PSI - Issue 8

Davide Zanellati et al. / Procedia Structural Integrity 8 (2018) 92–101 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

95

4

not impede the vertical bending and the torsional rotation of the specimen, while it prevents the horizontal bending of the specimen.

m tip

m tip

F t

m tip

m tip

m cant

m cant

F b

m spec

m spec

a H

a H

a V

a V

(a)

(b)

Fig. 3. Lumped-mass model and dynamic forces for: (a) bending; (b) torsion.

Under quasi-static condition, in first approximation, the formula F = m ∙ a is valid, where a is the input acceleration given by shaker and m is the concentrated mass in the model. To obtain a bending loading, a vertical acceleration a V is applied, which gives the following force F b = F tip + F spec , where F tip =(2 m tip + m cant )∙ a V acts on the specimen extremity and F spec = m spec ∙ a V acts on specimen barycenter. The eccentric tip mass is m tip , the cantilever mass is m cant and the specimen mass is m spec . The resultant bending moment at the notch is M b = F tip ∙ B + F spec ∙ B /2, where B is the distance between the specimen extremity and the notch. Thus, the maximum bending stress on the notch is σ p,notch =( M b / W b )∙ K t,b , where W b is the elastic bending section modulus. Similarly, to obtain a torsion loading, a horizontal acceleration a H is applied, which gives the force F t = F mass + F cant , where F mass =2 m tip ∙ a H acts on the cantilever extremity and F cant = m cant ∙ a H acts on cantilever barycenter. Under a horizontal acceleration, the plate impedes the movement of the specimen mass m spec , which in fact is not included into the force F t . The resultant torsional moment at the notch is M t =F mass ∙ L + F cant ∙ L /2, where L is the distance between the tip masses and the longitudinal axis of specimen. The maximum shear stress on the notch is τ p,notch =( M t / W t )∙ K t,t , where W t is the elastic torsional section modulus.

normal stresses shear stresses

300

6.502 g

200

17.165 g

5.475 g

13.430 g

Amplitude stress [MPa]

100

1.E+04

1.E+05

1.E+06

1.E+07

N [cycles]

Fig. 4. S-N curve for notched specimen for normal (solid line) and shear stresses (dashed line).