ISO/DIS 17561:2025(en)

ISO/TC 206

Secretariat: JISC

Date: 2025-10-31

Fine ceramics (advanced ceramics, advanced technical ceramics) — Test method for dynamic elastic moduli of monolithic ceramics at room temperature by sonic resonance and Impulse Excitation Technique (IET)

© ISO 2025

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Contents

Foreword iv

Introduction v

1 Scope 1

2 Normative references 1

3 Terms and definitions 1

4 Method A : Sonic Resonance 3

4.1 Principle 3

4.2 Apparatus 3

4.3 Test pieces 7

4.4 Test procedure 8

4.5 Calculations 10

4.6 Measurement uncertainty 11

5 Method B: Impulse excitation method 12

5.1 Principle 12

5.2 Apparatus 12

5.3 Test pieces 13

5.4 Procedure 14

5.5 Calculations 16

5.6 Measurement uncertainty 17

6 Report 17

6.1 General 17

6.2 Method A 17

6.3 Method B 18

Annex A (informative) Impact excitation method applied to disc test pieces 19

Annex B (informative) Round-robin validation of test methods 26

Bibliography 28

Foreword

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This document was prepared by Technical Committee ISO/TC 206, Fine ceramics.

This third edition cancels and replaces the second edition (ISO 17561:2016), which has been technically revised.

The main changes are as follows:

— addition of Method B – Impulse Excitation Technique

— revised equation (3) and (8) for the calculation of the dynamic shear modulus of a rectangular prism

— addition of informative Annex A : extension of the method B to disc shape test pieces

— addition of informative Annex B : results of a European round-robin comparing the merits of four methods among which the two test methods described in this document

Any feedback or questions on this document should be directed to the user’s national standards body. A complete listing of these bodies can be found at www.iso.org/members.html.

Introduction

Fine ceramics (advanced ceramics, advanced technical ceramics) — Test methods for dynamic elastic moduli of monolithic ceramics at room temperature by sonic resonance and Impulse Excitation Technique (IET)

This document describes test methods for determining the dynamic elastic moduli, specifically Young’s modulus, shear modulus and Poisson’s ratio, of fine ceramics at room temperature. This standard prescribes two alternative methods :

Both test methods assume the use of test pieces of homogeneous, isotropic and linear elastic materials^[3]

NOTE 1 Not all ceramic materials are equally and linearly elastic in tension and compression, such as some porous materials, and some piezoelectric materials.

NOTE 2 At high porosity levels these methods may become inappropriate.

NOTE 3 The maximum grain size (see ISO13383-1), excluding deliberately added whiskers, should be less than 10 % of the minimum dimension of the test piece.

NOTE 4 The merits of the two methods described in the present document have been addressed in a European round-robin comparing four methods for the determination of the elastic moduli of monolithic ceramics at room temperature. The results of this exercise are provided in the informative Annex B (see also reference [3]).

The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.

ISO 3611, Geometrical product specifications (GPS) — Dimensional measuring equipment — Design and metrological characteristics of micrometers for external measurements

ISO 13383‑1, Fine ceramics (advanced ceramics, advanced technical ceramics) — Microstructural characterization — Part 1: Determination of grain size and size distribution

ISO 13385‑1, Geometrical product specifications (GPS) — Dimensional measuring equipment — Part 1: Design and metrological characteristics of callipers

ISO/IEC 17025, General requirements for the competence of testing and calibration laboratories

For the purposes of this document, the following terms and definitions apply.

3.1

dynamic elastic moduli

elastic moduli determined non-quasistatically, i.e. under quasi-adiabatic conditions, such as in the sonic resonance and impulse excitation methods

3.2

Young’s modulus

E

stress required in a material to produce unit strain in uniaxial extension or compression

where

E is Young’s modulus in pascals (Pa);

σ is the tension or compression stress in pascals (Pa);

ε is the tension or compression strain.

3.3

shear modulus

G

shear stress required in a material to produce unit angular distortion

where

G is the shear modulus in pascals (Pa);

τ is the shear or torsional stress in pascals (Pa);

γ is the shear or torsional strain.

3.4

Poisson's ratio

ν

ratio of transverse strain to the corresponding axial strain resulting from uniformly distributed axial stress below the proportional limit of the material

Note 1 to entry: In isotropic materials, Young’s modulus (E), shear modulus (G) and Poisson's ratio (ν) are related by the following formula:

3.5

flexural vibration

vibration in a flexural mode

vibration apparent when the oscillation in a slender beam is in plane normal to the length dimension

3.6

torsional vibration

vibration in a torsional mode

vibration apparent when the oscillation in each cross-section plane of a slender bar is such that the plane twists around the length dimension axis

3.7

resonance

state if, when a slender bar driven into one of the above modes of vibration, the imposed frequency is such that the resultant displacements for a given amount of driving force are at a maximum

Note 1 to entry: The resonant frequencies are natural vibration frequencies which are determined by the elastic modulus, mass and dimensions of the test piece.

3.8

fundamental frequency

lowest frequency of a periodic waveform

3.9

nodes

locations in a vibrating shape where the displacements are zero for a given frequency of vibration

Note 1 to entry: For the fundamental flexural resonance in a slender beam, the nodes are located at 0,224 L from each end, where L is the length of the bar.

