Oluschinski at 05:25, 15 December 2025

2025-12-15T05:25:09Z

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	\|- valign="top"		\|- valign="top"
	\|width="50px"\|'''Fig. 6''':		\|width="50px"\|'''Fig. 6''':
	\|width="600px"\|Schematic representation of the [[Ultrasonic Transmission Technique\|ultrasonic transmission technique]] with [[Ultrasonic Standard Sensors\|standard sensors]] (a) and [[Ultrasonic Angle Beam Sensors\|angle beam sensors]] (b) as well as the [[~~Puls~~-Echo Ultrasonic Technique\|pulse-echo technique]] (c)		\|width="600px"\|Schematic representation of the [[Ultrasonic Transmission Technique\|ultrasonic transmission technique]] with [[Ultrasonic Standard Sensors\|standard sensors]] (a) and [[Ultrasonic Angle Beam Sensors\|angle beam sensors]] (b) as well as the [[Pulse-Echo Ultrasonic Technique\|pulse-echo technique]] (c)
	\|}		\|}

Line 237:		Line 237:
	==See also==		==See also==

	* [[Elastic Modulus ~~–Eexamples~~ and Material Values\|Elastic modulus – Examples and material values]]		* [[Elastic Modulus – Examples and Material Values\|Elastic modulus – Examples and material values]]
	* [[Elastic Modulus – Ultrasonic Measurement\|Elastic modulus – Ultrasonic measurement]]		* [[Elastic Modulus – Ultrasonic Measurement\|Elastic modulus – Ultrasonic measurement]]
	* [[Energy Elasticity\|Energy elasticity]]		* [[Energy Elasticity\|Energy elasticity]]

Oluschinski: /* Ultrasound testing */

2025-12-01T10:01:43Z

Ultrasound testing

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	===~~[[Ultrasound Testing\|~~Ultrasound testing]]===		===Ultrasound testing===

	In the high-frequency range, the dynamic modulus of elasticity can also be determined using a dielectric measuring station, or the propagation of sound and ultrasonic waves can be used to determine the characteristic values [9, 10].		In the high-frequency range, the dynamic modulus of elasticity can also be determined using a dielectric measuring station, or the propagation of sound and ultrasonic waves (see also: [[Ultrasound Testing]]) can be used to determine the characteristic values [9, 10].

	Above the resonance frequency, the wavelength λ of the oscillating mechanical [[Stress\|stress]] becomes small in comparison to the test specimen dimensions. This makes it possible to use the characteristics of wave propagation in the material to determine the [[Viscoelastic Material Behaviour\|viscoelastic properties]]. The measurements are usually carried out using ultrasound (''f'' > 20 kHz) in the [[Pulse-Echo Ultrasonic Technique\|pulse-echo ultrasonic technique]] or [[Ultrasonic Transmission Technique\|ultrasonic transmission technique]] [1]. The [[Sound Velocity\|sound velocities]] ''c'' ('''Eq. 10''') and the sound absorption coefficient ''α'' ('''Eq. 11''') are determined from the acoustic path length ''d'' and the associated pulse transit time ''t'', as well as the amplitudes ''A''<sub>1</sub> and ''A''<sub>2</sub> at different path lengths ''d''<sub>1</sub> and ''d''<sub>2</sub>.		Above the resonance frequency, the wavelength λ of the oscillating mechanical [[Stress\|stress]] becomes small in comparison to the test specimen dimensions. This makes it possible to use the characteristics of wave propagation in the material to determine the [[Viscoelastic Material Behaviour\|viscoelastic properties]]. The measurements are usually carried out using ultrasound (''f'' > 20 kHz) in the [[Pulse-Echo Ultrasonic Technique\|pulse-echo ultrasonic technique]] or [[Ultrasonic Transmission Technique\|ultrasonic transmission technique]] [1]. The [[Sound Velocity\|sound velocities]] ''c'' ('''Eq. 10''') and the sound absorption coefficient ''α'' ('''Eq. 11''') are determined from the acoustic path length ''d'' and the associated pulse transit time ''t'', as well as the amplitudes ''A''<sub>1</sub> and ''A''<sub>2</sub> at different path lengths ''d''<sub>1</sub> and ''d''<sub>2</sub>.

