Issue 43

F. Berto et alii, Frattura ed Integrità Strutturale, 43 (2018) 1-32; DOI: 10.3221/IGF-ESIS.43.01 4 value of SED can be expressed in the following form [11]        ( ) 2 ( ) max 0 1 1 (2 ) (2 , ) e e R E W F H E (3) where F(2 α ) depend on previously defined parameters H is summarised in Refs [11, 15-16] as a function of opening angles and Poisson’s ratios. Under mixed mode loading the problem becomes more complex than under mode I loading, mainly because the maximum elastic stress is out of the notch bisector line and its position varies as a function of mode I to mode II stress distributions. The problem was widely discussed considering different combination of mode mixity [70, 71]. The expression for U-notches under mixed mode is analogous to that valid for notches in mode I:            2 ( ) 0 max π * 2 , 4 e R W H E (4) where σ max is the maximum value of the principal stress along the notch edge and H * depends again on the normalised radius R/R 0 , the Poisson’s ratio ν and the loading conditions. For different configurations of mode mixity, the function H , analytically obtained under mode I loading, was shown to be very close to H *. This idea of equivalent local mode I was discussed in previous works [70-73]. M ASTER CURVES FOR STATIC AND FATIGUE LOADINGS ealing with static loading a large bulk of data taken from the literature have been summarized in a single master curve. The local SED values have been normalized to the critical SED values (as determined from unnotched specimens) and plotted as a function of the ρ/R 0 ratio. The final synthesis has been carried out by normalizing the local SED to the critical SED values (as determined from unnotched, plain specimens) and plotting this non-dimensional parameter as a function of the ρ/R 0 ratio. A scatterband is obtained whose mean value does not depend on ρ/R 0 , whereas the ratio between the upper and the lower limits are found to be about equal to 1.3/0.8=1.6 (Fig. 3). The strong variability of the non-dimensional radius ρ/R 0 (notch root radius to control volume radius ratio, ranging here from about zero to about 500) makes stringent the check of the approach based on the local SED. The complete scatterband presented here (Fig. 3) has been obtained by updating the database containing failure data from 20 different ceramics, 4 PVC foams and some metallic materials [15, 16]. Dealing with the fatigue assessment of welded joints a scatterband has been proposed by Lazzarin and collaborators [7- 10]. The mean value of the strain energy density (SED) in a circular sector of radius R 0 located at the fatigue crack initiation sites has been used to summarise fatigue strength data from steel welded joints of complex geometry (Fig. 4). The evaluation of the local strain energy density needs precise information about the control volume size. From a theoretical point of view the material properties in the vicinity of the weld toes and the weld roots depend on a number of parameters as residual stresses and distortions, heterogeneous metallurgical micro-structures, weld thermal cycles, heat source characteristics, load histories and so on. To device a model capable of predicting R 0 and fatigue life of welded components on the basis of all these parameters is really a task too complex. Thus, the spirit of the approach is to give a simplified method able to summarise the fatigue life of components only on the basis of geometrical information, treating all the other effects only in statistical terms, with reference to a well-defined group of welded materials and, for the time being, to arc welding processes. The material parameter R 0 has been estimated by using the fatigue strength Δ σ A of the butt ground welded joints (in order to quantify the influence of the welding process, in the absence of any stress concentration effect) and the NSIF-based fatigue strength of welded joints having a V-notch angle at the weld toe constant and large enough to ensure the non- singularity of mode II stress distributions. A convenient expression is [7, 10]:               1 1 1 1 1 0 2 N A A e K R (5) D