The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape

Vlassak, Joost J.; Ciavarella, M.; Barber, J. R.; Wang, X.

doi:10.1016/s0022-5096(03)00066-8

Cited by 190 publications

(158 citation statements)

References 9 publications

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“…Expressed using the crystallographic body-centered cubic (BCC) basis vectors, each edge of the tungsten mesh elements is <100>. The stiffnesses of tungsten are C11 = 522 GPa, C12 = 204 GPa, and C44 = 161 GPa (Lide, 2007); For the diamond indenter, the Young's modulus is selected from the published indentation modulus of {100} diamond (1126 GPa) and Poisson's ratio is 0.07 (Vlassak et al, 2003).…”

Section: Finite Element Modelingmentioning

confidence: 99%

“…A reduced elastic indentation modulus of R 317 GPa = E , found from the published indentation modulus of {100} diamond (Vlassak et al, 2003) and the stiffness coefficients of tungsten listed in Section 3.3 (for W 442 GPa = E ), was used to estimate R. Offset displacements found from fitting were less than 1 nm for both indentation experiments. Averaging over all of the accepted indentation tests, the mean radii are 163 nm ± 13 nm for the sharp indenter and 1160 nm ± 22 nm for the blunt indenter.…”

Section: Nanoindentation Experimentsmentioning

confidence: 99%

See 1 more Smart Citation

Effect of the Spherical Indenter Tip Assumption on the Initial Plastic Yield Stress

Ma¹,

Levine²,

Dixson³

et al. 2012

Nanoindentation in Materials Science

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Section: Finite Element Modelingmentioning

confidence: 99%

Section: Nanoindentation Experimentsmentioning

confidence: 99%

Effect of the Spherical Indenter Tip Assumption on the Initial Plastic Yield Stress

Ma¹,

Levine²,

Dixson³

et al. 2012

Nanoindentation in Materials Science

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“…Oliver and Pharr model assumed that the dynamic elastic modulus E * was proportional to the reduced modulus of elasticity Er provided by the Hertz model (Hertz, 1882;Ikai, 2007;Vlassak et al, 2003):…”

Section: Knee Modelmentioning

confidence: 99%

The measurement of biomechanical properties of porcine articular cartilage using atomic force microscopy

Imer

Akiyama

Rooij

et al. 2009

Arch. Histol. Cytol.

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relative to the surface under investigation were performed by means of eight inflatable balloons. An integrated threedimensional, piezoelectric scanner allowed raster scanning and probing of a small area of cartilage around the point of insertion. An AFM probe with an integrated deflection sensor was mounted at the distal end of the instrument. Using this instrument, several measurements were performed on agarose gel and on porcine cartilage samples. The load-displacement curves obtained were analyzed and the dynamic elastic moduli E * were calculated. A good correlation between these values and those published in the scientific literature was found. Therefore, we concluded that the SFA can provide quantitative measurements to detect early pathological changes in OA.

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“…However, one can still gain an insight into the meaning of the nominal Young's modulus of an elastically anisotropic material obtained from indentation, which is denoted as indentation modulus thereafter. According to the analysis of Vlassak et al, [22][23][24] the indentation modulus of an …”

Section: Experimental Examplesmentioning

confidence: 99%

An improved energy method for determining Young’s modulus by instrumented indentation using a Berkovich tip

Ma¹,

Ong

Zhang

2008

J. Mater. Res.

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We previously proposed a method for estimating Young's modulus from instrumented nanoindentation data based on a model assuming that the indenter had a spherical-capped Berkovich geometry to take account of the bluntness effect. The method is now further improved by releasing the constraint on the tip shape, allowing it to have a much broader arbitrariness to range from a conical-tipped shape to a flat-ended shape, whereas the spherical-capped shape is just a special case in between. This method requires two parameters to specify a tip geometry, namely, a volume bluntness ratio V r and a height bluntness ratio h r . A set of functional relationships correlating nominal hardness/reduced elastic modulus ratio (H n /E r ) and elastic work/total work ratio (W e /W) were established based on dimensional analysis and finite element simulations, with each relationship specified by a set of V r and h r . Young's modulus of an indented material can be estimated from these relationships. The method was shown to be valid when applied to S45C carbon steel and 6061 aluminum alloy.

show abstract

The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape

Cited by 190 publications

References 9 publications

Effect of the Spherical Indenter Tip Assumption on the Initial Plastic Yield Stress

Effect of the Spherical Indenter Tip Assumption on the Initial Plastic Yield Stress

The measurement of biomechanical properties of porcine articular cartilage using atomic force microscopy

An improved energy method for determining Young’s modulus by instrumented indentation using a Berkovich tip

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