Oluschinski: Created page with "{{Language_sel|LANG=ger|ARTIKEL=Elastizitätsmodul}} {{PSM_Infobox}} Elastic modulus FORCETOC ==Introduction== In addition to the Poisson's ratio, the modulus of elasticity (modulus ''E'') is also an important parameter for describing the energy-elastic properties (see: energy elasticity) of plastics. The short-term moduli ''E''_t..."

2025-12-01T08:39:00Z

Created page with "{{Language_sel|LANG=ger|ARTIKEL=Elastizitätsmodul}} {{PSM_Infobox}} Elastic modulus __FORCETOC__ ==Introduction== In addition to the Poisson's ratio, the modulus of elasticity (modulus ''E'') is also an important parameter for describing the energy-elastic properties (see: energy elasticity) of plastics. The short-term moduli ''E''t..."

New page

{{Language_sel|LANG=ger|ARTIKEL=Elastizitätsmodul}}
{{PSM_Infobox}}
Elastic modulus
__FORCETOC__

==Introduction==

In addition to the [[Poisson's Ratio|Poisson's ratio]], the modulus of elasticity (modulus ''E'') is also an important [[Material Parameter|parameter]] for describing the energy-elastic properties (see: [[Energy Elasticity|energy elasticity]]) of [[Plastics|plastics]]. The short-term moduli ''E''t, ''E''f and ''E''c determined in [[Quasi-static Test Methods|quasi-static tests]] such as [[Tensile Test|tensile]], [[Bend Test|bending]] or [[Compression Test|compression tests]] are suitable for quality assurance, [[Material & Werkstoff|material]] development and optimisation, as well as simple dimensioning tasks (see: [[Plastic Component|plastic component]]), but cannot be used for demanding structural applications. In this case, the creep modulus (see: [[Creep Behaviour – Determination|creep behaviour – determination]]) from long-term experiments must also be used, depending on the test temperature.

The structural cause of the [[Energy Elasticity|energy-elastic behaviour]] of plastics is the change (elongation, compression) in the average atomic distances and bond angles when subjected to mechanical [[Stress|stresses]]. The mechanical work performed in this process is stored in the form of potential energy (increase in internal energy) and is completely recovered when the [[Stress|stress]] is removed (1st law of thermodynamics). Due to its structural causes, energy-elastic behaviour is limited to the range of small deformations. The [[Deformation|deformation]] is completely reversible, whereby the relationship between stress and deformation can be linear or non-linear. The loading and unloading curve is identical in every case, which means that no hysteresis occurs. If a linear relationship between stress (force) and strain (see also: [[Deformation|deformation]]) is observed, then in the case of a [[Uniaxial Stress State|uniaxial]] tensile or compressive load, the relationship can be clearly described by [[HOOKE's Law|HOOKE's law]] ('''Eq. 1''') in analogy to a spring or proportionality constant ('''Fig. 1''').

[[File:Elastizitaetsmodul-1.JPG|500px]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px"|[[Deformation#Elastic deformation|Elastic deformation]] of the spring model and the solid body according to HOOKE
|}

[[Energy Elasticity|Energy elasticity]] dominates the behaviour of [[Polymer|polymer]] [[Material & Werkstoff|materials]], particularly in the case of small deformations and at low temperatures, as well as at high [[Deformation Rate|deformation rates]] (see also: [[Strain Rate Basics|strain rate basics]]), whereby classical energy elasticity theory contributes significantly to understanding the [[Deformation|deformation behaviour]] of plastics. In addition, it provides useful approximate solutions for the quantitative description of the stress–strain relationship (see also: [[Tensile Test True Stress–Strain Diagram|true stress–strain diagram]]) in this area, at least for uniaxial normal stress [1].

In testing practice, three methods are mainly used to determine the modulus of elasticity. These are [[Quasi-static Test Methods|quasi-static tests]] for [[Polymer Testing|polymer testing]], dynamic mechanical analysis and [[Ultrasound Testing|ultrasonic testing]], with short-term mechanical tests (see: [[Tensile Test|tensile test]]) being the most relevant in practice.

