GB/T 22315-2026Metallic materials — Determination of the modulus of elasticity and Poisson's ratio (English PDF)

5.1 Principle

An axial force is applied to the specimen, and the corresponding axial and transverse deformations are measured within its elastic range to determine one or more of the conditions defined in this document. Several mechanical properties.

5.2 Sample

5.2.1 Cutting of blanks and preparation of samples

5.2.1.1 The location, direction, and quantity of sample blanks cut shall meet the requirements of relevant standards or agreements. Unless otherwise specified, they shall be cut in accordance with... It shall be carried out in accordance with the requirements of GB/T 2975.

5.2.1.2 When cutting sample blanks and machining specimens, care should be taken to prevent cold working or heating from affecting the mechanical properties of the metal. For example, due to specimen preparation... If the material needs to be flattened, the test results should indicate that a subsequent heat treatment process to relieve residual stress was used. The material needs to be... Annealing at a temperature of Tm/3 for 30 minutes to relieve stress (Tm is the thermodynamic melting point of the material) is required to be noted in the report.

If the purpose of the test is to verify product performance, the heat treatment process can be omitted. The test report should record the condition of the test material, including the heat treatment process. Processing technology.

Note: The purpose of this method is to reveal the inherent properties of the material; therefore, the specimen must not contain residual stress.

5.2.1.3 The sample after final machining should be straight, free of burrs, and free of scratches and other human or mechanical damage.

5.2.1.4 Thin sheet specimens cut from rolls are permitted to have slight bending that does not affect performance determination.

5.2.2 Sample shape and size

5.2.2.1 Circular and rectangular tensile specimens shall meet the requirements of Annex E, Annex F and Annex G of GB/T 228.1-2021, and the specimen clamping... The radius of the transition section between the end and the parallel section should be as large as possible, and the parallel length of the specimen should at least exceed the gauge length plus twice the specimen diameter. width.

5.2.2.2 Circular and rectangular compression specimens shall meet the requirements of 6.1 in GB/T 7314-2017. The ends of the specimens shall be flat, parallel, and perpendicular. From the side.

5.2.2.3 Other types of test specimens may be used upon consultation among the relevant parties.

5.2.2.4 The shape and size of the specimen head should be suitable for the clamping of the testing machine chuck.

5.2.2.5 For rectangular tensile specimens with a bearing pin hole at the head, the pin hole surface should be smooth, and the center of the pin hole should be offset from the centerline of the gauge length portion.

It should not exceed 0.005 times the width of the gauge length.

5.2.2.6 For rectangular specimens machined on two or four sides, the surface roughness Ra of the machined surfaces should not exceed 1.6 µm. If two sides are used... For machined rectangular specimens, the dimensional and shape tolerances of the unmachined surfaces should meet the tolerance requirements of the machined surfaces.

5.2.2.7 For rectangular specimens made of sheet metal, small lugs can be prepared on both sides of the specimen width for mounting the extensometer. See [link to example] for rectangular specimens with lugs.

5.3 Test Equipment

5.3.1 Testing Machine

5.3.1.1 The accuracy class of the force measurement system of the testing machine shall meet the requirements of GB/T 16825.1 or JJG139, JJG475 within the corresponding measurement range. The requirements for Level 1 accuracy in JJG1063.

5.3.1.2 The testing machine used for compression testing, in addition to meeting the accuracy requirements in 5.3.1.1, must also meet other auxiliary device requirements (such as force guiding devices, adjustment...).

Requirements for flat pads and restraint devices, etc., shall comply with the provisions of 7.2 to 7.4 in GB/T 7314-2017.

5.3.2 Extensometer System

The extensometer system should meet the accuracy requirements of 0.5 class as specified in GB/T 12160 or JJG762 within the corresponding measurement range.

Note: If strain is measured only on one side of the specimen, the additional bending strain will introduce a large error into the measurement results.

5.3.3 Test System Resolution

The resolution of the test system should be able to obtain at least 50 different discrete measurements within the evaluation range.

