Obtaining mechanical parameters for metallisation stress sensor design using nanoindentation

Soare, S.; Bull, Steve; Oila, Adrian; O’Neill, Anthony; Wright, Nicolas G.; Horsfall, Alton B.; Santos, Jorge M.

doi:10.3139/146.101172

Cited by 10 publications

(24 citation statements)

References 7 publications

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“…consistently converge with the exponent 2 on h (e.g. [3]). There is thus never match with experimental results.…”

Section: Resultsmentioning

confidence: 99%

“…8), with the dimension of the penetration resistance k, opens an easy and simple way to obtain the physically sound hardness H phys (mN/µm 3/2 ), without iterations, only from the loading curve with the unbeatable penetration resistance k 1 (before the kink) by linear regression. The tip rounding initial effect is not part of the linear regression of the penetration resistance (but it plays a role for adjustments between different pyramids/cones [4,18] The results are exemplified in Table 1 from a paper [3] that published both experimental loading curve and finite element simulation loading curves far below of a phase change onset. One remarks considerable differences between H ISO (from unloading curve with excessive iterations of aluminum on silicon for fit with the standard) and H universal (invoking h 2 ) without correction.…”

Section: Hardness and Modulusmentioning

confidence: 93%

“…This found widespread belief in publications and textbooks, but experimental loading curves do not show such relation. Several iterative "excuses" for this inconsistency were proposed, and finite element (FE) simulations continue to converge with exponent 2 on h. Claims that these would reproduce experimental loading curves are incorrect [3,4], the published experimental curves analyze with exponent 3/2. In that situation ISO 14577 concentrated on the iterative analysis of the unloading curve with freely iterated exponent on h (between 1 and 3) for gaining values of indentation hardness H ISO and reduced elastic modulus E r-ISO .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Important Consequences of the Exponent 3/2 for Pyramidal/Conical Indentations-New Definitions of Physical Hardness and Modulus

Kaupp¹

2016

J Material Sci Eng

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The now physically founded exponent 3/2 that governs the relation of normal force to depth 3/2 in conical/pyramidal indentation is a physically founded (F N = k h 3/2 ). Strictly linear plots obtain non-iterated penetration resistance k (mN/ µm 3/2 ) as slope, initial effects (including tip rounding), adhesion energy, and phase transitions with their transformation energy and activation energy. The reason for the failing of the Sneddon theory, claiming wrong exponent 2 (as do ABAQUS or ANSYS finite element simulations) is their neglect of long-range effects by shearing. Previous undue trials to rationalize the non-occurrence of exponent 2 are polynomial fittings and "best or variable exponent" iterations for curve fittings that lose all unique information from the loading curve. Also ISO 14577 unloading hardness H ISO and reduced elastic modulus E r-ISO lack physical reality. They are redefined to physical dimensions as new indentation parameters H phys and E r-phys . For the first time physically sound indentation hardness H phys is obtained without iterations solely from loading curves. Also all mechanical indentation parameters relying on Sneddon's exponent 2 are unphysical. They require redefinition with new dimensions. This applies also to visco-elastic-plastic parameters in a recent NIST tutorial. The present ISO-standards create dilemma with physics. But the risk from using wrong mechanical parameters against physics is dangerous, subject to change.

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“…consistently converge with the exponent 2 on h (e.g. [3]). There is thus never match with experimental results.…”

Section: Resultsmentioning

confidence: 99%

Section: Hardness and Modulusmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Important Consequences of the Exponent 3/2 for Pyramidal/Conical Indentations-New Definitions of Physical Hardness and Modulus

Kaupp¹

2016

J Material Sci Eng

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“…When the direct calculation with A hc is changed for A projected , we obtain the absolute E r-direct =20.9 nN/nm 2 . The respective error factors 3.1 and 3.5 when compared with E r-iso-iterated =73 GPa [7] are enormous! They falsify convincingly these ISO iteration standards not only for this example.…”

