Functional gradient effects explain the low transverse shear modulus in spruce – Full-field strain data and a micromechanics model

An important failure mechanism in glulam beams is cracking caused by out-of-plane transverse loads. It has been demonstrated that the low transverse shear modulus GRT in spruce contributes to large transverse strain inhomogeneities due to the annual ring structure in combination with shear coupling effects. In the present study, improved understanding of annual ring effects is achieved by the development of a micromechanical model. It relates the functional density gradient in spruce annual rings to shear modulus GRT. The geometrical basis is a hexagonal cell model, and in shear it is demonstrated to deform primarily by cell wall bending. Full-field strain measurements by digital speckle photography (DSP) show very strong correlation with predicted shear strains at the annual ring scale. Predictions are obtained by implementation of the micromechanics model in a finite element (FE) model developed for the single cube apparatus shear specimen. The low GRT of spruce is due to the strong dependence of GRT on relative density ρ/ρs(GRT∝(ρ/ρs)3). This is particularly important in spruce. Even though average density is typically quite high, the functional gradient structure includes local densities as low as View the MathML source.