熱気乾燥における木材の表面割について

When along round timber dries under such a certain constant condition as the equilibrium moisture content of wood is U_1, the maximum tensile stress (σ_0) in the drying timber can be calculated by equation (11) on some assumptions, where E is the Young's modulus of wood perpendicular to the grain, α_t and α_r are coefficients of tangential and radial shrinking, respectively, θ is the drying period, a and b are radii of round timber and pith, respectively, k is the drying diffusion constant, h is a constant in equation (2) which represents a boundary condition, u_0 = U_0-U', U_0 is the initial moisture content of the timber and U' is the moisture content from which the shrinking begins, and u_1 = U_1-U'. If σ_0 is larger than the transverse thensile strength (σ_z) of the timber, checks will occur at surface of the timber.
We calculated σ_0 by equation (11) in the case of various drying conditions, and compared with σ_z, and thereby, tried to determine the critical codition which should cause surface-checks of the timber. However, we could not accomplish this purpose, i.e., there was a considerable discrepancy between the results of test on the surfacechecks and that of calculation, and the tilmber could dry without surface-checks even under the severer conditions than the calculated one.
In the derivation of equation(11), we assumed that E and α are constants and Hooke's law is adaptable. But all these assumptions are not always true in wood when its moisture content is changing. Therefore, other equation must be find to calculate the true value of stress in drying timber.