==Test methods for determining the modulus of elasticity==

===Quasi-static short-term tests===

To determine the modulus of elasticity ''E'', [[Tensile Test|tensile]], [[Bend Test|bending]] and [[Compression Test|compression tests]] are performed in quasi-static polymer testing using a [[Material Testing Machine|universal testing machine]]. In contrast to the testing of metallic materials (see also: [[Materials Testing|materials testing]]), where the modulus of elasticity (also known as Young's modulus) is determined as the tangent modulus at the origin of the stress–strain diagram, the secant modulus is determined in standard-compliant [[Polymer Testing|testing of plastics]]. The reason for this lies in the comparatively low elastic [[Deformation|deformation range]] of < 0.1 % elongation and in the [[Linear-viscoelastic Behaviour|linear-viscoelastic behaviour]], which is recorded up to approximately 0.3 %. The reversible strain range up to 0.3 %, although time-dependent, is followed by the range of non-linear viscoelasticity, in which the first irreversible [[Micro-damage Limit|micro-damage]] and deformations occur. For this reason, the strain limits in the three specified test methods [2–4] were specified as 0.05 and 0.25 %, and the corresponding stress values are determined in the test ('''Fig. 2'''). To avoid run-up effects in, for example, [[Tensile Test|tensile tests]], an offset of 0.05 % is set or a preload is specified that causes this strain value. The test, which is carried out at an [[Strain Rate Basics|elongation rate]] of approximately 1 %/min, is stopped above 0.3 % or is continued at a [[Test Speed|test speed]] of, for example, 50 mm/min as a [[Tensile Test|tensile]] test until the test specimen fails [6]. The elasticity moduli ''E''t, ''E''f or ''E''c are calculated uniformly according to '''Eq. (1)''', using the strain in the tensile test ''ε'', the [[Peripheral Fibre Strain|peripheral fibre strain]] in the [[Bend Test|bending test]] ''ε''f or the compression in the [[Compression Test|compression test]] ''ε''c as specified values.

[[File:Elastizitaetsmodul-2.JPG|500px]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px"|Determination of the tangent modulus for metals (a) and the secant modulus for plastics (b)
|}

{|
|-
|width="20px"|
|width="500px"|<math>E=\frac{\sigma_{2}-\sigma_{1}}{\epsilon_{2}-\epsilon_{1}}=\frac{\sigma_{2}-\sigma_{1}}{0,0025 - 0,0005}=\frac{\Delta\sigma}{0,002}</math>
|(1)
|}

If necessary, these tests can also be carried out in a temperature-controlled chamber, allowing the modulus of elasticity to be represented as a function of temperature.

===Dynamic-mechanical analysis (DMA)===

In dynamic-mechanical analysis or spectroscopy, the test specimen is subjected to periodically alternating, mostly sinusoidal stress. The advantage of this method when using a temperature control chamber (dynamic-mechanical thermal analysis – DMTA) is that the dynamic-mechanical characteristics are available as a function of temperature ('''Fig. 3'''). By varying the frequency, it is also possible to characterise the time dependence of the material behaviour. Dynamic mechanical analysis can be performed with free damped vibrations (pendulum vibrations) or in forced vibration and resonance mode. The types of [[Stress|stress]] torsion, bending and tension are commonly used. What all methods have in common is that the [[Deformation|deformation]] of the test [[Specimen|specimen]] is very small and should not exceed the [[Linear-viscoelastic Behaviour|linear-viscoelastic]] range. As a result of these small deformations, DMA or DMTA can be used to achieve high test frequencies with mechanical excitation up to 200 Hz in a temperature range from approx. –180 °C to 400 °C [1, 7].

[[File:Elastizitaetsmodul-3.JPG|300px]]
{|
|- valign="top"
|width="50px"|'''Fig. 3''':
|width="600px"|DMTA system Eplexor from NETSCH Instruments GmbH, Ahlen
|}

For [[Polymer Testing|polymer testing]] using [[Dynamic-mechanical Analysis (DMA) – Tensile Stress|DMA or DMTA under tensile stress]] [8], small hydraulic, pneumatic or electrodynamic testing machines and DMTA systems with additional equipment such as strain sensors and temperature control chambers ('''Fig. 3''') are primarily used to generate sinusoidal strains or stresses. The testing system then applies a constant sinusoidal strain or stress amplitude with a defined and constant frequency to the test specimen, whereby in plastics testing, the tensile threshold range is preferred due to the [[Specimen|specimen]] geometry. The amplitude of the stress or strain, as well as the mean stress or strain and the temperature, are kept at a constant level by means of PID control in order to compensate for [[Creep Plastics|creep]] or [[Relaxation Plastics|relaxation]] effects during the test. In the case of [[linear-viscoelastic Behaviour|linear-viscoelastic material behaviour]] and a normal stress state, the temporal changes in stress and [[Deformation|deformation]] in the steady state have the same frequency but different phase angles ('''Eq. (2)''' and '''(3)''') ('''Fig. 4'''), where ''δ'' is the phase angle, which can take values between 0 and π/2.

