Ultrasonic estimate of the modulus of rupture and quantification of the frequency dependent dynamic modulus in Norway Spruce

Abstract

Ultrasonic measurements allow non-destructive evaluation of mechanical properties of wood. However, it is unclear how these ultrasonically determined properties relate to comparable values obtained by traditional mechanical experiments, e.g., three point bending performed at different probing frequencies. In addition, although a link between the modulus of rupture (MOR) and the modulus of elasticity (MOE) obtained with static methods is established, little research exists on the correlation between the ultrasonically determined dynamic elastic modulus and MOR. Therefore, we set out to link the modulus values obtained by three-point bending to those obtained by ultrasonic measurements at different frequencies. We compared the modalities using a fractional derivative model that theoretically predicts a frequency dependency of the dynamic elastic modulus. We determined MOE and MOR in 102 Norway Spruce samples (340 to 510 kg/m3 density) by three-point bending followed by ultrasonic through-transmission measurements that quantified the dynamic modulus at 500 kHz, 4 MHz, and 8 MHz. This is the first report on such a frequency series for Norway Spruce. Our results provide a conversion factor that permits comparing ultrasonically and statically measured MOE values. Depending on the ultrasonic frequency, correlations ranging from 0.3 to 0.53 between the ultrasonic dynamic modulus and MOR were found.