PSI - Issue 25

Victor Rizov / Procedia Structural Integrity 25 (2020) 112–127

121

10

Author name / Structural Integrity Procedia 00 (2019) 000–000

qh bp qh bp   2

2

2 1

c



.

(32)

1

U E and L E in the length direction of the

The power laws (20) and (21) are used to express the distributions of

beam. The geometry of the beam cross-section is characterized by h b / , p b / and q b / ratios.

Fig. 6. T-shaped beam cross-section.

In order to evaluate the effects of the cross-section geometry calculations of the strain energy release rate are carried-out by applying the methodology developed in section 2 of the paper at various h b / , p b / and q b / ratios. The compliance method is used for verification of the strain energy release rate. One can get an idea about the effects of the geometry of the beam cross-section on the lengthwise fracture behaviour of the inhomogeneous beam in Fig. 7 where the strain energy release rate in non-dimensional form is plotted against h b / ratio at three p b / ratios for / 0.1  q b . The curves in Fig. 7 show that the strain energy release rate decreases with increasing of h b / and p b / ratios. The influence of q b / ratio on the lengthwise fracture behaviour of the beam is shown in Fig. 8. It can be observed in Fig. 8 that the strain energy release rate decreases with increasing of q b / ratio. The lengthwise fracture is analyzed further assuming that the inhomogeneous beam has a circular cross-section of radius, r , shown in Fig. 9. For this purpose, calculations of the strain energy release rate are performed by applying the methodology developed in the previous section of the beam. The compliance method is used for verification. The distribution of the modulus of elasticity along the beam height is written as





 m

r z 

  r E E E E 2   m U U

L

,

(33)

1

where

r z r    1 .

(34)

U E and L E in the beam length direction. The

Formulae (20) and (21) are applied to express the distributions of