{|
|-
|width="20px"|
|width="500px"|<math>\epsilon(t)=\epsilon_{0}\cdot \sin (\omega t)</math>
|(2)
|}

{|
|-
|width="20px"|
|width="500px"|<math>\sigma(t)=\sigma_{0}\cdot \sin (\omega t - \delta)</math>
|(3)
|}

'''Eq. (4)''' applies to the relationship between the stress duration ''t'' and frequency ''f'' or angular frequency ''ω'':

{|
|-
|width="20px"|
|width="500px"|<math>t=\frac{1}{2\pi f}=\frac{1}{\omega}</math>
|(4)
|}

[[File:Elastic Modulus-4.JPG|500px]]
{|
|- valign="top"
|width="50px"|'''Fig. 4''':
|width="600px"|Schematic structure of the test system and temporal change in stress and strain during DMA using forced vibrations
|}

Due to the phase shift ''δ'' between stress ''σ'' and strain ''ε'', the modulus of elasticity is introduced as a complex parameter ''E*'' to describe the stress–strain relationship. The complex modulus can be viewed as a vector in the complex number plane ('''Fig. 5'''), whose direction is determined by the phase angle ''δ'' and whose magnitude is determined by the ratio of the amplitude values of stress and strain ('''Eq. 5'''):

{|
|-
|width="20px"|
|width="500px"|<math>\left | E^{*} \right |=\frac{\sigma_{0}}{\epsilon_{0}}</math>
|(5)
|}

[[File:Elastizitaetsmodul-5.JPG|300px]]
{|
|- valign="top"
|width="50px"|'''Fig. 5''':
|width="600px"|Description of the complex tensile modulus from the DMTA
|}

Using simple trigonometric relationships, a split into a real part ''E''' (storage module) and the imaginary part ''E'''' (loss module) can be made according to '''Eqs. (6)''' and '''(7)''', whereby the storage module is of particular interest from an engineering perspective.

{|
|-
|width="20px"|
|width="500px"|<math>E^{\prime}=E\text{*}\cdot\cos\delta=\frac{\sigma_{0}}{\epsilon_{0}}\cdot\cos\delta </math>
|(6)
|}

{|
|-
|width="20px"|
|width="500px"|<math>E^{\prime\prime}=E\text{*}\cdot\sin\delta=\frac{\sigma_{0}}{\epsilon_{0}}\cdot\sin\delta </math>
|(7)
|}

The ratio of loss and storage modules results in the loss factor tan ''δ'', which characterises the damping behaviour of the material ('''Eq. 8''').

{|
|-
|width="20px"|
|width="500px"|<math>\tan\delta=\frac{E^{\prime\prime}}{E^{\prime}} </math>
|(8)
|}

As a rule, the dynamic modulus of elasticity is slightly higher than the modulus of elasticity from the [Quasi-static Test Methods|quasi-static tests]] due to the oscillating stress. The forced vibration method is limited to frequencies below the resonance frequency of the test specimen. The measurement can be controlled by both strain and stress (see: [[Tensile Test Control|tensile test control]]), which allows the complex modulus ''E*'' and the complex test [[Specimen Compliance|specimen compliance]] ''C*'' to be determined.

Due to their wide range of applications (torsion, tension, bending and shear), forced vibration methods now play a dominant role in the [[Dynamic-mechanical Analysis – General Principles|dynamic- mechanical analysis]] of [[Polymer|polymer]] [[Material & Werkstoff|materials]].

An approximate determination of the modulus of elasticity is also possible using the torsion vibration test from the shear modulus ''G'' if the Poisson's ratio ''μ'' is known in the corresponding temperature interval ('''Eq. 9''').

{|
|-
|width="20px"|
|width="500px"|<math>E^{\prime}=2G^{\prime}\cdot(1+\mu)</math>
|(9)
|}

===[[Ultrasound Testing|Ultrasound testing]]===

In the high-frequency range, the dynamic modulus of elasticity can also be determined using a dielectric measuring station, or the propagation of sound and ultrasonic waves can be used to determine the characteristic values [9, 10].