This test method measures the flexural or torsional frequencies of test specimens of a slender rectangular prism or cylindrical rod by exciting them at continuously variable frequencies. Mechanical excitation of the specimens is provided through the use of a transducer that transforms a cyclic electrical signal into a cyclic mechanical force on the test piece. A second transducer senses the resulting mechanical vibrations of the test piece and transforms them into an electrical signal. The amplitude and the frequency of the signal are measured by an oscilloscope or other means to detect resonance. The peak response is obtained at the resonant frequency. The fundamental resonant frequencies, dimensions and mass of the specimen are used to calculate the dynamic elastic moduli. The Young’s modulus is determined from the flexural resonance frequency, and the shear modulus is determined from the torsional resonance frequency, together with the test piece dimensions and mass. Poisson's ratio is determined from the Young’s modulus and the shear modulus.

4.3.1 General

There are various techniques that may be used to determine the resonant frequency of the test piece. The test piece may be excited by direct mechanical contact of a vibrator, or it may be suspended by a wire from a vibrator. It may be driven electromagnetically by attaching thin foils of magnetic material to one surface, or electrostatically by attaching an electrode to, or painting a conducting film of metal or graphite on, one surface.

One example of the test apparatus is shown in Figure 1. The driving circuit consists of an oscillator, an amplifier, a driver and a frequency counter. The detecting circuit consists of a detector, an amplifier and an oscilloscope. Figure 1 shows the suspension style of the apparatus. The direct contact support style of the test apparatus, shown in Figure 2, is also possible. It consists of a variable-frequency audio oscillator, used to generate a sinusoidal voltage, and a power amplifier and suitable transducer to convert the electrical signal to a mechanical driving vibration. A frequency meter (preferably digital) monitors the audio oscillator output to provide accurate frequency determination. A suitable suspension coupling system supports the test piece. A transducer detector acts to detect mechanical vibration in the specimen and to convert it into an electrical signal which is passed through an amplifier and displayed on an indicating meter. The meter may be a voltmeter, a microammeter or an oscilloscope. An oscilloscope is recommended because it enables the operator to positively identify resonances, including higher order harmonics, by Lissajous figure analysis, which is a superposition of two perpendicular harmonics. If a Lissajous figure is desired, the output of the oscillator is also coupled to the horizontal plates of the oscilloscope.

Key

1 frequency counter

2 oscillator

3 amplifier

4 driver

5 oscilloscope

6 detector

7 suspending string

Figure 1 — Example of the test apparatus and the suspension for fundamental flexural resonance

Key

1 driving

2 detecting

3 flexural

Figure 2 — Example of the direct contact support of the test piece for fundamental flexural resonance

4.2.2 Oscillator

The oscillator shall be able to vary the frequency from 100 Hz to at least 30 kHz, with a frequency resolution of 1 Hz and a maximum frequency drift of 1 Hz/min.

4.2.3 Amplifier

The audio amplifier shall have a power output sufficient to ensure that the type of transducer used can excite any specimen, the mass of which falls within a specified range. A power amplifier in the detector circuit shall be impedance-matched with the type of detector transducer selected and shall serve as a prescope amplifier.

4.2.4 Driver

The driver shall be able to convert electrical vibration to mechanical vibration. The frequency response of the driver transducer across the frequency range of interest shall have at least a 6,5 kHz bandwidth before −3 dB power loss occurs.

NOTE For flexibility in testing, the bandwidth can, with advantage, be at least as large as the frequency range given in Table 1.

4.2.5 Detector

The detector shall generate a voltage proportional to the amplitude, velocity or acceleration of the mechanical vibration of the specimen. The frequency response of the detector across the frequency range of interest shall have at least a 6,5 kHz bandwidth before a −3 dB power loss occurs.

NOTE For flexibility in testing, the bandwidth can, with advantage, be at least as large as the frequency range given in Table 1.

Table 1 — Examples of the test piece size and the calculated resonant frequencies

The frequency counter, preferably digital, shall be able to measure frequencies to within ±1 Hz.

Any method of specimen support that permits the free vibration of the test piece with no significant effect on the vibration frequencies shall be used. Test pieces are commonly supported either by suspension from threads or wires or on direct contact supports. If the test piece is to be supported from beneath, the support shall be made of rubber, cork or similar material, and shall have a minimum contact area with the test piece. If the test piece is suspended from the driving and detecting transducers, fine thread or metal wires shall be used. The vibrating mass of the suspension system shall be less than 0,1 % of the mass of the test piece. For the electromagnetic or electrostatic method, the mass of any magnetic foil or electrode attached to the test piece shall be negligible compared with the mass of the test piece.

NOTE For the electrostatic method it may be necessary to make the support electrically conducting.

A micrometer with a resolution of 0,002 mm or 0,1 % of the specimen, in accordance with ISO 3611, shall be used to measure the thickness, width and diameter of the test piece. Alternative dimension measuring instruments that have a resolution of 0,002 mm or finer may be used.