5.3.4 Measuring device for relevant sample dimensions

All measuring devices used to determine the original cross-sectional area should be calibrated according to relevant standards and traceable to the national measurement system.

The measuring device should ensure that the accuracy of the measured data is better than ±0.5% of the measured value.

5.4 Test Conditions

5.4.1 Measurement of sample size

5.4.1.1 The diameter of a circular specimen shall be measured in mutually perpendicular directions at both ends and the middle of the gauge length, and the arithmetic mean of each shall be taken. The diameter shall be calculated according to formula (1).

Calculate the cross-sectional area. Take the arithmetic mean of the cross-sectional areas measured at three locations as the original cross-sectional area of the specimen, and retain at least four significant figures.

5.4.1.2 The thickness and width of a rectangular specimen should be measured at both ends and the middle of the gauge length, and the cross-sectional area should be calculated according to formula (2). The cross-sectional area measured at the three locations should be... The arithmetic mean of the product is taken as the original cross-sectional area of the specimen and should retain at least 4 significant figures.

Note: The width of a specimen with lugs should not be measured near the base of the lugs.

5.4.2 Initial Test Force

For most testing machines and specimens, factors such as clearance, specimen curvature, and original clamping conditions can affect the performance of testing machines when small test conditions are applied to the specimen.

Applying an initial test force to the specimen can introduce significant deviations in the extensometer's output. During testing, an initial test force should be applied to the specimen to eliminate these effects, and the measurement should be performed... Starting with the initial test force, and progressing to a larger test force within the elastic range.

5.4.3 Test Rate

To avoid the effects of adiabatic expansion or contraction and to accurately measure axial force and corresponding deformation, the test speed should not be too high.

High elastic modulus, to avoid creep effects, should not be too low a test speed. Compared to other performance indicators determined by tensile testing, elastic modulus is less affected by test rate.

Sensitive. The test rate should meet the requirements of Method A, Scope 1 in GB/T 228.1-2021, and other test rates (including those of Method B) should be... A lower test rate is also permissible. The test rate should be low to achieve the required number of data points for analysis. A constant beam displacement rate should be used to avoid... Any discontinuities should be avoided. For compression tests, the test rate should comply with the requirements of 8.1 and 8.2 in GB/T 7314-2017, and the rate should be as fast as possible. It can remain constant.

5.4.4 Coaxiality of Forces

5.4.4.1 The clamping device of the testing machine should be able to withstand axial force on the specimen, and between the initial axial force and the final axial force, the specimen relative to the force in all directions should be stable.

The maximum difference between the strain change measured on both sides and its average value (i.e., the maximum bending strain) should not exceed 3% of the average value; for the use of double... In the case of an average extensometer, the maximum bending strain should not exceed 5% of the average value, and the coaxiality of the loading on the testing machine should conform to GB/T 34104. Fixed measurement.

5.4.4.2 The compression test shall use the leveling pads, force guiding devices and restraint devices specified in GB/T 7314-2017.

5.4.5 Use of the extensometer

5.4.5.1 Axial Extensometer

When measuring the axial deformation of a specimen, use an axial average extensometer that can measure the average deformation on both sides of the specimen, or measure the deformation on both sides of the specimen.

Do not fix the two axial extensometers in place. The accuracy of modulus measurement depends on the accuracy of strain measurement. Increasing the gauge length can improve the accuracy of strain measurement.

Accuracy should ensure the tolerance requirements of the parallel sections of the machined specimen. When using a rectangular specimen with lugs, the extensometer should be mounted on the outside of the two lugs on the same side.

The inner side. Its extensometer gauge length should be the distance between the center lines of the widths of the two lugs.

5.4.5.2 Lateral Extensometer

When measuring the transverse deformation of a specimen, the transverse extensometer should be mounted on the diameter (width) within the gauge length of the specimen. This diameter (or width) is used as the reference point.

The dimension (degrees) is used as the gauge length of the transverse extensometer.