Above the resonance frequency, the wavelength λ of the oscillating mechanical [[Stress|stress]] becomes small in comparison to the test specimen dimensions. This makes it possible to use the characteristics of wave propagation in the material to determine the [[Viscoelastic Material Behaviour|viscoelastic properties]]. The measurements are usually carried out using ultrasound (''f'' > 20 kHz) in the [[Pulse-Echo Ultrasonic Technique|pulse-echo ultrasonic technique]] or [[Ultrasonic Transmission Technique|ultrasonic transmission technique]] [1]. The [[Sound Velocity|sound velocities]] ''c'' ('''Eq. 10''') and the sound absorption coefficient ''α'' ('''Eq. 11''') are determined from the acoustic path length ''d'' and the associated pulse transit time ''t'', as well as the amplitudes ''A''1 and ''A''2 at different path lengths ''d''1 and ''d''2.

{|
|-
|width="20px"|
|width="500px"|<math>c=\frac{d}{t}</math>
|(10)
|}

{|
|-
|width="20px"|
|width="500px"|<math>\alpha=\frac{1}{d_{2}-d_{1}}\quad In\quad \frac{A_{1}}{A_{2}}</math>
|(11)
|}

Using longitudinal waves (''c''L, ''α''L) and transverse waves (''c''T, ''α''T), the longitudinal wave modulus ''L'' and the [[Shear Modulus|shear modulus]] ''G'' can be determined if the [[Density|density]] ''ρ'' of the material is known. With low attenuation (''α'' ''λ''/2π << 1), '''Eqs. (12)''' and '''(13)''' apply approximately.

{|
|-
|width="20px"|
|width="500px"|<math>L^{\prime}= \rho\cdot c_{L}^{2} \quad und\quad L^{\prime\prime}=\frac{2\rho\cdot\alpha_{L}\cdot c_{L}^{3}}{\omega}</math>
|(12)
|}

{|
|-
|width="20px"|
|width="500px"|<math>G^{\prime}= \rho\cdot c_{T}^{2}\quad und \quad G^{\prime\prime}=\frac{2\rho\cdot\alpha_{T}\cdot c_{T}^{3}}{\omega}</math>
|(13)
|}

The longitudinal wave and shear modulus can be used to calculate the modulus of elasticity ''E''' ('''Eq. 14''') in accordance with elasticity theory, which depends on the ratio of the propagation velocities of transverse and longitudinal waves.

{|
|-
|width="20px"|
|width="500px"|<math>E^{\prime}=\frac{(3L^{\prime}-4G^{\prime})\cdot(G^{\prime}-1)}{L^{\prime}}=4\rho\cdot c_{T}^{2}\left ( \frac{0,75-\left ( \frac{c_{T}}{c_{L}} \right )^{2}}{1-\left ( \frac{c_{T}}{c_{L}} \right )^{2}} \right )</math>
|(14)
|}

Ultrasonic measurements are usually performed at frequencies between 100 kHz and 100 MHz. The upper end of the frequency range is determined by the strong increase in damping. Working in this wide frequency range requires the use of different vibration sensors. Relatively large frequency ranges can be recorded after broadband excitation using Fourier or wavelet analysis (see: [[Frequency Analysis|frequency analysis]]).

A relatively simple method for determining the modulus of elasticity using ultrasound is to use plate-shaped test specimens of known thickness ''d'' and density ''ρ'' ('''Fig. 6''').

[[File:Elastic Modulus-6.JPG|500px]]
{|
|- valign="top"
|width="50px"|'''Fig. 6''':
|width="600px"|Schematic representation of the [[Ultrasonic Transmission Technique|ultrasonic transmission technique]] with [[Ultrasonic Standard Sensors|standard sensors]] (a) and [[Ultrasonic Angle Beam Sensors|angle beam sensors]] (b) as well as the [[Puls-Echo Ultrasonic Technique|pulse-echo technique]] (c)
|}

When using [[Ultrasonic Standard Sensors|standard sensors]] ('''Figs. 6a''' and '''c'''), longitudinal waves are used for measurement. It should be noted that with the [[Pulse-Echo Ultrasonic Technique|pulse-echo technique]], the transit time of the ultrasound is twice as long as with the [[Ultrasonic Transmission Technique|transmission method]]. The transit time Δ''t'' can then be measured from the [[A-Scan Technique|A-scan]] in direct coupling or [[Ultrasonic Immersion Bath Technique|immersion bath technique]] with known thickness and angle of incidence ''γ'' according to '''Eq. (15)''' (transmission) or '''(16)''' (pulse-echo technique) and the longitudinal wave velocity ''c''L can be calculated. The traverse wave velocity ''c''T is determined using [[Ultrasonic Angle Beam Sensors|angle beam sensors]] according to '''Eq. (17)'''.