A vernier calliper with a resolution of 0,05 mm or 0,1 % of the specimen, in accordance with ISO 13385-1, shall be used to measure the length of the test piece. Alternative dimension measuring instruments that have a resolution of 0,05 mm or finer may be used.

A balance with a resolution of 1 mg or 0,1 % of the specimen or finer, shall be used to measure the weight of the test piece.

This test method is not satisfactory for test pieces that have major discontinuities, such as large cracks (surface or internal) or internal voids.

The test piece shall be a rectangular prism in accordance with 4.3.2.1 and 4.3.3.1, or a circular cross section rod in accordance with 4.3.2.2 and 4.3.3.2.

The maximum grain size (see ISO13383-1), excluding deliberately added whiskers, shall be less than 10 % of the minimum dimension of the test piece.

The surface of the test piece shall be smooth and flat. The surface shall be finished using a fine grind (400 grit or finer). The machining procedure shall not affect the test results.

The edges of the specimen shall not be chamfered. However, if the chipping of the specimen from the edges affects the results, the edges may be chamfered, but the amount of the chamfering shall be as small as possible.

NOTE ASTM C1259, Annex A2^[1] describes how to correct the calculation of Young’s modulus for edge chamfers or radii in rectangular beams.

For the suspension method, the mass of the specimen is, with advantage, at least 5 g in order to assist keeping a suspension system straight.

Rectangular prism

The test piece shall have a length (L) greater than 40 mm and a ratio of length to thickness (t) greater than 10 and preferably greater than 20. The ratio of length to width (b) shall be greater than or equal to 10. The dimensions of the test piece shall be such as to have a fundamental flexural resonant frequency in the range 100 Hz to 20 kHz.

NOTE 1 For convenience, a flexural test piece as defined in ISO 14704^[2] can be used, provided that the ends of the bar are machined square and parallel, subject to the allowable frequency range above.

NOTE 2 If the moduli of the test material are high (E > 200 GPa), or when the available oscillator power is marginal, it is recommended that L/t >> 10 and that 10 > b/t > 2,5. It is also recommended that b/t is > 1,1 or < 0,9 to avoid confusion of different vibration modes.

The parallelism of the upper and lower surfaces perpendicular to the direction of flexural vibration shall be better than t/100, of the sides parallel to the direction of vibration, better than b/100, and of the ends of the test piece, better than L/200.

Cylindrical rod

The test piece shall have a length (L) greater than 40 mm and a ratio of length to diameter (d) greater than 10 and preferably greater than 20.

The diameter of the test piece shall be constant to within d/100 and the ends shall be flat and parallel to better than L/200

Rectangular prism

The test piece shall have a length (L) greater than 40 mm and a ratio of length to thickness (t) greater than 10, and preferably greater than 20. The ratio of width (b) to thickness (t) shall be in the range of 1,5 to 10 (5 is recommended).

The parallelism of the upper and lower surfaces perpendicular to the direction of flexural vibration shall be better than t/100, of the sides parallel to the direction of vibration, better than b/100, and of the ends of the test piece better than L/200.

Cylindrical rod

The test piece shall have a length (L) greater than 40 mm and a ratio of length to diameter (d) greater than 10 and preferably greater than 20.

The diameter of the test piece shall be constant to within d/100 and the ends shall be flat and parallel to better than L/200

The minimum number of test pieces prepared shall be three.

Dry the test pieces at 110 °C ± 10 °C until the mass is constant and cool in the desiccator.

Weigh each test piece to the nearest 1 mg or 0,1 % (whichever is greater). Measure the cross-sectional dimensions of each test piece (i.e. the thickness and the width, or the diameter) at three positions along its length to the nearest 0,002 mm or 0,1 % (whichever is greater) using the micrometer (4.2.8) and calculate the mean values. Measure the length with the vernier calliper (4.2.9) to the nearest 0,05 mm or 0,1 % (whichever is greater).

Position each test piece in turn properly. If the fundamental mode of the flexural resonance is measured, the vibration nodes appear at a distance of 0,224 of the total length from each end. If the specimen is suspended by threads or wires that will be used to drive and detect vibration, position the threads outside the nodal points, as shown in Figure 1 (distance of 0,2 of the length from each end is recommended). If the specimen is to be supported from below, position two supports at the nodal points, as shown in Figure 2. If the fundamental mode of the torsional resonance is measured, the vibration nodes appear as shown in Figure 3. If the specimen is supported from below, position one support at the centre of the specimen, as shown in Figure 3. If the specimen is suspended by threads, position the supports at diagonally opposed corners of the specimen, as shown in Figure 4. The suspending devices shall permit the free vibration of the test piece.

Cotton thread is recommended for suspending the specimen. Cork or rubber is recommended for supporting the specimen.

It is recommended that external noise is excluded as far as is practical to avoid extraneous excitations of the test piece. For very small test pieces, the use of a vacuum envelope for the apparatus is recommended.

