from sizes of a few microns to hundreds of microns. The scientific community has given considerable attention to this subject, in particular in the range where size effects have a dominant contribution.The purpose of this paper is certainly not to review the wide field of research that has permitted to experimentally identify and model size effects in metals. Whereas many explanations have been given for the measured effects (usually ''small is strong''), a number of issues remain at least quantitatively unclear. Different physical phenomena contribute to the reported size effects, whereas the interpretation is usually focusing on a single phenomenon. A quantitative analysis necessitates the complete overview of all contributing effects. To provide the relevant context of this contribution, the reader is referred to papers that either discuss the role of different size effects, [1][2][3][4] or papers that provide the state-of-the-art in higher-order crystal plasticity models. [5][6][7][8][9][10][11][12][13][14][15][16] From the modeling perspective, a large number of strain gradient models have been proposed in the literature, whereby the higher-order terms are largely phenomenological, often lacking a rigorous physical connection with the underlying problem.This paper has therefore a two-fold focus: 1) emphasize the critical role of size effects that tend to be easily forgotten; 2) underpin the need for a specific strain gradient enrichment in crystal plasticity modeling, as the result of coarse graining the interaction between discrete dislocations. The first part of the paper concentrates on the important role of processing-or manufacturing-induced size effects, where the intrinsic role of geometrically necessary dislocations (GNDs) is emphasized. The second part concentrates on the physical justification and interpretation of the energetic higher-order terms in strain gradient crystal plasticity. A deterministic analogy with the work of [17] is given, which fits entirely in an earlier adopted format for the incorporation of internal stress effects in FCC crystals. Most importantly, this paper aims to provide additional insight into the origin o...

show abstract

Size effects in single crystal thin films: nonlocal crystal plasticity simulations

Cited by 32 publications

References 19 publications

Statistical approach to dislocation dynamics: From dislocation correlations to a multiple-slip continuum theory of plasticity

Statistical approach to dislocation dynamics: From dislocation correlations to a multiple-slip continuum theory of plasticity

Statistical physical approach to describe the collective properties of dislocations

On a Proper Account of First‐ and Second‐Order Size Effects in Crystal Plasticity

Contact Info

Product

Resources

About