PSI - Issue 28

Victor Rizov et al. / Procedia Structural Integrity 28 (2020) 1237–1248 Author name / Structural Integrity Procedia 00 (2019) 000–000

1245

9

1

n



2





n

u

 

.

(33)

01

1

2

E



 n

1

n H



The strain energy density in the un-cracked bar portion is determined also by (33). For this purpose,  is replaced with g  . By substituting of (31) and (32) in (30), one obtains the following expression for the strain energy release rate:       g F G    0 01 u dA u dA . (34)

R  1 2 1

 

  





A

A

1

The integration in (34) should be performed by using the MatLab computer program.

Fig. 3. The non-dimensional strain energy release rate versus t p . Curve 1 - at non-linear behaviour of the material, curve 2 - at linear-elastic behaviour. The strain energy release rates obtained by (1) and (34) are identical. This fact proofs the correctness of the general solution procedure for the strain energy release rate in non-linear elastic inhomogeneous round bars loaded in tension developed in the present paper. The sensitivity of the solution of the strain energy release rate with respect to the number of members in the series of Maclaurin (15) and (16) is evaluated. For this purpose, fracture analyses of the cantilever (Fig. 2) are performed by keeping more than three members in the series of Maclaurin. The analyses reveal that the strain energy release rates obtained by keeping more members are very close to these derived by keeping the first three members in the series of Maclaurin (the difference is less than 3 %) which is an indication for the reliability of the solution procedure. The solution of the strain energy release rate is used to evaluate the influence of the material inhomogeneity and