PSI - Issue 57

Mathias Euler et al. / Procedia Structural Integrity 57 (2024) 298–306 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

303

6

1. The observed first cracks through the welds seem to be controlled by the same failure mechanism whereby shear stresses on preferred planes are considered as driving influence. The failure is initiated at the plane with the largest cyclic shear stress. 2. Accompanying normal stresses on the plane with the largest cyclic shear stress have presumedly an influence on the crack growth so that the same failure mechanism on a microscopic scale can result in different macro scopic crack patterns as observed in the tests with stationarily pulsating and travelling wheel loads (Findley, 1952). See the detailed description of the crack patterns in (Euler, 2017). 4. Derivation of new test-based detail categories The general approach,thatwas chosen to develop the design proposal in (Euler, 2017), is summarized by Figure 5. A new elastic calculation model is generated that analyses the web of the crane runway beam and the crane rail as an elastic shell. The model takes the weld flexibility into account. By means of this model, the cyclic wheel loads F of the fatigue tests are turned into the nominalstresses ¯  || , ¯  ⊥ and ¯  || in the tested rail welds and the nominalstresses  || ,  ⊥ and  || in the welds of the tested flange-to-web connections. As expected the web stresses of the new calculation model correspond well with the stresses obtained from Eq. (1). Next, the nominal stresses are transformed into effective notch stresses  x ,  z and  xz at the weld root (spot of crack initiation) according to the concept of Neuber & Radaj for example by means of notch stress factors (Radaj, 1985). In the following, the effective notch stresses are projected into different planes with angle θ . The history of the stresses  θ und  θ is evaluated in order to obtain the stress ranges   θ and the corresponding maximum normal stress  θ ,max . The plane with the largest stress range   eff =   θ + 2 k  θ,max according to Findley ’s hypothesis (Findley, 1959) is identified as critical. In addition, the kinematic compatibility of the critical plane is taken into account considering the fact that only a plane can be critical if the deflections on this plane are compatible with the macroscopic crack pattern (positive dissipation energy). See (Euler, 2017) for more details.   eff at the critical plane represents the fatigue resistance of the test girders based on effective notch stresses (50% survival probability). The characteristic reference value   C of the critical plane (notch stresses) at 2 million stress cycles is derived according to the safety requirements of EN 1993-1-9 (2005) using standardized scatter bands (Haibach, 2006). Finally, the characteristic reference values   C of the flange-to-web connections and of the rail welds based on nominal stresses are determined using the aforementioned link between the nominal stresses and effective notch stresses. For design purposes, the calculation of the local stress ¯  ⊥ in the rail welds is facilitated by Eq. (5) and Eq. (6) that take advantage of the effective loaded length eff,fat .

min

/ 2

 ⊥ = p

a

(5)

max

max eff,fat / = p F

(6)

Fig. 5. General approach for joint evaluation of fatigue tests on flange-to-web connections and rail welds to establish a fatigue resistance on basis of nominal stresses