{|
|-
|width="20px"|
|width="500px"|<math>c_{L}=\frac{d}{\Delta t}</math>
|(15)
|}

{|
|-
|width="20px"|
|width="500px"|<math>c_{L}=\frac{2d}{\Delta t}</math>
|(16)
|}

{|
|-
|width="20px"|
|width="500px"|<math>c_{L}=\frac{2d}{\Delta t \cdot \cos \gamma}</math>
|(17)
|}

Provided that the [[Poisson's Ratio|Poisson's ratio]] ''µ'' for the test temperature ''T'' is known, the modulus of elasticity ''E'' can then be calculated using '''Eq. (18)''' and the shear modulus ''G'' using '''Eq. (19)''', bearing in mind that these characteristic values are frequency-dependent.

{|
|-
|width="20px"|
|width="500px"|<math>E=c_{L}^{2}\cdot\rho\frac{(1+\mu)\cdot(1-2\mu)}{(1-\mu)}</math>
|(18)
|}

{|
|-
|width="20px"|
|width="500px"|<math>G=c_{T}^{2}\cdot\rho</math>
|(19)
|}

==See also==

* [[Elastic Modulus –Eexamples and Material Values|Elastic modulus – Examples and material values]]
* [[Elastic Modulus – Ultrasonic Measurement|Elastic modulus – Ultrasonic measurement]]
* [[Energy Elasticity|Energy elasticity]]
* [[Shear Modulus|Shear modulus]]
* [[HOOKE´s Law|HOOKE´s law]]

'''References'''

{|
|-valign="top"
|[1]
|Lüpke, T.: Fundamental Principles of Mechanical Behavior. In: [[Grellmann, Wolfgang|Grellmann, W.]], [[Seidler, Sabine|Seidler, S.]] (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition, pp. 75–77 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-8807-5; see [[AMK-Büchersammlung|AMK-Library]] under A 22)
|-valign="top"
|[2]
|ISO 527-1 (2019-04): Plastics – Determination of Tensile Properties – Part 1: General Principles
|-valign="top"
|[3]
|ISO 527-2 (2025-06): Plastics – Determination of Tensile Properties – Part 2: Test Conditions for Moulding and Extrusion Plastics
|-valign="top"
|[4]
|ISO 178 (2019-08): Plastics – Determination of Flexural Properties
|-valign="top"
|[5]
|ISO 604 (2002-03): Plastics – Determination of Compressive Properties
|-valign="top"
|[6]
|[[Bierögel, Christian|Bierögel, C.]]: Bend Test on Polymers. In: [https://www.researchgate.net/profile/Wolfgang-Grellmann Grellmann, W.], [https://www.researchgate.net/profile/Sabine-Seidler Seidler, S.]] (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition, pp. 133–143 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-807-5; see [[AMK-Büchersammlung|AMK-Library]] under A 22)
|-valign="top"
|[7]
|ISO 6721-1 (2019-04): Plastics – Determination of Dynamic Mechanical Properties – Part 1: General Principles
|-valign="top"
|[8]
|ISO 6721-4 (2019-05): Plastics – Determination of Dynamic Mechanical Properties – Part 4: Tensile Vibration – Non-resonance Method
|-valign="top"
|[9]
|ISO 6721-8 (2019-04): Plastics – Determination of Dynamic Mechanical Properties – Part 8: Longitudinal and Shear Vibration – Wave-propagation Method
|-valign="top"
|[10]
|ISO 6721-9 (2019-04): Plastics – Determination Dynamic Mechanical Properties – Part 9: Tensile Vibration – Sonic-pulse Propagation Method
|-valign="top"
|[11]
|Matthies, K. u. a.: Dickenmessung mit Ultraschall. Deutscher Verlag für Schweisstechnik (DVS), Berlin, 2nd Edition (1998) (ISBN 3-87155-940-7; see [[AMK-Büchersammlung|AMK-Library]] under M 44)
|}

[[Category:Deformation]]
[[Category:Tensile Test]]

Elastic Modulus - Revision history

Oluschinski at 05:25, 15 December 2025

Oluschinski: /* Ultrasound testing */