5.5 Performance Measurement

5.5.1 Determination of Young's Modulus

5.5.1.1 Graphical Method

The Young's modulus E is calculated according to formula (3), or the resistance strain gauge in Appendix A or the DIC method in Appendix B can be used to directly measure the axial strain. Calculate E using the variable method.

5.5.1.2 Fitting Method

5.5.1.2.1 During the test, record a set of numerical data pairs of axial force and corresponding axial deformation within the elastic range. Use least squares... The data is fitted to an axial stress-axial strain straight line, and the slope of the fitted line is Young's modulus, which is calculated according to equation (4).

5.5.1.2.2 When the modulus is obtained after the strain exceeds 0.25%, it is recommended to use the instantaneous cross-sectional area and instantaneous gauge length instead of the original cross-sectional area.

Stress and strain are calculated using area and original gauge length.

5.5.1.2.3 The coefficient of determination r² of the fitted straight line can be calculated according to equation (5). This coefficient should be close to 1 ( >0.9995), and the number of data points should not be less than [number missing]. The 50 values yielded valid Young's modulus values.

5.5.1.3 When specifying Young's modulus in relevant documents or agreements, it should be stated whether it is tensile Young's modulus or compressive Young's modulus, using Et and Ec respectively.

Indicated. Unless otherwise specified, the tensile method is generally used for determination, and the E value is reported.

5.5.2 Determination of chord modulus

5.5.2.1 Graphical Method

During the experiment, an automatic recording method was used to plot the axial force-axial deformation curve, as shown in Figure 6. On the recorded axial force-axial deformation curve, the... Through the specified upper and lower stress points (such as two stress points at 10% and 50% of the specified plastic elongation strength Rp0.2) or two strain points.

Draw a chord line corresponding to points A and B. Read the change in axial force and the corresponding change in axial deformation along the drawn chord line, according to equation (6).

Calculate the chord modulus. Alternatively, E can be calculated by directly measuring the axial strain using a resistance strain gauge as described in Appendix A.

During the experiment, an automatic recording method was used to plot the axial force-axial deformation curve, as shown in Figure 5. On the recorded axial force-axial deformation curve, it was confirmed that... For a given elastic straight line segment, read the change in axial force and the corresponding axial deformation between two points A and B that are as far apart as possible on this line segment.

5.5.2.2 Fitting Method

During the experiment, a set of numerical data pairs of axial force and corresponding axial deformation were recorded within the elastic range. This set of data pairs was then fitted with a... Mathematical expressions (such as polynomials) are used to obtain the fitted axial stress-axial strain curve. The elasticity of the fitted axial stress-axial strain curve is then analyzed.

The slope of the chord between two specified stress or strain values within the specified range is called the chord modulus.

5.5.3 Determination of Tangent Modulus

Note: For nonlinear elastic metallic materials, when specifying the chord modulus, relevant documents or agreements must specify the stress or strain values at the upper and lower points of the chord.

5.5.3.1 Graphical Method

During the experiment, an automatic recording method was used to plot the axial force-axial deformation curve, as shown in Figure 7. On the recorded axial force-axial deformation curve, [the following data was collected/distributed].

Draw a tangent line to the curve at point R corresponding to the specified stress or strain value. Read the distance between points A and B, which are as far apart as possible, on the drawn tangent line.

The axial force change and the corresponding axial deformation change are used to calculate the tangent modulus according to equation (7). Alternatively, the resistance strain gauge in Appendix A or... Appendix B describes the method for directly measuring axial strain using the DIC method to calculate E.

5.5.3.2 Fitting Method

During the experiment, a set of numerical data pairs of axial force and corresponding axial deformation were recorded within the elastic range. This set of data pairs was then fitted with a numerical model.

By learning the expression (such as a polynomial), the fitted axial stress-axial strain curve is obtained. The elasticity of the fitted axial stress-axial strain curve is then considered.

The slope of the curve calculated within the specified stress or strain value is the tangent modulus.

Note: For nonlinear elastic metallic materials, when specifying the tangent modulus, the relevant standards or agreements must specify the stress or strain value at the tangent point.

