Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Wedge indentation of thin films modelled by strain gradient plasticity
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).ORCID iD: 0000-0001-6232-8819
2008 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 45, no 21, 5556-5566 p.Article in journal (Refereed) Published
Abstract [en]

A plane strain study of wedge indentation of a thin film on a substrate is performed. The film is modelled with the strain gradient plasticity theory by Gudmundson [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. journal of the Mechanics and Physics of Solids 52, 1379-1406] and analysed using finite element simulations. Several trends that have been experimentally observed elsewhere are captured in the predictions of the mechanical behaviour of the thin film. Such trends include increased hardness at shallow depths due to gradient effects as well as increased hardness at larger depths due to the influence of the substrate. In between, a plateau is found which is observed to scale linearly with the material length scale parameter. It is shown that the degree of hardening of the material has a strong influence on the substrate effect, where a high hardening modulus gives a larger impact on this effect. Furthermore, pile-up deformation dominated by plasticity at small values of the internal length scale parameter is turned into sink-in deformation where plasticity is suppressed for larger values of the length scale parameter. Finally, it is demonstrated that the effect of substrate compliance has a significant effect on the hardness predictions if the effective stiffness of the substrate is of the same order as the stiffness of the film.

Place, publisher, year, edition, pages
2008. Vol. 45, no 21, 5556-5566 p.
Keyword [en]
Indentation; Hardness; Thin films; Size effects; Strain gradient plasticity; Finite element method; Length scales
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-8037DOI: 10.1016/j.ijsolstr.2008.06.001ISI: 000260354300004Scopus ID: 2-s2.0-51249099163OAI: oai:DiVA.org:kth-8037DiVA: diva2:13251
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

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Authority records BETA

Larsson, Per-Lennart

Search in DiVA

By author/editor
Fredriksson, PerLarsson, Per-Lennart
By organisation
Solid Mechanics (Dept.)
In the same journal
International Journal of Solids and Structures
Mechanical Engineering

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 76 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf