Oluschinski at 07:44, 12 January 2026

2026-01-12T07:44:59Z

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			{{Language_sel\|LANG=ger\|ARTIKEL=Eindringmodul}}
	{{PSM_Infobox}}		{{PSM_Infobox}}
	<span style="font-size:1.2em;font-weight:bold;">Indentation modulus</span>		<span style="font-size:1.2em;font-weight:bold;">Indentation modulus</span>

Oluschinski at 06:36, 15 December 2025

2025-12-15T06:36:14Z

← Older revision		Revision as of 08:36, 15 December 2025
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	\|Oliver, W. C., Pharr, G. M.: An Improved Technique for Determining Hardness and Elastic Modulus using Load and Displacement Sensing Indentation. J. of Materials Research 7 (1992) 1564–1583		\|Oliver, W. C., Pharr, G. M.: An Improved Technique for Determining Hardness and Elastic Modulus using Load and Displacement Sensing Indentation. J. of Materials Research 7 (1992) 1564–1583
	\|}		\|}



	[[category: Hardness]]		[[category: Hardness]]
	[[category: Surface Testing Technology]]		[[category: Surface Testing Technology]]

Oluschinski: Created page with "{{PSM_Infobox}} Indentation modulus FORCETOC ==Definition of the indentation modulus== The indentation modulus ''E''_IT (in MPa) is determined in the micro load range of the hardness test using a method described in detail in ISO 14577 [1] from the initial rise of the unloading curve of the load (''F'')–indentation depth (''h'') diagram (see: Instrumented Hardness Testing – Method..."

2025-12-02T09:40:24Z

Created page with "{{PSM_Infobox}} Indentation modulus __FORCETOC__ ==Definition of the indentation modulus== The indentation modulus ''E''IT (in MPa) is determined in the micro load range of the hardness test using a method described in detail in ISO 14577 [1] from the initial rise of the unloading curve of the load (''F'')–indentation depth (''h'') diagram (see: Instrumented Hardness Testing – Method..."

New page

{{PSM_Infobox}}
Indentation modulus
__FORCETOC__

==Definition of the indentation modulus==

The indentation modulus ''E''IT (in MPa) is determined in the micro load range of the [[Hardness | hardness test]] using a method described in detail in ISO 14577 [1] from the initial rise of the unloading curve of the load (''F'')–indentation depth (''h'') diagram (see: [[Instrumented Hardness Testing – Method & Material Parameters | instrumented hardness testing – method & material parameters]]) at the maximum load ''F''max (d''F''/d''h''|''F''max). In the nanolast range of hardness testing, the method according to Oliver and Pharr is usually used [2]. According to ISO 14577, it is taken into account that the mechanical resistances of the test specimen and diamond [[Indenter|indenter]] are connected in parallel (see '''Figure''' and Eq. 1)

[[file:Indentation Modulus_Figure.jpg]]

{|
|-
|width="20px"|
|width="650px" | <math>\frac {1} {E_{G}} = \frac {1\,-\,\nu^2}{E_{IT}}\,+\, \frac {1-\nu^2_D} {E_{D}}</math>
|(1)
|}

This results in ''E''IT:
{|
|-
|width="20px"|
|width="650px" | <math> E_{IT} = \frac{1-\nu^2}{\frac {1}{E_G}\,-\,\frac{1-\nu^2_D}{E_D}}</math>
|(2)
|}

from which the following expression can be derived using the relationships described in detail in ISO 14577:

{|
|-
|width="20px"|
|width="650px" | <math> E_{IT} = \frac {1-\nu^2} {0,5 \sqrt {\frac {24,5} {\pi}} \cdot \left( \frac {dh} {dF} \right )_{F_{max}} \cdot \left( 4h_t-3F_{max} \left(\frac {dh} {dF} \right)_{F_{max}} \right)-8,73 \cdot 10^{-13} Pa^{-1}}
</math>
|(3)
|}

The [[Poisson's Ratio | Poisson's ratio]] required to calculate ''E''IT is known for most [[Thermoplastic Material | materials]] and is relatively independent of temperature. The value 8.73 x 10-13 Pa-1 is the effective compliance of diamond.

==Application limits==

When using the indentation modulus ''E''IT, it is important to note that although ''E''IT is fundamentally equivalent to a [[Elastic Modulus | modulus of elasticity]], it only describes the [[Stiffness|stiffness]] behaviour very locally and under [[Multiaxial Stress State|triaxial loading]]. This results in a difference in value to the [[Material Value | characteristic values]] of the [[Elastic Modulus | modulus of elasticity]], which were determined using conventional [[Polymer Testing | plastic testing]] methods, such as the [[Uniaxial Stress State|uniaxial]] [[Tensile Test | tensile]] or [[Compression Test | compression test]] or the [[Bend Test#The three-point bending test method|three-]] or [[Bend Test#The four-point bending test method|four-point bending test]]. The indentation modulus can therefore not be used for dimensioning purposes.

==See also==

*[[Elastic Modulus|Elastic modulus]]
*[[Instrumented Hardness Testing – Method & Material Parameters|Instrumented hardness testing – method & material parameters]]
*[[Vickers Hardness|vickers hardness]]
*[[Ultrasound – Elastic Parameters|Ultrasound – elastic parameters]]
*[[Indentation Fracture Mechanics|Indentation fracture mechanics]]

'''References'''

{|
|-valign="top"
|[1]
|ISO 14577: Metallic Materials – Instrumented Indentation Test for Hardness and Materials Parameters
* Part 1 (2024-08): Test Method (Draft)
* Part 2 (2024-08): Verification and Calibration of Testing Machines (Draft)
* Part 3 (2024-07): Calibration of Reference Blocks (Draft)
* Part 4 (2016-11): Test Method for Metallic and Non-metallic Coatings
* Part 5 (2022-10): Linear Elastic Dynamic Instrumented Indentation Testing (DIIT)
* Part 6 (2025-11): Instrumented Indentation Test at Elevated Temperature
|-valign="top"
|[2]
|Oliver, W. C., Pharr, G. M.: An Improved Technique for Determining Hardness and Elastic Modulus using Load and Displacement Sensing Indentation. J. of Materials Research 7 (1992) 1564–1583
|}

[[category: Hardness]]
[[category: Surface Testing Technology]]

Indentation Modulus - Revision history

Oluschinski at 07:44, 12 January 2026

Oluschinski at 06:36, 15 December 2025