5.5.4 Determination of Poisson's Ratio

During the experiment, the transverse deformation-axial deformation curve was plotted using an automatic recording method (see Figure 8a). The recorded transverse deformation-axial deformation curve... Online, determine the elastic straight line segment, and read the lateral deformation change and corresponding axial deformation between two points C and D that are as far apart as possible on the straight line segment.

The amount of deformation change. Calculate Poisson's ratio according to formula (8). When Poisson's ratio and Young's modulus are measured together in the same experiment, it is recommended to plot them simultaneously.

The axial force-axial deformation curve and the transverse deformation-axial deformation curve are shown in Figure 8b). Alternatively, the axial force can be directly measured using the DIC method in Appendix B. The strain method is used to calculate µ.

During the experiment, the transverse deformation-axial force curve and the axial deformation-axial force curve were simultaneously plotted using an automatic recording method, as shown in Figure 9. In the transverse... On the elastic straight segments of the deformation-axial force curve and the axial deformation-axial force curve, read the axial force changes that are as far apart as possible and of the same value.

The Poisson's ratio is calculated using equation (8) based on the lateral deformation change between points C and D and the axial deformation change between points A and B.

If the changes in transverse and axial deformation are not read at different axial force values, then equation (8) cannot be used directly for calculation. They can be calculated separately... Calculate the ratio of the change in transverse strain to the change in axial stress, and the ratio of the change in axial strain to the change in axial stress, and calculate the former.

The ratio to the latter is Poisson's ratio, which can also be calculated by directly measuring axial strain using the DIC method in Appendix B.

5.5.4.1 Graphical Method 1

5.5.4.2 Graphical Method 2

5.5.4.3 Fitting Method

During the experiment, within the elastic range, a set of numerical data pairs of transverse and axial deformation were recorded under the same axial force. Least squares was then used to analyze the data.

The method involves fitting a transverse strain-axial strain straight line to this set of data, and the slope of the line is Poisson's ratio. It is calculated according to equation (9). For example, recording the transverse strain... For two sets of numerical data pairs, namely deformation-axial force and axial deformation-axial force, the least squares method is applied to fit the transverse strain-axial force to each data pair.

The axial stress and axial strain-axial stress straight lines are calculated, and the slope of the fitted line is calculated. The ratio of the slope of the former to that of the latter is Poisson's ratio. According to equation (5)... Calculate the coefficient of determination r² of the fitted straight line. This coefficient should ideally be close to 1 ( >0.9995). The number of data points should be no less than 50.The resulting Poisson's ratio is... efficient.

6.1 Principle

6.1.1 Using energy coupling or pulse excitation methods with continuously variable frequencies or pulse signals, a specimen with a suitable geometry is subjected to [the following method/method].

Mechanical excitation is applied, and the mechanical resonant frequency of the transducer test sample is detected. The results are then determined based on the sample size, mass (or density), and the measured resonant frequency.

The dynamic Young's modulus, dynamic shear modulus, and dynamic Poisson's ratio are calculated using the ratio.

6.1.2 Energy coupling methods include three types. suspension wire coupling, electrostatic coupling, and electromagnetic coupling. Suspension wire coupling is recommended.

Note: The advantages of the suspension wire coupling method are that the sample amplitude is large, resonance is easy to identify, the influence of the support is easy to eliminate, the vibration length is easy to determine accurately, and it has a wide temperature range. Scope of application.

6.2 Sample

6.2.1 Select the specimen size based on equipment conditions, estimated material density, and modulus. The minimum mass of the specimen is determined by the vibration pickup system.

Sensitivity determines the sample size and mass, which is generally not less than 5g. The maximum values are determined by the energy supplied by the excitation system and the allowable space. Decide.

6.2.2 The recommended sample length for the suspension wire coupling method is 120mm~180mm. For round rods and tubes, the diameter (outer) diameter is 4mm~ 8mm, with a length approximately 30 times the diameter; when only the bending resonant frequency is measured, the diameter can be as small as 2mm. For rectangular rods, the thickness is... 1mm~4mm, width 5mm~10mm.

