T.A.C.M. van der Put
TU-Delft, Civil Engineering and Geosciences, Timber Structures and Wood Technology, Delft, Netherlands
Series: Materials Science and Technologies
This second edition provides extensions of a new theory based on micro crack processes and leading to unification with strength theory. The completed derivation of the ultimate stress theory is also added as the last chapter.
The now solely applied singularity approach of fracture mechanics prevents the derivation of the right failure criterion and the possibility of exact solutions, and thus prevents real and reliable strength predictions. It therefore was necessary to leave the singularity approach and to apply the general applicable technical exact limit analysis theory for the boundary value problem of notches in wood. It then appeared possible to derive the mixed “Mode I – II” interaction equation with the relations between the Mode I and Mode II stress intensities and energy release rates. Further, the so-called non-linear fracture mechanics approaches, such as fictitious crack models, J-integral, etc., which only apply for singularity solutions, are superfluous because they are covered by limit analysis.
Because initial fracture starts in the isotropic wood matrix, it is necessary to solve the isotropic boundary value problem as a basis for the total stresses experienced. Therefore, for combined Mode I – II loading, there is always a virtual oblique crack extension in the opening mode by the same uniaxial ultimate tensile stress (cohesive strength) for the crack boundary at the fracture process zone. This ultimate stress acts as a full plastic stress of limit analysis in the fracture process zone. This leads to the mixed mode Coulomb equation as an exact failure criterion for total stresses, which is shown to follow the orthotropic critical distortional energy criterion, determining the critical energy release rate equation.
The actual stress (with the still intact material of the ligament) increases, with an increase in the crack length and hardening behavior (by the spreading effect with activated molecular bonds) characterizing the critical stress (not softening). Thus, fracture strain softening does not exist and is not a material property as assumed. This follows from the derivation of this softening called the yield drop curve with the explanation of the measurements. The points of this curve represent metastable equilibrium states at the actual present crack lengths. For overcritical crack lengths, at the end stage, the crack closure energy is lower than the bond breaking energy. Failure then is due to ultimate, clear wood failure strength, thus via a micro-crack formation in the intact material.
It is shown that the area under the yield drop curve method does not give the right fracture energy. The contribution of other viscoelastic and viscoplastic processes, as the mechano-sorptive influence will dominate, have to be corrected for deformation kinetics by determining the activation energies of the acting processes. This also applies to the R-curve construction.
Furthermore, the derivation of the power law; the extension of the notched beams energy method and joints loaded perpendicular to the grain; the Weibull Size Effect in the fracture mechanics of wide angle notches; the necessary rejection of the fictitious crack models; and the correction of crack growth models via the limit analysis of deformation kinetics are all discussed. (Imprint: Nova)