Determinations of both length scale and surface elastic parameters for fcc metals

Song, Jingru; Liu, Jianyun; Ma, Hongmei; Liang, Lihong; Yan, Weizhen

doi:10.1016/j.crme.2014.03.004

Cited by 13 publications

(6 citation statements)

References 34 publications

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“…For trans-scale mechanics theory considering both strain gradient effect and surface/interface effects, a variation equation of total potential can be expressed as follows [41,42] …”

Section: A Brief Introduction To the Trans-scale Mechanics Theorymentioning

confidence: 99%

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Hierarchical structure observation and nanoindentation size effect characterization for a limnetic shell

Song

Fan

et al. 2015

Acta Mech Sin

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In the present research, hierarchical structure observation and mechanical property characterization for a type of biomaterial are carried out. The investigated biomaterial is Hyriopsis cumingii, a typical limnetic shell, which consists of two different structural layers, a prismatic "pillar" structure and a nacreous "brick and mortar" structure. The prismatic layer looks like a "pillar forest" with variationsection pillars sized on the order of several tens of microns. The nacreous material looks like a "brick wall" with bricks sized on the order of several microns. Both pillars and bricks are composed of nanoparticles. The mechanical properties of the hierarchical biomaterial are measured by using the nanoindentation test. Hardness and modulus are measured for both the nacre layer and the prismatic layer, respectively. The nanoindentation size effects for the hierarchical structural materials are investigated experimentally. The results show that the prismatic nanostructured material has a higher stiffness and hardness than the nacre nanostructured material. In addition, the nanoindentation size effects for the hierarchical structural materials are described theoretically, by using the trans-scale mechanics theory considering both strain gradient effect and the surface/interface effect. The modeling results are consistent with experimental ones.

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“…For trans-scale mechanics theory considering both strain gradient effect and surface/interface effects, a variation equation of total potential can be expressed as follows [41,42] …”

Section: A Brief Introduction To the Trans-scale Mechanics Theorymentioning

confidence: 99%

“…(2), considering the small strain case and considering the current configuration in calculating the surface/interface energy, the surface/interface constitutive equations can be expressed as follows [42]:…”

Section: A Brief Introduction To the Trans-scale Mechanics Theorymentioning

confidence: 99%

Hierarchical structure observation and nanoindentation size effect characterization for a limnetic shell

Song

Fan

et al. 2015

Acta Mech Sin

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“…There are several well-known simplified versions of second gradient theory, such as the couple stress theory ( Koiter, 1964;Mindlin & Tiersten, 1962;Toupin, 1962 ) corresponding to letting the micro-deformation gradient be only rotation gradient, Kleinert strain gradient theory ( Kleinert, 1989 ) corresponding to considering the gradient of volumetric strain in addition to rotation gradient as the micro-deformation gradient, etc. Some other models, like Aifantis ( Altan & Aifantis, 1997;Gao & Park, 2007 ) and Wei & Hutchinson's strain gradient elasticity theory ( Song, Liu, Ma, Liang, & Wei, 2014;Wei, 2006;Wei & Hutchinson, 1997 ), use strain gradient or second gradient of displacement as the micro-deformation gradient and define different constitutive relations. The objective of developing these high order continuum theories is to characterize the size effect well observed when size of structure is decreasing to micro or nano scale ( Fleck, Muller, Ashby, & Hutchinson, 1994;Kouzeli & Mortensen, 2002 ), the microstructure comes into play in this case which is unable to be accounted for by Cauchy continuum theory without microstructure ( Hu, Liu, & Lu, 2005 ).…”

Section: Introductionmentioning

confidence: 99%

Inclusion problem in second gradient elasticity

Wei

et al. 2018

International Journal of Engineering Science

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The Green's function and Eshelby tensors of an infinite linear isotropic second gradient continuum are derived for an inclusion of arbitrary shape. Particularly for spherical, cylindrical and ellipsoidal inclusions, Eshelby tensors and their volume averages are obtained in an analytical form. It is found that the Eshelby tensors are not uniform inside the inclusion even for a spherical inclusion, and their variations depend on the two characteristic lengths of second gradient theory. When size of inclusion is large enough compared to the characteristic lengths, the Eshelby tensor of the second gradient medium is reduced to the classical one, as expected. It is also demonstrated that the existing Green's functions and Eshelby tensors of couple stress theory, Aifantis, Kleinert and Wei-Hutchinson special strain gradient theories could be recovered as special cases. This work paves the way for constructing micromechanical method to predict size effect of composite materials, as shown for the effective modulus of particulate composite derived with the proposed theory.

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“…Wei-Hutchinson strain gradient theory (Song et al, 2014;Wei, 2006;Wei and Hutchinson, 1997) is used to describe the organic matrix materials. Its basic equations are written as:…”

Section: The Modelmentioning

confidence: 99%

“…interlaminations, the rest 11.9% was in the mineral platelets, which divided the mineral platelet to many aragonite nanograins (Zhang et al, 2016 hardness showed a strong size effect. By a trans-scale mechanics theory (Song et al, 2014;Wu et al, 2012), which considered both strain gradient effect and the surface/interface effect, Song et al (2015) As mentioned above, the organic materials and the immersed mineral bridges, nanoasperities, etc. in the organic interlaminations can be regarded as an effective medium and its properties are size-dependence.…”

Section: Comparisons With Experiments and Simulationmentioning

confidence: 99%

Mechanical behavior and size effect of the staggered bio-structure materials

Wei

Song

et al. 2018

Mechanics of Materials

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • A strain gradient shear-lag model for the staggered bio-structure is developed in which the effects of microstructures and scale were incorporated. • The analytical expressions of the overall effective modulus, interfacial strengths and deformations of the staggered bio-structure material are obtained. • The size effects of the properties of the staggered bio-structure are studied. • The predicted effective moduli of nacreous layer in different shells are compared with corresponding experimental results and are in good agreement with experimental results.

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Determinations of both length scale and surface elastic parameters for fcc metals

Cited by 13 publications

References 34 publications

Hierarchical structure observation and nanoindentation size effect characterization for a limnetic shell

Hierarchical structure observation and nanoindentation size effect characterization for a limnetic shell

Inclusion problem in second gradient elasticity

Mechanical behavior and size effect of the staggered bio-structure materials

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