By David E. Malach
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Additional info for Advances in Mechanical Engineering Research; Volume 2
The general applicability of these models will be discussed in this section while criteria based on a critical energy are discussed in the next section. 2. The Fictitious Crack Models The high stresses near the crack tip, are replaced by a plastic zone in the Dugdale model following from elastic superposition of closing stresses, equal to the yield stress, on the crack tip zone of a fictitious enlarged crack of such a length that the stress in the elastic singularity point becomes zero. 1) where f is the yield stress or is regarded to be a cohesive stress.
Constitutive equations only can follow from the theory and not from general thermodynamic considerations. 1. Crack growth tests of Mindess (Figure 10 of ). 3). 28), discussed in Section 3. g. 3), is discussed below. g. 5) E c c , with E E0 t n and rp a t . g. K Ic , y , rp and E0 to obtain an equation in E, t, c and c . 5) thus is not a new derived crack rate equation but an alternative writing of the four relations. 2 of  showing comparable parameter manipulations of many critical parameter values which can not be applied independently because they are part of the same failure condition.
10) for the same crack length and now the energy of crack extension is equal to the decrease of elastic energy in the beam. 11) where again V 1 / 2 is the increase of the elastic energy and V ( 1 ) the plastic energy of the flow of the joint. 11) then follows: 44 T. A. C. M. 8), despite of the plastic deformation. For connections, plastic deformation in the last case will not yet occur because it is coupled with crack extension. When the dowels of the joint are pressed into the wood, the crack opening increases and thus also crack extension.