Issue34

F. Berto, Frattura ed Integrità Strutturale, 34 (2015) 11-26; DOI: 10.3221/IGF-ESIS.34.02 21 A convenient expression is [7]: 1 1 1 1 1 0 2 N A A e K R               (16) where both  1 and e 1 depend on the V-notch angle. Eq. (16) makes it possible to estimate the R 0 value as soon as 1 N A K  and   A are known. At N A = 5  10 6 cycles and in the presence of a nominal load ratio R  equal to zero a mean value 1 N A K  equal to 211 MPa mm 0.326 was found re-analysing experimental results taking from the literature [10]. For butt ground welds made of ferritic steels a mean value  A = 155 MPa (at N A = 5  10 6 cycles) was found [79]. Then, by introducing the above mentioned value into Eq.(16), one obtains for steel welded joints with failures from the weld toe R 0 =0.28 mm. It is interesting to learn that, for welded joints made of structural steels, different espressions for  K th taken from the literature were reported in Ref. [79], from which  K th = 180 MPa mm (5.7 MPa m 1/2 ). In the case 2  =0 and fatigue crack initiation at the weld root Eq.(16) gives R 0 =0.36 mm, by neglecting the mode II contribution and using e 1 =0.133, Eq.(7), 1 K N A  = 180 MPa mm 0.5 , and, once again,   A = 155 MPa. This means that the choice to use a critical radius equal to 0.28 mm both for toe and root failures is a sound engineering approximation. By modelling the weld toe regions as sharp V-notches and using the local strain energy, more than 900 fatigue strength data from welded joints with weld toe failure were analysed and the first theoretical scatter band in terms of SED was obtained [8]. The geometry exhibited a strong variability of the main plate thickness (from 6 to 100 mm), the transverse plate (from 3 to 200 mm) and the bead flank (from 110 to 150 degrees). Figure 5 : Fatigue strength of welded joints as a function of the averaged local strain energy density; R  is the nominal load ratio. The synthesis of all those data is shown in Figure 5, where the number of cycles to failure is given as a function of 1 W  (the Mode II stress distribution being non singular for all those geometries). The figure includes data obtained both under tension and bending loads, as well as from “as-welded” and “stress-relieved” joints. The scatter index T W , related to the two curves with probabilities of survival P S = 2.3% and 97.7%, is 3.3, to be compared with the variation of the strain energy density range, from about 4.0 to about 0.1 MJ/m 3 . T W =3.3 becomes equal to 1.50 when reconverted to an equivalent local stress range with probabilities of survival P S =10% and 90% (T  = 3.3 /1.21 1.5  ). The scatterband proposed was latter applied in [10] to a larger bulk of experimental data, which included also fatigue failures from the weld root. Dealing with static loading, the local SED values are normalised to the critical SED values (as determined from unnotched specimens) and plotted as a function of the R/R 0 ratio. The data related to the experimental program of PMMA tested at - 60°C [56-59] are summarised together with other data taken from a data base due related to PMMA tested at room 0.01 0.1 1.0 10 10 5 10 4 10 6 10 7 R 0 =0.28 mm 900 fatigue test data Various steels Inverse slope k=1.5 P.S. 97.7 % 2D, failure from the weld toe, R= 0 2D, failure from the weld root, R = 0 Butt welded joints -1 < R < 0.2 3D, -1 < R < 0.67 Hollow section joints, R= 0 Averaged strain energy density  W [Nmm/mm 3 ] T  W = 3.3 0.192 0.105 0.058 R 0 R 0 2  Cycles to failure, N