Key

1 driving

2 detecting

3 nodal

Figure 3 — Nodes and direct contact support on the fundamental torsional resonance

Key

1 driving

2 detecting

Figure 4 — Suspension for the fundamental torsional resonance

Activate the equipment so that the power adequate to excite the specimen is delivered to the driving transducer. Set the gain of the detector circuit high enough to detect vibration in the specimen and to display it on the oscilloscope screen with sufficient amplitude to accurately measure the frequency at which the signal amplitude is maximized. Adjust the oscilloscope so that a sharply defined horizontal baseline exists when the test piece is not excited. Scan frequencies with the audio oscillator until test piece resonance (flexural or torsional) is indicated by a sinusoidal pattern of maximum amplitude on the oscilloscope or by a single closed loop Lissajous pattern. It is recommended that the frequency scan starts at a low frequency and then increases.

Record the fundamental mode resonance frequency to an accuracy of better than 1 Hz or 0,1 % whichever is the greater. Repeat this at least five times to ensure repeatability of result.

To verify that the frequency is fundamental and not an overtone, either the node/antinode locations or one or more overtones should be identified. If a determination of the shear modulus is made, offset the coupling to the transducers so that the torsional mode of vibration may be induced and detected (see Figure 3 and Figure 4).

Currently, no certified reference artefacts for checking this measurement are available. Measurement system calibration for frequency should be undertaken using a suitable traceably certified frequency source. Laboratories should retain an identified test-piece for intermittent system repeatability checks, and for staff training.

NOTE The proper identification of the fundamental flexural mode is important as spurious frequencies inherent in the system may interfere, especially when greater excitation power and detection sensitivity are required for work with a specimen that has a poor response. One method of locating the nodes on the test piece is to move the detector along the length of the test piece; a node is indicated when the output amplitude goes to zero. An anti-node is indicated when the output amplitude reaches a local maximum. Another node location method (used often with string suspensions) is to lay a thin rod across the test piece at a presumed node or anti-node location. If the output amplitude is not affected, then the rod is on a node; if the output amplitude goes to zero, then the location is an anti-node. It is also possible to locate the nodes by spreading fine, free-flowing powder on the top surface of the test piece and observe its alignment at the nodal points. When several resonant flexural frequencies have been identified, the lowest frequency can be verified as the fundamental if the numerical ratios of the first three overtone frequencies to the lowest frequency are: 2,7, 5,4 and 8,9. Note that these ratios are for a Bernoulli-Euler (simple) beam under ideal conditions. Typically, the ratios will be slightly lower. A further possibility is localizing the nodes on the test piece by means of laser vibrometer.

4.5.1.1 For a rectangular prism, calculate the dynamic Young’s modulus using equation (1) ^[4]

(1)

where

E is the dynamic Young’s modulus in pascals (Pa);

m is the mass of the specimen in kilograms (kg);

f_f is the fundamental flexural resonant frequency in hertz (Hz);

b is the width of the specimen in metres (m);

L is the length of the specimen in metres (m);

t is the thickness of the specimen in metres (m).

4.5.1.2 For a rod of circular cross section, calculate the dynamic Young’s modulus using equation (2) ^[4].

(2)

where d is the diameter of the specimen in metres (m).

Equations (1) and (2) are considered accurate to within 0,2 % for beams of the specified geometry in the present document. Extended versions of this equation are available, and their use is essential for short aspect ratio test pieces. Such equations may be found in ASTM C1259^[1] and may be implemented in commercial calculation software.

4.5.2.1 For a rectangular prism, calculate the dynamic shear modulus using equation (3) ^[5]

(3)

where

NOTE The above equation for the correction factor R is accurate to within ~0,2 % for b / L ≤ 0,3 and b / t ≤ 10 in the fundamental mode of torsional vibration, otherwise the errors are estimated to be ≤1 %^[1].

4.5.2.2 For a rod of circular cross section, calculate the dynamic shear modulus using equation (4) ^[5]

(4)

Calculate the dynamic Poisson's ratio, ν, using equation (5)

(5)

The uncertainty of this method is considered to be governed principally by the dimensional regularity of the test piece (parallelism of faces) and the accuracy with which its dimensions, particularly the thickness in the flexural vibration mode, are measured. Adherence to the requirements of the present document usually enables an accuracy of typically ±1 % in Young’s modulus, ±2 % in shear modulus, and ±0,05 in Poisson’s ratio derived from E and G to be achieved.

The presence of directional microstructural texture in the test-piece may produce anisotropic elastic properties, the characterisation of which is outside the scope of this standard. In such a case, it may be found that the calculated value of Poisson’s ratio is outside the normal physical range of 0,1 to 0,35. If anisotropy is potentially present, the shear modulus and Poisson’s ratio values should be described as ‘apparent’ or ‘invalid’ in the test report as a caveat. The Young’s modulus value remans correct for the longitudinal direction in the test-piece.

A slender rectangular prism or cylindrical rod is supported at its nodes for the fundamental frequency of flexural or torsional vibration and is struck a light blow. The natural vibration is detected by a microphone or other transducer and the value of the fundamental natural frequency is determined by a frequency analyser. The Young’s modulus is calculated from the fundamental natural flexural frequency, and the shear modulus is determined from the fundamental natural torsional frequency, together with the test piece dimensions and mass. Poisson's ratio is determined from the Young’s modulus and the shear modulus.

A method appropriate for disc test pieces is given in Annex A.

5.2.1 General

This test is normally undertaken using proprietary apparatus designed for directly determining the dominant fundamental frequency of the test piece.

