PSI - Issue 26

Victor Rizov et al. / Procedia Structural Integrity 26 (2020) 63–74 Rizov / Structural Integrity Procedia 00 (2019) 000 – 000

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0.3 = a l , curve 2 – at /

0.5 = a l and

Fig. 4. The strain energy release rate in non-dimensional form plotted against  (curve 1 – at /

curve 3 – at / 0.7 = a l ). First, the influence of the continuously varying radius of the cross-section along the beam length no the fracture behaviour is evaluated. The variation of the radius is characterized by 2 1 / R R ratio. The strain energy release rate in non-dimensional form is plotted against 2 1 / R R ratio in Fig. 3. It is evident from Fig. 3 that the strain energy release rate decreases with increasing of 2 1 / R R ratio (this finding is attributed to the increase of the beam stiffness). The strain energy release rate obtained assuming linear-elastic mechanical behaviour of the material is plotted also in non dimensional form against 2 1 / R R ratio in Fig. 3 for comparison with the non-linear solution.

0 / Q L ratio (curve 1 – at

/ 3 1 = R R

0.2

, curve 2 – at

Fig. 5. The strain energy release rate in non-dimensional form plotted against

/ 3 1 = R R

/ 3 1 = R R

0.4

0.6

and curve 3 – at

).

It should be noted that the linear-elastic solution to the strain energy release rate is derived by substituting of 0 = Q in (18) since at 0 = Q the non-linear stress-strain relation (18 ) transforms in the Hooke’s law assuming that L 1/ is the modulus of elasticity of the inhomogeneous material. One can observe in Fig. 3 that the material non-linearity leads to increase of the strain energy release rate. The influence of the material property,  , and the crack length on the fracture behaviour is evaluated too. The crack length is characterized by a l / ratio. The influence of  and a l / ratio is illustrated in Fig. 4 where the strain