ASTM E1875 Test for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio by Sonic Resonance

Scope:

Materials that are elastic, isotropic, and homogeneous can be tested using ASTM E1875 test method. Cracks or voids represent inhomogeneities in the material therefore such materials cannot be tested with this method. Resonance frequency values can be used to calculate dynamic elastic properties. 

This test method can also be performed at cryogenic and high temperatures with appropriate equipment modifications and modifications to the calculations to compensate for thermal expansion.

ASTM E1875 is a nondestructive test method. Only minute stresses are applied to the specimen. The time during which stress is applied and removed is of the order of hundreds of microseconds.

This test method is also used in quality control. A range of acceptable resonant frequencies is determined for a specimen with a particular geometry and mass. Any specimen whose frequency falls outside this range is rejected.

Test Procedure:

In the ASTM E1875 test method, elastic properties are determined by calculating resonance frequencies. Resonance frequencies of test specimens are determined by exciting the specimens at different frequencies to find a particular frequency that matches the specimen’s natural resonance frequency. It is a hit-and-trial method. Specimens are excited by a transducer, a transducer transforms a set electric signal into a mechanical vibration which causes a vibration in the specimen. Another transducer converts the vibration in the specimen into an electric signal that is displayed on the screen of an oscilloscope to measure resonance. The dimensions of the specimen, its resonance frequency, and its mass are used to calculate Young’s modulus and shear’s modulus. 

Video 01: What is resonance?

Specimen size:

The specimens used in ASTM E1875 testing should be either rectangular or circular. Both can be used to calculate elastic properties.

Data:

The following data is calculated in ASTM E1875:

1. Young modulus: 

Y = (38.3 × f² × ρ × ℓ⁴)/d²

where:

Y = Young’s modulus

f = resonance frequency of oscillations

ρ = density

ℓ = length

d = width

2. Shear modulus:

E = 2G(1 + ν)

Where:

E =  Young’s modulus

G =  shear modulus 

ν =  Poisson’s ratio

3. Poisson’s ratio:

µ = Poisson’s ratio

E = Young’s modulus

G = shear modulus

4. Moduli at elevated and cryogenic temperatures:

M_T = modulus at temperature T 

M₀ = modulus at room temperature 

f_T = resonant frequency in a furnace or cryogenic chamber at temperature T

f_O = resonant frequency at room temperature in a furnace or cryogenic chamber,

α = average linear thermal expansion from room temperature to test temperature

∆T = temperature differential in °C between the test temperature T and room temperature

Conclusion:

Materials that are elastic, isotropic, and homogeneous can be tested using ASTM E1875 test method.