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Size-dependent yield strength of thin films
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).ORCID iD: 0000-0002-0307-8917
2005 (English)In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 21, no 9, 1834-1854 p.Article in journal (Refereed) Published
Abstract [en]

Biaxial strain and pure shear of a thin film are analysed using a strain gradient plasticity theory presented by Gudmundson [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 52, 1379-1406]. Constitutive equations are formulated based on the assumption that the free energy only depends on the elastic strain and that the dissipation is influenced by the plastic strain gradients. The three material length scale parameters controlling the gradient effects in a general case are here represented by a single one. Boundary conditions for plastic strains are formulated in terms of a surface energy that represents dislocation buildup at an elastic/plastic interface. This implies constrained plastic flow at the interface and it enables the simulation of interfaces with different constitutive properties. The surface energy is also controlled by a single length scale parameter, which together with the material length scale defines a particular material. Numerical results reveal that a boundary layer is developed in the film for both biaxial and shear loading, giving rise to size effects. The size effects are strongly connected to the buildup of surface energy at the interface. If the interface length scale is small, the size effect vanishes. For a stiffer interface, corresponding to a non-vanishing surface energy at the interface, the yield strength is found to scale with the inverse of film thickness.

Place, publisher, year, edition, pages
2005. Vol. 21, no 9, 1834-1854 p.
Keyword [en]
constitutive behaviour; viscoplastic material; strain gradient plasticity
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-8034DOI: 10.1016/j.ijplas.2004.09.005ISI: 000229867100008Scopus ID: 2-s2.0-18444369672OAI: oai:DiVA.org:kth-8034DiVA: diva2:13248
Note
QC 20100723Available 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
2. A strain gradient plasticity analysis of size effects in thin films
Open this publication in new window or tab >>A strain gradient plasticity analysis of size effects in thin films
2005 (English)Licentiate thesis, comprehensive summary (Other scientific)
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2005. 15 p.
Series
Trita-HFL. Report / Royal Institute of Technology, Solid Mechanics, ISSN 1654-1472 ; 0387
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-380 (URN)
Presentation
2005-06-07, Sal Q2, Osquldas väg 10, Stockholm, 13:15
Supervisors
Note

QC 20101129

Available from: 2005-08-09 Created: 2005-08-09 Last updated: 2013-01-15Bibliographically approved

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