5.2.2 Transducer

A transducer connected to an amplifier and a frequency analyser for sensing the frequency of vibration. The accuracy of the frequency analyser shall be checked using a reference frequency source or other suitable method.

5.2.3 Micrometer

A micrometer with a resolution of 0,002 mm or 0,1 % of the specimen, in accordance with ISO 3611, shall be used to measure the thickness, width and diameter of the test piece. Alternative dimension measuring instruments that have a resolution of 0,002 mm or finer may be used.

5.2.4 Vernier calliper

A vernier calliper with a resolution of 0,05 mm or 0,1 % of the specimen, in accordance with ISO 13385-1, shall be used to measure the length of the test piece. Alternative dimension measuring instruments that have a resolution of 0,05 mm or finer may be used.

5.2.5 Balance

A balance with a resolution of 1 mg or 0,1 % of the specimen or finer, shall be used to measure the weight of the test piece.

5.2.6 Oven for drying test pieces at 110 °C ± 10 °C, or other suitable device.

5.2.7 Desiccator for storage of dried test pieces.

This test method is not satisfactory for test pieces that have major discontinuities, such as large cracks (surface or internal) or internal voids.

The test piece shall be a rectangular prism in accordance with 5.3.2.1 and 5.3.3.1, or a circular cross section rod in accordance with 5.3.2.2.

The maximum grain size (see ISO13383-1), excluding deliberately added whiskers, shall be less than 10 % of the minimum dimension of the test piece.

The surface of the test piece shall be smooth and flat. The surface shall be finished using a fine grind (400 grit or finer). The machining procedure shall not affect the test results.

The edges of the specimen shall not be chamfered. However, if the chipping of the specimen from the edges affects the results, the edges may be chamfered, but the amount of the chamfering shall be as small as possible.

NOTE ASTM C1259, Annex A2^[1] describes how to correct the calculation of Young’s modulus for edge chamfers or radii in rectangular beams.

Rectangular prism

The test piece shall have a length (L) greater than 40 mm and a ratio of length to thickness (t) greater than 10 and preferably greater than 20. The ratio of length to width (b) shall be greater than or equal to 10.

The dimensions of the test piece shall be such as to have a fundamental natural flexural frequency in the range 100 Hz to 20 kHz.

NOTE 1 For convenience, a flexural test piece as defined in ISO 14704^[2] can be used, provided that the ends of the bar are machined square and parallel, subject to the allowable frequency range above.

NOTE 2 If the moduli of the test material are high (E > 200 GPa), it is recommended that L/t >> 10 and that 10 > b/t > 2,5. It is also recommended that b/t is > 1,1 or < 0,9 to avoid confusion of different vibration modes.

The parallelism of the upper and lower surfaces perpendicular to the direction of flexural vibration shall be better than t/100, of the sides parallel to the direction of vibration, better than b/100, and of the ends of the test piece, better than L/200.

Cylindrical rod

The test piece shall have a length (L) greater than 40 mm and a ratio of length to diameter (d) greater than 10 and preferably greater than 20.

The diameter of the test piece shall be constant to within d/100 and the ends shall be flat and parallel to better than L/200

NOTE Except in some special circumstances, it is impossible to strike up the fundamental torsional mode frequency on a simple round-section rod.

Rectangular prism

The test piece shall have a length (L) greater than 40 mm and a ratio of length to thickness (t) greater than 10, and preferably greater than 20. The ratio of width (b) to thickness (t) shall be in the range of 1,5 to 10 (5 is recommended in order to reliably strike up torsion).

The parallelism of the upper and lower surfaces perpendicular to the direction of flexural vibration shall be better than t/100, of the sides parallel to the direction of vibration, better than b/100, and of the ends of the test piece better than L/200.

The minimum number of test pieces prepared shall be three.

Dry the test pieces at 110 °C ± 10 °C until the mass is constant and cool in the desiccator.

Weigh each test piece to the nearest 1 mg or 0,1 % (whichever is greater). Measure the cross-sectional dimensions of each test piece (i.e. the thickness and the width, or the diameter) at three positions along its length to the nearest 0,002 mm or 0,1 % (whichever is greater) using the micrometer (5.2.3) and calculate the mean values. Measure the length with the vernier calliper (5.2.4) to the nearest 0,05 mm or 0,1 % (whichever is greater).

For flexural excitation, place each test piece in turn on two compliant supports, e.g. as shown in Figure 5, at a distance from each end of approximately 0,224 of the total test piece length. Place the vibration-detecting transducer near or in contact with the test piece as demonstrated in Figure 5a.

For torsional excitation, support the test piece near its centre on a compliant support. Place the transducer near or in contact with the test piece as shown in Figure 5b.

Key

1 microphone

2 ceramic rod to piezo-detector

3 flexural nodal positions

4 impact location

5 torsional nodal positions

Figure 5— The impulse excitation method: typical positions and directions (2) of striking for exciting vibration in (a) flexural, (b) torsional.