6.2.3 For the pulse excitation method, the recommended sample length is 60mm~100mm. The ratio of length (l) to thickness (h) (l/h) should not be less than 20, and the width... The ratio (b) to thickness (h) (b/h) should be 3 to 10, preferably 5.

6.2.4 The sample material should be uniform and flat; the axial non-uniformity of the transverse dimension should not exceed 0.7%; the surface should be free of defects and the roughness Ra should not be high.

For a depth of 1.6 µm, the parallelism between the relative surfaces should be less than 0.02 mm.

6.2.5 When detecting the torsional resonance frequency of a specimen at high temperature, if the resonance signal is weak, a dumbbell-shaped specimen or a suspension wire fixed with a pin can be used. The method involves relative measurement of torsional resonance frequencies.

6.3 Test Equipment

6.3.1 Measuring tools

6.3.1.1 Vernier calipers. used to measure the length of a sample, with a minimum graduation value not exceeding 0.02 mm.

6.3.1.2 Micrometer. Used to measure the diameter, width, or thickness of a sample, with a minimum graduation of no more than 0.002 mm.

6.3.1.3 Balance. Used to weigh the sample mass, with a scale division not exceeding 0.001g.

6.3.1.4 Temperature measuring device. Used to measure the ambient temperature of the sample during different temperature tests, using calibrated thermocouples, with an accuracy of [insert accuracy here].

At ±0.5°C, its position should be close to the middle of the sample, the distance from the sample should not be greater than 5mm, and it should not touch the sample.

6.3.2 Resonance Measurement Device

6.3.2.1 Overview

A schematic diagram of the suspension wire coupling method detection device is shown in Figure 10; a schematic diagram of the pulse excitation method detection device is shown in Figure 11.A digital frequency meter is used to complete the excitation.

Precise measurement of the output frequency of the oscillator that triggers sample resonance; transducers are classified into exciters and pickups according to their functions; frequency-selective amplifiers... The built-in AC voltmeter detects the resonance signal. If Lissajous figures are needed to determine false resonance, the oscillator and amplifier should be connected... The outputs are supplied to the horizontal and vertical deflection plates of the oscilloscope, respectively.

6.3.2.2 Audio Oscillator

It should have a continuously variable frequency output within the range of 100Hz to 30kHz; in general measurements, the frequency drift at any given location should be negligible.

If the frequency shift is below 0.1 Hz/min, its output power should ensure that the excitation transducer used can excite any sample with a mass within the specified range.

6.3.2.3 Pulse Exciter

A flexible striking hammer made of a solid metal or ceramic sphere with a diameter of 1mm to 10mm is recommended as a manual actuator. Use an automatic electromagnetic pulse generator.

6.3.2.4 Digital Frequency Meter

A counting frequency meter that can be used to measure vibration period. The measurement error should not exceed 0.01 Hz, and its crystal oscillator stability should not be lower than [value missing]. On the order of 10^-^8/d.

6.3.2.5 Transducer

6.3.2.5.1 Different types of transducers are selected based on the coupling method and the mass and resonant frequency of the test sample. In the tested... Within the range of sample frequency variation, the output power loss of the excitation should not exceed 3dB, and the vibration pickup should have the best possible frequency response.

6.3.2.5.2 Generally, piezoelectric transducers, such as box-type piezoelectric ceramic transducers, can be used; if the sample mass is small (generally 5g~15g), a smaller sample can be used.

Crystal cartridge. For rectangular rods, a moving-coil loudspeaker can be used as the exciter, and an in-ear monitor as the pickup.

6.3.2.6 Frequency Selective Amplifier

Its input impedance should be matched with the impedance of the resonant pickup transducer, the frequency range should meet the test requirements, and the test sensitivity to the resonant signal should not be insufficient.

Less than 1µV. A lock-in amplifier or a transducer amplifier with a bandpass filter is recommended.

6.3.2.7 Oscilloscope

The frequency response range and sensitivity should meet the requirements of a general-purpose oscilloscope for testing.

