Determination of Static and Dynamic Young's Modulus of A Cantilever Beam using Digital Image Correlation (DIC) Method

Abstract

The Young's modulus is a fundamental mechanical property that measures the stiffness of a solid material. Destructive material testing is the common method to determine Young's modulus. This paper presents the vibration measurement technique using Digital Image Correlation (DIC) as an alternative method to determine the Young's modulus of materials. The principle is based on the linear transverse vibrations of a Euler-Bernoulli cantilever beam with clamped-free boundary conditions. The dynamic responses of three materials (steel, aluminium and brass) were discussed. For each material, the beam was subjected to an initial static transverse displacement at its free end and then allowed to vibrate freely. The vibrations at the free end were captured using DIC measurements, and the results processed and presented in the form of displacement versus time, following which the natural frequencies of the beam can be obtained using the method of Fast Fourier Transform (FFT). The Young's modulus can then be derived using the first natural frequency and the geometry of the beam. The calculated Young's modulus values obtained using the DIC measurements of the free vibrations are compared with the modulus obtained using the static deflection approach, which shows highly favorable agreement. The use of the vibration method to determine Young's modulus using DIC method can help in the non-contact assessment of the existing structural integrity without subjecting test specimens to destructive testing.