NOTE The detecting transducer (1, 2) is positioned at suitable locations on the test piece, typically as shown, but depending on the direction in which it detects vibration

Lightly strike the test piece in the appropriate positions as shown in Figure 5 to excite flexural or torsional vibrations and record the principal vibration frequency with the frequency analyser to better than 1 Hz or 0,1 %, whichever is the greater. Repeat this at least five times to ensure repeatability of result.

The direction of striking shall be carefully controlled in order to produce repeatable results. When striking, a single impact shall be used, and repeated bouncing of the striker shall be avoided. Striking shall be normal to surface with any sideways component minimized.

NOTE It is important to ensure that the correct mode of vibration is detected. If there is any doubt about detection of the correct frequencies, consistency of results between the three modes of striking can be checked by estimating the expected frequencies for the test piece employed.

5.5.1.1 For a rectangular prism, calculate the dynamic Young’s modulus using equation (6) ^[4]

(6)

where

E is the dynamic Young’s modulus in pascals (Pa);

m is the mass of the specimen in kilograms (kg);

f_f is the fundamental flexural resonant frequency in hertz (Hz);

b is the width of the specimen in metres (m);

L is the length of the specimen in metres (m);

t is the thickness of the specimen in metres (m).

NOTE Some proprietary instruments do not determine the frequency directly but detect the time interval for a certain number of half-periods of vibration. To use the above equations, the time interval for one full period of sinusoidal vibration is converted to a frequency by taking its reciprocal.

5.5.1.2 For a rod of circular cross section, calculate the dynamic Young’s from Formula (7) ^[4]

(7)

where d is the diameter of the specimen in metres (m).

Equations (6) and (7) are considered accurate to within 0,2 % for beams of the specified geometry in the present document. Extended versions of this equation are available, and their use is essential for short aspect ratio test pieces. Such equations may be found in ASTM C1259^[1] and may be implemented in commercial calculation software.

For a rectangular prism, calculate the dynamic shear modulus using equation (8) ^[5]

(8)

where

NOTE The above equation for the correction factor R is accurate to within ~0,2 % for b / L ≤ 0,3 and b / t ≤ 10 in the fundamental mode of torsional vibration, otherwise the errors are estimated to be ≤1 %^[1].

Calculate the dynamic Poisson's ratio using equation (9)

(9)

where ν is the dynamic Poisson's ratio.

NOTE A more reliable method for determining Poisson’s ratio is by the disc method – see Annex A.

The accuracy level of this method is similar to that of Method A applied to the same dimensions of test pieces.

The test report shall be in accordance with the reporting requirements of ISO/IEC 17025, and shall contain the following information:

1. name of the testing establishment;

2. unique identification of the report and of each page, name and address of the customer, and the signatory of the report;

3. dates of receipt of the test item and of the test;

4. details of the material type, manufacturing code, batch number, etc.;

5. number of test pieces tested (minimum 3);

6. dimensions of each test piece, and if relevant, orientations in which test pieces are prepared from components or blocks;

For Method A (see Clause 4) the following information shall also be included

a) a reference to this ISO Standard, i.e. determined in accordance to ISO 17561, Method A;

b) brief details of the technique employed, including apparatus construction, excitation and pick-up transducers, and detecting circuit;

c) mass and dimensions of each test piece;

d) individual values of fundamental resonance frequency in flexural and torsional modes;

e) individual values of dynamic Young’s modulus (expressed in Pa or GPa), and if appropriate, shear modulus (expressed in Pa or GPa), to three significant figures, and Poisson’s ratio to two decimal places, calculated for each test piece;

f) any relevant comments on quality of resonance peaks or suspected anisotropy of test piece;

g) if required, the mean value of elastic moduli and standard deviations of all determinations;

h) any other relevant comments.

For Method B (see Clause 5) the following information shall also be included

a) a reference to this ISO Standard, i.e. determined in accordance to ISO 17561, Method B;

b) brief details of the of the equipment employed for undertaking the test;

c) mass and dimensions of each test piece;

d) individual values of natural vibration frequency determined with the frequency analyser for each determination (i.e. flexural or torsional) on each test piece;

e) individual values of dynamic Young’s modulus (expressed in Pa or GPa), and if appropriate, shear modulus (expressed in Pa or GPa), to three significant figures, and Poisson’s ratio to two decimal places, calculated for each test piece;

f) if required, the mean value of elastic moduli and standard deviations of all determinations;

g) any other relevant comments.

1. 
   (informative)
   
   Impact excitation method applied to disc test pieces
   1. Scope

Method B of this document may be extended to disc test pieces. The method is restricted to homogeneous isotropic materials.

NOTE This method can also be used in resonance if a driving method is available.

• 1. Apparatus

Apparatus should be in accordance with Method B.

• 1. Test pieces

Test pieces are in the form of discs which are parallel-faced to better than t/100 where t is the thickness, and which are round to better than d/200 where d is the diameter. This method works satisfactorily for discs with diameter to thickness ratio in the range 10 to 50. The discs should ideally be larger than 25 mm diameter. The edges shall not be visibly chamfered or chipped.

NOTE As-fired test pieces are usually not appropriate for this test without face and peripheral grinding to ensure geometrical perfection.