6.3.3 Temperature Variable Device

The temperature control device should allow for controlled heating and cooling, and prevent frost formation at low temperatures. Within the measured temperature range, temperature fluctuations along the sample length should be within acceptable limits. Within ±5°C.

6.4 Test conditions and operating requirements

6.4.1 Measurement of geometric dimensions and mass

After cleaning the sample, measurements were performed. The length was measured twice, to within 0.1%, and the average value was taken. When testing the dynamic elastic modulus, the measurement was performed along the sample... The diameter or thickness and width of the sample were measured at five locations along its length, to a value within 0.1%, and the average value was taken; the mass was measured to a value within 0.1%. Within.

6.4.2 Energy Coupling Method

6.4.2.1 General Rules

Depending on the testing requirements, any energy coupling method, such as mechanical, electrostatic, or electromagnetic coupling, can be used. Regardless of the coupling method used, the sample must be kept safe.

The specimen is placed in a horizontal position and in a free vibration state to eliminate the influence of support damping on the resonant frequency of the specimen.

6.4.2.2 Suspension Wire Coupling Method

6.4.2.2.1 Suspension wire coupling is a commonly used type of mechanical coupling. The coupling method is shown in Figure 12. Both suspension methods should ensure that the sample is suspended in one go.

The bending vibration frequency and torsional vibration frequency can then be measured successively.

6.4.2.2.2 For round rods and tubular specimens, the suspension method shown in Figure 12b) is recommended. If only the bending resonance frequency of the specimen is to be measured, then... The two suspension wires should ideally be in the same plane as the central axis of the specimen. The suspension wires used must be flexible yet possess the necessary strength to ensure proper suspension of the specimen. Tighten.

6.4.2.2.3 In tests below 100°C, it is recommended to use cotton thread as the suspension wire to ensure sufficient friction between the suspension wire and the sample surface. Friction.

6.4.2.2.4 In high-temperature measurements, quartz glass fiber is recommended. Alternatively, two different materials of suspension wire can be used inside and outside the furnace.

When measuring samples with large mass, copper wire or nickel-chromium wire with a diameter of less than 0.15 mm can be used.

6.4.2.2.5 The recommended suspension position is (0.200~0.215)l or 0.238l, where l is the length of the specimen; the resulting bending resonance fundamental frequency... The systematic deviation of the rate measurement should not exceed 0.01%, and the systematic deviation of the torsional resonance fundamental frequency should not exceed 0.1%.

6.4.2.2.6 If the resonance signal is weak, the suspension position can be moved outwards, but the measurement accuracy will decrease accordingly. Changing the suspension point can be used instead.

The method of extrapolating the obtained resonant frequency value to the node is used to eliminate the system deviation caused by deviation from the node.

6.4.2.2.7 During the measurement process, avoid interference with the sample resonance measurement caused by the suspension wire resonance.

6.4.2.3 Electrostatic Coupling Method

Electrostatic coupling can effectively eliminate the influence of system resonance and easily achieve high measurement accuracy. Figure 13a) is suitable for bending resonance fundamental frequency.

Frequency detection; Figure 13b) is suitable for detecting the torsional resonance fundamental frequency. In high-temperature measurements, care should be taken to eliminate the effects caused by gas molecule ionization. The impact of noise.

6.4.2.4 Electromagnetic Coupling Method

Electromagnetic coupling can achieve higher measurement sensitivity. Figure 14a) is suitable for detecting the fundamental frequency of bending resonance, and Figure 14b is suitable for... For the detection of the torsional resonance fundamental frequency. This measurement can be performed at temperatures below the Curie point of ferromagnetic materials. For precise measurements, the iron... The influence of the deltaE effect on magnetic materials is corrected, while the influence of added mass should be considered for non-ferromagnetic materials.

6.5.6 Measurement Uncertainty

When determining the dynamic Young's modulus, dynamic shear modulus, and dynamic Poisson's ratio of metallic materials using the dynamic method, the measurement uncertainty can be determined according to... The evaluation shall be conducted in accordance with JJF1059.1 and with reference to Appendix C.