Discussion and proposal of a general failure criterion for wood

Based on a polynomial expansion of the failure surface, a general failure criterion, satisfying equilibrium in all directions. was developed for wood long ago (IUFRO Borns 1982) and shown to apply for clear wood. For wood with (small) defects and (local) grain deviations, equivalent strengths can be defined in the main directions and a comparable equivalent failure criterion applies as was shown by K. Hemmer (PhD thesis 1985). It was shown at the last COST-508 meeting that the second order terms of the polynomial failure criterion represent the critical distorsional energy of initial yield (or failure at initial yield when the test becomes unstable at this point). It will be shown that the third order terms represent special hardening effects (clue to micro-crack arrest by strong layers), occurring after initial yield, determining ultimate failure in longitudinal direction in a stable test. As known. the singularity approach of fracture mechanics predicts for the critical energy release rate: G_C = G_IC + G_IIC for collinear crack propagation in grain direc­tion. As p.e. mentioned in the RILEM State of the Art report on fracture mechanics of wood, this is against experimental evidence and in stead, the empirical Wu-­equation is used for layered composites. It was shown at the COST SOS-meeting at Bordeaux that this wrong prediction is due to this singularity method that, by the critical stress intensities, does not satisfy in all cases the failure criterion and, although this method is generally applied in fracture mechanics of materials, it therefore has to be rejected. It further was shown that the Wu-criterion can be derived from oriented (in grain direction) crack propagation of elliptic micro-cracks and is a necessary condition for the (right form of the) energy principle. It now wilI be shown that this Wu- (or Mohr-) criterion is also determining the failure criterion of wood, showing the same oriented micro-cracking to be responsible for failure in general. Based on this criterion, the existing criteria can be explained as the Hankinson, Norris, and Coulomb criterion. A derivation is given of an exact modified Hankinson criterion and of the general form of the higher order constants and how they can (safely) be determined from uni-axial tests in the main plane. The exact criterion is as easy to apply as the invalid approximations, now used for the Codes.