• 1. Principle

A disc when struck at its centre will ring with a circularly symmetrical vibration mode (‘diaphragm’ or second mode) with a nodal circle at approximately 0,7 of its diameter (Figure A.1). When struck on the nodal circle a folding mode (‘saddle’ or first mode) of lower frequency will be preferentially produced. If these two frequencies are measured, their ratio, coupled with the dimensions of the disc, gives Poisson’s ratio. Either of these frequencies with Poisson’s ratio and the test piece dimensions and mass gives Young’s modulus. Shear modulus is computed from Young’s modulus and Poisson’s ratio.

Key

1 nodal circle for ‘diaphragm’ mode

2 optimum strike position to excite the mode

3 microphone

4 piezosensor

Figure A.1— Disc method, (a) second (‘diaphragm’) mode and (b) first (‘saddle’) mode of vibration of a disc when struck

• 1. Method

A.5.1 Dry the test pieces at 110 ± 10 ^oC to constant mass, and cool and store in a desiccator.

A.5.2 Weigh the test pieces to the nearest 1 mg.

A.5.3 Measure the thickness with a micrometer to the nearest 0,002 mm. Measure the diameter with a micrometer or vernier callipers to the nearest 0,02 mm.

A.5.4 Place the test piece either on four small equally spaced supports positioned on the nodal circle or on a small pad of cotton wool or fibre insulation. Position the detecting microphone above the test piece or alternatively position the piezoelectric transducer as shown in Figure A.1 for the respective modes. Strike the test piece at the centre to excite and detect the second (diaphragm) mode, and on the nodal circle (between the support points if used) to excite and detect the first (saddle) mode. Measure the two frequencies, f₂ and f₁, respectively, to the nearest 1 Hz or 0,01 % whichever is the greater. Repeat the strikes at least a further four times to ensure repeatability. If the frequency values vary by more than 1 %, review the suitability of the geometrical arrangement or the test piece.

NOTE 1 The correct identification of the two frequencies is best achieved by estimating the relevant frequency window for the test piece mass, dimensions and approximate elastic properties, and by using a system which displays the entire natural frequency spectrum. This will allow the correct peaks to be identified and to be measured accurately.

NOTE 2 The ratio of the two frequencies will typically lie in the range 1,4 to 1,7 for discs with thickness to radius ratios up to 0,5.

• 1. Calculations

A.6.1 Determine Poisson’s ratio from the look-up table (Table A.1) for the relevant thickness to radius ratio, t/r and the relevant ratio of the first and second natural frequency modes, f₂ /f₁.

A.6.2 Determine two values of dynamic Young’s modulus, E₁, E₂, from the following equations using the frequencies of the respective modes, together with the determined value of Poisson’s ratio:

(A.1)

(A.2)

where:

d disc diameter in mm

m disc mass in g

t disc thickness in mm

f₁ first (saddle) mode frequency in Hz

f₂ second (diaphragm) mode frequency in Hz

K₁ geometric factor for first vibration mode (see Table A.2)

K₂ geometric factor for second vibration mode (see Table A.3)

ν Poisson’s ratio

NOTE The derivation of these equations may be found in^[6] and^[7] (see Bibliography).

Determine the average value of dynamic Young’s modulus, E, from equation A3:

(A.3)

A.6.3 Compute the dynamic shear modulus, G, from equation A.4

(A.4)

• 1. Interferences

Disc test pieces which are not of accurate roundness or parallelism of faces to the tolerance specified may show a doubling of each of the frequencies of natural vibration. In this case, the fact should be reported in the report, and the computations of modulus should be based on the average of the two frequencies.

Disc test pieces which have inhomogeneous density may show a small variability in the recorded frequency, especially when using a piezoelectric detector in contact with a specific point on the test piece surface, depending on where the disc is struck. Similarly, test pieces which are anisotropic in the plane of the disc, for example if taken from an extruded sheet, or from a material with a hot-pressing direction lying in the plane of the disc may show similar variability. This variability should be reported in the report.

• 1. Measurement uncertainty

At present, the calculation method recommended in A.6 has limited traceability. The tabular data given in Tables A.1 to A.3 are based on smooth curve fitting by^[6] (see Bibliography) of a small number of computed data points given by^[7] (see Bibliography). Further, there are no known multiparameter curve-fits permitting an algebraic expression to be used confidently in substitution for Tables A.1 to A.3. Most software packages incorporating this method employ the Tables A.1 to A.3 in look-up and interpolation mode. Consequently, until there is documented experimental proof of the close equivalence of data produced by the beam impact excitation and the disc excitation methods, the overall uncertainties of the method are not fully known, but the disc method potentially gives results with uncertainties of less than 1 % in modulus and less than 5 % in Poisson’s ratio.

• 1. Report

The test report shall be in accordance with the reporting requirements of ISO 17025, and shall contain the following information:

a) name and address of the testing establishment;

b) unique identification of the report and of each page, name and address of the customer, and the signatory of the report;

c) dates of receipt of the test item and of the test;

d) details of the material type, manufacturing code, batch number, etc.;

e) number of test pieces tested (minimum 3);

f) dimensions and mass of each test piece, and if relevant, orientations in which test pieces are prepared from components or blocks;

g) a reference to this standard, i.e. determined in accordance to ISO 17561 Annex A;

h) average natural frequencies detected for the two modes of natural vibration;

i) computed values of Poisson’s ratio to two significant figures, dynamic Young’s modulus, expressed as Pa or GPa to three significant figures, and dynamic shear modulus, expressed as Pa or GPa to three significant figures for each test piece;

j) mean results if required;

k) any interferences noted, such as doubling of frequency peaks, positional dependence of frequency.

