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Finite element implementation and numerical issues of strain gradient plasticity with application to metal matrix composites
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).ORCID iD: 0000-0002-0307-8917
Tech Univ Denmark, Risø Natl Lab Sustainable Energy, Mat Res Dept.
2009 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 46, no 22-23, 3977-3987 p.Article in journal (Refereed) Published
Abstract [en]

A framework of finite element equations for strain gradient plasticity is presented. The theoretical framework requires plastic strain degrees of freedom in addition to displacements and a plane strain version is implemented into a commercial finite element code. A couple of different elements of quadrilateral type are examined and a few numerical issues are addressed related to these elements as well as to strain gradient plasticity theories in general. Numerical results are presented for an idealized cell model of a metal matrix composite under shear loading. It is shown that strengthening due to fiber size is captured but strengthening due to fiber shape is not. A few modelling aspects of this problem are discussed as well. An analytic solution is also presented which illustrates similarities to other theories.

Place, publisher, year, edition, pages
2009. Vol. 46, no 22-23, 3977-3987 p.
Keyword [en]
Finite element method; Strain gradient plasticity; Metal matrix composites; Strengthening; Dislocations
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-8036DOI: 10.1016/j.ijsolstr.2009.07.028ISI: 000271483900005Scopus ID: 2-s2.0-70349156782OAI: oai:DiVA.org:kth-8036DiVA: diva2:13250
Note
QC 20100723. Uppdaterad från submitted till published (20100723).Available from: 2008-02-26 Created: 2008-02-26 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Modelling and simulation of plastic deformation on small scales: interface conditions and size effects of thin films
Open this publication in new window or tab >>Modelling and simulation of plastic deformation on small scales: interface conditions and size effects of thin films
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Contrary to elastic deformation, plastic deformation of crystalline materials, such as metals, is size-dependent. Most commonly, this phenomenon is present but unnoticed, such as the effect of microstructural length scales. The grain size in metallic materials is a length scale that affects material parameters such as yield stress and hardening moduli. In addition, several experiments performed in recent years on specimens with geometrical dimensions on the micron scale have shown that these dimensions also influence the mechanical behaviour. The work presented in this thesis involves continuum modelling and simulation of size-dependent plastic deformation, with emphasis on thin films and the formulation of interface conditions.

A recently published strain gradient plasticity framework for isotropic materials [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 52, 1379-1406] is used as a basis for the work. The theory is higher-order in the sense that additional boundary conditions are required and, as a consequence, higher-order stresses appear in the theory. For dimensional consistency, length scale parameters enter the theory, which is not the case for conventional plasticity theory. In Paper A and B, interface conditions are formulated in terms of a surface energy. The surface energy is assumed to depend on the plastic strain state at the interface and different functional forms are investigated. Numerical results are generated with the finite element method and it is found that this type of interface condition can capture the boundary layers that develop at the substrate interface in thin films. Size-effects are captured in the hardening behaviour as well as the yield strength. In addition, it is shown that there is an equivalence between a surface energy varying linearly in plastic strain and a viscoplastic interface law for monotonous loading.

In paper C, a framework of finite element equations is formulated, of which a plane strain version is implemented in a commercial finite element program. Results are presented for an idealized problem of a metal matrix composite and several element types are examined numerically. In paper D, the implementation is used in a numerical study of wedge indentation of a thin film on an elastic substrate. Several trends that have been observed experimentally are captured in the theoretical predictions. Increased hardness at shallow depths due to gradient effects as well as increased hardness at more significant depths due to the presence of the substrate are found. It is shown that the hardening behaviour of the film has a large impact on the substrate effect and that either pile-up or sink-in deformation modes may be obtained depending on the material length scale parameter. Finally, it is qualitatively demonstrated that the substrate compliance has a significant effect on the calculated hardness of the film.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. x, 51 p.
Series
Trita-HFL. Report / Royal Institute of Technology, Solid mechanics, ISSN 1654-1472 ; 0451
Keyword
Strain gradient plasticity, Size effects, Thin films, Interface, Finite element method, Dislocations, Constitutive behaviour, Hardening behaviour, Indentation, Contact mechanics, Metal matrix composites
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-4652 (URN)
Public defence
2008-03-14, D2, Kungl Tekniska Högskolan, Lindstedtsvägen 5, Stockholm, 10:15
Opponent
Supervisors
Note

QC 20100723

Available from: 2008-02-26 Created: 2008-02-26 Last updated: 2013-01-14Bibliographically approved

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