Section: Flaws Of the Iso Indentation Modulusmentioning

confidence: 99%

“…The diversion between the two paths is enormous. By using the direct path we follow the defined underlying basis of [6] and obtain for the unloading curve of, for example, cubic aluminium [7] . When the direct calculation with A hc is changed for A projected , we obtain the absolute E r-direct =20.9 nN/nm 2 .…”

Section: Flaws Of the Iso Indentation Modulusmentioning

confidence: 99%

Dilemma between Physics and ISO Elastic Indentation Modulus

Kaupp¹

2017

J Material Sci Eng

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This paper challenges the ISO standard 14577 that determines the elastic indentation modulus by violating the first energy law, and omitting easily detected phase change onsets as well as initial surface effects under load. The double iteration for incorrect fitting indentation modulus to Hook's law Young's modulus of a standard with up to 11 free parameters must be cancelled and discontinued. The iterative evaluation of the elastic modulus E r-ISO can by far not be reproduced by iteration-free direct calculation of E r , when using the underlying formulas for S, h c , A hc , and . For cubic aluminium the divergence amounts to a factor of 3.5 or 3.1, respectively (both smaller for the non-iterated calculations). Every interpretation of indentation moduli as single unidirectional "Young's moduli" is false. They are mixtures from all directions and include shear moduli. The three different packing diagrams of body centered cubic -iron exemplify the mixture of three independent Young's moduli (and thus also three shear moduli) even in this simple but already anisotropic case. More linear moduli ensue in lower symmetry crystals as exemplified with -quartz. The first physical indentation modulus is deduced by removal of the physical errors of E r-ISO , or after indenter compliance correction E ISO . E phys does no longer violate the energy law. Five face-dependent elastic indentation moduli of -quartz at the obsolete E r-ISO level and two tensional Hook-law Young's moduli are compared with all of its six resonance ultrasound spectroscopy (RUS) evaluated Young's moduli, and with the bulk modulus. The dilemma between ISO and physics is particularly detrimental, as E ISO is used for the calculation of very frequently applied mechanical parameters. These propagate the errors into failure risks of falsely calculated materials with severe violation of the basic energy law and other physical laws for daily life. Difficulties with the urgent settlement by new ISO standards are discussed. First suggestions for the use of E phys , or S phys , or eventually measured bulk modulus K are made. This should be urgently evaluated and discussed.

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The exponent 3/2 at pyramidal nanoindentations

Kaupp

Naimi-Jamal

2010

Scanning

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The analysis of published loading curves reveals the exponent 3/2 to the depth for nanoindentations with sharp pyramidal or conical tips. This has geometric reasons, as it occurs independent on the bonding states and indentation mechanisms. Nevertheless, most mathematical deductions and finite element simulations of nanomechanical parameters in the literature continue using the experimentally not supported Hertzian exponent 2. Therefore, numerous published loading curves of various authors are plotted using the experimental exponent 3/2 to present unbiased proof for its generality with metals, oxides, semiconductors, biomaterials, polymers, and organics. Linearity is independent of equipment and valid for load controlled, or depth controlled, or continuous stiffness, or AFM force measurements. The linearity with exponent 3/2 often extends from the nano- into the microindentation ranges. The tip rounding and taper influence of the "geometrical similar" indenters are discussed. When kinks occur in such linear plots through the origin, these indicate change of the materials' mechanical properties under pressure by phase transition. These events are discussed for nanoindentations with respect to the known hydrostatic transformation pressures that are, of course, always higher than the necessary indentation mean pressure. Numerous Raman, as well as X-ray and electron diffraction results from the literature support the phase transitions that are now easily detected. Nanoporous materials first fill the pores upon indentation. Published loading curves exhibit more information than hitherto assumed.

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Obtaining mechanical parameters for metallisation stress sensor design using nanoindentation

Cited by 10 publications

References 7 publications

Important Consequences of the Exponent 3/2 for Pyramidal/Conical Indentations-New Definitions of Physical Hardness and Modulus

Important Consequences of the Exponent 3/2 for Pyramidal/Conical Indentations-New Definitions of Physical Hardness and Modulus

Dilemma between Physics and ISO Elastic Indentation Modulus

The exponent 3/2 at pyramidal nanoindentations

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