Table A.1 — Poisson’s ratio (v) as a function of the ratios t/r and f₂ /f₁

Table A.2 — Geometrical constant K₁ as a function of Poisson’s ratio (ν) and the ratio t/r

Expansion of region shown in bold above:

Table A.3 — Geometrical constant K₂ as a function of Poisson’s ratio (ν) and the ratio t/r

Expansion of region shown in bold above:

1. 
   (informative)
   
   Round-robin validation of test methods
   1. Objectives

The objective of this round-robin conducted within the framework of the EC sponsored project “Ceranorm”^[8] (see Bibliography) was to provide information on equivalence of results produced by four methods of determination of elastic moduli at room temperature, and on their repeatability, reproducibility. The four methods evaluated were quasi-static flexure (SF, three or four-point bending), beam resonance (R), beam impact excitation (IE), and ultrasonic pulse (UP). The data concerning the sonic resonance method and the IET method are of direct relevance for the present ISO document.

• 1. Materials

Five homogeneous and well-defined ceramics were selected to cover the range of Young’s modulus between 64 GPa and 400 GPa, including Macor® machinable glass-ceramic, fused silica, partially stabilised zirconia, debased alumina, and translucent alumina. These were prepared as standard flexural strength test pieces 3 x 4 x 50 mm without chamfers or as discs 30 mm diameter, and in thicknesses of 3 mm to 10 mm.

• 1. Test facilities

Six laboratories made measurements of moduli on five test pieces of each type in accordance with the instructions within the equivalent EN standard using their own facilities. Not all laboratories performed all the methods. The results were submitted to the lead laboratory for data analysis.

• 1. Results

At room temperature and for all five materials, no practical problems with measurement were encountered for any of the methods (Table B.1). Young’s modulus (E) for translucent alumina was found to be most reproducibly measured by the R and IE methods giving a very small within-laboratory scatter (<1 %), and between-laboratory scatter (<1 %). The SF resulted in rather more scatter (~ 4 %) with results tending to be lower than those for the other methods. The UP method proved to be difficult on thin discs because the pulse transit times were ~ 250 ns only, but with careful correction of the instrument baseline transit times, a reasonable agreement with the R and IE methods could be obtained. The set of data is shown in Table B.1. The data for the debased alumina showed rather greater scatter attributable to greater variability from test piece to test piece, but improved comparability of the UP method with the other methods was achieved when using thicker test pieces, and hence longer transit times. The data for the zirconia, fused silica and machinable glass-ceramic all showed similar statistics and trends, and the data produced were close to expected values. The reproducibility of results on fused silica was particularly good, suggesting that this material could make a useful reference for checking set-up and computation procedures.

Table B.1 — Summary of room temperature results for Young’s modulus, E (GPa)

• 1. Conclusions

When properly operated, all methods gave consistent results within the limits of scatter caused by material inhomogeneity, but the Resonant and Impulse Excitation methods gave the least scatter and were the least dependent on the set-up employed. The SF method was less reliable, but an error analysis suggested that improvements would result from using thinner test pieces. The use of a reference material for system set-up was recommended, and fused silica appears particularly suitable.

[Conducted under EU contract SMT-CT96-2078, “CERANORM”.]

Bibliography

[1] ASTM C1259, Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio for Advanced Ceramics by Impulse Excitation of Vibration

[2] ISO 14704, Fine ceramics (advanced ceramics, advanced technical ceramics) — Test method for flexural strength of monolithic ceramics at room temperature

[3] Spinner S., Tefft W.E. A Method for Determining Mechanical Resonance Frequencies and for Calculating Elastic Moduli from These Frequencies. Proceedings, ASTM, 1961, pp. 1221-1238

[4] Spinner S., Reichard T.W., Tefft W.E. A Comparison of Experimental and Theoretical Relations Between Young’s Modulus and the Flexural and Longitudinal Resonance Frequencies of Uniform Bars. J. Res. Natl. Bur. Stand., A Phys. Chem. 1960, 64A (2)

[5] Pickett G. Equations for Computing Elastic Constants from Flexural and Torsional Resonant Frequencies of Vibration of Prisms and Cylinders. Proceedings ASTM, (45), 1945, pp. 846-865

[6] Glandus J.C. “Rupture fragile et résistance aux chocs thermiques des céramiques à usage mécaniques”, Thesis, University of Limoges, France, 1981.

[7] Martincek, G., “The determination of Poisson’s ratio and dynamic modulus of elasticity from the frequencies of natural vibration in thick circular plates”, J.Sound & Vibration, 1965, 2(2), 116-27.

[8] Hendrix, M., De With, G., Morrell, R., “Young’s modulus of ceramic materials – an intercomparison of methods”, Brit. Ceram. Proc. 1999, 60(2), 565-6