PSI - Issue 25

Victor Rizov / Procedia Structural Integrity 25 (2020) 112–127 Author name / Structural Integrity Procedia 00 (2019) 000–000

122

11

  h r / 2 1 ratio.

location of the crack along the beam height is characterized by

Fig. 7. The strain energy release rate in non-dimensional form plotted against h b / ratio (curve 1 – at /

0.05  p b , curve 2 – at

/ 0.10  p b and curve 3 – at / 0.15  p b ). In order to evaluate the effects of the cross-section radius and the crack location along the beam height on the lengthwise fracture behaviour of the inhomogeneous beam configuration, the strain energy release rate in non dimensional form is plotted against   h r / 2 1 ratio in Fig. 10 at three values of the radius. It is evident form Fig. 10 that the strain energy release rate has minimum when the crack is located near the mid-plane of the beam and increases when the crack approaches the lower or the upper surfaces of the beam. It can also be observed in Fig. 10 that the strain energy release rate decreases with increasing of the radius of the cross-section. Lengthwise fracture behaviour is analyzed also when the inhomogeneous beam has different moduli of elasticity in compression and tension, c E and t E . The beam has a circular cross-section. The distribution of these moduli along the beam height is written as





 m

r z 

  r E E E E 2   m cU cU c

cL

,

(35)

1





 m

r z 

  r E E E E 2   m tU t t

tL

,

(36)

1

where

r z r    1 .

(37)

In (36) and (37), cU E and cL E are the values of the compression modulus in the upper and lower surfaces of the beam, respectively. The values of the tension modulus in the upper and lower surfaces of the beam are tU E and